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2023/(ML)$^2$P-Encoder_ On Exploration of Channel-Class Correlation for Multi-Label Zero-Shot Learning/2f5d72e4-31bc-4c21-9948-28d1063a50fb_content_list.json

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+        "text": "$(\\mathbf{ML})^{2}\\mathbf{P}$ -Encoder: On Exploration of Channel-class Correlation for Multi-label Zero-shot Learning",
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+        "text": "Ziming Liu<sup>1</sup>, Song Guo<sup>1,2</sup>, Xiaocheng Lu<sup>1</sup>, Jingcai Guo<sup>1,2*</sup>, Jiewei Zhang<sup>1</sup>, Yue Zeng<sup>1</sup>, Fushuo Huo<sup>1</sup>  \n<sup>1</sup>Department of Computing, The Hong Kong Polytechnic University, Hong Kong SAR, China  \n<sup>2</sup>The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, China",
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+        "text": "{ziming.liu, jiewei.zhang, fushuo.huo}@connect.polyu.hk {song.quo, xiaoclu, jc-jingcai.quo, zengyue.zeng}@polyu.edu.hk",
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+        "text": "Abstract",
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+        "text": "Recent studies usually approach multi-label zero-shot learning (MLZSL) with visual-semantic mapping on spatial-class correlation, which can be computationally costly, and worse still, fails to capture fine-grained class-specific semantics. We observe that different channels may usually have different sensitivities on classes, which can correspond to specific semantics. Such an intrinsic channel-class correlation suggests a potential alternative for the more accurate and class-harmonious feature representations. In this paper, our interest is to fully explore the power of channel-class correlation as the unique base for MLZSL. Specifically, we propose a light yet efficient Multi-Label MultiLayer Perceptron-based Encoder, dubbed  $(ML)^{2}P$ -Encoder, to extract and preserve channel-wise semantics. We reorganize the generated feature maps into several groups, of which each of them can be trained independently with  $(ML)^{2}P$ -Encoder. On top of that, a global group-wise attention module is further designed to build the multilabel specific class relationships among different classes, which eventually fulfills a novel Channel-Class Correlation MLZSL framework  $(C^{3}$ -MLZSL). Extensive experiments on large-scale MLZSL benchmarks including NUS-WIDE and Open-Images-V4 demonstrate the superiority of our model against other representative state-of-the-art models.",
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+        "text": "1. Introduction",
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+        "text": "The proliferation of smart devices has greatly enriched human life when it comes to the era of big data. These smart devices are usually equipped with cameras such that users can easily produce and share their images. With the increasing abundance of public images, how to analyze them accurately has become a challenging problem. Recent years",
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+            "Figure 1. Example of Channel-Class Correlation. Our method achieves the prediction of unseen classes by exploiting the unique distribution of channel responses as semantic information for the class and building correlations with responses from the same channel (zoom in for a better view)."
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+        "text": "have witnessed great success in classifying an image into a specific class [20, 37, 39], namely, single-label classification. However, in reality, the images [17,46] usually contain abundant information and thereby consist of multiple labels.",
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+        "text": "In recent years, the multi-label classification has been widely investigated by exploring the relationship among different labels from multiple aspects [9, 13, 14, 16, 42]. However, in some scenarios where extensive collections of images exist, e.g., Flickr $^2$ , users can freely set one or more individual tags/labels for each image, while the presented objects and labels in these images may not be fully shown in any previous collection, and thus result in a domain gap for the recognition. Therefore, in real-world applications, the model is required to gain the ability to predict unseen classes as well. As one of the thriving research topics, zero-",
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+        "text": "CVF",
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+    {
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+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "*Jingcai Guo is the corresponding author.  \n<sup>1</sup>Released code: github.com/simonzmliu/cvpr23_mlzsl",
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+        "text": "$^{2}$ https://www.flickr.com",
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+        "text": "shot learning (ZSL) [1, 12, 15, 34] is designed to transfer tasks from seen classes to unseen classes, and naturally recognizes novel objects of unseen classes. Specifically, ZSL has made continuous success in single-label classification [19, 26, 31, 45, 48]. However, these methods can hardly be extended to the multi-label scenario since exploring the cross-class relationships in an image is non-trivial.",
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+        "text": "Recently, some works have focused on multi-label zero-shot learning (MLZSL) tasks and obtained some promising results [33, 36, 49]. Other works considered incorporating attention mechanisms into their models, such as  $LESA$  [22] and  $BiAM$  [35].  $LESA$  [22] designed an attention-sharing mechanism for different patches in the image so that each patch can output the corresponding class. In another way,  $BiAM$  [35] designed a bi-level attention to extract relations from regional context and scene context, which can enrich the regional features of the model and separate the features of different classes.",
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+        "text": "Although previous works have made considerable progress, their designed methods have been limited to the processing of spatial-domain information. First of all, the over-reliance on spatial-class correlation fails to capture fine-grained class-specific semantics. In addition, the additional processing of spatial information greatly increases the computational cost of the model and limits the inference speed. Given the shortcomings of the above methods, we found through analysis that the channel response can be used as the semantic information of the class. Firstly, the response of each class in the channel is unique, which creates conditions for obtaining the unique semantics. Secondly, for classes with certain semantic associations, there must be some channels that capture their common information. Therefore, channel information, as an easily overlooked part after feature extraction, can complete the task of capturing multi-label information. In MLZSL, we can complete the prediction of unseen classes by obtaining the responses of seen classes in the channel domain, and the relationship between seen and unseen classes. Finally, the subsequent analysis of the channel response greatly saves computational costs.",
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+        "text": "Specifically, as shown in Figure 1, as seen classes, \"water\" and \"tree\" have unique response distributions on feature channels, and these responses can be used as semantic information for classification tasks. Besides, in order to explore the correlation of classes, we found that although the semantic information of \"water\" and \"tree\" is different, there are still some channels that respond simultaneously (i.e. the blue channel). We need to build this correlation during the training process through modeling so that the model can learn multi-label correlations. In the ZSL process, for the unseen class \"garden\", we know that it is related to \"water\" (i.e. purple layer) and \"tree\" (i.e. green, orange, and gray layer) by obtaining its semantic information and matching",
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+        "text": "with seen classes. This observation suggests that channels can help not only to classify objects but also to establish associations between classes. Previous methods which only consider spatial information are unable to obtain this intrinsic channel-class correlation and dissimilarity, thus achieving sub-optimal performance on the MLZSL task.",
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+        "text": "To address the above challenges and construct a more accurate and robust MLZSL system, we propose to group the generated feature maps and process them in a group-wise manner, thus enhancing the model by fully exploring the channel-class correlations. Besides, by properly designing a light yet efficient Multi-Label Multi-Layer Perceptron-based Encoder, i.e.,  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder, we can easily analyze the local relationship between channels while significantly reducing the computation overhead. Finally, these groups are recombined and then perform the calculation of group attention, indicating that the model is analyzed locally and globally from the perspective of the channels, which can ensure the integrity of the representation.",
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+        "text": "In summary, our contributions are four-fold:",
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+            "1. To the best of our knowledge, our method first suggests the concept of channel-class correlation in MLZSL, and proposes a channel-sensitive attention module  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder to extract and preserve channel-wise semantics for channel groups.",
+            "2. Different from previous works that use spatial-class correlation to extract global and local features, we alternatively explore the channel-class correlation as the unique base for MLZSL.",
+            "3. In conjunction with  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder, a global group-wise attention is also designed to establish the multi-label specific class relationships among classes.",
+            "4. Extensive experiments on large-scale datasets NUS-WIDE and Open-Images-V4 demonstrate the effectiveness of our method against other state-of-the-art models."
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+        "text": "2. Related Work",
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+        "text": "2.1. Multi-Label Classification",
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+        "text": "The establishment of graph neural networks (GNNs) brings remarkable success to multi-label classification tasks [8, 25]. Among them, Chen et al. [8] constructs directed graphs for object labels and uses graph convolutional networks (GCN) to map label nodes, which contain word embeddings, into classifiers. In addition, the CNN-based multi-label classification models enable the learning of the characteristics of each label from the spatial information of the image and design a new multi-label classifier [13, 14, 16, 17, 42, 43, 46]. Gao et al. [16] suggests a two-stream framework to identify global and local information",
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+        "img_path": "images/5c95f6e5e4e83008579a6320d2bbd777ec3c50f5b321ab9aef414704b93cb307.jpg",
+        "image_caption": [
+            "Figure 2. Pipeline for  $\\mathbf{C}^3$ -MLZSL. The input image is first passed through the feature extraction network (eg. VGG19), and then multi-layer feature maps are extracted through the Forward Pyramid module. After the feature maps are shuffled and grouped, each group uses  $(\\mathbf{ML})^{2}\\mathbf{P}$ -Encoder to extract semantic information. Then, the semantic information generated by all groups is associated through Group Attention to generate the final semantic matrix  $\\mathcal{S}$  (zoom in for a better view)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "separately and a multi-class regional attention module to align them. However, the above methods cannot generalize to unseen classes.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Zero-Shot Learning",
+        "text_level": 1,
+        "bbox": [
+            76,
+            433,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Zero-shot learning provides a solution to recognize unseen classes. Current studies mostly consider a relatively simple single-label scenario [4, 6, 26, 30, 32, 47, 50, 51]. In practice, existing methods usually focus on finding the main semantic information of training images, and then exploit the semantic relationship, i.e., word vectors [15, 38, 44, 45] or attribute vectors [3, 27, 28], between seen and unseen classes for prediction. The generated semantic information can be inferred from seen to unseen labels by comparing the similarity of the relation vectors between them. For example, Chen et al. [7] proposes a generative flow framework and uses a combinatorial strategy to solve the problems of semantic inconsistency, variance collapse, and structural disorder in zero-shot learning. Gune et al. [18] generates visual proxy samples to simulate the average entropy of the label distribution of the unseen class. However, the above methods only predict single labels with a single representation of images, which can hardly generalize to a more realistic multi-label scenario.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3. Multi-Label Zero-Shot Learning",
+        "text_level": 1,
+        "bbox": [
+            76,
+            755,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Multi-label zero-shot learning has received increasing attention recently. For example, Norouzi et al. [36] designs two separate spaces, i.e., the image and semantic embedding spaces, jointly with the convex combination of the label embedding vectors to achieve multi-label recognition in the zero-shot learning framework. Zhang et al. [49] proposes a fast and general model based on the fact that the word vectors of the relevant labels are ranked before",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "the irrelevant word vectors in the main vector of the image. Different from the above methods, Lee et al. [29] uses the knowledge graph to connect different labels. In recent years, attention-based methods become the mainstream. For example, LESA [22] applies an attention-sharing mechanism to the multi-label environment, allowing the model to focus on the key areas of each label. Narayan et al. [35] uses a bi-layer attention module to combine global context information and local features and map the generated information to the semantic space. However, the above methods only stay at the two-dimensional space level  $(H\\times W)$ , and do not consider the response between different feature channels with respect to classes.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Methods",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Problem Setting",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Before proposing our method, we first explain the definition of the MLZSL problem. Given  $n$  input samples  $\\{(I_1,Y_1),\\ldots ,(I_i,Y_i),\\ldots ,(I_n,Y_n)\\}$ , where  $I_{i}$  represents the input image of the  $i$ -th train-set, and  $Y_{i}$  represents the training labels corresponding to the input images, which are also called 'seen labels'. On the label distribution, let us set the seen label in the dataset as  $C_s$ , where the seen label refers to the label known by the model.  $C_s$  is mainly used for the train-set of the model in zero-shot learning. We set the unseen label to  $C_u$ , and the unseen label is generally used in the test-set. The label relationship in the dataset is defined as  $\\mathcal{C} = \\mathcal{C}_s\\cup \\mathcal{C}_u$ , where  $\\mathcal{C}$  represents the set of all labels in the dataset. Based on the above definition, after the model is trained on the train-set, in the testing part of MLZSL, given the image  $I_{u}$ , the model can output the prediction result  $y_{u}\\subset C_{u}$ . While in the generalized zero-shot learning task, given an image  $I_{u}$ , the output of the model is",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "23861",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "$y_{u} \\subset \\mathcal{C}$ , which means the model needs to output both the seen label and the unseen label that exist in the image.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2.  $(\\mathbf{ML})^{2}\\mathbf{P}$  -Encoder",
+        "text_level": 1,
+        "bbox": [
+            76,
+            128,
+            243,
+            145
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The proposed network structure is shown in Figure 2. For input images  $I$ , we first use a pre-trained feature extraction network to obtain the corresponding image features  $\\mathcal{F}$ . We extract the features from the last three layers of the feature extraction network, and keep the two layers with the larger size consistent with the smallest size layer by downsampling. For example, assuming that the used and training network is VGG19 [37], the size of the last three layers of feature maps is  $\\{28 \\times 28, 14 \\times 14, 7 \\times 7\\}$ . We use max-pooling to down-sample the large-scale feature maps to obtain equivalent  $7 \\times 7$  feature maps. This step is called the \"Forward Pyramid\". After that, we obtain feature maps at different levels with the same scale. Then we randomly shuffle them to get the feature map  $\\mathcal{F}_a$  and re-group them into  $g$  different groups, each group has  $d_w$  channels, which is the same length as the word vectors in the ground-truth semantic space. The purpose of this operation is to generate specific semantic vectors to express the semantic information contained in each group.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Next, the features of each group are fed into  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder. First, we need to calculate the correlation between channels within each group. In traditional self-attention, the cost of computation greatly consumes the inference speed of the model, and the traditional self-attention module cannot accurately reflect the relationship between each channel. To solve the loss caused by the amount of calculation and accurately reflect the channel correlation, we designed a new self-attention structure to achieve this.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For features  $\\mathcal{F}_a$  in group  $i$ , which is  $\\mathcal{F}_a^i \\in \\mathbb{R}^{H \\times W \\times d_w}$ . We first generate Query (Q), Value (V) and Key (K) through three convolution operations:",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {Q} = W _ {p} ^ {Q} \\mathcal {F} _ {a} ^ {i} \\quad \\mathbf {K} = W _ {p} ^ {K} \\mathcal {F} _ {a} ^ {i} \\quad \\mathbf {V} = W _ {p} ^ {V} \\mathcal {F} _ {a} ^ {i} \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            125,
+            631,
+            468,
+            651
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $W_{p}^{(\\cdot)}$  means the convolution operation. Next, to obtain the channel correlation matrix  $\\mathcal{R}$ , we reshape  $\\mathbf{Q},\\mathbf{K}$  and  $\\mathbf{V}$  in the spatial domain  $(H\\times W)$  to get  $\\widehat{\\mathbf{Q}}\\in \\mathbb{R}^{HW\\times d_w}$ ,  $\\widehat{\\mathbf{K}}\\in \\mathbb{R}^{d_w\\times HW}$  and  $\\widehat{\\mathbf{V}}\\in \\mathbb{R}^{HW\\times d_w}$ . Then perform a dot product operation on  $\\mathbf{Q}$  and  $\\mathbf{K}$  to obtain the channel correlation matrix  $\\mathcal{R}\\in \\mathbb{R}^{d_w\\times d_w}$ . After that, we do the dot product between  $\\mathcal{R}$  and  $\\mathbf{V}$ , finally, add with the input  $\\mathcal{F}_a^i$  to get the output  $\\widehat{\\mathcal{F}}_a^i\\in \\mathbb{R}^{H\\times W\\times d_w}$ :",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {A t t} (\\widehat {\\mathbf {Q}}, \\widehat {\\mathbf {K}}, \\widehat {\\mathbf {V}}) = \\widehat {\\mathbf {V}} \\cdot \\underset {\\mathcal {R}} {\\operatorname {s o f t m a x}} (\\underbrace {\\widehat {\\mathbf {K}} \\cdot \\widehat {\\mathbf {Q}}} _ {\\mathcal {R}}) \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            147,
+            795,
+            468,
+            832
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\widehat {\\mathcal {F}} _ {a} ^ {i} = \\mathcal {F} _ {a} ^ {i} + \\operatorname {A t t} (\\widehat {\\mathbf {Q}}, \\widehat {\\mathbf {K}}, \\widehat {\\mathbf {V}}) \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            844,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "After enhancing the correlation between channels, we need to extract and analyze the feature information contained in",
+        "bbox": [
+            76,
+            869,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "each channel. We reshape the information in the spatial domain into a one-dimensional vector, then we decide to use the Multi-Layer Perceptron (MLP) to encode the features. Compared with the traditional convolution structure, the MLP structure is convenient to perform information fusion between local regions. Specifically, for the input feature  $\\widehat{\\mathcal{F}}_a^i\\in \\mathbb{R}^{H\\times W\\times d_w}$ , we first change the dimension from  $H\\times W\\times d_w$  to  $\\mathcal{F}_{mlp}^i\\in \\mathbb{R}^{d_w\\times HW}$ , then we use LayerNorm to normalize the input. Our MLP structure includes two different MLPs: MLP1 is used to extract the spatial information contained in each channel, and MLP2 is proposed to obtain local information of different channels in the spatial domain:",
+        "bbox": [
+            496,
+            90,
+            890,
+            286
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {F} _ {m l p 1} ^ {i} = \\mathcal {F} _ {m l p} ^ {i} + \\mathbf {W} _ {2} \\sigma \\left(\\mathbf {W} _ {1} \\text {L a y e r N o r m} \\left(\\mathcal {F} _ {m l p} ^ {i}\\right)\\right) \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            524,
+            295,
+            890,
+            314
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {M} = \\mathcal {F} _ {m l p 1} ^ {i} + \\mathbf {W} _ {4} \\sigma \\left(\\mathbf {W} _ {3} \\text {L a y e r N o r m} \\left(\\mathcal {F} _ {m l p 1} ^ {i}\\right)\\right) \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            537,
+            321,
+            890,
+            340
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{F}_{mlp1}^i$  is the output after MLP1.  $\\mathbf{W}_1$ ,  $\\mathbf{W}_2$  is the parameter of MLP1, and  $\\mathbf{W}_3$ ,  $\\mathbf{W}_4$  is the parameter of MLP2.  $\\sigma$  is an element-wise non-linearity GELU [21]. Then we use max-pooling to filter out the best semantic vector in the spatial domain, which can more accurately represent the semantic information of this group. This max-pooling operation is also to be able to directly extract the channel response. So we obtain group semantic vectors  $\\mathcal{X} \\in \\mathbb{R}^{g \\times d_w}$  and send them into Group Attention.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Group Attention",
+        "text_level": 1,
+        "bbox": [
+            500,
+            489,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Although we obtained group semantic vectors  $\\mathcal{X}$  through  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder, the semantic vectors generated by each group did not establish a relationship with each other at this time. As we already know, the key to improving the accuracy of multi-label image classification is to construct the correlation of labels within the image. So we use Group Attention to build the mutual information and also to find similar responses between different labels. We pass a series of linear layers to  $\\mathcal{X}$ :",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {Q} _ {\\mathbf {x}} = W _ {x} ^ {Q} \\mathcal {X} \\quad \\mathbf {K} _ {\\mathbf {x}} = W _ {x} ^ {K} \\mathcal {X} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            596,
+            655,
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+            674
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {S} = \\left(\\mathbf {Q} _ {\\mathbf {x}} \\cdot \\mathbf {K} _ {\\mathbf {x}}\\right) \\cdot \\mathcal {X} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            627,
+            681,
+            890,
+            698
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{Q}_{\\mathbf{x}} \\in \\mathbb{R}^{g \\times d_w}$ , and we transpose  $\\mathbf{K}_{\\mathbf{x}}$  into  $\\mathbf{K}_{\\mathbf{x}} \\in \\mathbb{R}^{d_w \\times g}$ .  $W_x^Q$  and  $W_x^K$  are different linear weights.  $S \\in \\mathbb{R}^{g \\times d_w}$  is the semantic matrix, which contains all the semantic information of the input image. In the loss function, we will make each semantic vector in  $S$  approximate the semantic information of seen classes appearing in the image. Therefore, from another perspective, the semantic vectors in  $S$  are related to seen classes.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4. Loss Function",
+        "text_level": 1,
+        "bbox": [
+            500,
+            832,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "During training, some semantic vectors are generated for each input image. The semantic matrix  $S$  includes the semantic information in the image and is sent to the prediction",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "23862",
+        "bbox": [
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+            944,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "module. The loss function consists of two parts. First of all, to make the positive class (seen class appear in each training image) get a higher ranking than the negative class (seen class which does not appear in the training image). Inspired by [49], we choose to adopt ranknet loss [5] as the main component of the loss function. We use",
+        "bbox": [
+            75,
+            90,
+            468,
+            181
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mu_ {i j} = \\max  \\left(\\mathcal {S} \\cdot n _ {i}\\right) - \\max  \\left(\\mathcal {S} \\cdot p _ {j}\\right), \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            150,
+            195,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "to indicate the number of violations of any of these ranking constraints, where  $n_i$  represents the semantic vector of the negative class, and  $p_j$  denotes the semantic vector of the positive class. max is used to maximize this gap between negative and positive, and constrain it in subsequent steps.",
+        "bbox": [
+            75,
+            223,
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+            299
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Next, to minimize the gap, we design the loss function as the following:",
+        "bbox": [
+            76,
+            300,
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+            330
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {r a n k}} = \\frac {1}{(| P | | \\bar {P} |)} \\sum_ {i} \\sum_ {j} \\log \\left(1 + e ^ {\\mu_ {i j}}\\right), \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            127,
+            340,
+            468,
+            378
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\frac{1}{(|P| |\\bar{P}|)}$  is used to normalize the ranknet loss, and  $|P|$  denotes the number of positive class,  $|\\bar{P}|$  represents the number of negative class. When an image contains a large number of positive labels, the image becomes difficult to classify. So we need the model to value these hard samples during training. Therefore, we add the class weight  $\\omega$  to improve the performance of the model in the face of hard samples.  $\\omega$  is represented as:",
+        "bbox": [
+            75,
+            391,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\omega = 1 + \\sum_ {i} v a r (P ^ {i}), \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            194,
+            532,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $P^i$  represents the vector of the  $i$ -th positive class,  $var$  means the variance. The higher  $\\omega$  means the image contains more complex labels. To prevent the direction of the semantic vectors generated by the model from being too divergent, it needs to be controlled by the loss function. Therefore, we believe that the addition of regularization terms can reduce the difference between the generated semantic vectors when the model faces complex input images. This reduction in variance helps the model learn relevant information between different classes.",
+        "bbox": [
+            75,
+            575,
+            468,
+            726
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {r e g} = \\left\\| \\sum_ {n} v a r \\left(\\mathcal {S} _ {n}\\right) \\right\\| _ {1}. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            736,
+            468,
+            777
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, the loss function of the model is defined as:",
+        "bbox": [
+            76,
+            789,
+            418,
+            804
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} ((1 - \\lambda) \\cdot \\omega \\mathcal {L} _ {\\text {r a n k}} (\\mathcal {S} _ {i}, Y _ {i}) + \\lambda \\mathcal {L} _ {\\text {r e g}} (\\mathcal {S} _ {i})) \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            91,
+            816,
+            468,
+            869
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $N$  means the number of batch size, and  $\\lambda$  is a hyperparameter that denotes the regularization term's weight.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            90,
+            633,
+            107
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            500,
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+            132
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets: First, we use the NUS-WIDE dataset [10] to conduct MLZSL experiments. The NUS-WIDE dataset contains about 270,000 images, and each image contains 925 labels, which are automatically extracted from Flickr user tags. In addition, it also contains 81 labels that are manually annotated by humans, and these labels are called 'GroundTruth'. During the experiment, 925 labels were used as 'seen labels', and 81 labels were used as 'unseen labels'. This setting is similar with [22]. Another dataset is called the Open-Images-V4 dataset. This dataset contains nearly 9 million training images, 125,456 images as test images, and 41,620 images in the validation set. The train-set contains 7,186 labels, which are 'seen labels' that appear at least 100 times in the train-set. While the remaining 400 most frequent labels that do not appear in the train-set are used as test-set labels, they are also used as 'unseen labels'. Each unseen label has at least appeared 75 times.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Evaluation Metrics: To better allow our proposed new model and other comparative models to perform an unbiased comparison on the task of MLZSL, we use the two most common evaluation metrics, the mean Average Precision (mAP) [22, 41] and F1-Score. Among them, top-K F1-Score is used to measure the accuracy of the model for label prediction, and mAP is used to reflect the accuracy for unseen label retrieval of the image.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation Details: Our model can support end-to-end training. We choose VGG19 [37], pre-trained on ImageNet dataset [11], as the backbone network. Unlike other methods, our model uses multi-scale feature maps and aggregates them. The sizes of the feature maps are  $28 \\times 28$ ,  $14 \\times 14$ , and  $7 \\times 7$ , respectively.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In terms of the optimizer, we choose to use the Adam optimizer [24], which requires less memory and is suitable for large datasets. The weight decay of the Adam optimizer is set to  $4e^{-3}$ . In the NUS-WIDE dataset experiments, the initial learning rate of the model is  $5e^{-5}$ , and then the learning rate decreases by  $\\frac{1}{10}$  at the 7th epoch. The entire experimental process of the NUS-WIDE dataset requires a total of 20 epochs with a batch size of 48. In the experiments using the Open-Images-V4 dataset, our learning rate, batch size, and decay rate remain the same as the NUS-WIDE dataset, but the number of epochs is 7.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Baselines: We will compare the proposed method with several state-of-the-art deep learning-based MLZSL models. These comparative methods have been published in recent years and cover a fairly rich variety of techniques, such as the attention mechanism with the most common CNNs. These comparison methods include: CONSE [36], LabelEM [2], Fast0Tag [49], Kim et al. [23], LESA Attention per Cluster (ApC) [22], LESA [22], and BiAM [35]. All",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "23863",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "comparison methods using VGG19 [37] are not fine-tuned. In addition to comparing with comparison models, we will also test the model's performance under different settings of hyper-parameters  $g$  and  $\\lambda$ . At the same time, we will conduct ablation experiments to verify the integrity of the model's architecture.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. State-of-the-art Comparison",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "NUS-WIDE: Table 1 shows the performance of ours and competitive methods on the NUS-WIDE test-set. The table contains the results of both ZSL and GZSL. CONSE [36] and LabelEM [2], as the methods proposed earlier, do not perform well on large-scale datasets. Fast0Tag [49] achieves more competitive results by sorting the positive labels to find the principal directions of the image. LESA [22] and BiAM [35] are currently the most advanced models that rely on spatial attention mechanism to generate semantic information. Compared to BiAM, our method achieves a  $3.6\\%$  improvement on mAP in the ZSL task. Besides, we lead BiAM by  $0.8\\%$  and  $2.9\\%$  in F1-Score of  $K = 3$  and  $K = 5$ , respectively. On the GZSL task, we also surpass BiAM. BiAM deals with higher-dimensional and richer spatial information, while our method is more inclined to single-dimensional channel responses. Therefore, it is not easy to achieve such results with  $1.3\\%$  improvement in mAP and  $0.3\\%$  and  $0.7\\%$  in F1-Score of  $K = 3$  and  $K = 5$ , respectively. Good results on NUS-WIDE dataset imply the effectiveness of our method.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Attention Visualization on NUS-WIDE: Figure 6 illustrate the attention regions of the model when our method predicts unseen labels. Figure 6(a) shows that our model can clearly distinguish scene information from all unseen classes. The attention areas of \"Rocks\" and \"Mountain\" in the figure are roughly the same, which indicates that the two classes have similar semantics and dependencies, and the existence of Group Attention enables the model to learn this mutual information well. Figure 6(b) is a comparison with BiAM [35], the best existing model for mining spatial domain information. This result fully shows the effective use of channel information can more accurately grasp the response between classes. While BiAM's over-exploration of spatial information improves the acquisition of regional information, it loses the scene-level response at the same time. For more comparison results, please refer to appendix.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Open-Images-V4: From Table 2, we show the results of ours and the baseline models on Open-Images-V4. We follow the evaluation setting of [22, 35]. This dataset contains more seen and unseen labels than NUS-WIDE. With a large increase in the number of classes, all methods get poor F1-Score on the ZSL task. Among them, Fast0Tag has made great progress compared with past methods, especially in the GZSL task. LESA [22] and BiAM [35], as the two best methods, represent the highest level of extracting spatial re",
+        "bbox": [
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+            763,
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/53129e7f868080edbe375db7824014f7964f483c936020db97aa7120d8b23462.jpg",
+        "table_caption": [
+            "Table 1. State-of-the-art comparison for multi-label ZSL and GZSL tasks on the NUS-WIDE dataset. We show the indicators of F1-Score in the case of  $K \\in 3,5$  and mAP. The best results are shown in bold."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Task</td><td>mAP</td><td>F1 (K = 3)</td><td>F1 (K = 5)</td></tr><tr><td rowspan=\"2\">CONSE [36]</td><td>ZSL</td><td>9.4</td><td>21.6</td><td>20.2</td></tr><tr><td>GZSL</td><td>2.1</td><td>7.0</td><td>8.1</td></tr><tr><td rowspan=\"2\">LabelEM [2]</td><td>ZSL</td><td>7.1</td><td>19.2</td><td>19.5</td></tr><tr><td>GZSL</td><td>2.2</td><td>9.5</td><td>11.3</td></tr><tr><td rowspan=\"2\">Fast0Tag [49]</td><td>ZSL</td><td>15.1</td><td>27.8</td><td>26.4</td></tr><tr><td>GZSL</td><td>3.7</td><td>11.5</td><td>13.5</td></tr><tr><td rowspan=\"2\">Kim et al. [23]</td><td>ZSL</td><td>10.4</td><td>25.8</td><td>23.6</td></tr><tr><td>GZSL</td><td>3.7</td><td>10.9</td><td>13.2</td></tr><tr><td rowspan=\"2\">Attention per Cluster [22]</td><td>ZSL</td><td>12.9</td><td>24.6</td><td>22.9</td></tr><tr><td>GZSL</td><td>2.6</td><td>6.4</td><td>7.7</td></tr><tr><td rowspan=\"2\">LESA [22]</td><td>ZSL</td><td>19.4</td><td>31.6</td><td>28.7</td></tr><tr><td>GZSL</td><td>5.6</td><td>14.4</td><td>16.8</td></tr><tr><td rowspan=\"2\">BiAM [35]</td><td>ZSL</td><td>25.8</td><td>32.0</td><td>29.4</td></tr><tr><td>GZSL</td><td>8.9</td><td>15.5</td><td>18.5</td></tr><tr><td rowspan=\"2\">Our Approach</td><td>ZSL</td><td>29.4</td><td>32.8</td><td>32.3</td></tr><tr><td>GZSL</td><td>10.2</td><td>15.8</td><td>19.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/ab89dc01ca74cb24bd667d6cc1ec20d8ebfab87b3653f7442de766cd4e134fd5.jpg",
+        "table_caption": [
+            "Table 2. State-of-the-art comparison for multi-label ZSL and GZSL tasks on the Open-Images-V4 dataset. We show the indicators of F1-Score in the case of  $K \\in  {10},{20}$  and mAP. Best results are shown in bold."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Task</td><td>mAP</td><td>F1 (K = 10)</td><td>F1 (K = 20)</td></tr><tr><td rowspan=\"2\">CONSE [36]</td><td>ZSL</td><td>40.4</td><td>0.4</td><td>0.3</td></tr><tr><td>GZSL</td><td>43.5</td><td>2.6</td><td>2.4</td></tr><tr><td rowspan=\"2\">LabelEM [2]</td><td>ZSL</td><td>40.5</td><td>0.5</td><td>0.4</td></tr><tr><td>GZSL</td><td>45.2</td><td>5.2</td><td>5.1</td></tr><tr><td rowspan=\"2\">Fast0Tag [49]</td><td>ZSL</td><td>41.2</td><td>0.7</td><td>0.6</td></tr><tr><td>GZSL</td><td>45.2</td><td>16.0</td><td>13.0</td></tr><tr><td rowspan=\"2\">Attention per Cluster [22]</td><td>ZSL</td><td>40.7</td><td>1.2</td><td>0.9</td></tr><tr><td>GZSL</td><td>44.9</td><td>16.9</td><td>13.5</td></tr><tr><td rowspan=\"2\">LESA [22]</td><td>ZSL</td><td>41.7</td><td>1.4</td><td>1.0</td></tr><tr><td>GZSL</td><td>45.4</td><td>17.4</td><td>14.3</td></tr><tr><td rowspan=\"2\">BiAM [35]</td><td>ZSL</td><td>62.8</td><td>4.1</td><td>3.7</td></tr><tr><td>GZSL</td><td>79.6</td><td>17.6</td><td>15.1</td></tr><tr><td rowspan=\"2\">Our Approach</td><td>ZSL</td><td>65.7</td><td>7.5</td><td>6.5</td></tr><tr><td>GZSL</td><td>79.9</td><td>27.6</td><td>24.1</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "sponses. BiAM achieves very large progress in mAP metrics on both ZSL and GZSL tasks. But our method achieves the best results in the mAP of ZSL, while leading by  $3.4\\%$  and  $2.8\\%$  in F1-Score with  $K = 3$  and  $K = 5$ , respectively. Most importantly, for the GZSL task, our F1-Score results also achieve huge advantages by  $10.0\\%$  and  $9.0\\%$ . This shows that the channel-class correlation as semantic information can fully cope with the complex situation of a large number of labels.",
+        "bbox": [
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+            703,
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+            838
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Figure 5 shows the mAP, inference time, and GFLOPs comparisons between our model for obtaining semantic information based on channel responses and the two methods (LESA [22] and BiAM [35]) for acquiring semantic informa",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "23864",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "tion based on spatial features and achieving optimal results. In the mAP comparison, it can be seen that we have the highest accuracy for prediction in the ZSL task. At the same time, due to the small amount of data to be processed, the inference speed is the fastest of all comparison methods when we use the same GPU of NVIDIA RTX 3090. Finally, precisely because the model only needs to deal with a single-dimensional channel response, our  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder module requires much less computation than  $LESA$  and  $BiAM$  that deal with spatial attention. At the same time, the feature map is grouped to avoid the geometric increase of the computational complexity caused by the feature pyramid. This shows that our  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder can be more efficient.",
+        "bbox": [
+            75,
+            90,
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+            287
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/b9cc6f11cdb2e6723a9f25ccd2ae12b178a3ecf8a6c6305042d2560d22679364.jpg",
+        "table_caption": [
+            "Table 3. Ablation study shows the contribution of the different components in our proposed approach. The baseline methods are performed on the NUS-WIDE test-set."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td><td>a</td><td>b</td><td>c</td><td>d</td><td>ours</td></tr><tr><td rowspan=\"3\" colspan=\"2\">Forward Pyramid (ML)2P-Encoder Group Attention</td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td></td><td></td><td>✓</td><td></td><td>✓</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>✓</td></tr><tr><td rowspan=\"2\">mAP</td><td>ZSL</td><td>25.3</td><td>27.3</td><td>28.4</td><td>27.9</td><td>29.4</td></tr><tr><td>GZSL</td><td>8.1</td><td>8.5</td><td>9.2</td><td>8.8</td><td>10.2</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/8458772c1181ee73b3a85ca3b2e670d4a44bffd3c2387a13e1980532fbf7d75e.jpg",
+        "image_caption": [
+            "(a) W/O (ML) $^2$ P-Encoder"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            124,
+            484,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/7fcdb68df0c0c5df9c57d97fe0df8368ca7255d03e4d7cbd853a81342d753669.jpg",
+        "image_caption": [
+            "(b) With  $(\\mathrm{ML})^{2}\\mathrm{P}$  -Encoder",
+            "Figure 3. Evaluation of t-SNE (zoom in for a better view)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Hyper-parameter Selection",
+        "text_level": 1,
+        "bbox": [
+            76,
+            635,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Our method includes two hyper-parameters, the number of groups  $g$  and the weight of the regularization term  $\\lambda$ . We use the control variable method. In terms of initializing hyper-parameters, the number of output semantic vectors  $g$  is set to 7, and the value of  $\\lambda$  is set to 0.4. The line graph in Figure 4 shows the mAP results achieved on the ZSL and GZSL tasks with different hyper-parameters, respectively. In addition, we can also see the impact of changes in hyperparameters on the prediction accuracy of the model. It can be seen that the number of  $g$  does not have a very significant effect on the mAP of the ZSL task. But the impact on GZSL is more obvious. After comparison, we believe that when  $g = 7$ , two different tasks can be well balanced. For the choice of the value of  $\\lambda$ , we found that its change will have a greater impact on mAP. But only when  $\\lambda = 0.4$ , the performance of GZSL is far better than other results, and",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "ZSL also achieves the optimal result. So the optimal hyperparameters we choose  $g = 7$  and  $\\lambda = 0.4$ .",
+        "bbox": [
+            498,
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/a1657c3c9aeb342e41cd7a891fefffd25bd38870895024e77f74a63090faedec.jpg",
+        "image_caption": [
+            "(a)  $g$"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            509,
+            136,
+            694,
+            229
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/bea5c061b33965db1460c351ea8d6dc9e5548fde810a154ead8e86167d85a405.jpg",
+        "image_caption": [
+            "(b) Weights"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            699,
+            137,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/2e12f6e418094ab26027de6309daa2eb11ad2e6a6744aca0b614f345deb31613.jpg",
+        "image_caption": [
+            "Figure 4. Hyper-Parameter selection. The higher the mAP the better. All the experiments are performed on the NUS-WIDE test-set.",
+            "(a) mAP"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            504,
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+            620,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/be864e674cccd18cea12bbdcc3f4e639ca3700f6bc6523390a63dd95126fd3e0.jpg",
+        "image_caption": [
+            "(b) Inference time (ms)",
+            "Figure 5. Comparison of our  $(\\mathbf{ML})^2\\mathbf{P}$ -Encoder with BiAM and LESA in mAP, inference time, and FLOPs. The higher the mAP the better, the lower the Inference time and GFLOPs the better. All methods are performed on the NUS-WIDE test-set."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            635,
+            329,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/2455e527a5bdeb3bb22c7b815463f0c08e291f6c7add9f25ddff4192a6829139.jpg",
+        "image_caption": [
+            "(c) GFLOPs"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Ablation Study: To illustrate the effectiveness of each module designed in our method, we arrange three comparative experiments. The specific results are shown in Table 3. As the most primitive structure, model 'a' only contains shuffle and grouping operations. But after adding the 'Forward Pyramid', the model expands the number of features. As the number of optional feature channels increases, the amount of information brought by the channel also increases, thus achieving more competitive results. The addition of  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder enables the model to process the channel response of specific classes. The supplement of Group Attention is to give the model-specific information for solving multi-label tasks, that is, inter-class correlation. The combination of  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder and Group Attention greatly improves the prediction ability of the model in ZSL and GZSL tasks, indicating that our model construction has achieved great success.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "t-SNE: Figure 3 shows the performance of  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder in t-SNE visualization. It can be seen that after using  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder, the boundaries of inter-class become much clearer, proving the correctness of our exploration for class-specific channel responses.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Different Backbones: Table 4 shows the results produced by our method using different backbones. It can be seen from the results that ResNet [20] has obvious advantages",
+        "bbox": [
+            496,
+            854,
+            890,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "23865",
+        "bbox": [
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+            944,
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+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "over VGG [37]. As the ResNet network deepens and the number of parameters increases, the results obtained by our model become better. This is exactly in line with the result variation of an end-to-end model.",
+        "bbox": [
+            75,
+            90,
+            470,
+            151
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/0ededf22f384f4ae5ec4f8b10f45a702bb8521ddc0a28618eb5eecf6a9dfdb1f.jpg",
+        "table_caption": [
+            "Table 4. Our  $\\mathbf{C}^3$ -MLZSL approach with different backbones for multi-label ZSL and GZSL tasks on the NUS-WIDE dataset. We show the indicators of F1-Score in the case of  $K \\in 3, 5$  and mAP. The best results are shown in bold."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Backbones</td><td>Task</td><td>mAP</td><td>F1 (K = 3)</td><td>F1 (K = 5)</td></tr><tr><td rowspan=\"2\">VGG19 [37]</td><td>ZSL</td><td>29.4</td><td>32.8</td><td>32.3</td></tr><tr><td>GZSL</td><td>10.2</td><td>15.8</td><td>19.2</td></tr><tr><td rowspan=\"2\">ResNet50 [20]</td><td>ZSL</td><td>30.9</td><td>33.6</td><td>33.2</td></tr><tr><td>GZSL</td><td>10.7</td><td>15.9</td><td>19.4</td></tr><tr><td rowspan=\"2\">ResNet101 [20]</td><td>ZSL</td><td>31.2</td><td>33.9</td><td>33.9</td></tr><tr><td>GZSL</td><td>10.9</td><td>16.1</td><td>19.5</td></tr></table>",
+        "bbox": [
+            81,
+            229,
+            460,
+            351
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/35da844c0da731cac057f029763ba3bb2787c08a55a9372c0d286eebe3ef9a00.jpg",
+        "image_caption": [
+            "Figure 6. Attention visualization. where (a) is the attention response of our  $\\mathbf{C}^3$ -MLZSL when faced with unseen labels. (b) is the comparison of attention visualization results of our  $\\mathbf{C}^3$ -MLZSL and BiAM [35] models. See appendix for more results."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "4.5. Multi-Label Learning",
+        "text_level": 1,
+        "bbox": [
+            76,
+            665,
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+            681
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 5 shows the results of the model for multi-label image classification. The baselines we compare include not only state-of-the-art MLZSL models, but also multi-label image classification models including Logistic Regression [40], WSABIE [43], WARP [17] and CNN-RNN [42]. As can be seen from the results, our model far surpasses many multi-label image classification models and the classic Fast0Tag [49] algorithm in mAP performance. This is because the above models only process the input image into a single semantic vector, and limited image embedding cannot build the semantic diversity for multi-label classification. For other methods such as LESA [22] and BiAM [35], they noticed that the attention regions of different objects in multi-label images are different, and thus define the label",
+        "bbox": [
+            75,
+            688,
+            470,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/2d41ff5bccca30a3291db40de3b266d2f897d4e468be17fac5193a0af7e92cc9.jpg",
+        "table_caption": [
+            "Table 5. Performance of Multi-label image classification task on NUS-WIDE datasets. The best results are in bold."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>F1(K=3)(↑)</td><td>F1(K=5)(↑)</td><td>mAP(↑)</td></tr><tr><td>Logistic [40]</td><td>51.1</td><td>46.1</td><td>21.6</td></tr><tr><td>WARP [17]</td><td>54.4</td><td>49.4</td><td>3.1</td></tr><tr><td>WSABIE [43]</td><td>53.8</td><td>49.2</td><td>3.1</td></tr><tr><td>Fast0Tag [49]</td><td>53.8</td><td>48.6</td><td>22.4</td></tr><tr><td>CNN-RNN [42]</td><td>55.2</td><td>50.8</td><td>28.3</td></tr><tr><td>Kim et al. [23]</td><td>56.8</td><td>51.3</td><td>32.6</td></tr><tr><td>LESA ApC [22]</td><td>56.6</td><td>50.7</td><td>31.7</td></tr><tr><td>LESA [22]</td><td>58.0</td><td>52.0</td><td>31.5</td></tr><tr><td>BiAM [35]</td><td>59.6</td><td>53.4</td><td>47.8</td></tr><tr><td>Ours</td><td>59.8</td><td>53.8</td><td>48.0</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "related embeddings from the perspective of the spatial domain. However, after feature extraction, our model takes into account that the channel response can be important information representing the class semantics, and this superior performance just verifies the rationality of the exploration.",
+        "bbox": [
+            496,
+            325,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            445,
+            617,
+            460
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we focus on the neglect of channel-wise class information and over-reliance on spatial-wise class information in previous MLZSL models, then propose C3-MLZSL structure and the  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder component. The C3-MLZSL structure first group multi-scale features, then use the  $(\\mathrm{ML})^{2}\\mathrm{P}$ -Encoder to calculate the correlation of channels within each group and perform information fusion to get the semantic vectors. These semantic vectors are then aggregated through group attention to learn mutual information between groups. Finally, the model successfully learns channel-class correlation. Extensive experiments on the large-scale NUS-WIDE and Open-Images-V4 datasets show that our model has achieved very competitive results on MLZSL compared with other state-of-the-art models.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Acknowledgment",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "This research was supported by fundings from the Key-Area Research and Development Program of Guangdong Province (No. 2021B0101400003), Hong Kong RGC Research Impact Fund (No. R5060-19), Areas of Excellence Scheme (AoE/E-601/22-R), General Research Fund (No. 152203/20E, 152244/21E, 152169/22E, 152211/23E), Shenzhen Science and Technology Innovation Commission (JCYJ20200109142008673), the National Natural Science Foundation of China (No. 62102327), and PolyU Internal Fund (No. P0043932).",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "23866",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
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2023/(ML)$^2$P-Encoder_ On Exploration of Channel-Class Correlation for Multi-Label Zero-Shot Learning/2f5d72e4-31bc-4c21-9948-28d1063a50fb_origin.pdf

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2023/(ML)$^2$P-Encoder_ On Exploration of Channel-Class Correlation for Multi-Label Zero-Shot Learning/full.md

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+# $(\mathbf{ML})^{2}\mathbf{P}$ -Encoder: On Exploration of Channel-class Correlation for Multi-label Zero-shot Learning
+
+Ziming Liu<sup>1</sup>, Song Guo<sup>1,2</sup>, Xiaocheng Lu<sup>1</sup>, Jingcai Guo<sup>1,2*</sup>, Jiewei Zhang<sup>1</sup>, Yue Zeng<sup>1</sup>, Fushuo Huo<sup>1</sup>  
+<sup>1</sup>Department of Computing, The Hong Kong Polytechnic University, Hong Kong SAR, China  
+<sup>2</sup>The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, China
+
+{ziming.liu, jiewei.zhang, fushuo.huo}@connect.polyu.hk {song.quo, xiaoclu, jc-jingcai.quo, zengyue.zeng}@polyu.edu.hk
+
+# Abstract
+
+Recent studies usually approach multi-label zero-shot learning (MLZSL) with visual-semantic mapping on spatial-class correlation, which can be computationally costly, and worse still, fails to capture fine-grained class-specific semantics. We observe that different channels may usually have different sensitivities on classes, which can correspond to specific semantics. Such an intrinsic channel-class correlation suggests a potential alternative for the more accurate and class-harmonious feature representations. In this paper, our interest is to fully explore the power of channel-class correlation as the unique base for MLZSL. Specifically, we propose a light yet efficient Multi-Label MultiLayer Perceptron-based Encoder, dubbed  $(ML)^{2}P$ -Encoder, to extract and preserve channel-wise semantics. We reorganize the generated feature maps into several groups, of which each of them can be trained independently with  $(ML)^{2}P$ -Encoder. On top of that, a global group-wise attention module is further designed to build the multilabel specific class relationships among different classes, which eventually fulfills a novel Channel-Class Correlation MLZSL framework  $(C^{3}$ -MLZSL). Extensive experiments on large-scale MLZSL benchmarks including NUS-WIDE and Open-Images-V4 demonstrate the superiority of our model against other representative state-of-the-art models.
+
+# 1. Introduction
+
+The proliferation of smart devices has greatly enriched human life when it comes to the era of big data. These smart devices are usually equipped with cameras such that users can easily produce and share their images. With the increasing abundance of public images, how to analyze them accurately has become a challenging problem. Recent years
+
+![](images/012ebce2bca2908a1ed88b5b724c2627dd75ef1002f2138229d4a579b04f8c43.jpg)  
+Figure 1. Example of Channel-Class Correlation. Our method achieves the prediction of unseen classes by exploiting the unique distribution of channel responses as semantic information for the class and building correlations with responses from the same channel (zoom in for a better view).
+
+have witnessed great success in classifying an image into a specific class [20, 37, 39], namely, single-label classification. However, in reality, the images [17,46] usually contain abundant information and thereby consist of multiple labels.
+
+In recent years, the multi-label classification has been widely investigated by exploring the relationship among different labels from multiple aspects [9, 13, 14, 16, 42]. However, in some scenarios where extensive collections of images exist, e.g., Flickr $^2$ , users can freely set one or more individual tags/labels for each image, while the presented objects and labels in these images may not be fully shown in any previous collection, and thus result in a domain gap for the recognition. Therefore, in real-world applications, the model is required to gain the ability to predict unseen classes as well. As one of the thriving research topics, zero-
+
+shot learning (ZSL) [1, 12, 15, 34] is designed to transfer tasks from seen classes to unseen classes, and naturally recognizes novel objects of unseen classes. Specifically, ZSL has made continuous success in single-label classification [19, 26, 31, 45, 48]. However, these methods can hardly be extended to the multi-label scenario since exploring the cross-class relationships in an image is non-trivial.
+
+Recently, some works have focused on multi-label zero-shot learning (MLZSL) tasks and obtained some promising results [33, 36, 49]. Other works considered incorporating attention mechanisms into their models, such as  $LESA$  [22] and  $BiAM$  [35].  $LESA$  [22] designed an attention-sharing mechanism for different patches in the image so that each patch can output the corresponding class. In another way,  $BiAM$  [35] designed a bi-level attention to extract relations from regional context and scene context, which can enrich the regional features of the model and separate the features of different classes.
+
+Although previous works have made considerable progress, their designed methods have been limited to the processing of spatial-domain information. First of all, the over-reliance on spatial-class correlation fails to capture fine-grained class-specific semantics. In addition, the additional processing of spatial information greatly increases the computational cost of the model and limits the inference speed. Given the shortcomings of the above methods, we found through analysis that the channel response can be used as the semantic information of the class. Firstly, the response of each class in the channel is unique, which creates conditions for obtaining the unique semantics. Secondly, for classes with certain semantic associations, there must be some channels that capture their common information. Therefore, channel information, as an easily overlooked part after feature extraction, can complete the task of capturing multi-label information. In MLZSL, we can complete the prediction of unseen classes by obtaining the responses of seen classes in the channel domain, and the relationship between seen and unseen classes. Finally, the subsequent analysis of the channel response greatly saves computational costs.
+
+Specifically, as shown in Figure 1, as seen classes, "water" and "tree" have unique response distributions on feature channels, and these responses can be used as semantic information for classification tasks. Besides, in order to explore the correlation of classes, we found that although the semantic information of "water" and "tree" is different, there are still some channels that respond simultaneously (i.e. the blue channel). We need to build this correlation during the training process through modeling so that the model can learn multi-label correlations. In the ZSL process, for the unseen class "garden", we know that it is related to "water" (i.e. purple layer) and "tree" (i.e. green, orange, and gray layer) by obtaining its semantic information and matching
+
+with seen classes. This observation suggests that channels can help not only to classify objects but also to establish associations between classes. Previous methods which only consider spatial information are unable to obtain this intrinsic channel-class correlation and dissimilarity, thus achieving sub-optimal performance on the MLZSL task.
+
+To address the above challenges and construct a more accurate and robust MLZSL system, we propose to group the generated feature maps and process them in a group-wise manner, thus enhancing the model by fully exploring the channel-class correlations. Besides, by properly designing a light yet efficient Multi-Label Multi-Layer Perceptron-based Encoder, i.e.,  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder, we can easily analyze the local relationship between channels while significantly reducing the computation overhead. Finally, these groups are recombined and then perform the calculation of group attention, indicating that the model is analyzed locally and globally from the perspective of the channels, which can ensure the integrity of the representation.
+
+In summary, our contributions are four-fold:
+
+1. To the best of our knowledge, our method first suggests the concept of channel-class correlation in MLZSL, and proposes a channel-sensitive attention module  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder to extract and preserve channel-wise semantics for channel groups.  
+2. Different from previous works that use spatial-class correlation to extract global and local features, we alternatively explore the channel-class correlation as the unique base for MLZSL.  
+3. In conjunction with  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder, a global group-wise attention is also designed to establish the multi-label specific class relationships among classes.  
+4. Extensive experiments on large-scale datasets NUS-WIDE and Open-Images-V4 demonstrate the effectiveness of our method against other state-of-the-art models.
+
+# 2. Related Work
+
+# 2.1. Multi-Label Classification
+
+The establishment of graph neural networks (GNNs) brings remarkable success to multi-label classification tasks [8, 25]. Among them, Chen et al. [8] constructs directed graphs for object labels and uses graph convolutional networks (GCN) to map label nodes, which contain word embeddings, into classifiers. In addition, the CNN-based multi-label classification models enable the learning of the characteristics of each label from the spatial information of the image and design a new multi-label classifier [13, 14, 16, 17, 42, 43, 46]. Gao et al. [16] suggests a two-stream framework to identify global and local information
+
+![](images/5c95f6e5e4e83008579a6320d2bbd777ec3c50f5b321ab9aef414704b93cb307.jpg)  
+Figure 2. Pipeline for  $\mathbf{C}^3$ -MLZSL. The input image is first passed through the feature extraction network (eg. VGG19), and then multi-layer feature maps are extracted through the Forward Pyramid module. After the feature maps are shuffled and grouped, each group uses  $(\mathbf{ML})^{2}\mathbf{P}$ -Encoder to extract semantic information. Then, the semantic information generated by all groups is associated through Group Attention to generate the final semantic matrix  $\mathcal{S}$  (zoom in for a better view).
+
+separately and a multi-class regional attention module to align them. However, the above methods cannot generalize to unseen classes.
+
+# 2.2. Zero-Shot Learning
+
+Zero-shot learning provides a solution to recognize unseen classes. Current studies mostly consider a relatively simple single-label scenario [4, 6, 26, 30, 32, 47, 50, 51]. In practice, existing methods usually focus on finding the main semantic information of training images, and then exploit the semantic relationship, i.e., word vectors [15, 38, 44, 45] or attribute vectors [3, 27, 28], between seen and unseen classes for prediction. The generated semantic information can be inferred from seen to unseen labels by comparing the similarity of the relation vectors between them. For example, Chen et al. [7] proposes a generative flow framework and uses a combinatorial strategy to solve the problems of semantic inconsistency, variance collapse, and structural disorder in zero-shot learning. Gune et al. [18] generates visual proxy samples to simulate the average entropy of the label distribution of the unseen class. However, the above methods only predict single labels with a single representation of images, which can hardly generalize to a more realistic multi-label scenario.
+
+# 2.3. Multi-Label Zero-Shot Learning
+
+Multi-label zero-shot learning has received increasing attention recently. For example, Norouzi et al. [36] designs two separate spaces, i.e., the image and semantic embedding spaces, jointly with the convex combination of the label embedding vectors to achieve multi-label recognition in the zero-shot learning framework. Zhang et al. [49] proposes a fast and general model based on the fact that the word vectors of the relevant labels are ranked before
+
+the irrelevant word vectors in the main vector of the image. Different from the above methods, Lee et al. [29] uses the knowledge graph to connect different labels. In recent years, attention-based methods become the mainstream. For example, LESA [22] applies an attention-sharing mechanism to the multi-label environment, allowing the model to focus on the key areas of each label. Narayan et al. [35] uses a bi-layer attention module to combine global context information and local features and map the generated information to the semantic space. However, the above methods only stay at the two-dimensional space level  $(H\times W)$ , and do not consider the response between different feature channels with respect to classes.
+
+# 3. Methods
+
+# 3.1. Problem Setting
+
+Before proposing our method, we first explain the definition of the MLZSL problem. Given  $n$  input samples  $\{(I_1,Y_1),\ldots ,(I_i,Y_i),\ldots ,(I_n,Y_n)\}$ , where  $I_{i}$  represents the input image of the  $i$ -th train-set, and  $Y_{i}$  represents the training labels corresponding to the input images, which are also called 'seen labels'. On the label distribution, let us set the seen label in the dataset as  $C_s$ , where the seen label refers to the label known by the model.  $C_s$  is mainly used for the train-set of the model in zero-shot learning. We set the unseen label to  $C_u$ , and the unseen label is generally used in the test-set. The label relationship in the dataset is defined as  $\mathcal{C} = \mathcal{C}_s\cup \mathcal{C}_u$ , where  $\mathcal{C}$  represents the set of all labels in the dataset. Based on the above definition, after the model is trained on the train-set, in the testing part of MLZSL, given the image  $I_{u}$ , the model can output the prediction result  $y_{u}\subset C_{u}$ . While in the generalized zero-shot learning task, given an image  $I_{u}$ , the output of the model is
+
+$y_{u} \subset \mathcal{C}$ , which means the model needs to output both the seen label and the unseen label that exist in the image.
+
+# 3.2.  $(\mathbf{ML})^{2}\mathbf{P}$  -Encoder
+
+The proposed network structure is shown in Figure 2. For input images  $I$ , we first use a pre-trained feature extraction network to obtain the corresponding image features  $\mathcal{F}$ . We extract the features from the last three layers of the feature extraction network, and keep the two layers with the larger size consistent with the smallest size layer by downsampling. For example, assuming that the used and training network is VGG19 [37], the size of the last three layers of feature maps is  $\{28 \times 28, 14 \times 14, 7 \times 7\}$ . We use max-pooling to down-sample the large-scale feature maps to obtain equivalent  $7 \times 7$  feature maps. This step is called the "Forward Pyramid". After that, we obtain feature maps at different levels with the same scale. Then we randomly shuffle them to get the feature map  $\mathcal{F}_a$  and re-group them into  $g$  different groups, each group has  $d_w$  channels, which is the same length as the word vectors in the ground-truth semantic space. The purpose of this operation is to generate specific semantic vectors to express the semantic information contained in each group.
+
+Next, the features of each group are fed into  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder. First, we need to calculate the correlation between channels within each group. In traditional self-attention, the cost of computation greatly consumes the inference speed of the model, and the traditional self-attention module cannot accurately reflect the relationship between each channel. To solve the loss caused by the amount of calculation and accurately reflect the channel correlation, we designed a new self-attention structure to achieve this.
+
+For features  $\mathcal{F}_a$  in group  $i$ , which is  $\mathcal{F}_a^i \in \mathbb{R}^{H \times W \times d_w}$ . We first generate Query (Q), Value (V) and Key (K) through three convolution operations:
+
+$$
+\mathbf {Q} = W _ {p} ^ {Q} \mathcal {F} _ {a} ^ {i} \quad \mathbf {K} = W _ {p} ^ {K} \mathcal {F} _ {a} ^ {i} \quad \mathbf {V} = W _ {p} ^ {V} \mathcal {F} _ {a} ^ {i} \tag {1}
+$$
+
+where  $W_{p}^{(\cdot)}$  means the convolution operation. Next, to obtain the channel correlation matrix  $\mathcal{R}$ , we reshape  $\mathbf{Q},\mathbf{K}$  and  $\mathbf{V}$  in the spatial domain  $(H\times W)$  to get  $\widehat{\mathbf{Q}}\in \mathbb{R}^{HW\times d_w}$ ,  $\widehat{\mathbf{K}}\in \mathbb{R}^{d_w\times HW}$  and  $\widehat{\mathbf{V}}\in \mathbb{R}^{HW\times d_w}$ . Then perform a dot product operation on  $\mathbf{Q}$  and  $\mathbf{K}$  to obtain the channel correlation matrix  $\mathcal{R}\in \mathbb{R}^{d_w\times d_w}$ . After that, we do the dot product between  $\mathcal{R}$  and  $\mathbf{V}$ , finally, add with the input  $\mathcal{F}_a^i$  to get the output  $\widehat{\mathcal{F}}_a^i\in \mathbb{R}^{H\times W\times d_w}$ :
+
+$$
+\operatorname {A t t} (\widehat {\mathbf {Q}}, \widehat {\mathbf {K}}, \widehat {\mathbf {V}}) = \widehat {\mathbf {V}} \cdot \underset {\mathcal {R}} {\operatorname {s o f t m a x}} (\underbrace {\widehat {\mathbf {K}} \cdot \widehat {\mathbf {Q}}} _ {\mathcal {R}}) \tag {2}
+$$
+
+$$
+\widehat {\mathcal {F}} _ {a} ^ {i} = \mathcal {F} _ {a} ^ {i} + \operatorname {A t t} (\widehat {\mathbf {Q}}, \widehat {\mathbf {K}}, \widehat {\mathbf {V}}) \tag {3}
+$$
+
+After enhancing the correlation between channels, we need to extract and analyze the feature information contained in
+
+each channel. We reshape the information in the spatial domain into a one-dimensional vector, then we decide to use the Multi-Layer Perceptron (MLP) to encode the features. Compared with the traditional convolution structure, the MLP structure is convenient to perform information fusion between local regions. Specifically, for the input feature  $\widehat{\mathcal{F}}_a^i\in \mathbb{R}^{H\times W\times d_w}$ , we first change the dimension from  $H\times W\times d_w$  to  $\mathcal{F}_{mlp}^i\in \mathbb{R}^{d_w\times HW}$ , then we use LayerNorm to normalize the input. Our MLP structure includes two different MLPs: MLP1 is used to extract the spatial information contained in each channel, and MLP2 is proposed to obtain local information of different channels in the spatial domain:
+
+$$
+\mathcal {F} _ {m l p 1} ^ {i} = \mathcal {F} _ {m l p} ^ {i} + \mathbf {W} _ {2} \sigma \left(\mathbf {W} _ {1} \text {L a y e r N o r m} \left(\mathcal {F} _ {m l p} ^ {i}\right)\right) \tag {4}
+$$
+
+$$
+\mathcal {M} = \mathcal {F} _ {m l p 1} ^ {i} + \mathbf {W} _ {4} \sigma \left(\mathbf {W} _ {3} \text {L a y e r N o r m} \left(\mathcal {F} _ {m l p 1} ^ {i}\right)\right) \tag {5}
+$$
+
+where  $\mathcal{F}_{mlp1}^i$  is the output after MLP1.  $\mathbf{W}_1$ ,  $\mathbf{W}_2$  is the parameter of MLP1, and  $\mathbf{W}_3$ ,  $\mathbf{W}_4$  is the parameter of MLP2.  $\sigma$  is an element-wise non-linearity GELU [21]. Then we use max-pooling to filter out the best semantic vector in the spatial domain, which can more accurately represent the semantic information of this group. This max-pooling operation is also to be able to directly extract the channel response. So we obtain group semantic vectors  $\mathcal{X} \in \mathbb{R}^{g \times d_w}$  and send them into Group Attention.
+
+# 3.3. Group Attention
+
+Although we obtained group semantic vectors  $\mathcal{X}$  through  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder, the semantic vectors generated by each group did not establish a relationship with each other at this time. As we already know, the key to improving the accuracy of multi-label image classification is to construct the correlation of labels within the image. So we use Group Attention to build the mutual information and also to find similar responses between different labels. We pass a series of linear layers to  $\mathcal{X}$ :
+
+$$
+\mathbf {Q} _ {\mathbf {x}} = W _ {x} ^ {Q} \mathcal {X} \quad \mathbf {K} _ {\mathbf {x}} = W _ {x} ^ {K} \mathcal {X} \tag {6}
+$$
+
+$$
+\mathcal {S} = \left(\mathbf {Q} _ {\mathbf {x}} \cdot \mathbf {K} _ {\mathbf {x}}\right) \cdot \mathcal {X} \tag {7}
+$$
+
+where  $\mathbf{Q}_{\mathbf{x}} \in \mathbb{R}^{g \times d_w}$ , and we transpose  $\mathbf{K}_{\mathbf{x}}$  into  $\mathbf{K}_{\mathbf{x}} \in \mathbb{R}^{d_w \times g}$ .  $W_x^Q$  and  $W_x^K$  are different linear weights.  $S \in \mathbb{R}^{g \times d_w}$  is the semantic matrix, which contains all the semantic information of the input image. In the loss function, we will make each semantic vector in  $S$  approximate the semantic information of seen classes appearing in the image. Therefore, from another perspective, the semantic vectors in  $S$  are related to seen classes.
+
+# 3.4. Loss Function
+
+During training, some semantic vectors are generated for each input image. The semantic matrix  $S$  includes the semantic information in the image and is sent to the prediction
+
+module. The loss function consists of two parts. First of all, to make the positive class (seen class appear in each training image) get a higher ranking than the negative class (seen class which does not appear in the training image). Inspired by [49], we choose to adopt ranknet loss [5] as the main component of the loss function. We use
+
+$$
+\mu_ {i j} = \max  \left(\mathcal {S} \cdot n _ {i}\right) - \max  \left(\mathcal {S} \cdot p _ {j}\right), \tag {8}
+$$
+
+to indicate the number of violations of any of these ranking constraints, where  $n_i$  represents the semantic vector of the negative class, and  $p_j$  denotes the semantic vector of the positive class. max is used to maximize this gap between negative and positive, and constrain it in subsequent steps.
+
+Next, to minimize the gap, we design the loss function as the following:
+
+$$
+\mathcal {L} _ {\text {r a n k}} = \frac {1}{(| P | | \bar {P} |)} \sum_ {i} \sum_ {j} \log \left(1 + e ^ {\mu_ {i j}}\right), \tag {9}
+$$
+
+where  $\frac{1}{(|P| |\bar{P}|)}$  is used to normalize the ranknet loss, and  $|P|$  denotes the number of positive class,  $|\bar{P}|$  represents the number of negative class. When an image contains a large number of positive labels, the image becomes difficult to classify. So we need the model to value these hard samples during training. Therefore, we add the class weight  $\omega$  to improve the performance of the model in the face of hard samples.  $\omega$  is represented as:
+
+$$
+\omega = 1 + \sum_ {i} v a r (P ^ {i}), \tag {10}
+$$
+
+where  $P^i$  represents the vector of the  $i$ -th positive class,  $var$  means the variance. The higher  $\omega$  means the image contains more complex labels. To prevent the direction of the semantic vectors generated by the model from being too divergent, it needs to be controlled by the loss function. Therefore, we believe that the addition of regularization terms can reduce the difference between the generated semantic vectors when the model faces complex input images. This reduction in variance helps the model learn relevant information between different classes.
+
+$$
+\mathcal {L} _ {r e g} = \left\| \sum_ {n} v a r \left(\mathcal {S} _ {n}\right) \right\| _ {1}. \tag {11}
+$$
+
+Finally, the loss function of the model is defined as:
+
+$$
+\mathcal {L} = \frac {1}{N} \sum_ {i = 1} ^ {N} ((1 - \lambda) \cdot \omega \mathcal {L} _ {\text {r a n k}} (\mathcal {S} _ {i}, Y _ {i}) + \lambda \mathcal {L} _ {\text {r e g}} (\mathcal {S} _ {i})) \tag {12}
+$$
+
+where  $N$  means the number of batch size, and  $\lambda$  is a hyperparameter that denotes the regularization term's weight.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Datasets: First, we use the NUS-WIDE dataset [10] to conduct MLZSL experiments. The NUS-WIDE dataset contains about 270,000 images, and each image contains 925 labels, which are automatically extracted from Flickr user tags. In addition, it also contains 81 labels that are manually annotated by humans, and these labels are called 'GroundTruth'. During the experiment, 925 labels were used as 'seen labels', and 81 labels were used as 'unseen labels'. This setting is similar with [22]. Another dataset is called the Open-Images-V4 dataset. This dataset contains nearly 9 million training images, 125,456 images as test images, and 41,620 images in the validation set. The train-set contains 7,186 labels, which are 'seen labels' that appear at least 100 times in the train-set. While the remaining 400 most frequent labels that do not appear in the train-set are used as test-set labels, they are also used as 'unseen labels'. Each unseen label has at least appeared 75 times.
+
+Evaluation Metrics: To better allow our proposed new model and other comparative models to perform an unbiased comparison on the task of MLZSL, we use the two most common evaluation metrics, the mean Average Precision (mAP) [22, 41] and F1-Score. Among them, top-K F1-Score is used to measure the accuracy of the model for label prediction, and mAP is used to reflect the accuracy for unseen label retrieval of the image.
+
+Implementation Details: Our model can support end-to-end training. We choose VGG19 [37], pre-trained on ImageNet dataset [11], as the backbone network. Unlike other methods, our model uses multi-scale feature maps and aggregates them. The sizes of the feature maps are  $28 \times 28$ ,  $14 \times 14$ , and  $7 \times 7$ , respectively.
+
+In terms of the optimizer, we choose to use the Adam optimizer [24], which requires less memory and is suitable for large datasets. The weight decay of the Adam optimizer is set to  $4e^{-3}$ . In the NUS-WIDE dataset experiments, the initial learning rate of the model is  $5e^{-5}$ , and then the learning rate decreases by  $\frac{1}{10}$  at the 7th epoch. The entire experimental process of the NUS-WIDE dataset requires a total of 20 epochs with a batch size of 48. In the experiments using the Open-Images-V4 dataset, our learning rate, batch size, and decay rate remain the same as the NUS-WIDE dataset, but the number of epochs is 7.
+
+Baselines: We will compare the proposed method with several state-of-the-art deep learning-based MLZSL models. These comparative methods have been published in recent years and cover a fairly rich variety of techniques, such as the attention mechanism with the most common CNNs. These comparison methods include: CONSE [36], LabelEM [2], Fast0Tag [49], Kim et al. [23], LESA Attention per Cluster (ApC) [22], LESA [22], and BiAM [35]. All
+
+comparison methods using VGG19 [37] are not fine-tuned. In addition to comparing with comparison models, we will also test the model's performance under different settings of hyper-parameters  $g$  and  $\lambda$ . At the same time, we will conduct ablation experiments to verify the integrity of the model's architecture.
+
+# 4.2. State-of-the-art Comparison
+
+NUS-WIDE: Table 1 shows the performance of ours and competitive methods on the NUS-WIDE test-set. The table contains the results of both ZSL and GZSL. CONSE [36] and LabelEM [2], as the methods proposed earlier, do not perform well on large-scale datasets. Fast0Tag [49] achieves more competitive results by sorting the positive labels to find the principal directions of the image. LESA [22] and BiAM [35] are currently the most advanced models that rely on spatial attention mechanism to generate semantic information. Compared to BiAM, our method achieves a  $3.6\%$  improvement on mAP in the ZSL task. Besides, we lead BiAM by  $0.8\%$  and  $2.9\%$  in F1-Score of  $K = 3$  and  $K = 5$ , respectively. On the GZSL task, we also surpass BiAM. BiAM deals with higher-dimensional and richer spatial information, while our method is more inclined to single-dimensional channel responses. Therefore, it is not easy to achieve such results with  $1.3\%$  improvement in mAP and  $0.3\%$  and  $0.7\%$  in F1-Score of  $K = 3$  and  $K = 5$ , respectively. Good results on NUS-WIDE dataset imply the effectiveness of our method.
+
+Attention Visualization on NUS-WIDE: Figure 6 illustrate the attention regions of the model when our method predicts unseen labels. Figure 6(a) shows that our model can clearly distinguish scene information from all unseen classes. The attention areas of "Rocks" and "Mountain" in the figure are roughly the same, which indicates that the two classes have similar semantics and dependencies, and the existence of Group Attention enables the model to learn this mutual information well. Figure 6(b) is a comparison with BiAM [35], the best existing model for mining spatial domain information. This result fully shows the effective use of channel information can more accurately grasp the response between classes. While BiAM's over-exploration of spatial information improves the acquisition of regional information, it loses the scene-level response at the same time. For more comparison results, please refer to appendix.
+
+Open-Images-V4: From Table 2, we show the results of ours and the baseline models on Open-Images-V4. We follow the evaluation setting of [22, 35]. This dataset contains more seen and unseen labels than NUS-WIDE. With a large increase in the number of classes, all methods get poor F1-Score on the ZSL task. Among them, Fast0Tag has made great progress compared with past methods, especially in the GZSL task. LESA [22] and BiAM [35], as the two best methods, represent the highest level of extracting spatial re
+
+Table 1. State-of-the-art comparison for multi-label ZSL and GZSL tasks on the NUS-WIDE dataset. We show the indicators of F1-Score in the case of  $K \in 3,5$  and mAP. The best results are shown in bold.  
+
+<table><tr><td>Method</td><td>Task</td><td>mAP</td><td>F1 (K = 3)</td><td>F1 (K = 5)</td></tr><tr><td rowspan="2">CONSE [36]</td><td>ZSL</td><td>9.4</td><td>21.6</td><td>20.2</td></tr><tr><td>GZSL</td><td>2.1</td><td>7.0</td><td>8.1</td></tr><tr><td rowspan="2">LabelEM [2]</td><td>ZSL</td><td>7.1</td><td>19.2</td><td>19.5</td></tr><tr><td>GZSL</td><td>2.2</td><td>9.5</td><td>11.3</td></tr><tr><td rowspan="2">Fast0Tag [49]</td><td>ZSL</td><td>15.1</td><td>27.8</td><td>26.4</td></tr><tr><td>GZSL</td><td>3.7</td><td>11.5</td><td>13.5</td></tr><tr><td rowspan="2">Kim et al. [23]</td><td>ZSL</td><td>10.4</td><td>25.8</td><td>23.6</td></tr><tr><td>GZSL</td><td>3.7</td><td>10.9</td><td>13.2</td></tr><tr><td rowspan="2">Attention per Cluster [22]</td><td>ZSL</td><td>12.9</td><td>24.6</td><td>22.9</td></tr><tr><td>GZSL</td><td>2.6</td><td>6.4</td><td>7.7</td></tr><tr><td rowspan="2">LESA [22]</td><td>ZSL</td><td>19.4</td><td>31.6</td><td>28.7</td></tr><tr><td>GZSL</td><td>5.6</td><td>14.4</td><td>16.8</td></tr><tr><td rowspan="2">BiAM [35]</td><td>ZSL</td><td>25.8</td><td>32.0</td><td>29.4</td></tr><tr><td>GZSL</td><td>8.9</td><td>15.5</td><td>18.5</td></tr><tr><td rowspan="2">Our Approach</td><td>ZSL</td><td>29.4</td><td>32.8</td><td>32.3</td></tr><tr><td>GZSL</td><td>10.2</td><td>15.8</td><td>19.2</td></tr></table>
+
+Table 2. State-of-the-art comparison for multi-label ZSL and GZSL tasks on the Open-Images-V4 dataset. We show the indicators of F1-Score in the case of  $K \in  {10},{20}$  and mAP. Best results are shown in bold.  
+
+<table><tr><td>Method</td><td>Task</td><td>mAP</td><td>F1 (K = 10)</td><td>F1 (K = 20)</td></tr><tr><td rowspan="2">CONSE [36]</td><td>ZSL</td><td>40.4</td><td>0.4</td><td>0.3</td></tr><tr><td>GZSL</td><td>43.5</td><td>2.6</td><td>2.4</td></tr><tr><td rowspan="2">LabelEM [2]</td><td>ZSL</td><td>40.5</td><td>0.5</td><td>0.4</td></tr><tr><td>GZSL</td><td>45.2</td><td>5.2</td><td>5.1</td></tr><tr><td rowspan="2">Fast0Tag [49]</td><td>ZSL</td><td>41.2</td><td>0.7</td><td>0.6</td></tr><tr><td>GZSL</td><td>45.2</td><td>16.0</td><td>13.0</td></tr><tr><td rowspan="2">Attention per Cluster [22]</td><td>ZSL</td><td>40.7</td><td>1.2</td><td>0.9</td></tr><tr><td>GZSL</td><td>44.9</td><td>16.9</td><td>13.5</td></tr><tr><td rowspan="2">LESA [22]</td><td>ZSL</td><td>41.7</td><td>1.4</td><td>1.0</td></tr><tr><td>GZSL</td><td>45.4</td><td>17.4</td><td>14.3</td></tr><tr><td rowspan="2">BiAM [35]</td><td>ZSL</td><td>62.8</td><td>4.1</td><td>3.7</td></tr><tr><td>GZSL</td><td>79.6</td><td>17.6</td><td>15.1</td></tr><tr><td rowspan="2">Our Approach</td><td>ZSL</td><td>65.7</td><td>7.5</td><td>6.5</td></tr><tr><td>GZSL</td><td>79.9</td><td>27.6</td><td>24.1</td></tr></table>
+
+sponses. BiAM achieves very large progress in mAP metrics on both ZSL and GZSL tasks. But our method achieves the best results in the mAP of ZSL, while leading by  $3.4\%$  and  $2.8\%$  in F1-Score with  $K = 3$  and  $K = 5$ , respectively. Most importantly, for the GZSL task, our F1-Score results also achieve huge advantages by  $10.0\%$  and  $9.0\%$ . This shows that the channel-class correlation as semantic information can fully cope with the complex situation of a large number of labels.
+
+Figure 5 shows the mAP, inference time, and GFLOPs comparisons between our model for obtaining semantic information based on channel responses and the two methods (LESA [22] and BiAM [35]) for acquiring semantic informa
+
+tion based on spatial features and achieving optimal results. In the mAP comparison, it can be seen that we have the highest accuracy for prediction in the ZSL task. At the same time, due to the small amount of data to be processed, the inference speed is the fastest of all comparison methods when we use the same GPU of NVIDIA RTX 3090. Finally, precisely because the model only needs to deal with a single-dimensional channel response, our  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder module requires much less computation than  $LESA$  and  $BiAM$  that deal with spatial attention. At the same time, the feature map is grouped to avoid the geometric increase of the computational complexity caused by the feature pyramid. This shows that our  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder can be more efficient.
+
+Table 3. Ablation study shows the contribution of the different components in our proposed approach. The baseline methods are performed on the NUS-WIDE test-set.  
+
+<table><tr><td colspan="2"></td><td>a</td><td>b</td><td>c</td><td>d</td><td>ours</td></tr><tr><td rowspan="3" colspan="2">Forward Pyramid (ML)2P-Encoder Group Attention</td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td></tr><tr><td></td><td></td><td>✓</td><td></td><td>✓</td></tr><tr><td></td><td></td><td></td><td>✓</td><td>✓</td></tr><tr><td rowspan="2">mAP</td><td>ZSL</td><td>25.3</td><td>27.3</td><td>28.4</td><td>27.9</td><td>29.4</td></tr><tr><td>GZSL</td><td>8.1</td><td>8.5</td><td>9.2</td><td>8.8</td><td>10.2</td></tr></table>
+
+![](images/8458772c1181ee73b3a85ca3b2e670d4a44bffd3c2387a13e1980532fbf7d75e.jpg)  
+(a) W/O (ML) $^2$ P-Encoder
+
+![](images/7fcdb68df0c0c5df9c57d97fe0df8368ca7255d03e4d7cbd853a81342d753669.jpg)  
+(b) With  $(\mathrm{ML})^{2}\mathrm{P}$  -Encoder  
+Figure 3. Evaluation of t-SNE (zoom in for a better view).
+
+# 4.3. Hyper-parameter Selection
+
+Our method includes two hyper-parameters, the number of groups  $g$  and the weight of the regularization term  $\lambda$ . We use the control variable method. In terms of initializing hyper-parameters, the number of output semantic vectors  $g$  is set to 7, and the value of  $\lambda$  is set to 0.4. The line graph in Figure 4 shows the mAP results achieved on the ZSL and GZSL tasks with different hyper-parameters, respectively. In addition, we can also see the impact of changes in hyperparameters on the prediction accuracy of the model. It can be seen that the number of  $g$  does not have a very significant effect on the mAP of the ZSL task. But the impact on GZSL is more obvious. After comparison, we believe that when  $g = 7$ , two different tasks can be well balanced. For the choice of the value of  $\lambda$ , we found that its change will have a greater impact on mAP. But only when  $\lambda = 0.4$ , the performance of GZSL is far better than other results, and
+
+ZSL also achieves the optimal result. So the optimal hyperparameters we choose  $g = 7$  and  $\lambda = 0.4$ .
+
+![](images/a1657c3c9aeb342e41cd7a891fefffd25bd38870895024e77f74a63090faedec.jpg)  
+(a)  $g$
+
+![](images/bea5c061b33965db1460c351ea8d6dc9e5548fde810a154ead8e86167d85a405.jpg)  
+(b) Weights
+
+![](images/2e12f6e418094ab26027de6309daa2eb11ad2e6a6744aca0b614f345deb31613.jpg)  
+Figure 4. Hyper-Parameter selection. The higher the mAP the better. All the experiments are performed on the NUS-WIDE test-set.  
+(a) mAP
+
+![](images/be864e674cccd18cea12bbdcc3f4e639ca3700f6bc6523390a63dd95126fd3e0.jpg)  
+(b) Inference time (ms)  
+Figure 5. Comparison of our  $(\mathbf{ML})^2\mathbf{P}$ -Encoder with BiAM and LESA in mAP, inference time, and FLOPs. The higher the mAP the better, the lower the Inference time and GFLOPs the better. All methods are performed on the NUS-WIDE test-set.
+
+![](images/2455e527a5bdeb3bb22c7b815463f0c08e291f6c7add9f25ddff4192a6829139.jpg)  
+(c) GFLOPs
+
+# 4.4. Ablation Study
+
+Ablation Study: To illustrate the effectiveness of each module designed in our method, we arrange three comparative experiments. The specific results are shown in Table 3. As the most primitive structure, model 'a' only contains shuffle and grouping operations. But after adding the 'Forward Pyramid', the model expands the number of features. As the number of optional feature channels increases, the amount of information brought by the channel also increases, thus achieving more competitive results. The addition of  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder enables the model to process the channel response of specific classes. The supplement of Group Attention is to give the model-specific information for solving multi-label tasks, that is, inter-class correlation. The combination of  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder and Group Attention greatly improves the prediction ability of the model in ZSL and GZSL tasks, indicating that our model construction has achieved great success.
+
+t-SNE: Figure 3 shows the performance of  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder in t-SNE visualization. It can be seen that after using  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder, the boundaries of inter-class become much clearer, proving the correctness of our exploration for class-specific channel responses.
+
+Different Backbones: Table 4 shows the results produced by our method using different backbones. It can be seen from the results that ResNet [20] has obvious advantages
+
+over VGG [37]. As the ResNet network deepens and the number of parameters increases, the results obtained by our model become better. This is exactly in line with the result variation of an end-to-end model.
+
+Table 4. Our  $\mathbf{C}^3$ -MLZSL approach with different backbones for multi-label ZSL and GZSL tasks on the NUS-WIDE dataset. We show the indicators of F1-Score in the case of  $K \in 3, 5$  and mAP. The best results are shown in bold.  
+
+<table><tr><td>Backbones</td><td>Task</td><td>mAP</td><td>F1 (K = 3)</td><td>F1 (K = 5)</td></tr><tr><td rowspan="2">VGG19 [37]</td><td>ZSL</td><td>29.4</td><td>32.8</td><td>32.3</td></tr><tr><td>GZSL</td><td>10.2</td><td>15.8</td><td>19.2</td></tr><tr><td rowspan="2">ResNet50 [20]</td><td>ZSL</td><td>30.9</td><td>33.6</td><td>33.2</td></tr><tr><td>GZSL</td><td>10.7</td><td>15.9</td><td>19.4</td></tr><tr><td rowspan="2">ResNet101 [20]</td><td>ZSL</td><td>31.2</td><td>33.9</td><td>33.9</td></tr><tr><td>GZSL</td><td>10.9</td><td>16.1</td><td>19.5</td></tr></table>
+
+![](images/35da844c0da731cac057f029763ba3bb2787c08a55a9372c0d286eebe3ef9a00.jpg)  
+Figure 6. Attention visualization. where (a) is the attention response of our  $\mathbf{C}^3$ -MLZSL when faced with unseen labels. (b) is the comparison of attention visualization results of our  $\mathbf{C}^3$ -MLZSL and BiAM [35] models. See appendix for more results.
+
+# 4.5. Multi-Label Learning
+
+Table 5 shows the results of the model for multi-label image classification. The baselines we compare include not only state-of-the-art MLZSL models, but also multi-label image classification models including Logistic Regression [40], WSABIE [43], WARP [17] and CNN-RNN [42]. As can be seen from the results, our model far surpasses many multi-label image classification models and the classic Fast0Tag [49] algorithm in mAP performance. This is because the above models only process the input image into a single semantic vector, and limited image embedding cannot build the semantic diversity for multi-label classification. For other methods such as LESA [22] and BiAM [35], they noticed that the attention regions of different objects in multi-label images are different, and thus define the label
+
+Table 5. Performance of Multi-label image classification task on NUS-WIDE datasets. The best results are in bold.  
+
+<table><tr><td>Method</td><td>F1(K=3)(↑)</td><td>F1(K=5)(↑)</td><td>mAP(↑)</td></tr><tr><td>Logistic [40]</td><td>51.1</td><td>46.1</td><td>21.6</td></tr><tr><td>WARP [17]</td><td>54.4</td><td>49.4</td><td>3.1</td></tr><tr><td>WSABIE [43]</td><td>53.8</td><td>49.2</td><td>3.1</td></tr><tr><td>Fast0Tag [49]</td><td>53.8</td><td>48.6</td><td>22.4</td></tr><tr><td>CNN-RNN [42]</td><td>55.2</td><td>50.8</td><td>28.3</td></tr><tr><td>Kim et al. [23]</td><td>56.8</td><td>51.3</td><td>32.6</td></tr><tr><td>LESA ApC [22]</td><td>56.6</td><td>50.7</td><td>31.7</td></tr><tr><td>LESA [22]</td><td>58.0</td><td>52.0</td><td>31.5</td></tr><tr><td>BiAM [35]</td><td>59.6</td><td>53.4</td><td>47.8</td></tr><tr><td>Ours</td><td>59.8</td><td>53.8</td><td>48.0</td></tr></table>
+
+related embeddings from the perspective of the spatial domain. However, after feature extraction, our model takes into account that the channel response can be important information representing the class semantics, and this superior performance just verifies the rationality of the exploration.
+
+# 5. Conclusion
+
+In this paper, we focus on the neglect of channel-wise class information and over-reliance on spatial-wise class information in previous MLZSL models, then propose C3-MLZSL structure and the  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder component. The C3-MLZSL structure first group multi-scale features, then use the  $(\mathrm{ML})^{2}\mathrm{P}$ -Encoder to calculate the correlation of channels within each group and perform information fusion to get the semantic vectors. These semantic vectors are then aggregated through group attention to learn mutual information between groups. Finally, the model successfully learns channel-class correlation. Extensive experiments on the large-scale NUS-WIDE and Open-Images-V4 datasets show that our model has achieved very competitive results on MLZSL compared with other state-of-the-art models.
+
+# 6. Acknowledgment
+
+This research was supported by fundings from the Key-Area Research and Development Program of Guangdong Province (No. 2021B0101400003), Hong Kong RGC Research Impact Fund (No. R5060-19), Areas of Excellence Scheme (AoE/E-601/22-R), General Research Fund (No. 152203/20E, 152244/21E, 152169/22E, 152211/23E), Shenzhen Science and Technology Innovation Commission (JCYJ20200109142008673), the National Natural Science Foundation of China (No. 62102327), and PolyU Internal Fund (No. P0043932).
+
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+        "text": "1% VS 100%: Parameter-Efficient Low Rank Adapter for Dense Predictions",
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+        "text": "Dongshuo Yin $^{1,2,\\dagger}$ , Yiran Yang $^{1,2,\\dagger}$ , Zhechao Wang $^{1,2}$ , Hongfeng Yu $^{1}$ , Kaiwen Wei $^{1,2}$ , Xian Sun $^{1,2,*}$ $^{1}$ Key Laboratory of Network Information System Technology, Aerospace Information Research Institute, Chinese Academy of Sciences  \n $^{2}$ School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences",
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+        "text": "{yindongshuo19, yangyiran19, wangzhechao21, weikaiwen19}@mails.ucas.ac.cn {yuhf, sunxian}@aircas.ac.cn",
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+        "text": "Abstract",
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+        "text": "Fine-tuning large-scale pre-trained vision models to downstream tasks is a standard technique for achieving state-of-the-art performance on computer vision benchmarks. However, fine-tuning the whole model with millions of parameters is inefficient as it requires storing a samesized new model copy for each task. In this work, we propose LoRand, a method for fine-tuning large-scale vision models with a better trade-off between task performance and the number of trainable parameters. LoRand generates tiny adapter structures with low-rank synthesis while keeping the original backbone parameters fixed, resulting in high parameter sharing. To demonstrate LoRand's effectiveness, we implement extensive experiments on object detection, semantic segmentation, and instance segmentation tasks. By only training a small percentage (1% to 3%) of the pre-trained backbone parameters, LoRand achieves comparable performance to standard fine-tuning on COCO and ADE20K and outperforms fine-tuning in low-resource PASCAL VOC dataset.",
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+        "text": "1. Introduction",
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+        "text": "With the rapid development of computer vision, parameters in deep models are surging. Giant models need to be trained with massive resources to achieve superior performance [3, 17, 47, 58], which is often unavailable to many academics and institutions. \"Pretrain & Finetuning\" paradigm is widely used to alleviate this dilemma. Teams with sufficient computation resources utilise enormous datasets [2, 9, 40, 50] to train superior backbones [4, 32, 40, 48] and optimise the models with ideal performances. Models pretrained in this way usually have a su",
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+        "image_caption": [
+            "Figure 1. Comparisons of trainable backbone parameters between our methods (red) and fine-tuning (black). In COCO, we achieve advanced performances and outperform most existing backbones with only  $0.9\\sim 2.5\\mathrm{M}$  new backbone parameters (Cascade-RCNN is employed as the detector). The fine-tuning paradigm produces massive redundant backbone parameters, whereas our approach saves over  $97\\%$  of hardware resources with competitive performances. The sizes of the circles intuitively compare the number of trainable parameters."
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+    {
+        "type": "text",
+        "text": "perior understanding of homogeneous data. After that, researchers with limited computational resources can transfer the understanding capabilities of the pre-trained models to downstream tasks with promising performances by finetuning [1,26,46,53].",
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+        "text": "However, the fine-tuned model will produce a new set of parameters as large as the pre-trained model. New parameters are independent of the pre-trained models and unshareable, which are very hardware intensive for cloud service providers [23, 49]. Figure 1 compares the parameter quantities of some remarkable backbones and their performances on the COCO [28] dataset. Recent advances in natural language processing (NLP) [30, 38] show that large pre-trained models trained with rich data have strong gener",
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+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "*Corresponding author.",
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+        "text": "20116",
+        "bbox": [
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/b58c6b179031f202b13762129589750230c30d575d80af5f850f0a002de939e8.jpg",
+        "image_caption": [
+            "Swin-Transformer Block"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            122,
+            87,
+            251,
+            318
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/7edbd25abc95b7d7da6fcc332f29fee39ad6e9b53dd1dfb97cf12b8d90b381de.jpg",
+        "image_caption": [
+            "LoRand Layer",
+            "Figure 2. Architecture of the adapter module and its integration with the Transformer. Left: We add two LoRand structures to each SwinBlock located behind the W/SW-MSA and MLP structures respectively. Right: LoRand contains two Multi-branch low-rank projections and nonlinearity. We include skip-connection to LoRand to enhance its robustness."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            267,
+            87,
+            424,
+            320
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "alisability, which means most parameters in the pre-trained models can be shared with the new tasks [22, 36, 37, 44, 59]. Moreover, recent literature demonstrates that the feature understanding of pre-trained models could be reduced when they are fine-tuned in low-resource situations [12, 36]. To tackle these issues, NLP researchers propose two new training paradigms based on pre-trained models: Adapter Tuning [22] and Prompt Tuning [30], both of which tune the new models by fixing the pre-trained parameters and adding a few trainable structures (less than  $10\\%$  of the backbone). These paradigms create a new buzz in NLP and achieve impressive performances which can be competitive with finetuning [12, 22, 30, 36-38, 44, 59]. Advances in NLP also shed new light on computer vision. Jia et al. [24] propose Visual Prompt Tuning (VPT) and demonstrate that VPT can outperform fine-tuning on image classification tasks by training a small number of trainable parameters. Nevertheless, VPT shows weakness on more challenging dense predictions like semantic segmentation compared with finetuning [24].",
+        "bbox": [
+            75,
+            458,
+            468,
+            760
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To find a parameter-efficient paradigm with promising performance in computer vision, we explore the potential of Adapter Tuning for visual dense predictions. We employ the advanced Swin Transformer [32] trained with ImageNet-22K [9] as the pre-trained model. After that, we add bottleneck adapter structures [22] behind each SwinBlock and freeze the original backbone parameters when training, but this approach cannot achieve comparable performance to fine-tuning as mentioned in [24]. In the experi",
+        "bbox": [
+            75,
+            763,
+            467,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "periments, we find that the models perform better with sparser adapter structures. To improve the performance of Adapter Tuning, we propose Low-Rank Adapter (LoRand) to reduce the adapter parameters, as shown in Figure 2. LoRand sparsely parameterizes the matrices in adapters by low-rank synthesis. Specifically, the projection matrix of the fully-connected layer (FC) in LoRand is a product of multiple low-rank matrices, which reduces FC parameters by more than  $80\\%$ . We implement extensive experiments on object detection (PASCAL VOC [14]), semantic segmentation (ADE20K [62]), and instance segmentation (MS COCO [28]) to verify the capability of LoRand. Experimental results show that LoRand-Tuning is comparable to fine-tuning on multiple tasks with only  $1.8\\%$  to  $2.8\\%$  new backbone parameters, which suggests that the pre-trained backbone parameters can be fully shared. More interestingly, our method completely outperforms fine-tuning on the PASCAL VOC dataset, illustrating that LoRand-Tuning can reduce the impairment of fine-tuning on pre-trained models in low-resource configurations. Our method demonstrates that the LoRand-Tuning paradigm can substantially save storage resources and achieve competitive performances on most dense prediction tasks. In summary, our contributions are three-fold:",
+        "bbox": [
+            496,
+            90,
+            890,
+            452
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We demonstrate that visual pre-trained models are highly generalisable and shareable. With our training methods, new tasks require only a few trainable parameters to achieve performances comparable to finetuning, which can save massive hardware resources.",
+            "- We propose the LoRand structure for sparser adapters based on low-rank synthesis. We demonstrate that the backbone parameters in fine-tuning are highly redundant, which can be replaced by  $1.8\\%$  to  $2.8\\%$  additional parameters in LoRand.",
+            "- Extensive experiments on object detection, semantic segmentation, and instance segmentation show that LoRand-Tuning can achieve remarkable performances and reduce massive new parameters in challenging dense prediction tasks."
+        ],
+        "bbox": [
+            516,
+            462,
+            890,
+            705
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
+            715,
+            640,
+            732
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. Training Paradigms in NLP",
+        "text_level": 1,
+        "bbox": [
+            500,
+            741,
+            750,
+            758
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Computer vision has been continuously inspired by NLP in recent years, including the visual transformer series [5,13,29,32] and self-supervised MAE series [15,19,60]. In fact, NLP is leading new training trends different from finetuning. Fine-tuning produces a new parameter set for each new task, which is parametrically inefficient for plenty of linguistic tasks [22,30]. To solve this problem, [30] and [22] have proposed \"Prompt Tuning\" and \"Adapter Tuning\" respectively, both of which fix all parameters of the backbone",
+        "bbox": [
+            496,
+            763,
+            890,
+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "20117",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "and plug a few tiny trainable structures (less than  $10\\%$  of the backbone) to adapt the pre-trained model to the new tasks. \"Prompt tuning\" adds learnable parameters (also known as prompts) to the input or intermediate layers to change the input space of the new tasks. \"Prompts\" can motivate the model to remember knowledge learned in the previous tasks. \"Adapter tuning\" adds learnable bottleneck structures after each block to connect the pre-trained model with new tasks. Adapter and prompt demonstrate the coexistence of parameter efficiency and high performances in NLP, stimulating studies in CV. [24] proposes Visual Prompt Tuning (VPT) for image classification and semantic segmentation, but the performance of VPT on semantic segmentation is still far from fine-tuning. This phenomenon motivates us to explore whether adapter tuning can bring a new paradigm in computer vision with fewer parameters and better performances. In this work, we try to explore parameter-efficient and high-performance adapter structures.",
+        "bbox": [
+            75,
+            90,
+            472,
+            363
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.2. Adapter Tuning",
+        "text_level": 1,
+        "bbox": [
+            76,
+            377,
+            236,
+            393
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Adapters have been widely studied in NLP. Houlsby et al. [22] first add a bottleneck adapter structure to the transformer blocks and fix the original backbone, which achieves comparable performances to fine-tuning. Figure 3 illustrates the differences between fine-tuning and adaptertuning. [37,44,59] further reduce parameters in the adapter with closer performances to fine-tuning. [18,34,39] outperform fine-tuning on low-resource tasks, demonstrating that more parameters may not improve performance when finetuning pre-trained models [36]. In computer vision, [41] add convolutional adapters to the ResNet [20] and obtain competitive results in image classification. Adapter concept has also been applied in multimodal [33], vision-and-language [51], and domain adaptation [56], but these methods are only applicable under specific conditions. [7, 21, 25, 31] investigate the potential of adapter-tuning for visual classification. [8] apply the adapter structure to visual dense predictions without fixing any original parameters, which indeed trades more parameters for better performances.",
+        "bbox": [
+            75,
+            401,
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+            690
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3. Low-rank Approximation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            702,
+            312,
+            718
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The low-rank approximation uses multiple low-dimensional tensors to approximate a larger tensor with higher dimensions. Tensor dimensions and sizes in machine learning are very large, so low-rank approximations are widely used in face recognition [61], distributed training [54], transfer learning [11], and cross-domain [10]. A  $b \\times c$  matrix  $M$  can be approximated with  $N$  low-rank matrices  $Q$  by the following equation:",
+        "bbox": [
+            75,
+            727,
+            468,
+            849
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nM _ {b \\times c} = \\prod_ {i = 1} ^ {N} Q _ {r _ {i} \\times s _ {i}}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            202,
+            862,
+            468,
+            904
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/076b68aad349b00b6a3bfa1feb3c01031b3a22e132f2f3e1d5dbafcabaff3fd7.jpg",
+        "image_caption": [
+            "Figure 3. Comparison between Adapter-Tuning and Fine-Tuning paradigms. Fine-Tuning tunes (  $\\mathcal{A}$ ) all parameters delivered by the pre-trained model. Adapter-Tuning freezes ( $\\mathcal{A}$ ) all structures and parameters in the pre-trained model and only trains ( $\\mathcal{A}$ ) the additional parameters in adapters. Parameters in the decoder and head are trainable in both paradigms."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            506,
+            90,
+            888,
+            287
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $N$  has different values depending on the approximation methods, we implement low-rank approximation of the adapter matrices by heuristic learning.",
+        "bbox": [
+            496,
+            407,
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+            455
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            500,
+            467,
+            589,
+            482
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we will elaborate on the proposed low-rank adapter (LoRand) in three parts: adapter tuning paradigm, LoRand, and parameter analysis.",
+        "bbox": [
+            496,
+            492,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Adapter Tuning Paradigm",
+        "text_level": 1,
+        "bbox": [
+            500,
+            547,
+            738,
+            564
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For dataset  $D = \\{(x_{i},y_{i})\\}_{i = 1}^{N}$ , fine-tuning calculates the loss between inference results and labels according to the formula:",
+        "bbox": [
+            496,
+            570,
+            890,
+            614
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL (D, \\theta) = \\sum_ {i = 1} ^ {N} \\operatorname {l o s s} \\left(f _ {\\theta} \\left(x _ {i}\\right), y _ {i}\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            583,
+            623,
+            890,
+            666
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $f_{\\theta}$  denotes the network forward function and loss represents the loss function. After that,  $\\theta$  is optimized through",
+        "bbox": [
+            496,
+            674,
+            890,
+            719
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\theta \\leftarrow \\underset {\\theta} {\\arg \\min } L (D, \\theta). \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            617,
+            719,
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+            744
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In adapter tuning paradigm, parameters consist of two parts, including parameters in adapter  $\\theta_{A}$  and parameters in the original architecture  $\\theta$ . Here,  $\\theta$  is further divided into frozen part  $\\theta_{F}$  and trainable part  $\\theta_{T}$ , noted as  $\\theta = \\{\\theta_{F},\\theta_{T}\\}$ . Let  $\\Omega$  be all the trainable parameters, then  $\\Omega = \\{\\theta_{A},\\theta_{T}\\}$ . The loss function and optimization formula in adapter can be written as:",
+        "bbox": [
+            496,
+            750,
+            890,
+            853
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL \\left(D, \\theta_ {F}, \\Omega\\right) = \\sum_ {i = 1} ^ {N} \\operatorname {l o s s} \\left(f _ {\\theta_ {F}, \\Omega} \\left(x _ {i}\\right), y _ {i}\\right), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            557,
+            862,
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+            902
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "20118",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/1121da732dac8d417df762986ffe346f6c0ca9d44752793fbadaa91c64385b68.jpg",
+        "image_caption": [
+            "Figure 4. Left: Multi-branch projection in LoRand. The down-projection  $W^{D}$  and up-projection  $W^{U}$  matrices are the summation of  $\\alpha$  branches  $W_{1}^{D}(W_{1}^{U})\\ldots W_{\\alpha}^{D}(W_{\\alpha}^{U})$ .  $K_{i}$  in  $i$ -th branch is shared between  $W_{i}^{D}$  and  $W_{i}^{U}$ . All the  $P, Q,$  and  $K$  are trainable, while all the  $W$  matrices are calculated. Right: Comparisons of the same-sized projection matrices between LoRand and Adapter.  $(m,n)$  in the table are typical values in SwinBlocks. LoRand has far fewer parameters than Adapter. With the same projection dimension, LoRand saves over 80% parameters of the Adapter in Swin Transformers.  $(\\alpha ,\\beta)$  here are (2,8), the same as the experiments."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            86,
+            90,
+            665,
+            335
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "table",
+        "img_path": "images/5eca91dd2736066fb84fb54d46ca61d14724c9686fdcea2d77de0ad60e1368a3.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>(m,n)</td><td>PLoRand</td><td>PAdapter</td><td>%</td></tr><tr><td>(96,48)</td><td>4736</td><td>9216</td><td>51.39%</td></tr><tr><td>(192,96)</td><td>9344</td><td>36864</td><td>25.35%</td></tr><tr><td>(384,192)</td><td>18560</td><td>147456</td><td>12.59%</td></tr><tr><td>(768,384)</td><td>36992</td><td>589824</td><td>6.27%</td></tr><tr><td>……</td><td>……</td><td>……</td><td>……</td></tr></table>",
+        "bbox": [
+            669,
+            148,
+            880,
+            279
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Omega \\leftarrow \\underset {\\Omega} {\\arg \\min } L (D, \\theta_ {F}, \\Omega). \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            179,
+            441,
+            468,
+            467
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. LoRand",
+        "text_level": 1,
+        "bbox": [
+            76,
+            474,
+            176,
+            489
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Before introducing LoRand, we first review the existing adapter structure. Conventional adapters are bottleneck structures containing a down-projection, an up-projection, and a non-linear activation function. Besides, adapters ensure the robustness of the model by adding residual [20] structures. Adapter layer can be formulated as follows:",
+        "bbox": [
+            75,
+            497,
+            468,
+            589
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nA ^ {l} = U ^ {l} \\left(G e L U (D ^ {l} (x))\\right) + x, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            163,
+            595,
+            468,
+            616
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $U^l$  and  $D^l$  represent the up and down projections in the  $l$ -th adapter layer, and GeLU is the activation function. It is clear that the parameters in adapter come from the projections. The projection process can be written as:",
+        "bbox": [
+            75,
+            623,
+            468,
+            684
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ny = W x + b, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            223,
+            694,
+            468,
+            709
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "which means most adapter parameters are in  $W$ .",
+        "bbox": [
+            76,
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+            398,
+            734
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To reduce the adapter parameters, we propose a low-rank adapter (LoRand) structure to replace the  $W$  in the projection structures. Figure 2 shows the simplified structure of LoRand. Here we approximate not a specific matrix  $W$  but an ideal matrix  $W_{best}$  that can transform the feature space of the pre-trained model into new tasks by heuristic learning. The approximation matrix  $\\hat{W}$  has the same size as  $W$ , but the low-rank design makes  $\\hat{W}$  have far fewer free degrees than a common  $W$ .",
+        "bbox": [
+            75,
+            734,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Specifically, we synthesize each  $W$  by multiplying three low-rank matrices  $P \\in \\mathbb{R}^{\\beta \\times m}$ ,  $K \\in \\mathbb{R}^{\\beta \\times \\beta}$ ,  $Q \\in \\mathbb{R}^{\\beta \\times n}$",
+        "bbox": [
+            76,
+            869,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "that is:",
+        "bbox": [
+            500,
+            444,
+            547,
+            455
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nW = P ^ {T} K Q, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            645,
+            458,
+            890,
+            474
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\beta \\ll \\min(m, n)$  ensuring that  $P$  and  $Q$  are low-rank matrices.  $K$  can be regarded as a kernel matrix that controls the parameter size of LoRand.",
+        "bbox": [
+            498,
+            483,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "After that, we add multi-branch structures to LoRand to increase the robustness and stability of low-rank matrices, which is inspired by MoE [43] and adaboost [45,52]. Every  $W$  consists of  $\\alpha$  branches, that is:",
+        "bbox": [
+            498,
+            529,
+            890,
+            589
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nW = \\sum_ {i = 1} ^ {\\alpha} W _ {i} = \\sum_ {i = 1} ^ {\\alpha} P _ {i} ^ {T} K _ {i} Q _ {i}. \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            593,
+            601,
+            890,
+            640
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In addition, we share the kernel matrix  $K$  of the two projection layers within each branch. We hope the sharing mechanism can promote the coherence of two projection layers during training process. Besides, the shared  $K$  also slightly reduces the number of LoRand parameters. Up to now, the  $W^{U}$  and  $W^{D}$  in a complete LoRand structure can be represented as:",
+        "bbox": [
+            496,
+            651,
+            893,
+            756
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nW ^ {U} = \\sum_ {i = 1} ^ {\\alpha} W _ {i} ^ {U} = \\sum_ {i = 1} ^ {\\alpha} \\left(P _ {i} ^ {U}\\right) ^ {T} K _ {i} Q _ {i} ^ {U}, \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            568,
+            768,
+            890,
+            809
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nW ^ {D} = \\sum_ {i = 1} ^ {\\alpha} W _ {i} ^ {D} = \\sum_ {i = 1} ^ {\\alpha} \\left(P _ {i} ^ {D}\\right) ^ {T} K _ {i} Q _ {i} ^ {D}, \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            566,
+            821,
+            890,
+            861
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $K_{i}$  is shared in  $W^{U}$  and  $W^{D}$ . Figure 4 presents the detailed designs of the multi-branch projection.",
+        "bbox": [
+            498,
+            869,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "20119",
+        "bbox": [
+            478,
+            944,
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+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Parameter Analysis",
+        "text_level": 1,
+        "bbox": [
+            76,
+            90,
+            266,
+            107
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we will compare the parameters of Lo-Rand and typical adapter [22] with the same size of projection matrix.",
+        "bbox": [
+            76,
+            114,
+            468,
+            159
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Adapter Let  $m$  be the input dimension of the adapter and  $n$  be the middle layer dimension after down projection. Then the number of parameters in each adapter is  $2mn$  (ignoring the few biases). In general, adapter tuning places two adapter modules in each block, so the space complexity of all adapter parameters in  $\\gamma$  blocks can be written as:",
+        "bbox": [
+            76,
+            167,
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+            258
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nO (4 \\gamma m n). \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            233,
+            271,
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+            287
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "LoRand According to section 3.2, each  $W$  contains  $\\alpha$  sets of  $\\{P,Q,K\\}$ , that is:",
+        "bbox": [
+            76,
+            306,
+            468,
+            339
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\alpha \\left(m \\beta + \\beta^ {2} + n \\beta\\right). \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            204,
+            349,
+            468,
+            367
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Each LoRand consists of two  $W$  and  $\\alpha$  shared  $K$ , so the parameter quantity of each LoRand is:",
+        "bbox": [
+            76,
+            378,
+            468,
+            409
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n2 \\alpha (m \\beta + \\beta^ {2} + n \\beta) - \\alpha \\beta^ {2} = 2 \\alpha \\beta (m + n + \\beta / 2). \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            84,
+            419,
+            468,
+            438
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Each block has two LoRand structures, so the number of parameters in  $\\gamma$  blocks is:",
+        "bbox": [
+            76,
+            449,
+            468,
+            479
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n4 \\alpha \\beta \\gamma (m + n) + 2 \\alpha \\beta^ {2} \\gamma . \\tag {15}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            491,
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+            508
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As  $\\alpha, \\beta, \\gamma \\ll \\min(m, n)$ , the space complexity here can be written as:",
+        "bbox": [
+            76,
+            520,
+            468,
+            547
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nO \\left(4 \\alpha \\beta \\gamma (m + n)\\right). \\tag {16}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            202,
+            550,
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+            566
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Comparison between Formulas 12 and 16 can be simplified as:",
+        "bbox": [
+            76,
+            573,
+            468,
+            602
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nO (m n), \\tag {17}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            243,
+            603,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "and",
+        "bbox": [
+            76,
+            627,
+            106,
+            638
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nO (\\alpha \\beta (m + n)). \\tag {18}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            215,
+            642,
+            468,
+            657
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Given that  $\\alpha, \\beta \\ll \\min(m, n)$ , the space complexity of LoRand is far lower than the typical adapter. The table in Figure 4 illustrates that LoRand saves most Adapter parameters with the same projecting dimension.",
+        "bbox": [
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+            726
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We evaluate LoRand on multiple dense prediction tasks, including object detection, semantic segmentation, and instance segmentation. We also evaluate LoRand under low-resource conditions. We first describe our experimental setup in Section 4.1, including pre-trained backbones, baselines, LoRand settings, and downstream tasks. Then we present the main results of three benchmarks in Section 4.2. We also implement ablation study in Section 4.3 to investigate the impact of structural settings in LoRand.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            500,
+            90,
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+            107
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Pretrained Backbones We conduct experiments on the advanced Swin Transformer [32] architectures. All backbones in this section are pre-trained by ImageNet-22k [9]. Pre-trained models are provided by OpenMMLab [6].",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Baselines We compare LoRand with three other common training methods:",
+        "bbox": [
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+            215,
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+            247
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "(a) FULL: update all parameters in the architecture.",
+            "(b) FIXED: fix pre-trained parameters in Swin and train other parts of the architecture (neck, head).",
+            "(c) ADAPTER: add two trainable adapter structures in each SwinBlock following [22], and freeze other parts of the backbone. We evaluate two forms of adapter with different middle layer dimensions  $(D_{ML})$ :",
+            "- ADAPTER-B:  $D_{ML}$  is a half of input dimension.",
+            "- ADAPTER-T:  $D_{ML}$  is a quarter of input dimension."
+        ],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "LoRand Settings We conducted experiments on three Lo-Rand variants, which have different branch numbers  $\\alpha$  and kernel matrix dimensions  $\\beta$ .",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- LoRand:  $\\alpha = 2$ ,  $\\beta = 8$  (Standard).",
+            "- LoRand+:  $\\alpha = 4, \\beta = 8$ .",
+            "- LoRand++:  $\\alpha = 4, \\beta = 16$ ."
+        ],
+        "bbox": [
+            517,
+            500,
+            764,
+            564
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Downstream Tasks We conducted experiments on COCO [28], ADE20K [62], and PASCAL VOC [14] benchmarks to widely evaluate LoRand's performance on main dense prediction tasks.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "COCO 2017 [28] is the most commonly used dataset for object detection and instance segmentation, which contains 118K training and 5K validation images. We perform experiments on the validation set. For a fair comparison, all experiments performed on COCO employ Cascade MASK R-CNN [32] as the detector.",
+        "bbox": [
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+            643,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "ADE20K [62] is the most widely used semantic segmentation dataset, which contains 20K training and 2K validation images. We also conduct experiments on the ADE20K validation set and utilise UperNet [57] as the framework.",
+        "bbox": [
+            498,
+            734,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "PASCAL VOC 0712 [14] is also widely used in object detection, which contains about 16K training and 5K validation images. VOC 0712 is much smaller than the latest benchmarks, so we treat it as a low-resource case. We adopt Faster RCNN [42] as the detector for VOC 0712.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "All our experiments are conducted with 8x NVIDIA Tesla V100 GPUs. The experiments on PASCAL VOC and",
+        "bbox": [
+            498,
+            869,
+            890,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "20120",
+        "bbox": [
+            478,
+            944,
+            519,
+            957
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/78ed1d7df5666048085291a177d60527e41079be4303c0fa2fdf632339889cc3.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Swin-L (198M)</td><td rowspan=\"2\">Trained* Params</td><td rowspan=\"2\">%</td><td rowspan=\"2\">ΔFull</td><td rowspan=\"2\">Extra Structure</td><td colspan=\"2\">Pascal VOC (Faster RCNN)</td><td colspan=\"2\">ADE20K (UperNet)</td></tr><tr><td>APBox</td><td>ΔLoRand</td><td>mIoU</td><td>ΔLoRand</td></tr><tr><td colspan=\"9\">Baselines</td></tr><tr><td>FULL</td><td>198.58 M</td><td>100.00 %</td><td>-</td><td>X</td><td>84.43 %</td><td>- 2.69 %</td><td>53.25 %</td><td>+ 1.34 %</td></tr><tr><td>FIXED</td><td>0.00 M</td><td>0.00 %</td><td>- 100.00 %</td><td>X</td><td>85.19 %</td><td>- 1.93 %</td><td>32.21 %</td><td>- 19.70 %</td></tr><tr><td>ADAPTER-B</td><td>32.04 M</td><td>16.13 %</td><td>- 83.87 %</td><td>✓</td><td>80.93 %</td><td>- 6.19 %</td><td>46.23 %</td><td>- 5.68 %</td></tr><tr><td>ADAPTER-T</td><td>16.04 M</td><td>8.08 %</td><td>- 91.92 %</td><td>✓</td><td>78.10 %</td><td>- 9.02 %</td><td>43.51 %</td><td>- 8.40 %</td></tr><tr><td colspan=\"9\">Our Methods</td></tr><tr><td>LORAND</td><td>3.59 M</td><td>1.84 %</td><td>- 98.16 %</td><td>✓</td><td>87.12 %</td><td>-</td><td>50.67 %</td><td>-</td></tr><tr><td>LORAND+</td><td>7.19 M</td><td>3.62 %</td><td>- 96.38 %</td><td>✓</td><td>87.63 %</td><td>+ 0.51 %</td><td>51.13 %</td><td>+ 0.46 %</td></tr><tr><td>LORAND++</td><td>14.24 M</td><td>7.17 %</td><td>- 92.83 %</td><td>✓</td><td>88.11 %</td><td>+ 0.99 %</td><td>51.87 %</td><td>+ 1.20 %</td></tr></table>",
+        "bbox": [
+            86,
+            88,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/4c26357a7976afde004ccdb1b5d7da94ceef118863e7dcbd3c2763f83235aa15.jpg",
+        "table_caption": [
+            "Table 1. Results of baselines and our methods on Pascal VOC and ADE20K benchmarks. Swin-L is employed as the pre-trained model here. We present the numbers and percentages of trainable backbone parameters on the left and all the performances on the right. * denotes the trainable parameters in backbones."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Swin-B (89M)</td><td rowspan=\"2\">Trained* Params</td><td rowspan=\"2\">%</td><td rowspan=\"2\">ΔFull</td><td rowspan=\"2\">Extra Structure</td><td colspan=\"4\">COCO (Cascade Mask R-CNN)</td></tr><tr><td>APBox</td><td>ΔLoRand</td><td>APMask</td><td>ΔLoRand</td></tr><tr><td colspan=\"9\">Baselines</td></tr><tr><td>FULL</td><td>89.14 M</td><td>100.00 %</td><td>-</td><td>X</td><td>51.90 %</td><td>+0.80 %</td><td>45.00 %</td><td>+0.90 %</td></tr><tr><td>FIXED</td><td>0.00 M</td><td>0.00 %</td><td>-100.00 %</td><td>X</td><td>15.30 %</td><td>-35.80 %</td><td>10.80 %</td><td>-33.8 %</td></tr><tr><td>ADAPTER-B</td><td>14.38 M</td><td>16.13 %</td><td>-83.87 %</td><td>✓</td><td>46.50 %</td><td>-4.60 %</td><td>40.20 %</td><td>-3.90 %</td></tr><tr><td>ADAPTER-T</td><td>7.20 M</td><td>8.08 %</td><td>-91.92 %</td><td>✓</td><td>43.20 %</td><td>-7.90 %</td><td>38.70 %</td><td>-5.40 %</td></tr><tr><td colspan=\"9\">Our Methods</td></tr><tr><td>LORAND</td><td>2.39 M</td><td>2.76 %</td><td>-97.24 %</td><td>✓</td><td>51.10 %</td><td>-</td><td>44.10 %</td><td>-</td></tr><tr><td>LORAND+</td><td>4.73 M</td><td>5.31 %</td><td>-94.69 %</td><td>✓</td><td>51.20 %</td><td>+0.10 %</td><td>44.30 %</td><td>+0.20 %</td></tr><tr><td>LORAND++</td><td>9.32 M</td><td>10.46 %</td><td>-89.54 %</td><td>✓</td><td>51.50 %</td><td>+0.40 %</td><td>44.40 %</td><td>+0.30 %</td></tr></table>",
+        "bbox": [
+            86,
+            347,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Results of baselines and our methods on COCO benchmarks. Swin-B is employed as the pre-trained model here. We present the numbers and percentages of trainable backbone parameters on the left and all the performances on the right. * denotes the trainable parameters in backbones.",
+        "bbox": [
+            75,
+            558,
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+            599
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "ADE20K are based on Swin-S, Swin-B, and Swin-L pretrained models. Limited by GPU memory, the COCO experiments are based on Swin-T, Swin-S, and Swin-B.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. Main Results",
+        "text_level": 1,
+        "bbox": [
+            76,
+            665,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We first compare the trainable backbone parameters and performance of these methods on three benchmarks in Tables 1 and 2. Table 1 shows the results of PASCAL VOC and ADE20K datasets based on Swin-L, and Table 2 shows the results of COCO based on Swin-B. From Tables 1 and 2, we can see that:",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "1) LoRand can effectively address the dilemma of fine-tuning in low-resource situations. Table 1 shows that FIXED outperforms FULL on the PASCAL VOC dataset, which implies that the powerful generalization ability of pre-trained model is severely weakened during fine-tuning. Fine-tuning with low-resource data reduces the feature understanding of pre-trained models, which leads to the poor performance on downstream tasks. LoRand avoids this dis",
+        "bbox": [
+            75,
+            779,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "advantage by fixing the original parameters. More importantly, LoRand can absorb features from the new data by its smaller trainable structures. Table 1 indicates that LoRand outperforms FULL and FIXED by  $2.69\\%$  and  $1.93\\%$  on the low-resource dataset with only  $1.84\\%$  trainable backbone parameters. LoRand+ and LoRand++ also outperform FULL by  $3.2\\%$  and  $3.68\\%$  with  $3.62\\%$  and  $7.17\\%$  backbone parameters. In fact, there are many other common computer vision datasets with similar volumes to the PASCAL VOC, including CUB-200-2011 [55], Oxford 102 Flowers [35], Stanford Cars [27], and Caltech-256 [16]. The prevalence of \"Pretrained & Finetuning\" leads us to focus more on giant benchmarks, but Table 1 suggests we need a better training paradigm to cope with many low-resource situations in industrial applications. LoRand-Tuning proves to be a competitive candidate who brings promising performance and parameter-efficient approaches to low-resource cases.",
+            "2) LoRand effectively balances the number of trainable backbone parameters and downstream task per"
+        ],
+        "bbox": [
+            496,
+            609,
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+            901
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "20121",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "formance. Tables 1 and 2 demonstrate that LoRand (standard) performs very closely to FULL on large benchmarks with only  $1.84\\%$  to  $2.76\\%$  trainable parameters. By tuning less than 3.6M backbone parameters, LoRand (standard) achieves  $50.67\\%$  (mIOU) on ADE20K, and  $51.10\\%$ $(\\mathrm{AP}_{\\mathrm{Box}})$  /  $44.10\\%$ $(\\mathrm{AP}_{\\mathrm{Mask}})$  on COCO, which is only about  $1.5\\%$  off on average compared to FULL. LoRand+ and LoRand++ further reduce the gap between these two paradigms to approximately  $1\\%$  with slight parameter increases. For Swin-L, LoRand saves about 195M parameters per copy compared to FULL. For Swin-B, LoRand saves about  $86\\mathrm{M}$ . These results are interesting, which means we do not have to spend plenty of hardware resources to store these redundant parameters. Industrial service providers deliver thousands of model training tasks every day. With LoRand-Tuning, millions of gigabytes per year for model storage could be saved.",
+        "bbox": [
+            76,
+            90,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "3) LoRand effectively broadens the potential of conventional parameter-efficient adapter structures in dense predictions. From the results, we can draw similar conclusions to [24] that the standard adapter [22] performs worse than fine-tuning on dense predictions. Tables 1 and 2 illustrate that the ADAPTER's performance is far from FULL, although it reduces  $80\\%$  of trainable backbone parameters. Also adding new structures, LoRand achieves comparable performance to FULL by training fewer parameters than the ADAPTER. Overall, Tables 1 and 2 demonstrate the feasibility of parameter-efficient tuning paradigm in visual dense prediction tasks.",
+        "bbox": [
+            76,
+            349,
+            470,
+            532
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Comparisons with other fine-tuned backbone. We then show the comparisons of LoRand with some other remarkable fine-tuned backbones in Table 3. Table 3a shows the results based on UperNet and ADE20K, and 3b shows the results based on Cascade MASK R-CNN and COCO. Table 3 shows that LoRand (based on Swin-Transformer) can outperform most existing fine-tuned backbones with less than 2M parameters. Compared to these backbones, LoRand not only presents more robust and superior results but also saves massive hardware resources in this era of parameter explosion. Specifically, LoRand (Swin-T) exceeds COCO by  $1.9\\%$ $\\mathrm{(AP_{Box})}$  and  $1.2\\%$ $\\mathrm{(AP_{Mask})}$  with 80.12M fewer new backbone parameters than ResNeXt-101-64. Similarly, LoRand (Swin-L) surpasses  $5.82\\%$  (mIoU) on ADE20K with 40.41M fewer trainable backbone parameters than ResNet-101.",
+        "bbox": [
+            76,
+            535,
+            472,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Comparisons on different backbone scales. In addition to Swin-L and Swin-B, we also conduct extensive experiments on Swin-S and Swin-T. We illustrate the performance of baselines and LoRand on multiple backbones. Figure 5 shows the performance of the six methods on different backbone scales, which includes three Swin variants for each benchmark. As FIXED's performance on COCO and ADE20K is too low to display, we only show FIXED's re",
+        "bbox": [
+            76,
+            779,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/ac81b040aef3ed5169607b06418b5ad765aa8022c1df5b4c5231108821303a27.jpg",
+        "table_caption": [
+            "(a) Comparisons between LoRand-Tuning and Fine-Tuning on COCO."
+        ],
+        "table_footnote": [
+            "Table 3. Comparisons between LoRand-Tuning and Fine-Tuning on ADE20K and COCO. We fine-tune multiple backbones and compare their performances with LoRand series. Architectures in (a) and (b) are Cascade Mask R-CNN and UperNet. Parameters in decoder and head are updated in both paradigms. * denotes the trainable parameters in backbones."
+        ],
+        "table_body": "<table><tr><td>Backbone</td><td>Trained \nParams*</td><td>APBox</td><td>APMask</td></tr><tr><td colspan=\"4\">Fine-Tuning Paradigm</td></tr><tr><td>ResNet-101</td><td>44 M</td><td>47.9 %</td><td>41.5 %</td></tr><tr><td>ResNeXt-101-32</td><td>40 M</td><td>48.1 %</td><td>41.6 %</td></tr><tr><td>ResNeXt-101-64</td><td>81 M</td><td>48.3 %</td><td>41.7 %</td></tr><tr><td>DeiT-S</td><td>22 M</td><td>48.0 %</td><td>41.4 %</td></tr><tr><td>Swin-T</td><td>29 M</td><td>50.5 %</td><td>43.7 %</td></tr><tr><td>Swin-S</td><td>50 M</td><td>51.8 %</td><td>44.7 %</td></tr><tr><td>Swin-B</td><td>88 M</td><td>51.9 %</td><td>45.0 %</td></tr><tr><td colspan=\"4\">LoRand-Tuning</td></tr><tr><td>LoRand (Swin-T)</td><td>0.88 M</td><td>50.2 %</td><td>42.9 %</td></tr><tr><td>LoRand (Swin-S)</td><td>1.80 M</td><td>50.7 %</td><td>43.8 %</td></tr><tr><td>LoRand (Swin-B)</td><td>2.39 M</td><td>51.1 %</td><td>44.3 %</td></tr><tr><td colspan=\"4\">(b) Comparisons between LoRand-Tuning and Fine-Tuning on ADE20K.</td></tr><tr><td>Backbone</td><td colspan=\"2\">Trained Params*</td><td>APMask</td></tr><tr><td colspan=\"4\">Fine-Tuning</td></tr><tr><td>ResNet-18</td><td colspan=\"2\">12 M</td><td>39.97 %</td></tr><tr><td>ResNet-50</td><td colspan=\"2\">25 M</td><td>42.78 %</td></tr><tr><td>ResNet-101</td><td colspan=\"2\">44 M</td><td>44.85 %</td></tr><tr><td>DeiT-S</td><td colspan=\"2\">22 M</td><td>44.01 %</td></tr><tr><td>Swin-S</td><td colspan=\"2\">50 M</td><td>49.30 %</td></tr><tr><td>Swin-B</td><td colspan=\"2\">88 M</td><td>51.60 %</td></tr><tr><td>Swin-L</td><td colspan=\"2\">197 M</td><td>53.25 %</td></tr><tr><td colspan=\"4\">LoRand-Tuning</td></tr><tr><td>LoRand (Swin-S)</td><td colspan=\"2\">1.80 M</td><td>47.33 %</td></tr><tr><td>LoRand (Swin-B)</td><td colspan=\"2\">2.39 M</td><td>49.62 %</td></tr><tr><td>LoRand (Swin-L)</td><td colspan=\"2\">3.59 M</td><td>50.67 %</td></tr></table>",
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+        "type": "text",
+        "text": "sults in the PASCAL VOC. Figure 5 indicates that the performance of most methods improves as the backbone scale gets larger. For the LoRand series, more parameters bring better performance, but it is still challenging to outperform FULL on large datasets. For the ADAPTER, ADAPTER-B performs better than ADAPTER-T, suggesting that adding extra parameters does help improve adapter-tuning performance. Experiments on Swin variants systematically",
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+        "text": "20122",
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+            "Figure 5. Seven methods on different backbone scales. Figures show results on PASCAL VOC, COCO, and ADE20K from left to right. Swin-S, Swin-B, and Swin-L are employed as the pre-trained models for PASCAL VOC and ADE20K. Swin-T, Swin-S, and Swin-B are employed for COCO. FIXED's performances are so low on COCO and ADE20K that they reduce the intuitiveness of the other six methods, so FIXED is only presented in PASCAL VOC comparisons."
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+        "image_caption": [
+            "Figure 6. Ablation Study for  $\\alpha$  and  $\\beta$ .  $\\alpha$  ranges from 2, 4, 6, and  $\\beta$  ranges from 4, 8, 16. Figures from left to right present experiments on three benchmarks respectively. We only present  $\\mathrm{AP_{Box}}$  changes for COCO benchmark considering the strong correlation between the values of  $\\mathrm{AP_{Box}}$  and  $\\mathrm{AP_{Mask}}$  in COCO."
+        ],
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+    {
+        "type": "text",
+        "text": "demonstrate that LoRand can outperform both FULL and traditional adapter structures in low-resource cases and perform very closely to FULL in large benchmarks.",
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+    {
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+        "text": "4.3. Ablation Study",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this section, we ablate two key hyperparameters in LoRand: the LoRand branch number  $\\alpha$  and the kernel matrix dimension  $\\beta$ .  $\\alpha$  affects the distributed decision-making of LoRand, while  $\\beta$  focuses on a single branch's learning capability and consistency.",
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+    {
+        "type": "text",
+        "text": "Several sets of ablation experiments are designed and implemented to investigate the effect of  $\\alpha$  and  $\\beta$  on the performance of LoRand. The ablation experiments were conducted on the same three benchmarks. In order to improve the upper limit of LoRand, our experiments are conducted on the largest backbone of each dataset (ADE20K/PASCAL VOC: Swin-L, COCO: Swin-B). The value sets of  $\\alpha$  and  $\\beta$  are  $\\{2,4,6\\}$  and  $\\{4,8,16\\}$ . Figure 6 shows the results of ablation studies on three datasets. In most cases, LoRand's performance increases slightly as  $\\alpha$  and  $\\beta$  become larger but hardly outperforms fine-tuning on large benchmarks. Besides, exponentially increasing the size of the LoRand does",
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+    {
+        "type": "text",
+        "text": "not result in an equivalent performance improvement and even leads to a reduction ( $\\alpha = 6$  in VOC and COCO). Ablation studies demonstrate that larger LoRands have fewer gains both in parameter efficiency and performance. We have considered this trade-off when designing the LoRand standard, LoRand+, and LoRand++.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "This paper presents LoRand, a parameter-efficient low-rank adapter for dense predictions, which completely shares the feature understanding of advanced pre-trained models and effectively transfers it to downstream tasks. LoRand performs on par with fine-tuning in COCO instance segmentation, ADE20K semantic segmentation, and PASCAL VOC object detection with only  $1\\%$  to  $3\\%$  trainable backbone parameters. Moreover, LoRand effectively avoids the disadvantages of the fine-tuning paradigm and delivers better performance in low-resource situations. We hope that parameter-efficient LoRand can save massive redundant storage resources and facilitate a unified training paradigm for vision and language.",
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+        "type": "page_number",
+        "text": "20123",
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+    {
+        "type": "text",
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+        "page_idx": 9
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2023/1% VS 100%_ Parameter-Efficient Low Rank Adapter for Dense Predictions/3b75c6c9-33bc-4e41-9df3-2e14ac85ef59_origin.pdf

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2023/1% VS 100%_ Parameter-Efficient Low Rank Adapter for Dense Predictions/full.md

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+# 1% VS 100%: Parameter-Efficient Low Rank Adapter for Dense Predictions
+
+Dongshuo Yin $^{1,2,\dagger}$ , Yiran Yang $^{1,2,\dagger}$ , Zhechao Wang $^{1,2}$ , Hongfeng Yu $^{1}$ , Kaiwen Wei $^{1,2}$ , Xian Sun $^{1,2,*}$ $^{1}$ Key Laboratory of Network Information System Technology, Aerospace Information Research Institute, Chinese Academy of Sciences  
+ $^{2}$ School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences
+
+{yindongshuo19, yangyiran19, wangzhechao21, weikaiwen19}@mails.ucas.ac.cn {yuhf, sunxian}@aircas.ac.cn
+
+# Abstract
+
+Fine-tuning large-scale pre-trained vision models to downstream tasks is a standard technique for achieving state-of-the-art performance on computer vision benchmarks. However, fine-tuning the whole model with millions of parameters is inefficient as it requires storing a samesized new model copy for each task. In this work, we propose LoRand, a method for fine-tuning large-scale vision models with a better trade-off between task performance and the number of trainable parameters. LoRand generates tiny adapter structures with low-rank synthesis while keeping the original backbone parameters fixed, resulting in high parameter sharing. To demonstrate LoRand's effectiveness, we implement extensive experiments on object detection, semantic segmentation, and instance segmentation tasks. By only training a small percentage (1% to 3%) of the pre-trained backbone parameters, LoRand achieves comparable performance to standard fine-tuning on COCO and ADE20K and outperforms fine-tuning in low-resource PASCAL VOC dataset.
+
+# 1. Introduction
+
+With the rapid development of computer vision, parameters in deep models are surging. Giant models need to be trained with massive resources to achieve superior performance [3, 17, 47, 58], which is often unavailable to many academics and institutions. "Pretrain & Finetuning" paradigm is widely used to alleviate this dilemma. Teams with sufficient computation resources utilise enormous datasets [2, 9, 40, 50] to train superior backbones [4, 32, 40, 48] and optimise the models with ideal performances. Models pretrained in this way usually have a su
+
+![](images/284244850d213821e678546c56bd87e129870b5533c18d88c83c8caed88f03ff.jpg)  
+Figure 1. Comparisons of trainable backbone parameters between our methods (red) and fine-tuning (black). In COCO, we achieve advanced performances and outperform most existing backbones with only  $0.9\sim 2.5\mathrm{M}$  new backbone parameters (Cascade-RCNN is employed as the detector). The fine-tuning paradigm produces massive redundant backbone parameters, whereas our approach saves over  $97\%$  of hardware resources with competitive performances. The sizes of the circles intuitively compare the number of trainable parameters.
+
+perior understanding of homogeneous data. After that, researchers with limited computational resources can transfer the understanding capabilities of the pre-trained models to downstream tasks with promising performances by finetuning [1,26,46,53].
+
+However, the fine-tuned model will produce a new set of parameters as large as the pre-trained model. New parameters are independent of the pre-trained models and unshareable, which are very hardware intensive for cloud service providers [23, 49]. Figure 1 compares the parameter quantities of some remarkable backbones and their performances on the COCO [28] dataset. Recent advances in natural language processing (NLP) [30, 38] show that large pre-trained models trained with rich data have strong gener
+
+![](images/b58c6b179031f202b13762129589750230c30d575d80af5f850f0a002de939e8.jpg)  
+Swin-Transformer Block
+
+![](images/7edbd25abc95b7d7da6fcc332f29fee39ad6e9b53dd1dfb97cf12b8d90b381de.jpg)  
+LoRand Layer  
+Figure 2. Architecture of the adapter module and its integration with the Transformer. Left: We add two LoRand structures to each SwinBlock located behind the W/SW-MSA and MLP structures respectively. Right: LoRand contains two Multi-branch low-rank projections and nonlinearity. We include skip-connection to LoRand to enhance its robustness.
+
+alisability, which means most parameters in the pre-trained models can be shared with the new tasks [22, 36, 37, 44, 59]. Moreover, recent literature demonstrates that the feature understanding of pre-trained models could be reduced when they are fine-tuned in low-resource situations [12, 36]. To tackle these issues, NLP researchers propose two new training paradigms based on pre-trained models: Adapter Tuning [22] and Prompt Tuning [30], both of which tune the new models by fixing the pre-trained parameters and adding a few trainable structures (less than  $10\%$  of the backbone). These paradigms create a new buzz in NLP and achieve impressive performances which can be competitive with finetuning [12, 22, 30, 36-38, 44, 59]. Advances in NLP also shed new light on computer vision. Jia et al. [24] propose Visual Prompt Tuning (VPT) and demonstrate that VPT can outperform fine-tuning on image classification tasks by training a small number of trainable parameters. Nevertheless, VPT shows weakness on more challenging dense predictions like semantic segmentation compared with finetuning [24].
+
+To find a parameter-efficient paradigm with promising performance in computer vision, we explore the potential of Adapter Tuning for visual dense predictions. We employ the advanced Swin Transformer [32] trained with ImageNet-22K [9] as the pre-trained model. After that, we add bottleneck adapter structures [22] behind each SwinBlock and freeze the original backbone parameters when training, but this approach cannot achieve comparable performance to fine-tuning as mentioned in [24]. In the experi
+
+periments, we find that the models perform better with sparser adapter structures. To improve the performance of Adapter Tuning, we propose Low-Rank Adapter (LoRand) to reduce the adapter parameters, as shown in Figure 2. LoRand sparsely parameterizes the matrices in adapters by low-rank synthesis. Specifically, the projection matrix of the fully-connected layer (FC) in LoRand is a product of multiple low-rank matrices, which reduces FC parameters by more than  $80\%$ . We implement extensive experiments on object detection (PASCAL VOC [14]), semantic segmentation (ADE20K [62]), and instance segmentation (MS COCO [28]) to verify the capability of LoRand. Experimental results show that LoRand-Tuning is comparable to fine-tuning on multiple tasks with only  $1.8\%$  to  $2.8\%$  new backbone parameters, which suggests that the pre-trained backbone parameters can be fully shared. More interestingly, our method completely outperforms fine-tuning on the PASCAL VOC dataset, illustrating that LoRand-Tuning can reduce the impairment of fine-tuning on pre-trained models in low-resource configurations. Our method demonstrates that the LoRand-Tuning paradigm can substantially save storage resources and achieve competitive performances on most dense prediction tasks. In summary, our contributions are three-fold:
+
+- We demonstrate that visual pre-trained models are highly generalisable and shareable. With our training methods, new tasks require only a few trainable parameters to achieve performances comparable to finetuning, which can save massive hardware resources.  
+- We propose the LoRand structure for sparser adapters based on low-rank synthesis. We demonstrate that the backbone parameters in fine-tuning are highly redundant, which can be replaced by  $1.8\%$  to  $2.8\%$  additional parameters in LoRand.  
+- Extensive experiments on object detection, semantic segmentation, and instance segmentation show that LoRand-Tuning can achieve remarkable performances and reduce massive new parameters in challenging dense prediction tasks.
+
+# 2. Related Work
+
+# 2.1. Training Paradigms in NLP
+
+Computer vision has been continuously inspired by NLP in recent years, including the visual transformer series [5,13,29,32] and self-supervised MAE series [15,19,60]. In fact, NLP is leading new training trends different from finetuning. Fine-tuning produces a new parameter set for each new task, which is parametrically inefficient for plenty of linguistic tasks [22,30]. To solve this problem, [30] and [22] have proposed "Prompt Tuning" and "Adapter Tuning" respectively, both of which fix all parameters of the backbone
+
+and plug a few tiny trainable structures (less than  $10\%$  of the backbone) to adapt the pre-trained model to the new tasks. "Prompt tuning" adds learnable parameters (also known as prompts) to the input or intermediate layers to change the input space of the new tasks. "Prompts" can motivate the model to remember knowledge learned in the previous tasks. "Adapter tuning" adds learnable bottleneck structures after each block to connect the pre-trained model with new tasks. Adapter and prompt demonstrate the coexistence of parameter efficiency and high performances in NLP, stimulating studies in CV. [24] proposes Visual Prompt Tuning (VPT) for image classification and semantic segmentation, but the performance of VPT on semantic segmentation is still far from fine-tuning. This phenomenon motivates us to explore whether adapter tuning can bring a new paradigm in computer vision with fewer parameters and better performances. In this work, we try to explore parameter-efficient and high-performance adapter structures.
+
+# 2.2. Adapter Tuning
+
+Adapters have been widely studied in NLP. Houlsby et al. [22] first add a bottleneck adapter structure to the transformer blocks and fix the original backbone, which achieves comparable performances to fine-tuning. Figure 3 illustrates the differences between fine-tuning and adaptertuning. [37,44,59] further reduce parameters in the adapter with closer performances to fine-tuning. [18,34,39] outperform fine-tuning on low-resource tasks, demonstrating that more parameters may not improve performance when finetuning pre-trained models [36]. In computer vision, [41] add convolutional adapters to the ResNet [20] and obtain competitive results in image classification. Adapter concept has also been applied in multimodal [33], vision-and-language [51], and domain adaptation [56], but these methods are only applicable under specific conditions. [7, 21, 25, 31] investigate the potential of adapter-tuning for visual classification. [8] apply the adapter structure to visual dense predictions without fixing any original parameters, which indeed trades more parameters for better performances.
+
+# 2.3. Low-rank Approximation
+
+The low-rank approximation uses multiple low-dimensional tensors to approximate a larger tensor with higher dimensions. Tensor dimensions and sizes in machine learning are very large, so low-rank approximations are widely used in face recognition [61], distributed training [54], transfer learning [11], and cross-domain [10]. A  $b \times c$  matrix  $M$  can be approximated with  $N$  low-rank matrices  $Q$  by the following equation:
+
+$$
+M _ {b \times c} = \prod_ {i = 1} ^ {N} Q _ {r _ {i} \times s _ {i}}, \tag {1}
+$$
+
+![](images/076b68aad349b00b6a3bfa1feb3c01031b3a22e132f2f3e1d5dbafcabaff3fd7.jpg)  
+Figure 3. Comparison between Adapter-Tuning and Fine-Tuning paradigms. Fine-Tuning tunes (  $\mathcal{A}$ ) all parameters delivered by the pre-trained model. Adapter-Tuning freezes ( $\mathcal{A}$ ) all structures and parameters in the pre-trained model and only trains ( $\mathcal{A}$ ) the additional parameters in adapters. Parameters in the decoder and head are trainable in both paradigms.
+
+where  $N$  has different values depending on the approximation methods, we implement low-rank approximation of the adapter matrices by heuristic learning.
+
+# 3. Method
+
+In this section, we will elaborate on the proposed low-rank adapter (LoRand) in three parts: adapter tuning paradigm, LoRand, and parameter analysis.
+
+# 3.1. Adapter Tuning Paradigm
+
+For dataset  $D = \{(x_{i},y_{i})\}_{i = 1}^{N}$ , fine-tuning calculates the loss between inference results and labels according to the formula:
+
+$$
+L (D, \theta) = \sum_ {i = 1} ^ {N} \operatorname {l o s s} \left(f _ {\theta} \left(x _ {i}\right), y _ {i}\right), \tag {2}
+$$
+
+where  $f_{\theta}$  denotes the network forward function and loss represents the loss function. After that,  $\theta$  is optimized through
+
+$$
+\theta \leftarrow \underset {\theta} {\arg \min } L (D, \theta). \tag {3}
+$$
+
+In adapter tuning paradigm, parameters consist of two parts, including parameters in adapter  $\theta_{A}$  and parameters in the original architecture  $\theta$ . Here,  $\theta$  is further divided into frozen part  $\theta_{F}$  and trainable part  $\theta_{T}$ , noted as  $\theta = \{\theta_{F},\theta_{T}\}$ . Let  $\Omega$  be all the trainable parameters, then  $\Omega = \{\theta_{A},\theta_{T}\}$ . The loss function and optimization formula in adapter can be written as:
+
+$$
+L \left(D, \theta_ {F}, \Omega\right) = \sum_ {i = 1} ^ {N} \operatorname {l o s s} \left(f _ {\theta_ {F}, \Omega} \left(x _ {i}\right), y _ {i}\right), \tag {4}
+$$
+
+![](images/1121da732dac8d417df762986ffe346f6c0ca9d44752793fbadaa91c64385b68.jpg)  
+Figure 4. Left: Multi-branch projection in LoRand. The down-projection  $W^{D}$  and up-projection  $W^{U}$  matrices are the summation of  $\alpha$  branches  $W_{1}^{D}(W_{1}^{U})\ldots W_{\alpha}^{D}(W_{\alpha}^{U})$ .  $K_{i}$  in  $i$ -th branch is shared between  $W_{i}^{D}$  and  $W_{i}^{U}$ . All the  $P, Q,$  and  $K$  are trainable, while all the  $W$  matrices are calculated. Right: Comparisons of the same-sized projection matrices between LoRand and Adapter.  $(m,n)$  in the table are typical values in SwinBlocks. LoRand has far fewer parameters than Adapter. With the same projection dimension, LoRand saves over 80% parameters of the Adapter in Swin Transformers.  $(\alpha ,\beta)$  here are (2,8), the same as the experiments.
+
+<table><tr><td>(m,n)</td><td>PLoRand</td><td>PAdapter</td><td>%</td></tr><tr><td>(96,48)</td><td>4736</td><td>9216</td><td>51.39%</td></tr><tr><td>(192,96)</td><td>9344</td><td>36864</td><td>25.35%</td></tr><tr><td>(384,192)</td><td>18560</td><td>147456</td><td>12.59%</td></tr><tr><td>(768,384)</td><td>36992</td><td>589824</td><td>6.27%</td></tr><tr><td>……</td><td>……</td><td>……</td><td>……</td></tr></table>
+
+$$
+\Omega \leftarrow \underset {\Omega} {\arg \min } L (D, \theta_ {F}, \Omega). \tag {5}
+$$
+
+# 3.2. LoRand
+
+Before introducing LoRand, we first review the existing adapter structure. Conventional adapters are bottleneck structures containing a down-projection, an up-projection, and a non-linear activation function. Besides, adapters ensure the robustness of the model by adding residual [20] structures. Adapter layer can be formulated as follows:
+
+$$
+A ^ {l} = U ^ {l} \left(G e L U (D ^ {l} (x))\right) + x, \tag {6}
+$$
+
+where  $U^l$  and  $D^l$  represent the up and down projections in the  $l$ -th adapter layer, and GeLU is the activation function. It is clear that the parameters in adapter come from the projections. The projection process can be written as:
+
+$$
+y = W x + b, \tag {7}
+$$
+
+which means most adapter parameters are in  $W$ .
+
+To reduce the adapter parameters, we propose a low-rank adapter (LoRand) structure to replace the  $W$  in the projection structures. Figure 2 shows the simplified structure of LoRand. Here we approximate not a specific matrix  $W$  but an ideal matrix  $W_{best}$  that can transform the feature space of the pre-trained model into new tasks by heuristic learning. The approximation matrix  $\hat{W}$  has the same size as  $W$ , but the low-rank design makes  $\hat{W}$  have far fewer free degrees than a common  $W$ .
+
+Specifically, we synthesize each  $W$  by multiplying three low-rank matrices  $P \in \mathbb{R}^{\beta \times m}$ ,  $K \in \mathbb{R}^{\beta \times \beta}$ ,  $Q \in \mathbb{R}^{\beta \times n}$
+
+that is:
+
+$$
+W = P ^ {T} K Q, \tag {8}
+$$
+
+where  $\beta \ll \min(m, n)$  ensuring that  $P$  and  $Q$  are low-rank matrices.  $K$  can be regarded as a kernel matrix that controls the parameter size of LoRand.
+
+After that, we add multi-branch structures to LoRand to increase the robustness and stability of low-rank matrices, which is inspired by MoE [43] and adaboost [45,52]. Every  $W$  consists of  $\alpha$  branches, that is:
+
+$$
+W = \sum_ {i = 1} ^ {\alpha} W _ {i} = \sum_ {i = 1} ^ {\alpha} P _ {i} ^ {T} K _ {i} Q _ {i}. \tag {9}
+$$
+
+In addition, we share the kernel matrix  $K$  of the two projection layers within each branch. We hope the sharing mechanism can promote the coherence of two projection layers during training process. Besides, the shared  $K$  also slightly reduces the number of LoRand parameters. Up to now, the  $W^{U}$  and  $W^{D}$  in a complete LoRand structure can be represented as:
+
+$$
+W ^ {U} = \sum_ {i = 1} ^ {\alpha} W _ {i} ^ {U} = \sum_ {i = 1} ^ {\alpha} \left(P _ {i} ^ {U}\right) ^ {T} K _ {i} Q _ {i} ^ {U}, \tag {10}
+$$
+
+$$
+W ^ {D} = \sum_ {i = 1} ^ {\alpha} W _ {i} ^ {D} = \sum_ {i = 1} ^ {\alpha} \left(P _ {i} ^ {D}\right) ^ {T} K _ {i} Q _ {i} ^ {D}, \tag {11}
+$$
+
+where  $K_{i}$  is shared in  $W^{U}$  and  $W^{D}$ . Figure 4 presents the detailed designs of the multi-branch projection.
+
+# 3.3. Parameter Analysis
+
+In this section, we will compare the parameters of Lo-Rand and typical adapter [22] with the same size of projection matrix.
+
+Adapter Let  $m$  be the input dimension of the adapter and  $n$  be the middle layer dimension after down projection. Then the number of parameters in each adapter is  $2mn$  (ignoring the few biases). In general, adapter tuning places two adapter modules in each block, so the space complexity of all adapter parameters in  $\gamma$  blocks can be written as:
+
+$$
+O (4 \gamma m n). \tag {12}
+$$
+
+LoRand According to section 3.2, each  $W$  contains  $\alpha$  sets of  $\{P,Q,K\}$ , that is:
+
+$$
+\alpha \left(m \beta + \beta^ {2} + n \beta\right). \tag {13}
+$$
+
+Each LoRand consists of two  $W$  and  $\alpha$  shared  $K$ , so the parameter quantity of each LoRand is:
+
+$$
+2 \alpha (m \beta + \beta^ {2} + n \beta) - \alpha \beta^ {2} = 2 \alpha \beta (m + n + \beta / 2). \tag {14}
+$$
+
+Each block has two LoRand structures, so the number of parameters in  $\gamma$  blocks is:
+
+$$
+4 \alpha \beta \gamma (m + n) + 2 \alpha \beta^ {2} \gamma . \tag {15}
+$$
+
+As  $\alpha, \beta, \gamma \ll \min(m, n)$ , the space complexity here can be written as:
+
+$$
+O \left(4 \alpha \beta \gamma (m + n)\right). \tag {16}
+$$
+
+Comparison between Formulas 12 and 16 can be simplified as:
+
+$$
+O (m n), \tag {17}
+$$
+
+and
+
+$$
+O (\alpha \beta (m + n)). \tag {18}
+$$
+
+Given that  $\alpha, \beta \ll \min(m, n)$ , the space complexity of LoRand is far lower than the typical adapter. The table in Figure 4 illustrates that LoRand saves most Adapter parameters with the same projecting dimension.
+
+# 4. Experiments
+
+We evaluate LoRand on multiple dense prediction tasks, including object detection, semantic segmentation, and instance segmentation. We also evaluate LoRand under low-resource conditions. We first describe our experimental setup in Section 4.1, including pre-trained backbones, baselines, LoRand settings, and downstream tasks. Then we present the main results of three benchmarks in Section 4.2. We also implement ablation study in Section 4.3 to investigate the impact of structural settings in LoRand.
+
+# 4.1. Experimental Setup
+
+Pretrained Backbones We conduct experiments on the advanced Swin Transformer [32] architectures. All backbones in this section are pre-trained by ImageNet-22k [9]. Pre-trained models are provided by OpenMMLab [6].
+
+Baselines We compare LoRand with three other common training methods:
+
+(a) FULL: update all parameters in the architecture.  
+(b) FIXED: fix pre-trained parameters in Swin and train other parts of the architecture (neck, head).  
+(c) ADAPTER: add two trainable adapter structures in each SwinBlock following [22], and freeze other parts of the backbone. We evaluate two forms of adapter with different middle layer dimensions  $(D_{ML})$ :  
+- ADAPTER-B:  $D_{ML}$  is a half of input dimension.  
+- ADAPTER-T:  $D_{ML}$  is a quarter of input dimension.
+
+LoRand Settings We conducted experiments on three Lo-Rand variants, which have different branch numbers  $\alpha$  and kernel matrix dimensions  $\beta$ .
+
+- LoRand:  $\alpha = 2$ ,  $\beta = 8$  (Standard).  
+- LoRand+:  $\alpha = 4, \beta = 8$ .  
+- LoRand++:  $\alpha = 4, \beta = 16$ .
+
+Downstream Tasks We conducted experiments on COCO [28], ADE20K [62], and PASCAL VOC [14] benchmarks to widely evaluate LoRand's performance on main dense prediction tasks.
+
+COCO 2017 [28] is the most commonly used dataset for object detection and instance segmentation, which contains 118K training and 5K validation images. We perform experiments on the validation set. For a fair comparison, all experiments performed on COCO employ Cascade MASK R-CNN [32] as the detector.
+
+ADE20K [62] is the most widely used semantic segmentation dataset, which contains 20K training and 2K validation images. We also conduct experiments on the ADE20K validation set and utilise UperNet [57] as the framework.
+
+PASCAL VOC 0712 [14] is also widely used in object detection, which contains about 16K training and 5K validation images. VOC 0712 is much smaller than the latest benchmarks, so we treat it as a low-resource case. We adopt Faster RCNN [42] as the detector for VOC 0712.
+
+All our experiments are conducted with 8x NVIDIA Tesla V100 GPUs. The experiments on PASCAL VOC and
+
+<table><tr><td rowspan="2">Swin-L (198M)</td><td rowspan="2">Trained* Params</td><td rowspan="2">%</td><td rowspan="2">ΔFull</td><td rowspan="2">Extra Structure</td><td colspan="2">Pascal VOC (Faster RCNN)</td><td colspan="2">ADE20K (UperNet)</td></tr><tr><td>APBox</td><td>ΔLoRand</td><td>mIoU</td><td>ΔLoRand</td></tr><tr><td colspan="9">Baselines</td></tr><tr><td>FULL</td><td>198.58 M</td><td>100.00 %</td><td>-</td><td>X</td><td>84.43 %</td><td>- 2.69 %</td><td>53.25 %</td><td>+ 1.34 %</td></tr><tr><td>FIXED</td><td>0.00 M</td><td>0.00 %</td><td>- 100.00 %</td><td>X</td><td>85.19 %</td><td>- 1.93 %</td><td>32.21 %</td><td>- 19.70 %</td></tr><tr><td>ADAPTER-B</td><td>32.04 M</td><td>16.13 %</td><td>- 83.87 %</td><td>✓</td><td>80.93 %</td><td>- 6.19 %</td><td>46.23 %</td><td>- 5.68 %</td></tr><tr><td>ADAPTER-T</td><td>16.04 M</td><td>8.08 %</td><td>- 91.92 %</td><td>✓</td><td>78.10 %</td><td>- 9.02 %</td><td>43.51 %</td><td>- 8.40 %</td></tr><tr><td colspan="9">Our Methods</td></tr><tr><td>LORAND</td><td>3.59 M</td><td>1.84 %</td><td>- 98.16 %</td><td>✓</td><td>87.12 %</td><td>-</td><td>50.67 %</td><td>-</td></tr><tr><td>LORAND+</td><td>7.19 M</td><td>3.62 %</td><td>- 96.38 %</td><td>✓</td><td>87.63 %</td><td>+ 0.51 %</td><td>51.13 %</td><td>+ 0.46 %</td></tr><tr><td>LORAND++</td><td>14.24 M</td><td>7.17 %</td><td>- 92.83 %</td><td>✓</td><td>88.11 %</td><td>+ 0.99 %</td><td>51.87 %</td><td>+ 1.20 %</td></tr></table>
+
+Table 1. Results of baselines and our methods on Pascal VOC and ADE20K benchmarks. Swin-L is employed as the pre-trained model here. We present the numbers and percentages of trainable backbone parameters on the left and all the performances on the right. * denotes the trainable parameters in backbones.  
+
+<table><tr><td rowspan="2">Swin-B (89M)</td><td rowspan="2">Trained* Params</td><td rowspan="2">%</td><td rowspan="2">ΔFull</td><td rowspan="2">Extra Structure</td><td colspan="4">COCO (Cascade Mask R-CNN)</td></tr><tr><td>APBox</td><td>ΔLoRand</td><td>APMask</td><td>ΔLoRand</td></tr><tr><td colspan="9">Baselines</td></tr><tr><td>FULL</td><td>89.14 M</td><td>100.00 %</td><td>-</td><td>X</td><td>51.90 %</td><td>+0.80 %</td><td>45.00 %</td><td>+0.90 %</td></tr><tr><td>FIXED</td><td>0.00 M</td><td>0.00 %</td><td>-100.00 %</td><td>X</td><td>15.30 %</td><td>-35.80 %</td><td>10.80 %</td><td>-33.8 %</td></tr><tr><td>ADAPTER-B</td><td>14.38 M</td><td>16.13 %</td><td>-83.87 %</td><td>✓</td><td>46.50 %</td><td>-4.60 %</td><td>40.20 %</td><td>-3.90 %</td></tr><tr><td>ADAPTER-T</td><td>7.20 M</td><td>8.08 %</td><td>-91.92 %</td><td>✓</td><td>43.20 %</td><td>-7.90 %</td><td>38.70 %</td><td>-5.40 %</td></tr><tr><td colspan="9">Our Methods</td></tr><tr><td>LORAND</td><td>2.39 M</td><td>2.76 %</td><td>-97.24 %</td><td>✓</td><td>51.10 %</td><td>-</td><td>44.10 %</td><td>-</td></tr><tr><td>LORAND+</td><td>4.73 M</td><td>5.31 %</td><td>-94.69 %</td><td>✓</td><td>51.20 %</td><td>+0.10 %</td><td>44.30 %</td><td>+0.20 %</td></tr><tr><td>LORAND++</td><td>9.32 M</td><td>10.46 %</td><td>-89.54 %</td><td>✓</td><td>51.50 %</td><td>+0.40 %</td><td>44.40 %</td><td>+0.30 %</td></tr></table>
+
+Table 2. Results of baselines and our methods on COCO benchmarks. Swin-B is employed as the pre-trained model here. We present the numbers and percentages of trainable backbone parameters on the left and all the performances on the right. * denotes the trainable parameters in backbones.
+
+ADE20K are based on Swin-S, Swin-B, and Swin-L pretrained models. Limited by GPU memory, the COCO experiments are based on Swin-T, Swin-S, and Swin-B.
+
+# 4.2. Main Results
+
+We first compare the trainable backbone parameters and performance of these methods on three benchmarks in Tables 1 and 2. Table 1 shows the results of PASCAL VOC and ADE20K datasets based on Swin-L, and Table 2 shows the results of COCO based on Swin-B. From Tables 1 and 2, we can see that:
+
+1) LoRand can effectively address the dilemma of fine-tuning in low-resource situations. Table 1 shows that FIXED outperforms FULL on the PASCAL VOC dataset, which implies that the powerful generalization ability of pre-trained model is severely weakened during fine-tuning. Fine-tuning with low-resource data reduces the feature understanding of pre-trained models, which leads to the poor performance on downstream tasks. LoRand avoids this dis
+
+advantage by fixing the original parameters. More importantly, LoRand can absorb features from the new data by its smaller trainable structures. Table 1 indicates that LoRand outperforms FULL and FIXED by  $2.69\%$  and  $1.93\%$  on the low-resource dataset with only  $1.84\%$  trainable backbone parameters. LoRand+ and LoRand++ also outperform FULL by  $3.2\%$  and  $3.68\%$  with  $3.62\%$  and  $7.17\%$  backbone parameters. In fact, there are many other common computer vision datasets with similar volumes to the PASCAL VOC, including CUB-200-2011 [55], Oxford 102 Flowers [35], Stanford Cars [27], and Caltech-256 [16]. The prevalence of "Pretrained & Finetuning" leads us to focus more on giant benchmarks, but Table 1 suggests we need a better training paradigm to cope with many low-resource situations in industrial applications. LoRand-Tuning proves to be a competitive candidate who brings promising performance and parameter-efficient approaches to low-resource cases.  
+2) LoRand effectively balances the number of trainable backbone parameters and downstream task per
+
+formance. Tables 1 and 2 demonstrate that LoRand (standard) performs very closely to FULL on large benchmarks with only  $1.84\%$  to  $2.76\%$  trainable parameters. By tuning less than 3.6M backbone parameters, LoRand (standard) achieves  $50.67\%$  (mIOU) on ADE20K, and  $51.10\%$ $(\mathrm{AP}_{\mathrm{Box}})$  /  $44.10\%$ $(\mathrm{AP}_{\mathrm{Mask}})$  on COCO, which is only about  $1.5\%$  off on average compared to FULL. LoRand+ and LoRand++ further reduce the gap between these two paradigms to approximately  $1\%$  with slight parameter increases. For Swin-L, LoRand saves about 195M parameters per copy compared to FULL. For Swin-B, LoRand saves about  $86\mathrm{M}$ . These results are interesting, which means we do not have to spend plenty of hardware resources to store these redundant parameters. Industrial service providers deliver thousands of model training tasks every day. With LoRand-Tuning, millions of gigabytes per year for model storage could be saved.
+
+3) LoRand effectively broadens the potential of conventional parameter-efficient adapter structures in dense predictions. From the results, we can draw similar conclusions to [24] that the standard adapter [22] performs worse than fine-tuning on dense predictions. Tables 1 and 2 illustrate that the ADAPTER's performance is far from FULL, although it reduces  $80\%$  of trainable backbone parameters. Also adding new structures, LoRand achieves comparable performance to FULL by training fewer parameters than the ADAPTER. Overall, Tables 1 and 2 demonstrate the feasibility of parameter-efficient tuning paradigm in visual dense prediction tasks.
+
+Comparisons with other fine-tuned backbone. We then show the comparisons of LoRand with some other remarkable fine-tuned backbones in Table 3. Table 3a shows the results based on UperNet and ADE20K, and 3b shows the results based on Cascade MASK R-CNN and COCO. Table 3 shows that LoRand (based on Swin-Transformer) can outperform most existing fine-tuned backbones with less than 2M parameters. Compared to these backbones, LoRand not only presents more robust and superior results but also saves massive hardware resources in this era of parameter explosion. Specifically, LoRand (Swin-T) exceeds COCO by  $1.9\%$ $\mathrm{(AP_{Box})}$  and  $1.2\%$ $\mathrm{(AP_{Mask})}$  with 80.12M fewer new backbone parameters than ResNeXt-101-64. Similarly, LoRand (Swin-L) surpasses  $5.82\%$  (mIoU) on ADE20K with 40.41M fewer trainable backbone parameters than ResNet-101.
+
+Comparisons on different backbone scales. In addition to Swin-L and Swin-B, we also conduct extensive experiments on Swin-S and Swin-T. We illustrate the performance of baselines and LoRand on multiple backbones. Figure 5 shows the performance of the six methods on different backbone scales, which includes three Swin variants for each benchmark. As FIXED's performance on COCO and ADE20K is too low to display, we only show FIXED's re
+
+(a) Comparisons between LoRand-Tuning and Fine-Tuning on COCO.  
+
+<table><tr><td>Backbone</td><td>Trained 
+Params*</td><td>APBox</td><td>APMask</td></tr><tr><td colspan="4">Fine-Tuning Paradigm</td></tr><tr><td>ResNet-101</td><td>44 M</td><td>47.9 %</td><td>41.5 %</td></tr><tr><td>ResNeXt-101-32</td><td>40 M</td><td>48.1 %</td><td>41.6 %</td></tr><tr><td>ResNeXt-101-64</td><td>81 M</td><td>48.3 %</td><td>41.7 %</td></tr><tr><td>DeiT-S</td><td>22 M</td><td>48.0 %</td><td>41.4 %</td></tr><tr><td>Swin-T</td><td>29 M</td><td>50.5 %</td><td>43.7 %</td></tr><tr><td>Swin-S</td><td>50 M</td><td>51.8 %</td><td>44.7 %</td></tr><tr><td>Swin-B</td><td>88 M</td><td>51.9 %</td><td>45.0 %</td></tr><tr><td colspan="4">LoRand-Tuning</td></tr><tr><td>LoRand (Swin-T)</td><td>0.88 M</td><td>50.2 %</td><td>42.9 %</td></tr><tr><td>LoRand (Swin-S)</td><td>1.80 M</td><td>50.7 %</td><td>43.8 %</td></tr><tr><td>LoRand (Swin-B)</td><td>2.39 M</td><td>51.1 %</td><td>44.3 %</td></tr><tr><td colspan="4">(b) Comparisons between LoRand-Tuning and Fine-Tuning on ADE20K.</td></tr><tr><td>Backbone</td><td colspan="2">Trained Params*</td><td>APMask</td></tr><tr><td colspan="4">Fine-Tuning</td></tr><tr><td>ResNet-18</td><td colspan="2">12 M</td><td>39.97 %</td></tr><tr><td>ResNet-50</td><td colspan="2">25 M</td><td>42.78 %</td></tr><tr><td>ResNet-101</td><td colspan="2">44 M</td><td>44.85 %</td></tr><tr><td>DeiT-S</td><td colspan="2">22 M</td><td>44.01 %</td></tr><tr><td>Swin-S</td><td colspan="2">50 M</td><td>49.30 %</td></tr><tr><td>Swin-B</td><td colspan="2">88 M</td><td>51.60 %</td></tr><tr><td>Swin-L</td><td colspan="2">197 M</td><td>53.25 %</td></tr><tr><td colspan="4">LoRand-Tuning</td></tr><tr><td>LoRand (Swin-S)</td><td colspan="2">1.80 M</td><td>47.33 %</td></tr><tr><td>LoRand (Swin-B)</td><td colspan="2">2.39 M</td><td>49.62 %</td></tr><tr><td>LoRand (Swin-L)</td><td colspan="2">3.59 M</td><td>50.67 %</td></tr></table>
+
+Table 3. Comparisons between LoRand-Tuning and Fine-Tuning on ADE20K and COCO. We fine-tune multiple backbones and compare their performances with LoRand series. Architectures in (a) and (b) are Cascade Mask R-CNN and UperNet. Parameters in decoder and head are updated in both paradigms. * denotes the trainable parameters in backbones.
+
+sults in the PASCAL VOC. Figure 5 indicates that the performance of most methods improves as the backbone scale gets larger. For the LoRand series, more parameters bring better performance, but it is still challenging to outperform FULL on large datasets. For the ADAPTER, ADAPTER-B performs better than ADAPTER-T, suggesting that adding extra parameters does help improve adapter-tuning performance. Experiments on Swin variants systematically
+
+![](images/4799d8629c462496de8ce6fadebc123984f57f3c6291d7d764ef3994d63168c8.jpg)
+
+![](images/f1de32ed5f910da96337d105f6c2a278695e25f9594dff66acc215e4c8e21230.jpg)
+
+![](images/cf498dcc0f0551d854e6089165108833da42aef14b8789312e63f10306302f53.jpg)
+
+![](images/780459435f7dcd851bc2a17b3a882ae4f0dd704c150286faeb4d32782ced5b5b.jpg)
+
+![](images/c8f8fb199094b4d44297a887101b9142ca0aa4a8533d9a78d2804c16a7a98a80.jpg)  
+Figure 5. Seven methods on different backbone scales. Figures show results on PASCAL VOC, COCO, and ADE20K from left to right. Swin-S, Swin-B, and Swin-L are employed as the pre-trained models for PASCAL VOC and ADE20K. Swin-T, Swin-S, and Swin-B are employed for COCO. FIXED's performances are so low on COCO and ADE20K that they reduce the intuitiveness of the other six methods, so FIXED is only presented in PASCAL VOC comparisons.
+
+![](images/8beae4f9a09d00f90cecc036a470adcd74773704abd7430320102b6b1e266291.jpg)
+
+![](images/128d7434bbe4dec4e4d11a3c91b0ddb00bf1ce980db749fe4ff84624fbeb0a25.jpg)
+
+![](images/80ef1c9114fff622842c4aebee06a2c60b1be5b51ab9208d703be709a5193c33.jpg)  
+Figure 6. Ablation Study for  $\alpha$  and  $\beta$ .  $\alpha$  ranges from 2, 4, 6, and  $\beta$  ranges from 4, 8, 16. Figures from left to right present experiments on three benchmarks respectively. We only present  $\mathrm{AP_{Box}}$  changes for COCO benchmark considering the strong correlation between the values of  $\mathrm{AP_{Box}}$  and  $\mathrm{AP_{Mask}}$  in COCO.
+
+demonstrate that LoRand can outperform both FULL and traditional adapter structures in low-resource cases and perform very closely to FULL in large benchmarks.
+
+# 4.3. Ablation Study
+
+In this section, we ablate two key hyperparameters in LoRand: the LoRand branch number  $\alpha$  and the kernel matrix dimension  $\beta$ .  $\alpha$  affects the distributed decision-making of LoRand, while  $\beta$  focuses on a single branch's learning capability and consistency.
+
+Several sets of ablation experiments are designed and implemented to investigate the effect of  $\alpha$  and  $\beta$  on the performance of LoRand. The ablation experiments were conducted on the same three benchmarks. In order to improve the upper limit of LoRand, our experiments are conducted on the largest backbone of each dataset (ADE20K/PASCAL VOC: Swin-L, COCO: Swin-B). The value sets of  $\alpha$  and  $\beta$  are  $\{2,4,6\}$  and  $\{4,8,16\}$ . Figure 6 shows the results of ablation studies on three datasets. In most cases, LoRand's performance increases slightly as  $\alpha$  and  $\beta$  become larger but hardly outperforms fine-tuning on large benchmarks. Besides, exponentially increasing the size of the LoRand does
+
+not result in an equivalent performance improvement and even leads to a reduction ( $\alpha = 6$  in VOC and COCO). Ablation studies demonstrate that larger LoRands have fewer gains both in parameter efficiency and performance. We have considered this trade-off when designing the LoRand standard, LoRand+, and LoRand++.
+
+# 5. Conclusion
+
+This paper presents LoRand, a parameter-efficient low-rank adapter for dense predictions, which completely shares the feature understanding of advanced pre-trained models and effectively transfers it to downstream tasks. LoRand performs on par with fine-tuning in COCO instance segmentation, ADE20K semantic segmentation, and PASCAL VOC object detection with only  $1\%$  to  $3\%$  trainable backbone parameters. Moreover, LoRand effectively avoids the disadvantages of the fine-tuning paradigm and delivers better performance in low-resource situations. We hope that parameter-efficient LoRand can save massive redundant storage resources and facilitate a unified training paradigm for vision and language.
+
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+        "text": "1000 FPS HDR Video with a Spike-RGB Hybrid Camera",
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+        "text": "Yakun Chang $^{1,2}$  Chu Zhou $^{3}$  Yuchen Hong $^{1,2}$  Liwen Hu $^{2}$  Chao Xu $^{3}$  Tiejun Huang $^{1,2}$  Boxin Shi $^{1,2*}$",
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+            "$^{1}$  National Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University",
+            "$^{2}$  National Engineering Research Center of Visual Technology, School of Computer Science, Peking University",
+            "$^{3}$  National Key Laboratory of General AI, School of Intelligence Science and Technology, Peking University {yakunchang, zhou_chu, huliwen, tjhuang, shiboxin}@pku.edu.cn yuchenhong.cn@gmail.com, xuchao@cis.pku.edu"
+        ],
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+        "type": "text",
+        "text": "Abstract",
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+        "type": "text",
+        "text": "Capturing high frame rate and high dynamic range (HFR&HDR) color videos in high-speed scenes with conventional frame-based cameras is very challenging. The increasing frame rate is usually guaranteed by using shorter exposure time so that the captured video is severely interfered by noise. Alternating exposures can alleviate the noise issue but sacrifice frame rate due to involving long-exposure frames. The neuromorphic spiking camera records high-speed scenes of high dynamic range without colors using a completely different sensing mechanism and visual representation. We introduce a hybrid camera system composed of a spiking and an alternating-exposure RGB camera to capture HFR&HDR scenes with high fidelity. Our insight is to bring each camera's superiority into full play. The spike frames, with accurate fast motion information encoded, are firstly reconstructed for motion representation, from which the spike-based optical flows guide the recovery of missing temporal information for long-exposure RGB images while retaining their reliable color appearances. With the strong temporal constraint estimated from spike trains, both missing and distorted colors cross RGB frames are recovered to generate time-consistent and HFR color frames. We collect a new Spike-RGB dataset that contains 300 sequences of synthetic data and 20 groups of real-world data to demonstrate 1000 FPS HDR videos outperforming HDR video reconstruction methods and commercial high-speed cameras.",
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+        "text": "1. Introduction",
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+        "type": "text",
+        "text": "The spiking camera [17] and event camera [10] are neuromorphic sensors working differently from conventional frame-based digital cameras, which have many attractive characteristics, e.g., high-speed (perceiving scene",
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+        "image_caption": [
+            "Figure 1. (a) We build a spike-RGB hybrid camera system to achieve 1000 FPS HDR video reconstruction<sup>1</sup>. (b) The RGB camera uses alternating-exposure mode with a frame rate of 60 FPS, where  $t_s$ ,  $4t_s$ , and  $12t_s$  are the short, middle, and long exposure in our setup, respectively. The sampling frequency of the spiking camera is  $20000\\mathrm{Hz}$ ."
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+    {
+        "type": "text",
+        "text": "radiance changes at the microsecond level), high dynamic range (HDR,  $\\geq 100$  dB). However, since they only record neuromorphic signals, i.e., spike trains [64] and event streams [25], which are less friendly to the human visual system and cannot be directly processed by CNN-based models for video frames [40, 41], preprocessing modules that convert neuromorphic signals into compatible formats are usually required when applying them to frame-based vision algorithms [61, 65]. In comparison with event streams, spike trains contain concrete textured information of scene radiances, which are more suitable for reconstructing high frame rate (HFR) videos [61-64]. However, since the spiking camera only encodes the absolute intensities of environments, colors are absent in the reconstructed video frames.",
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+        "type": "text",
+        "text": "When capturing with a frame-based RGB camera, quality of recorded colors for each frame is determined by trading off the exposure time, ambient light, and target objects' moving speed [57]. For high-speed dynamic scenes, it often",
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+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "type": "page_footnote",
+        "text": "*Corresponding author.",
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+    {
+        "type": "page_footnote",
+        "text": "Project page: https://changyakun.github.io/1000FPS-HDR",
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+    {
+        "type": "page_footnote",
+        "text": "The video result is available on our project page.",
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+    },
+    {
+        "type": "page_number",
+        "text": "22180",
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+    },
+    {
+        "type": "text",
+        "text": "requires to set shorter exposure time to guarantee a higher frame rate and avoid motion blur. In such a situation, since the exposure time is extremely short, the quality of video frames would be severely degenerated due to noise. Merging a burst of short-exposure images is a simple yet effective approach to reduce the noise level [8, 11], however, the color shift caused by noise is difficult to be corrected. Fusing alternating-exposure (using short, middle, and long exposures) RGB frames is commonly used for synthesizing well-exposed images [3, 19, 21]. However, they are not suitable for high-speed scenes. As illustrated in Fig. 1(b), given a sequence of alternating-exposure RGB images, the total time from the starting of the current exposure to the starting of the next frame, denoted by  $T$ , is consistent for all frames, and it is composed of the exposure time  $T_{\\mathrm{exp}}$  and interval time  $T_{\\mathrm{itv}}$  (containing the readout and waiting time). It can be seen that the information during interval time is lost, and the frame rate they could achieve is thus limited to dozens of FPS. Another possible solution is to build a hybrid camera system to capture low frame rate (LFR) color sequence and high-speed neuromorphic signals simultaneously, then use the neuromorphic signals to interpolate [51, 52] and deblur [14, 18, 59] the RGB frames. However, the saturated regions are usually ignored, leaving the colors of the interpolated frames still unsatisfactory. HDR intensity map (does not contain any chromatic information) built from the neuromorphic signals can also be used to compensate the missing textures in the saturated regions [15]. But such an approach is not robust for scenes with large areas of saturated regions, due to the heavy reliance on the chrominance compensation network to hallucinate the color.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we propose an all-in-one framework to reconstruct HRF (Fig. 1(a), at the level of 1000 FPS) color videos with high fidelity from the spike trains and a series of alternating-exposure frames captured by a Spike-RGB hybrid camera system simultaneously (Fig. 1(b)). To make full use of the color information in RGB images, we propose a three-stage strategy to deal with different situations using specific modules: (i) For the blurry middle- and long-exposure images, we design a spike guided deblurring module to recover the corresponding sharp images with faithful colors; (ii) for missing colors during the interval time, we design a spike guided interpolation module that exploits the abundant motion information (SC-Flow [16]) obtained from spike trains; (iii) for suppressing noise in short-exposure images and maintaining temporal consistency, we design a merging module, which exploits the variant of recurrent U-Net [42] as its backbone, to complete the HFR&HDR color video reconstruction process. To summarize, this paper makes contributions by proposing:",
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+    {
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+        "text": "- an all-in-one framework to reconstruct high-speed HDR color video by jointly fusing spike trains and a sequence of alternating-exposure frames;",
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+    {
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+        "list_items": [
+            "- a three-stage strategy fusing alternating exposures of RGB frames for the generation of well-exposure colors, via a recurrent convolution neural network for continuous frames interpolation guided by spike trains;",
+            "- a Spike-RGB hybrid camera system to demonstrate the applicability of the proposed method for capturing high-speed and high dynamic range scenes."
+        ],
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+    {
+        "type": "text",
+        "text": "Experimental results show that the proposed method outperforms the state-of-the-art HDR video reconstruction method [3] and commercial cameras with the slow-motion photography capability in reconstructing 1000 FPS HDR color videos on synthetic data and real-world data.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "HDR image and video reconstruction. The most common way to reconstruct HDR images is to fuse a set of LDR images with bracketed exposures [7, 34]. Since the results for dynamic scenes often contain ghosting artifacts, image alignment [28, 45] and deep learning [20, 55] are employed to reconstruct sharp HDR images. To better reduce ghosting artifacts, Lee et al. [24] and Shaw et al. [46] apply the estimated motion information from a high frame rate sequence to facilitate the HDR image synthesis. Messikommer et al. [35] also achieve HDR reconstruction by combining bracketed-exposure RGB images and events. There are methods being designed for HDR reconstruction from a single image. These methods cannot recover the missing textures in clipped regions [9, 44]. Abhiram and Chan [1] reconstruct HDR images with a quanta image sensor (QIS). Han et al. [15] find that the reconstructed intensity maps from event streams and spike trains contain abundant textures saturated in LDR images. Therefore, they exploit intensity maps to guide HDR image restoration. For the capturing of HDR videos, many existing methods use specialized hardware, such as scanline exposure [13], per-pixel exposure [37], or multiple sensors [33, 50]. Due to the particularity of hardware, these methods are limited to narrow applications. Merging alternating-exposure image sequences is the most common yet effective way to reconstruct HDR videos [12, 19, 21, 22, 30, 31]. Recently, Chen et al. [3] propose a coarse-to-fine network that performs alignment and fusion sequentially both in the image and feature space. However, these methods can only deal with LFR videos with about 20-60 FPS.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "HFR video reconstruction. There is plenty of data redundancy in capturing HFR videos directly by commercial high-speed cameras, e.g., the Phatom camera². Building a hybrid system with a high-resolution LFR camera and a low-resolution HFR camera, and utilizing HFR signals to reconstruct a sequence of sharp images from blurred images [2, 49] is a more data-efficient way for HFR video",
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+        "page_idx": 1
+    },
+    {
+        "type": "page_footnote",
+        "text": "2https://www.phantomhighspeed.com/",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "22181",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/98c720d4cece126ecdfa4451934d7d939ae0de158ecc49548ba1c53ceaaf3e0d.jpg",
+        "image_caption": [
+            "Figure 2. (a) The pipeline of the proposed solution. It contains three steps: Step  $①$  spike preprocessing (Sec. 3.2), Step  $②$  RGB frame processing (Sec. 3.3), and Step  $③$  merging into HFR video (Sec. 3.4). Given the spike trains, we firstly estimate the optical flow from them as well as reconstruct spike frames. Secondly, we rectify the uneven brightness with a linear mapping function and use spike-guided deblurring (SG-deblur) to reconstruct sharp color frames. Finally, we use spike-guided frame interpolation (SG-interpolation) to recover the missing colors during  $T_{\\mathrm{itv}}$ , and reconstruct time-consistent color frames. (b) and (c) show the detailed pipeline of SG-deblur and SG-interpolation."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/a3796d73d2d27d9cb39525bfe02cc066e9e00718bd42123a115adabad161f76c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "reconstruction. Li et al. [26] use a stereo pair of low-resolution HFR and high-resolution LFR cameras to calculate the fast motion and the depth map. Avinash et al. [38] compute optical flows between two existing frames by utilizing the content of auxiliary HFR videos. Jiang et al. [18] recover a sharp video sequence from a motion-blurred image by integrating the visual and temporal knowledge that is contained in the events. Xu et al. [54] achieve real-world event-based deblurring with a self-supervised learning method. Tulyakov et al. [52] propose the Time Lens that utilizes high-speed events to achieve video frame interpolation (VFI). Following that, Time Lens++ [51] further improves the performance. For the reason that real data are absent, Yu et al. [56] propose a weakly supervised method with the help of subpixel attention learning. Although the event-based interpolation realizes HFR video reconstruction [51, 52], the recovered quality of colors is usually unsatisfactory due to that single exposure cannot balance artifacts from noise and blur, we therefore propose to jointly fuse the high-speed spike signals and alternating-exposure RGB frames to achieve high-quality reconstruction.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Approach",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Overview",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our goal is to reconstruct HFR&HDR videos from the binary spike trains  $\\mathbb{S}(x,y) = \\{s(x,y,t)\\} (s(x,y,t) = 1$  if the accumulated photons reach a certain threshold, then the accumulator is reset and  $s(x,y,t) = 0$  before the next spike is fired [17]) and LFR alternating-exposure RGB frames  $\\mathbb{B} = \\{\\mathbf{B}_k\\} ^3$ , where  $(x,y)$  denote the coordinates of spikes,  $t$",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "denotes the timestamp, and  $k$  denotes the index of an RGB image in the sequence. As shown in Fig. 2(a), to achieve this goal, we design a pipeline that consists of three steps:",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Step ①: Spike preprocessing (Sec. 3.2). We estimate the optical flow  $\\mathbf{F}_i$  and spike frames  $\\mathbf{I}_i$  from the spike trains:",
+        "bbox": [
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {F} _ {i} (x, y) = \\mathcal {S C} \\left(s \\left(x, y, t _ {i} \\rightarrow t _ {i + 1}\\right)\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {I} _ {i} (x, y) = \\int_ {t _ {i} t _ {f} / 2} ^ {t _ {i} + t _ {f} / 2} s (x, y, t) d t, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{SC}(\\cdot)$  denotes optical flow estimation with Hu et al.'s [16] method,  $i$  and  $t_i$  denote the index and timestamp of spike frames, and  $t_f$  is the time window. In Sec. 3.2, we further super-resolve  $\\mathbf{I}_i$  at the feature space.",
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+        "type": "text",
+        "text": "Step ②: RGB frame preprocessing (Sec. 3.3). For the 60 FPS RGB images captured with alternating exposures, i.e.,  $t_s, 4t_s$ , and  $12t_s$ , we firstly unify the uneven brightness with a linear mapping function. Then we conduct motion deblurring for  $4t_s$  and  $12t_s$  images. For the  $t_s$  images, when  $t_s$  is sufficiently short, i.e., 1 ms, we assume the short-exposure image is free from motion blur, and take  $t_s$  as the reference time for the motion deblurring. Consequently, we can recover 4 and 12 sharp images from  $4t_s$  and  $12t_s$  images, respectively. As shown in Fig. 2(b), we use  $\\mathbf{B}^l$  to denote a blurry image, and the motion deblurring operation can be formulated as:  $\\{\\mathbf{B}_j^l\\} = \\mathcal{R}(\\mathbf{B}^l, \\{\\mathbf{I}_j | j \\in \\mathcal{N}_l\\}, \\mathbf{B}^s)$ , where  $j$  is the index of a recovered sharp image,  $\\mathcal{R}(\\cdot)$  is sharp image reconstruction,  $\\{\\mathbf{I}_j | j \\in \\mathcal{N}_l\\}$  is the corresponding spike frames, and  $\\mathbf{B}^s$  is the nearest short-exposure RGB frame.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Step ③: Merging into HFR video (Sec. 3.4). Following Step ②, for the interval time  $(T_{\\mathrm{itv}})$  that colors are not recorded, we bidirectionally query two nearest sharp RGB",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "3In this paper, we use  $\\{\\cdot\\}$  to denote collections.",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "22182",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/69d8b311ce36a4530ecf232650dd28197899054c0313144d824fc179e70d4d2f.jpg",
+        "image_caption": [
+            "warping",
+            "Figure 3. For the sake of increasing spatial resolution, we adopt flow-based warping to merge adjacent 5 spike frames."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/49bbef8a2cd1ba9b8519bf1120a392f74430894e19e52a34957f5c27c82657ef.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "images  $\\{\\mathbf{B}_i^+, \\mathbf{B}_i\\}$  for each spike frame  $\\mathbf{I}_i$ , and get the warped images  $\\{\\hat{\\mathbf{B}}_i^+, \\hat{\\mathbf{B}}_i\\}$  with optical flow, where  $+$  and  $-$  denote the forward and backward warping, respectively. In Fig. 2(c), we provide an illustration of the interpolation procedure. Finally, as shown in Fig. 4, we reconstruct time-consistent color frames, and each frame  $\\mathbf{C}_i$  is generated by merging the spike frame  $\\mathbf{I}_i$  with  $\\{\\mathbf{C}_i\\}_{1}, \\hat{\\mathbf{B}}_i^+, \\hat{\\mathbf{B}}_i\\}$  with the strong constraint of optical flow.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Spike preprocessing",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The optical flow estimation and spike frame reconstruction using in Eqn. (1) and Eqn. (2) are theoretically, yet the reconstructed frames practically have two issues: Since the integration time  $t_f$  is very short, noise is relatively strong; the spatial resolution of the first generation spiking camera (VidarOne [17]) is much lower than the RGB camera. To reduce the noise and increase the spatial resolution, inspired by the burst-based super-resolution [4] and denoising [27] for conventional RGB images, it is feasible to merge a group of adjacent spike frames with the help of spatial alignment. Moreover, thanks to the continuous motion recording capability of spiking cameras, the optical flow [16] estimated from spike trains makes the alignment even more stable than RGB images. As illustrated in Fig. 3, we design a computationally efficient module for spike frames, which is formulated as:  $\\hat{\\mathbf{I}}_i = \\{\\mathcal{W}_{\\mathbf{F}_{j\\to i}}(\\mathbf{I}_j)|j\\in \\mathcal{N}_i\\}$ , where  $\\mathcal{W}_{\\mathcal{F}_{j\\to i}}(\\cdot)$  denotes the flow-based warping operation,  $\\mathcal{N}_i$  denotes a collection of adjacent frames. Then, we feed  $\\hat{\\mathbf{I}}_i$  to a set of convolutional layers, and we use PixelShuffle [47] to increase the spatial resolution while decreasing the channel of features. It should be noted that the method for spike frame reconstruction is not unique, which means users can choose other learning-based methods [61, 62, 64]. However, those deep learning models are relatively heavy, and less efficient as a submodule fitting to our pipeline.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. RGB image preprocessing",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "RGB linear mapping. Following previous methods for HDR video reconstruction [3, 19, 21], we first unify the brightness of alternating-exposure RGB frames. Since we use an industrial camera (details in Sec. 3.5) that can acquire data without a nonlinear radiometric response function, the linearity of the captured frames is maintained. We find that the brightness of the frames can maintain a linear relationship with the duration of exposure time. Hence we use the global linear mapping to unify the frame brightness:  $\\alpha \\cdot \\mathbf{B}_k(x,y)\\rightarrow \\mathbf{B}_k(x,y)$ , where  $\\alpha$  denotes a linear scalar.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Spike-guided deblurring. The physical model of the blurring process can be simply formulated as the average of a group of sharp images, i.e.,  $\\mathbf{B}^l (x,y) = \\frac{1}{N}\\sum_{j = 1}^{N}\\mathbf{B}_j^l (x,y)$ , where  $N$  denotes the number of sharp images. However, due to the limited dynamic range of the RGB camera, that simplified equation does not hold in the clipped regions of real-world long-exposure frames. In general we should have:  $\\mathbf{B}^l (x,y)\\leq \\frac{1}{N}\\sum_{j = 1}^{N}\\mathbf{B}_j^l (x,y)$ . Therefore, for reconstructing a sequence of sharp HDR images from  $\\mathbf{B}^l$ , we divide it into two sub-tasks: (i) For the well-exposure regions, we use the sharp spike frames to guide motion deblurring; (ii) for the clipped regions where colors are lost, we compensate them with well-retained colors extracted from the adjacent short-exposure image  $\\mathbf{B}^s$ .",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Figure 2(b) shows the spike-guided deblurring (SG-deblur) from  $\\mathbf{B}_l$  ( $\\mathbf{B}_l$  may be a middle- or long-exposure image). Similar to Xu et al. [54] that exploit event frames to motion deblurring, we first concatenate  $\\mathbf{B}_l$  with  $\\{\\mathbf{I}_l^j\\}$ , then extract shallow features and increase feature channels with PixelShuffle [47], which is followed by a set of residual dense blocks (RDBs) [60] and a decoder. To make the colors in over-exposure regions be compensated by the adjacent short-exposure RGB image  $\\mathbf{B}_j^s$ , we warp the short-exposure image with the optical flow estimated from spike trains:  $\\mathbf{B}_j^s = \\mathcal{W}_{\\mathbf{F}_{s\\rightarrow j}}(\\mathbf{B}^s)$ , where  $\\mathcal{W}_{\\mathbf{F}_{s\\rightarrow j}}(\\cdot)$  denotes the warping operation from timestamp  $t_s$  to the timestamp of  $t_j$ . Subsequently, we extract features from  $\\{\\mathbf{B}_l^{s\\rightarrow j}\\}$  and add residual links between them and the decoder. Finally, we obtain a sequence of sharp color images. Note that the SG-deblur for the middle- and long-exposure RGB images share the same architecture while the parameters are not shareable. SG-deblur outputs four images for both  $4t_s$  and  $12t_s$  frames. For the case of  $12t_s$  frame, we interpolate the 4 frames to 12 frames with flow-based warping.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Next, we briefly explain the reason why this event-based model [54] can be applied to a spike-based task. Both event streams and spike trains with the high-speed property have been used for motion deblurring and latent frame reconstruction [14,18,54]. It is necessary to convert them to event frames and spike frames, both of which belong to the category of 2D images. But event frames and spike frames have different physical meanings: Pixel values in an event frame reveal the residual (relatively sparse information) between two adjacent frames, while pixel values in a spike frame represent exactly the texture (relatively dense information) of the corresponding frame. Since both event frames and spike frames are 2D images and the spike frames have denser texture information, we can replace event frames in such a model with spike frames, so as to make the solution to the problem more well-posed.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4. Merging into HFR video",
+        "text_level": 1,
+        "bbox": [
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+            861,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "RGB interpolation. Given each middle- and long-exposure",
+        "bbox": [
+            500,
+            885,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "22183",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/f70c457f89317c1a8dfbd75c2c3839b8139e7a74e3c29226b3c581376d4d252a.jpg",
+        "image_caption": [
+            "Figure 4. Network architecture of the CNN-RNN-based merging module for reconstructing HFR&HDR videos from alternating-exposure RGB frames and HFR spike frames. This module outputs HDR color frames in a step-wise manner. We unroll the module for  $M$  steps during training."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "frame, SG-deblur recovers 4 and 12 images. Therefore, the recovered RGB frames have a frame rate of  $340^{4}$  FPS. But temporal distribution of them is quite uneven, e.g., there is no recovered color frame interval time  $T_{\\mathrm{itv}}$ . Fortunately, the spike train contains continuous and dense texture information in the temporal domain. In Step ③, we use the SG-interpolation module to interpolate RGB frames into a sequence of uniformly distributed images. For each spike frame  $\\mathbf{I}_i$ , we bidirectionally query its two nearest recovered RGB frames  $\\{\\mathbf{B}_i^+, \\mathbf{B}_i\\}$  and interpolate two color frames  $\\{\\hat{\\mathbf{B}}_i^+, \\hat{\\mathbf{B}}_i\\}$  with the optical flow estimated from spike trains. When  $\\{\\hat{\\mathbf{B}}_i^+, \\hat{\\mathbf{B}}_i\\}$  are fed into our merging module, they are weighted by a linear coefficient  $(\\oplus$  in Fig. 4) related to the distance between  $t_i$  and  $\\{t_+, t\\}$ , where  $\\{t_+, t\\}$  denote the timestamp of  $\\{\\hat{\\mathbf{B}}_i^+, \\hat{\\mathbf{B}}_i\\}$ .",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Merging module. The aforementioned modules reconstruct coarse HFR video frames, which need to be refined for smoothing over time. We build a CNN-RNN-based HFR&HDR video reconstruction network to merge the spike frames and RGB frames, which is shown in Fig. 4. The merging module consists of three encoders, i.e.,  $\\mathcal{E}_I$ ,  $\\mathcal{E}_B$ , and  $\\mathcal{E}_C$ , which are respectively designed for feature extraction from the current spike frame  $\\hat{\\mathbf{I}}_i$ , the interpolated RGB images  $\\{\\hat{\\mathbf{B}}_i^+, \\hat{\\mathbf{B}}_i\\}$ , and the previously reconstructed image  $\\mathbf{C}_{i-1}$ . In  $\\mathcal{E}_I$ , we use PixelShuffle [47] to make the spatial resolution of spike features consistent with RGB features. The extracted features are denoted as  $\\mathbf{E}_I$ ,  $\\{\\mathbf{E}_B, \\mathbf{E}_{B+}\\}$ , and  $\\mathbf{E}_{C_i-1}$ , respectively.",
+        "bbox": [
+            75,
+            598,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Considering the spike frames and RGB frames may not be perfectly aligned at pixel level for real-world data, we add deformable convolution layers [6] to improve the robustness to this issue. In order to output flicker-free color frames, we adopt two constraints in the merging module:",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/9754e7ba0b3f019bb54d91503f166a8e553e6c6c01ac31fde44a015920f2d53f.jpg",
+        "table_caption": [
+            "Table 1. Details of the composition of the dataset (res. is the abbreviation of resolution)."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>data</td><td>RGB res.</td><td>spike res.</td><td>train/test</td><td>time</td></tr><tr><td>full-synthetic</td><td>500×800</td><td>250×400</td><td>80/20</td><td>0.1s</td></tr><tr><td>real-synthetic</td><td>600×800</td><td>250×400</td><td>160/40</td><td>0.101s</td></tr><tr><td>real-world</td><td>484×784</td><td>242×392</td><td>-/20</td><td>0.101s</td></tr></table>",
+        "bbox": [
+            521,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "(i) We add three ConvLSTM layers [48] to feed previous states forward in temporal domain; (ii) we feed  $\\mathbf{E}_{C_i}$  into the current step and align it with the current features with flow-based warping. We then use a decoder to reversely map deep features to the current output HDR frame  $\\mathbf{C}_i$ . We achieve the multi-module signal fusion by adding concatenation links between  $\\{\\mathbf{E}_{C_i}$ ,  $\\mathbf{E}_B$ ,  $\\mathbf{E}_{B+}\\}$  and the decoder.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5. Implementation Details",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Due to the setting of our method being different from existing HDR and video frame interpolation methods, there are no suitable datasets for training and testing our method. Therefore, we collect a new one with three components, whose details are summarized in Table 1 and sample images are provided in Fig. 5.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Part 1: Full-synthetic data. This part of data is obtained by using the spike simulator proposed by Hu et al. [16]. We render 2000 RGB images with their computer graphics based solution as ground truth and generate 2000 spike planes (0.1 s). Since the photons arriving at the sensor follow Poisson probability distribution [43], we synthesize alternating-exposure 60 FPS RGB frames with a Poisson noise model. For the full synthetic data, we randomly select starting time of each group of training data. We randomly shift the RGB frames within 3 pixels to make the trained model more robust to the misalignment in real-world data.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Part 2: Real-synthetic data. To reduce the domain gap between full-synthetic data and real-world data, we design a method to collect real-synthetic (the scenes are real while",
+        "bbox": [
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+            854,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_footnote",
+        "text": "4From  $60 = 20\\times 3$  to  $340 = 20\\times (1 + 4 + 12)$",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "22184",
+        "bbox": [
+            478,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/176aa9dfa2ecaf20f74ee48cdeb45fed0d736431be6a2a3e803a4ccf3f70da7d.jpg",
+        "image_caption": [
+            "Figure 5. Example frames from the proposed dataset. Each group shows three alternating-exposure RGB frames (left, from top to bottom rows) and the corresponding spike signals (right)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "the spike trains are synthetic) data, and we use this part of data to fine-tune our model. The RGB frames are captured with an alternating-exposure mode in slow-motion scenes. Then we synthesize blurry middle-exposure RGB frames by averaging 4 adjacent middle-exposure RGB images, and blurry long-exposure RGB frames are synthesized in a similar way. We synthesize spike trains from ground truth RGB frames with the integrate-and-fire methodology [61].",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Part 3: Real-world data. We build a Spike-RGB hybrid camera (Fig. 6) to capture real-world data. The system is composed of an industrial camera (Basler acA800-510uc $^5$ ) with alternating exposure capability and a spiking camera [17]. There is a beam splitter in front of the two sensors. We conduct geometric calibration and time synchronization to align bimodal signals collected by them.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Loss and training. The SG-deblur module and the merging module reconstruct images in the linear luminance domain, which covers a high dynamic range of pixel values. Following existing methods for HDR reconstruction, for the output images  $\\mathbf{C}$ , we compress the range of pixel values by applying the following function proposed by Kalantari et al. [20]:  $\\mathcal{T}(\\mathbf{C}) = \\log (1 + \\mu \\mathbf{C}) / \\log (1 + \\mu)$ , where  $\\mathcal{T}(\\cdot)$  denotes the tone mapping operation and  $\\mu$  denotes the amount of compression. For these two modules, we employ widely used  $l_{1}$  loss, Structure similarity (SSIM) loss [53], and Learned Perceptual Image Patch Similarity (LPIPS) loss [58]. The total loss at step  $i$  for both the motion deblurring and merging modules is",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} (i) = \\mathcal {L} _ {l _ {1}} (i) + \\beta_ {1} \\mathcal {L} _ {\\text {S S I M}} (i) + \\beta_ {2} \\mathcal {L} _ {\\text {L P I P S}} (i), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $\\beta_{1} = 1$  and  $\\beta_{2} = 1$ . For spike-based optical flow estimation using [16], we fine-tune the parameters with full-synthetic data. During training, we resize the RGB images and spike frames to  $512 \\times 800$  and  $256 \\times 400$ . We implement our model with PyTorch, set the batch size to 4, and use ADAM optimizer during the training process. We first train the model on full-synthetic data. The SG-deblur module is trained with 50 epochs, before training the merging",
+        "bbox": [
+            75,
+            744,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/3a9785b5e9c025abd121037f9499ff36cfcf100a90bcaf5ae65255ec856a5815.jpg",
+        "image_caption": [
+            "Figure 6. The prototype of our Spike-RGB imaging system composed of a spiking camera and an RGB camera."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            87,
+            890,
+            220
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "module. We unroll the merging module for  $M$  steps, and we find  $M = 4$  achieves a suitable balance between training time and recovery quality. The total loss for the unrolled  $M$  steps is  $\\mathcal{L}_{\\mathrm{merge}} = \\sum_{i=1}^{M} \\mathcal{L}_{\\mathrm{total}}^{\\mathrm{M}}(i)$ , where  $\\mathcal{L}_{\\mathrm{total}}^{\\mathrm{M}}(i)$  denotes the total loss for the merging module at step  $i$ . The initial learning rate for both two modules is 0.001, we decay it to  $10^{-6}$  with a linear strategy. For the real-synthetic data, we fine-tune another group of parameters to reduce the gap between synthetic data and real-world data. We use one NVIDIA Tesla A100 for training, and the training procedure consumes about 30 hours.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Quantitative Evaluation using Synthetic Data",
+        "text_level": 1,
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+        "text": "Validation on full-synthetic data. Figure 8 shows a group of results on full-synthetic data. We can see that both the flying objects in the short-exposure image and the oversaturated clouds (see the regions marked by boxes) in the long-exposure image are recovered successfully. The results with rich textures and consistent colors show the feasibility of our proposed method.",
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+        "text": "Evaluation on real-synthetic data. To the best of our knowledge, the proposed method is the first framework to reconstruct HFR&HDR videos with the combination of spike trains and alternating-exposure RGB frames. Therefore, it is unfair to compare our method with existing ones, i.e., Kalantari13 [21], Kalantari19 [19], and Chen21  $[3]^{6}$ , which are designed for low frame rate HDR videos.",
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+        "text": "We choose a state-of-the-art HDR video reconstruction method Chen21 [3], which also uses alternating-exposure RGB frames (the closest setup to ours) as a reference. Figure 7 shows the reconstruction results on real-synthetic data of the proposed method and Chen21 [3]. Thanks to the complementary motion information provided by spike trains, the abundant color extracted from alternating-exposure RGB frames, and the accurate textures contained in spike frames, the proposed method is capable of reconstructing rich texture details with less motion blur. For ex",
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+        "text": "5https://www.baslerweb.com/en/products/camera/ area-scan-cameras/ace/aca800-510uc/",
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+        "text": "In this section, we use \"Last name of the first author+year\" as synonyms of methods for comparison.",
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+        "image_caption": [
+            "Figure 7. Visual equality comparison of real-synthetic data between the proposed method and the state-of-the-art HDR video reconstruction method: Chen 21 [3]. We present two sets of results in (a) and (b). Please zoom-in electronic versions for better details, and watch the HFR videos on the project page.",
+            "Figure 8. Validation on the synthetic data."
+        ],
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+    {
+        "type": "text",
+        "text": "ample, in the long-exposure frame in the first row of (a), the building marked by a yellow box suffers from severe motion blur and overexposure. Chen21 [3] partially recovers the colors of this building, but it fails to remove the blurry artifacts. In the results generated by our method, the edges are sharp and the colors are vivid. In Fig. 7(b), the motions across RGB frames have a very large span, Chen21 [3] can only recover the corresponding LFR videos, while our method can reconstruct an HFR video with smooth motion.",
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+    {
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+        "text": "We evaluate the reconstructed HDR in terms of PSNR, SSIM, HDR-VDP-2 [32], and HDR-VQM [36]. Table 2 clearly shows that our framework outperforms the state-of-the-art method [3] in all the metrics on the real-synthetic data in the condition of 60 FPS. And we achieve excellent performance in the condition of 1000 FPS. We designed ablation experiments and used them to demonstrate the effectiveness of the modules in our framework. For \"w/o I\", we simply stack the spike trains with a time window, and upsample them using bilinear interpolation; for \"w/o PS\", we replace PixelShuffle with a convolutional layer. The two groups of experiments verify the effectiveness of spike frame preprocessing in Step ①. For \"w/o F1\" and \"w/o F2\", we remove the flow-based interpolation in the deblurring module and the merging module. The two groups of ex",
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+    {
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+        "table_caption": [
+            "Table 2. Quantitative results and ablation study on our realistic synthetic data. We sample 60 FPS videos from our results for the comparison with Chen21 [3].  $\\uparrow (\\downarrow)$  indicates larger (smaller) values are better."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"6\">Comparison with the state-of-th-art method</td></tr><tr><td>Method</td><td>PSNR↑</td><td>SSIM↑</td><td>HDR-VDP2↑</td><td>HDR-VQM↓</td><td>FPS</td></tr><tr><td>Chen21 [3]</td><td>18.46</td><td>0.697</td><td>27.34</td><td>0.536</td><td rowspan=\"2\">60</td></tr><tr><td>Ours</td><td>30.14</td><td>0.921</td><td>60.14</td><td>0.093</td></tr><tr><td>Chen21 [3]</td><td>/</td><td>/</td><td>/</td><td>/</td><td rowspan=\"2\">1000</td></tr><tr><td>Ours</td><td>24.38</td><td>0.903</td><td>47.79</td><td>0.120</td></tr><tr><td colspan=\"6\">Ablation study</td></tr><tr><td>w/o I</td><td>23.15</td><td>0.886</td><td>46.03</td><td>0.143</td><td rowspan=\"7\">1000</td></tr><tr><td>w/o PS</td><td>23.98</td><td>0.881</td><td>46.47</td><td>0.141</td></tr><tr><td>w/o F1</td><td>19.76</td><td>0.723</td><td>38.95</td><td>0.314</td></tr><tr><td>w/o F2</td><td>18.04</td><td>0.716</td><td>35.89</td><td>0.356</td></tr><tr><td>w/ t-loss</td><td>22.41</td><td>0.864</td><td>43.64</td><td>0.142</td></tr><tr><td>w/o DeConv</td><td>24.31</td><td>0.897</td><td>47.66</td><td>0.127</td></tr><tr><td>w/o DM</td><td>19.01</td><td>0.714</td><td>37.97</td><td>0.338</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "periments verify the effectiveness of SC-Flow [16] based interpolation in Steps ② and ③. To further verify the effectiveness of deblurring module, we completely remove it in \"w/o DM\". For \"w/o DeConv\", we replace the deformable convolutional layers with traditional convolution layers. For \"w/ t-loss\", we remove the warping operation on  $\\mathbf{C}_{i-1}$  and add the temporal consistent loss that is estimated by a pretrained optical flow model [23], which is widely used in video processing [5, 39]. Since the  $\\mathbf{C}_{i-1}$  is warped by accurate optical flow  $\\mathbf{F}_{i-1}$  and merged into the current step  $i$ , our method fundamentally has a strong temporal consistent constraint for video processing. Thus, our merging module does not need this loss during training.",
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+    {
+        "type": "text",
+        "text": "4.2. Qualitative Evaluation using Real Data",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In order to demonstrate the effectiveness of the proposed framework on real-world scenes, we collect 20 sets of real-world data, which are captured by our hybrid camera system shown in Fig. 6. We have compared our slow-motion capability with that of the commercial cameras. As shown in Fig. 9(a), the electric fan is moving at about 40 rounds",
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+        "image_caption": [
+            "Figure 9. Visual quality comparison of real-world data between the proposed method and commercial cameras with the slow-motion capability. In (a), we show two adjacent frames for the video captured by smartphones that have slow-motion capability. The commercial cameras are not calibrated so their results are not strictly aligned with ours. (b) is the comparison with Phantom camera set to 1000 FPS."
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+    {
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+        "img_path": "images/e93c85761807f3ca93c18962918da723c0e397456cdc1707f1e86ea56554f370.jpg",
+        "image_caption": [
+            "Figure 10. Qualitative visualization of our method in a super fast scene: a balloon bursting. We select 38 frames from our results for showing."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "per second. The short-exposure image is severely underexposed with less blurry artifacts, and the middle- and long-exposure images have severe blurring and oversaturated artifacts. With the accurate motion and texture information captured by the spiking camera, we have recovered temporally smooth video sequences. Four recovered images are shown for the middle- and long-exposure images. For the videos captured by iPhone 13 and Mi 10, the motions between frames are not continuous. And the electric fan captured by Mi 10 is deformed due to the rolling shutter. In Fig. 9(b), we compare our method with the Phantom<sup>7</sup> camera set to 1000 FPS. Since the exposure time of the Phantom camera is extremely short, it fails to capture regions where scene radiance is weak.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We propose an HFR&HDR video reconstruction method with a hybrid camera that is composed of an alternating-exposure RGB sensor and a spiking sensor. Extensive experiments on synthetic and real-world data demonstrate the superior performance of the proposed method.",
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+    {
+        "type": "text",
+        "text": "Discussion. (i) For super fast scenes, e.g., a balloon bursting, it is difficult to capture clear motions with a conventional RGB camera at 60 FPS. Therefore, the well-exposed color of the bursting balloon is not captured with the short exposure, which brings challenges to our reconstruction of accurate color. In our results, although the colors are somewhat distorted, we can still recover a smooth video sequence. Once the frame rate of the RGB camera is increased, e.g., 120 FPS, temporally smoother video with more accurate color is expected to be more reliably recovered. (ii) Since QIS [1, 29] share the same imaging model with the spiking camera, our method is ready to be applied to it. We show the simulation in supplementary material.",
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+    {
+        "type": "text",
+        "text": "Limitation and future work. Beam splitter is arguable for making a practical system on mobile devices. But when compact design is not a hard constraint, beam splitter has unique advantages in spatial alignment, that is why it is broadly adopted in building a hybrid prototype for HDR [15, 24, 33, 50]. Side-by-side arrangement with parallax unavoidably introduces occlusions and alignment issues, which is a promising direction to explore for our future work. Due to the low spatial resolution  $(250\\times 400)$  of the current model we use is, we have to super-resolve the spike frames in feature space. If higher-resolution spike signals can be directly obtained, our method can achieve better visual quality. Besides, there is a domain gap between synthetic spike trains and real-captured spike trains since the noise of the spiking camera is more complex than the simulator. For time complexity, our approach is better suited as a post-processing module. The number of parameters is  $45.7\\mathrm{M}$  and the time cost per frame is 0.371s with a single NVIDIA GeForce RTX 3090 graphics card. We hope to tackle these issues in the future work and achieve higher frame rate reconstruction.",
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+    {
+        "type": "text",
+        "text": "Acknowledgement",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "This work was supported by National Key R&D Program of China (2021ZD0109803), National Natural Science Foundation of China under Grant No. 62088102, 62136001. Yakun Chang was also supported by China Postdoctoral Science Foundation (8206300710).",
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+    {
+        "type": "page_footnote",
+        "text": "7Refer to footnote 2. Camera model: VEO 640, F/1.8, 85mm lens.",
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+        "text": "22187",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            174,
+            106
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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2023/1000 FPS HDR Video With a Spike-RGB Hybrid Camera/1c93f555-c37f-43ed-866a-0e7c5d4458e6_origin.pdf

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+# 1000 FPS HDR Video with a Spike-RGB Hybrid Camera
+
+Yakun Chang $^{1,2}$  Chu Zhou $^{3}$  Yuchen Hong $^{1,2}$  Liwen Hu $^{2}$  Chao Xu $^{3}$  Tiejun Huang $^{1,2}$  Boxin Shi $^{1,2*}$
+
+$^{1}$  National Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University  
+$^{2}$  National Engineering Research Center of Visual Technology, School of Computer Science, Peking University  
+$^{3}$  National Key Laboratory of General AI, School of Intelligence Science and Technology, Peking University {yakunchang, zhou_chu, huliwen, tjhuang, shiboxin}@pku.edu.cn yuchenhong.cn@gmail.com, xuchao@cis.pku.edu
+
+# Abstract
+
+Capturing high frame rate and high dynamic range (HFR&HDR) color videos in high-speed scenes with conventional frame-based cameras is very challenging. The increasing frame rate is usually guaranteed by using shorter exposure time so that the captured video is severely interfered by noise. Alternating exposures can alleviate the noise issue but sacrifice frame rate due to involving long-exposure frames. The neuromorphic spiking camera records high-speed scenes of high dynamic range without colors using a completely different sensing mechanism and visual representation. We introduce a hybrid camera system composed of a spiking and an alternating-exposure RGB camera to capture HFR&HDR scenes with high fidelity. Our insight is to bring each camera's superiority into full play. The spike frames, with accurate fast motion information encoded, are firstly reconstructed for motion representation, from which the spike-based optical flows guide the recovery of missing temporal information for long-exposure RGB images while retaining their reliable color appearances. With the strong temporal constraint estimated from spike trains, both missing and distorted colors cross RGB frames are recovered to generate time-consistent and HFR color frames. We collect a new Spike-RGB dataset that contains 300 sequences of synthetic data and 20 groups of real-world data to demonstrate 1000 FPS HDR videos outperforming HDR video reconstruction methods and commercial high-speed cameras.
+
+# 1. Introduction
+
+The spiking camera [17] and event camera [10] are neuromorphic sensors working differently from conventional frame-based digital cameras, which have many attractive characteristics, e.g., high-speed (perceiving scene
+
+![](images/60240d2e429f7bbaa254aba2a45842b1ba35e1ca5ec1952b36f6954e438ed27c.jpg)  
+Figure 1. (a) We build a spike-RGB hybrid camera system to achieve 1000 FPS HDR video reconstruction<sup>1</sup>. (b) The RGB camera uses alternating-exposure mode with a frame rate of 60 FPS, where  $t_s$ ,  $4t_s$ , and  $12t_s$  are the short, middle, and long exposure in our setup, respectively. The sampling frequency of the spiking camera is  $20000\mathrm{Hz}$ .
+
+radiance changes at the microsecond level), high dynamic range (HDR,  $\geq 100$  dB). However, since they only record neuromorphic signals, i.e., spike trains [64] and event streams [25], which are less friendly to the human visual system and cannot be directly processed by CNN-based models for video frames [40, 41], preprocessing modules that convert neuromorphic signals into compatible formats are usually required when applying them to frame-based vision algorithms [61, 65]. In comparison with event streams, spike trains contain concrete textured information of scene radiances, which are more suitable for reconstructing high frame rate (HFR) videos [61-64]. However, since the spiking camera only encodes the absolute intensities of environments, colors are absent in the reconstructed video frames.
+
+When capturing with a frame-based RGB camera, quality of recorded colors for each frame is determined by trading off the exposure time, ambient light, and target objects' moving speed [57]. For high-speed dynamic scenes, it often
+
+requires to set shorter exposure time to guarantee a higher frame rate and avoid motion blur. In such a situation, since the exposure time is extremely short, the quality of video frames would be severely degenerated due to noise. Merging a burst of short-exposure images is a simple yet effective approach to reduce the noise level [8, 11], however, the color shift caused by noise is difficult to be corrected. Fusing alternating-exposure (using short, middle, and long exposures) RGB frames is commonly used for synthesizing well-exposed images [3, 19, 21]. However, they are not suitable for high-speed scenes. As illustrated in Fig. 1(b), given a sequence of alternating-exposure RGB images, the total time from the starting of the current exposure to the starting of the next frame, denoted by  $T$ , is consistent for all frames, and it is composed of the exposure time  $T_{\mathrm{exp}}$  and interval time  $T_{\mathrm{itv}}$  (containing the readout and waiting time). It can be seen that the information during interval time is lost, and the frame rate they could achieve is thus limited to dozens of FPS. Another possible solution is to build a hybrid camera system to capture low frame rate (LFR) color sequence and high-speed neuromorphic signals simultaneously, then use the neuromorphic signals to interpolate [51, 52] and deblur [14, 18, 59] the RGB frames. However, the saturated regions are usually ignored, leaving the colors of the interpolated frames still unsatisfactory. HDR intensity map (does not contain any chromatic information) built from the neuromorphic signals can also be used to compensate the missing textures in the saturated regions [15]. But such an approach is not robust for scenes with large areas of saturated regions, due to the heavy reliance on the chrominance compensation network to hallucinate the color.
+
+In this paper, we propose an all-in-one framework to reconstruct HRF (Fig. 1(a), at the level of 1000 FPS) color videos with high fidelity from the spike trains and a series of alternating-exposure frames captured by a Spike-RGB hybrid camera system simultaneously (Fig. 1(b)). To make full use of the color information in RGB images, we propose a three-stage strategy to deal with different situations using specific modules: (i) For the blurry middle- and long-exposure images, we design a spike guided deblurring module to recover the corresponding sharp images with faithful colors; (ii) for missing colors during the interval time, we design a spike guided interpolation module that exploits the abundant motion information (SC-Flow [16]) obtained from spike trains; (iii) for suppressing noise in short-exposure images and maintaining temporal consistency, we design a merging module, which exploits the variant of recurrent U-Net [42] as its backbone, to complete the HFR&HDR color video reconstruction process. To summarize, this paper makes contributions by proposing:
+
+- an all-in-one framework to reconstruct high-speed HDR color video by jointly fusing spike trains and a sequence of alternating-exposure frames;
+
+- a three-stage strategy fusing alternating exposures of RGB frames for the generation of well-exposure colors, via a recurrent convolution neural network for continuous frames interpolation guided by spike trains;  
+- a Spike-RGB hybrid camera system to demonstrate the applicability of the proposed method for capturing high-speed and high dynamic range scenes.
+
+Experimental results show that the proposed method outperforms the state-of-the-art HDR video reconstruction method [3] and commercial cameras with the slow-motion photography capability in reconstructing 1000 FPS HDR color videos on synthetic data and real-world data.
+
+# 2. Related Work
+
+HDR image and video reconstruction. The most common way to reconstruct HDR images is to fuse a set of LDR images with bracketed exposures [7, 34]. Since the results for dynamic scenes often contain ghosting artifacts, image alignment [28, 45] and deep learning [20, 55] are employed to reconstruct sharp HDR images. To better reduce ghosting artifacts, Lee et al. [24] and Shaw et al. [46] apply the estimated motion information from a high frame rate sequence to facilitate the HDR image synthesis. Messikommer et al. [35] also achieve HDR reconstruction by combining bracketed-exposure RGB images and events. There are methods being designed for HDR reconstruction from a single image. These methods cannot recover the missing textures in clipped regions [9, 44]. Abhiram and Chan [1] reconstruct HDR images with a quanta image sensor (QIS). Han et al. [15] find that the reconstructed intensity maps from event streams and spike trains contain abundant textures saturated in LDR images. Therefore, they exploit intensity maps to guide HDR image restoration. For the capturing of HDR videos, many existing methods use specialized hardware, such as scanline exposure [13], per-pixel exposure [37], or multiple sensors [33, 50]. Due to the particularity of hardware, these methods are limited to narrow applications. Merging alternating-exposure image sequences is the most common yet effective way to reconstruct HDR videos [12, 19, 21, 22, 30, 31]. Recently, Chen et al. [3] propose a coarse-to-fine network that performs alignment and fusion sequentially both in the image and feature space. However, these methods can only deal with LFR videos with about 20-60 FPS.
+
+HFR video reconstruction. There is plenty of data redundancy in capturing HFR videos directly by commercial high-speed cameras, e.g., the Phatom camera². Building a hybrid system with a high-resolution LFR camera and a low-resolution HFR camera, and utilizing HFR signals to reconstruct a sequence of sharp images from blurred images [2, 49] is a more data-efficient way for HFR video
+
+![](images/98c720d4cece126ecdfa4451934d7d939ae0de158ecc49548ba1c53ceaaf3e0d.jpg)  
+Figure 2. (a) The pipeline of the proposed solution. It contains three steps: Step  $①$  spike preprocessing (Sec. 3.2), Step  $②$  RGB frame processing (Sec. 3.3), and Step  $③$  merging into HFR video (Sec. 3.4). Given the spike trains, we firstly estimate the optical flow from them as well as reconstruct spike frames. Secondly, we rectify the uneven brightness with a linear mapping function and use spike-guided deblurring (SG-deblur) to reconstruct sharp color frames. Finally, we use spike-guided frame interpolation (SG-interpolation) to recover the missing colors during  $T_{\mathrm{itv}}$ , and reconstruct time-consistent color frames. (b) and (c) show the detailed pipeline of SG-deblur and SG-interpolation.
+
+![](images/a3796d73d2d27d9cb39525bfe02cc066e9e00718bd42123a115adabad161f76c.jpg)
+
+reconstruction. Li et al. [26] use a stereo pair of low-resolution HFR and high-resolution LFR cameras to calculate the fast motion and the depth map. Avinash et al. [38] compute optical flows between two existing frames by utilizing the content of auxiliary HFR videos. Jiang et al. [18] recover a sharp video sequence from a motion-blurred image by integrating the visual and temporal knowledge that is contained in the events. Xu et al. [54] achieve real-world event-based deblurring with a self-supervised learning method. Tulyakov et al. [52] propose the Time Lens that utilizes high-speed events to achieve video frame interpolation (VFI). Following that, Time Lens++ [51] further improves the performance. For the reason that real data are absent, Yu et al. [56] propose a weakly supervised method with the help of subpixel attention learning. Although the event-based interpolation realizes HFR video reconstruction [51, 52], the recovered quality of colors is usually unsatisfactory due to that single exposure cannot balance artifacts from noise and blur, we therefore propose to jointly fuse the high-speed spike signals and alternating-exposure RGB frames to achieve high-quality reconstruction.
+
+# 3. Approach
+
+# 3.1. Overview
+
+Our goal is to reconstruct HFR&HDR videos from the binary spike trains  $\mathbb{S}(x,y) = \{s(x,y,t)\} (s(x,y,t) = 1$  if the accumulated photons reach a certain threshold, then the accumulator is reset and  $s(x,y,t) = 0$  before the next spike is fired [17]) and LFR alternating-exposure RGB frames  $\mathbb{B} = \{\mathbf{B}_k\} ^3$ , where  $(x,y)$  denote the coordinates of spikes,  $t$
+
+denotes the timestamp, and  $k$  denotes the index of an RGB image in the sequence. As shown in Fig. 2(a), to achieve this goal, we design a pipeline that consists of three steps:
+
+Step ①: Spike preprocessing (Sec. 3.2). We estimate the optical flow  $\mathbf{F}_i$  and spike frames  $\mathbf{I}_i$  from the spike trains:
+
+$$
+\mathbf {F} _ {i} (x, y) = \mathcal {S C} \left(s \left(x, y, t _ {i} \rightarrow t _ {i + 1}\right)\right), \tag {1}
+$$
+
+$$
+\mathbf {I} _ {i} (x, y) = \int_ {t _ {i} t _ {f} / 2} ^ {t _ {i} + t _ {f} / 2} s (x, y, t) d t, \tag {2}
+$$
+
+where  $\mathcal{SC}(\cdot)$  denotes optical flow estimation with Hu et al.'s [16] method,  $i$  and  $t_i$  denote the index and timestamp of spike frames, and  $t_f$  is the time window. In Sec. 3.2, we further super-resolve  $\mathbf{I}_i$  at the feature space.
+
+Step ②: RGB frame preprocessing (Sec. 3.3). For the 60 FPS RGB images captured with alternating exposures, i.e.,  $t_s, 4t_s$ , and  $12t_s$ , we firstly unify the uneven brightness with a linear mapping function. Then we conduct motion deblurring for  $4t_s$  and  $12t_s$  images. For the  $t_s$  images, when  $t_s$  is sufficiently short, i.e., 1 ms, we assume the short-exposure image is free from motion blur, and take  $t_s$  as the reference time for the motion deblurring. Consequently, we can recover 4 and 12 sharp images from  $4t_s$  and  $12t_s$  images, respectively. As shown in Fig. 2(b), we use  $\mathbf{B}^l$  to denote a blurry image, and the motion deblurring operation can be formulated as:  $\{\mathbf{B}_j^l\} = \mathcal{R}(\mathbf{B}^l, \{\mathbf{I}_j | j \in \mathcal{N}_l\}, \mathbf{B}^s)$ , where  $j$  is the index of a recovered sharp image,  $\mathcal{R}(\cdot)$  is sharp image reconstruction,  $\{\mathbf{I}_j | j \in \mathcal{N}_l\}$  is the corresponding spike frames, and  $\mathbf{B}^s$  is the nearest short-exposure RGB frame.
+
+Step ③: Merging into HFR video (Sec. 3.4). Following Step ②, for the interval time  $(T_{\mathrm{itv}})$  that colors are not recorded, we bidirectionally query two nearest sharp RGB
+
+![](images/69d8b311ce36a4530ecf232650dd28197899054c0313144d824fc179e70d4d2f.jpg)  
+warping  
+Figure 3. For the sake of increasing spatial resolution, we adopt flow-based warping to merge adjacent 5 spike frames.
+
+![](images/cf39b78ad3ae1e85fd6294c3574fe337a9e139e2680711172548c5216ff96c0f.jpg)
+
+![](images/ae9042900c55487e39988804c1314cb26d945fa12eb7432a4fe8c52019a9b1ae.jpg)
+
+![](images/c8d6dedbab383c4cabfdbf4100b648119d41bdf85f6b86c070cb6ca3c7313a25.jpg)
+
+![](images/49bbef8a2cd1ba9b8519bf1120a392f74430894e19e52a34957f5c27c82657ef.jpg)
+
+images  $\{\mathbf{B}_i^+, \mathbf{B}_i\}$  for each spike frame  $\mathbf{I}_i$ , and get the warped images  $\{\hat{\mathbf{B}}_i^+, \hat{\mathbf{B}}_i\}$  with optical flow, where  $+$  and  $-$  denote the forward and backward warping, respectively. In Fig. 2(c), we provide an illustration of the interpolation procedure. Finally, as shown in Fig. 4, we reconstruct time-consistent color frames, and each frame  $\mathbf{C}_i$  is generated by merging the spike frame  $\mathbf{I}_i$  with  $\{\mathbf{C}_i\}_{1}, \hat{\mathbf{B}}_i^+, \hat{\mathbf{B}}_i\}$  with the strong constraint of optical flow.
+
+# 3.2. Spike preprocessing
+
+The optical flow estimation and spike frame reconstruction using in Eqn. (1) and Eqn. (2) are theoretically, yet the reconstructed frames practically have two issues: Since the integration time  $t_f$  is very short, noise is relatively strong; the spatial resolution of the first generation spiking camera (VidarOne [17]) is much lower than the RGB camera. To reduce the noise and increase the spatial resolution, inspired by the burst-based super-resolution [4] and denoising [27] for conventional RGB images, it is feasible to merge a group of adjacent spike frames with the help of spatial alignment. Moreover, thanks to the continuous motion recording capability of spiking cameras, the optical flow [16] estimated from spike trains makes the alignment even more stable than RGB images. As illustrated in Fig. 3, we design a computationally efficient module for spike frames, which is formulated as:  $\hat{\mathbf{I}}_i = \{\mathcal{W}_{\mathbf{F}_{j\to i}}(\mathbf{I}_j)|j\in \mathcal{N}_i\}$ , where  $\mathcal{W}_{\mathcal{F}_{j\to i}}(\cdot)$  denotes the flow-based warping operation,  $\mathcal{N}_i$  denotes a collection of adjacent frames. Then, we feed  $\hat{\mathbf{I}}_i$  to a set of convolutional layers, and we use PixelShuffle [47] to increase the spatial resolution while decreasing the channel of features. It should be noted that the method for spike frame reconstruction is not unique, which means users can choose other learning-based methods [61, 62, 64]. However, those deep learning models are relatively heavy, and less efficient as a submodule fitting to our pipeline.
+
+# 3.3. RGB image preprocessing
+
+RGB linear mapping. Following previous methods for HDR video reconstruction [3, 19, 21], we first unify the brightness of alternating-exposure RGB frames. Since we use an industrial camera (details in Sec. 3.5) that can acquire data without a nonlinear radiometric response function, the linearity of the captured frames is maintained. We find that the brightness of the frames can maintain a linear relationship with the duration of exposure time. Hence we use the global linear mapping to unify the frame brightness:  $\alpha \cdot \mathbf{B}_k(x,y)\rightarrow \mathbf{B}_k(x,y)$ , where  $\alpha$  denotes a linear scalar.
+
+Spike-guided deblurring. The physical model of the blurring process can be simply formulated as the average of a group of sharp images, i.e.,  $\mathbf{B}^l (x,y) = \frac{1}{N}\sum_{j = 1}^{N}\mathbf{B}_j^l (x,y)$ , where  $N$  denotes the number of sharp images. However, due to the limited dynamic range of the RGB camera, that simplified equation does not hold in the clipped regions of real-world long-exposure frames. In general we should have:  $\mathbf{B}^l (x,y)\leq \frac{1}{N}\sum_{j = 1}^{N}\mathbf{B}_j^l (x,y)$ . Therefore, for reconstructing a sequence of sharp HDR images from  $\mathbf{B}^l$ , we divide it into two sub-tasks: (i) For the well-exposure regions, we use the sharp spike frames to guide motion deblurring; (ii) for the clipped regions where colors are lost, we compensate them with well-retained colors extracted from the adjacent short-exposure image  $\mathbf{B}^s$ .
+
+Figure 2(b) shows the spike-guided deblurring (SG-deblur) from  $\mathbf{B}_l$  ( $\mathbf{B}_l$  may be a middle- or long-exposure image). Similar to Xu et al. [54] that exploit event frames to motion deblurring, we first concatenate  $\mathbf{B}_l$  with  $\{\mathbf{I}_l^j\}$ , then extract shallow features and increase feature channels with PixelShuffle [47], which is followed by a set of residual dense blocks (RDBs) [60] and a decoder. To make the colors in over-exposure regions be compensated by the adjacent short-exposure RGB image  $\mathbf{B}_j^s$ , we warp the short-exposure image with the optical flow estimated from spike trains:  $\mathbf{B}_j^s = \mathcal{W}_{\mathbf{F}_{s\rightarrow j}}(\mathbf{B}^s)$ , where  $\mathcal{W}_{\mathbf{F}_{s\rightarrow j}}(\cdot)$  denotes the warping operation from timestamp  $t_s$  to the timestamp of  $t_j$ . Subsequently, we extract features from  $\{\mathbf{B}_l^{s\rightarrow j}\}$  and add residual links between them and the decoder. Finally, we obtain a sequence of sharp color images. Note that the SG-deblur for the middle- and long-exposure RGB images share the same architecture while the parameters are not shareable. SG-deblur outputs four images for both  $4t_s$  and  $12t_s$  frames. For the case of  $12t_s$  frame, we interpolate the 4 frames to 12 frames with flow-based warping.
+
+Next, we briefly explain the reason why this event-based model [54] can be applied to a spike-based task. Both event streams and spike trains with the high-speed property have been used for motion deblurring and latent frame reconstruction [14,18,54]. It is necessary to convert them to event frames and spike frames, both of which belong to the category of 2D images. But event frames and spike frames have different physical meanings: Pixel values in an event frame reveal the residual (relatively sparse information) between two adjacent frames, while pixel values in a spike frame represent exactly the texture (relatively dense information) of the corresponding frame. Since both event frames and spike frames are 2D images and the spike frames have denser texture information, we can replace event frames in such a model with spike frames, so as to make the solution to the problem more well-posed.
+
+# 3.4. Merging into HFR video
+
+RGB interpolation. Given each middle- and long-exposure
+
+![](images/f70c457f89317c1a8dfbd75c2c3839b8139e7a74e3c29226b3c581376d4d252a.jpg)  
+Figure 4. Network architecture of the CNN-RNN-based merging module for reconstructing HFR&HDR videos from alternating-exposure RGB frames and HFR spike frames. This module outputs HDR color frames in a step-wise manner. We unroll the module for  $M$  steps during training.
+
+frame, SG-deblur recovers 4 and 12 images. Therefore, the recovered RGB frames have a frame rate of  $340^{4}$  FPS. But temporal distribution of them is quite uneven, e.g., there is no recovered color frame interval time  $T_{\mathrm{itv}}$ . Fortunately, the spike train contains continuous and dense texture information in the temporal domain. In Step ③, we use the SG-interpolation module to interpolate RGB frames into a sequence of uniformly distributed images. For each spike frame  $\mathbf{I}_i$ , we bidirectionally query its two nearest recovered RGB frames  $\{\mathbf{B}_i^+, \mathbf{B}_i\}$  and interpolate two color frames  $\{\hat{\mathbf{B}}_i^+, \hat{\mathbf{B}}_i\}$  with the optical flow estimated from spike trains. When  $\{\hat{\mathbf{B}}_i^+, \hat{\mathbf{B}}_i\}$  are fed into our merging module, they are weighted by a linear coefficient  $(\oplus$  in Fig. 4) related to the distance between  $t_i$  and  $\{t_+, t\}$ , where  $\{t_+, t\}$  denote the timestamp of  $\{\hat{\mathbf{B}}_i^+, \hat{\mathbf{B}}_i\}$ .
+
+Merging module. The aforementioned modules reconstruct coarse HFR video frames, which need to be refined for smoothing over time. We build a CNN-RNN-based HFR&HDR video reconstruction network to merge the spike frames and RGB frames, which is shown in Fig. 4. The merging module consists of three encoders, i.e.,  $\mathcal{E}_I$ ,  $\mathcal{E}_B$ , and  $\mathcal{E}_C$ , which are respectively designed for feature extraction from the current spike frame  $\hat{\mathbf{I}}_i$ , the interpolated RGB images  $\{\hat{\mathbf{B}}_i^+, \hat{\mathbf{B}}_i\}$ , and the previously reconstructed image  $\mathbf{C}_{i-1}$ . In  $\mathcal{E}_I$ , we use PixelShuffle [47] to make the spatial resolution of spike features consistent with RGB features. The extracted features are denoted as  $\mathbf{E}_I$ ,  $\{\mathbf{E}_B, \mathbf{E}_{B+}\}$ , and  $\mathbf{E}_{C_i-1}$ , respectively.
+
+Considering the spike frames and RGB frames may not be perfectly aligned at pixel level for real-world data, we add deformable convolution layers [6] to improve the robustness to this issue. In order to output flicker-free color frames, we adopt two constraints in the merging module:
+
+Table 1. Details of the composition of the dataset (res. is the abbreviation of resolution).  
+
+<table><tr><td>data</td><td>RGB res.</td><td>spike res.</td><td>train/test</td><td>time</td></tr><tr><td>full-synthetic</td><td>500×800</td><td>250×400</td><td>80/20</td><td>0.1s</td></tr><tr><td>real-synthetic</td><td>600×800</td><td>250×400</td><td>160/40</td><td>0.101s</td></tr><tr><td>real-world</td><td>484×784</td><td>242×392</td><td>-/20</td><td>0.101s</td></tr></table>
+
+(i) We add three ConvLSTM layers [48] to feed previous states forward in temporal domain; (ii) we feed  $\mathbf{E}_{C_i}$  into the current step and align it with the current features with flow-based warping. We then use a decoder to reversely map deep features to the current output HDR frame  $\mathbf{C}_i$ . We achieve the multi-module signal fusion by adding concatenation links between  $\{\mathbf{E}_{C_i}$ ,  $\mathbf{E}_B$ ,  $\mathbf{E}_{B+}\}$  and the decoder.
+
+# 3.5. Implementation Details
+
+Due to the setting of our method being different from existing HDR and video frame interpolation methods, there are no suitable datasets for training and testing our method. Therefore, we collect a new one with three components, whose details are summarized in Table 1 and sample images are provided in Fig. 5.
+
+Part 1: Full-synthetic data. This part of data is obtained by using the spike simulator proposed by Hu et al. [16]. We render 2000 RGB images with their computer graphics based solution as ground truth and generate 2000 spike planes (0.1 s). Since the photons arriving at the sensor follow Poisson probability distribution [43], we synthesize alternating-exposure 60 FPS RGB frames with a Poisson noise model. For the full synthetic data, we randomly select starting time of each group of training data. We randomly shift the RGB frames within 3 pixels to make the trained model more robust to the misalignment in real-world data.
+
+Part 2: Real-synthetic data. To reduce the domain gap between full-synthetic data and real-world data, we design a method to collect real-synthetic (the scenes are real while
+
+![](images/176aa9dfa2ecaf20f74ee48cdeb45fed0d736431be6a2a3e803a4ccf3f70da7d.jpg)  
+Figure 5. Example frames from the proposed dataset. Each group shows three alternating-exposure RGB frames (left, from top to bottom rows) and the corresponding spike signals (right).
+
+the spike trains are synthetic) data, and we use this part of data to fine-tune our model. The RGB frames are captured with an alternating-exposure mode in slow-motion scenes. Then we synthesize blurry middle-exposure RGB frames by averaging 4 adjacent middle-exposure RGB images, and blurry long-exposure RGB frames are synthesized in a similar way. We synthesize spike trains from ground truth RGB frames with the integrate-and-fire methodology [61].
+
+Part 3: Real-world data. We build a Spike-RGB hybrid camera (Fig. 6) to capture real-world data. The system is composed of an industrial camera (Basler acA800-510uc $^5$ ) with alternating exposure capability and a spiking camera [17]. There is a beam splitter in front of the two sensors. We conduct geometric calibration and time synchronization to align bimodal signals collected by them.
+
+Loss and training. The SG-deblur module and the merging module reconstruct images in the linear luminance domain, which covers a high dynamic range of pixel values. Following existing methods for HDR reconstruction, for the output images  $\mathbf{C}$ , we compress the range of pixel values by applying the following function proposed by Kalantari et al. [20]:  $\mathcal{T}(\mathbf{C}) = \log (1 + \mu \mathbf{C}) / \log (1 + \mu)$ , where  $\mathcal{T}(\cdot)$  denotes the tone mapping operation and  $\mu$  denotes the amount of compression. For these two modules, we employ widely used  $l_{1}$  loss, Structure similarity (SSIM) loss [53], and Learned Perceptual Image Patch Similarity (LPIPS) loss [58]. The total loss at step  $i$  for both the motion deblurring and merging modules is
+
+$$
+\mathcal {L} _ {\text {t o t a l}} (i) = \mathcal {L} _ {l _ {1}} (i) + \beta_ {1} \mathcal {L} _ {\text {S S I M}} (i) + \beta_ {2} \mathcal {L} _ {\text {L P I P S}} (i), \tag {3}
+$$
+
+where  $\beta_{1} = 1$  and  $\beta_{2} = 1$ . For spike-based optical flow estimation using [16], we fine-tune the parameters with full-synthetic data. During training, we resize the RGB images and spike frames to  $512 \times 800$  and  $256 \times 400$ . We implement our model with PyTorch, set the batch size to 4, and use ADAM optimizer during the training process. We first train the model on full-synthetic data. The SG-deblur module is trained with 50 epochs, before training the merging
+
+![](images/3a9785b5e9c025abd121037f9499ff36cfcf100a90bcaf5ae65255ec856a5815.jpg)  
+Figure 6. The prototype of our Spike-RGB imaging system composed of a spiking camera and an RGB camera.
+
+module. We unroll the merging module for  $M$  steps, and we find  $M = 4$  achieves a suitable balance between training time and recovery quality. The total loss for the unrolled  $M$  steps is  $\mathcal{L}_{\mathrm{merge}} = \sum_{i=1}^{M} \mathcal{L}_{\mathrm{total}}^{\mathrm{M}}(i)$ , where  $\mathcal{L}_{\mathrm{total}}^{\mathrm{M}}(i)$  denotes the total loss for the merging module at step  $i$ . The initial learning rate for both two modules is 0.001, we decay it to  $10^{-6}$  with a linear strategy. For the real-synthetic data, we fine-tune another group of parameters to reduce the gap between synthetic data and real-world data. We use one NVIDIA Tesla A100 for training, and the training procedure consumes about 30 hours.
+
+# 4. Experiments
+
+# 4.1. Quantitative Evaluation using Synthetic Data
+
+Validation on full-synthetic data. Figure 8 shows a group of results on full-synthetic data. We can see that both the flying objects in the short-exposure image and the oversaturated clouds (see the regions marked by boxes) in the long-exposure image are recovered successfully. The results with rich textures and consistent colors show the feasibility of our proposed method.
+
+Evaluation on real-synthetic data. To the best of our knowledge, the proposed method is the first framework to reconstruct HFR&HDR videos with the combination of spike trains and alternating-exposure RGB frames. Therefore, it is unfair to compare our method with existing ones, i.e., Kalantari13 [21], Kalantari19 [19], and Chen21  $[3]^{6}$ , which are designed for low frame rate HDR videos.
+
+We choose a state-of-the-art HDR video reconstruction method Chen21 [3], which also uses alternating-exposure RGB frames (the closest setup to ours) as a reference. Figure 7 shows the reconstruction results on real-synthetic data of the proposed method and Chen21 [3]. Thanks to the complementary motion information provided by spike trains, the abundant color extracted from alternating-exposure RGB frames, and the accurate textures contained in spike frames, the proposed method is capable of reconstructing rich texture details with less motion blur. For ex
+
+![](images/afa1aa45dd7684f40beb4726479a3aba9c3cd0d96ec6f4bf23778aeeefabdc8f.jpg)  
+short
+
+![](images/71cdc16eea019dcd1bd0dd0177ee5024f38cc34f796330d5d1eac074cf09b1e0.jpg)  
+middle  
+(a)
+
+![](images/6162aa256a287f2f993030fdd823e1c193c5a5945396f892262b2ef1595ff2d3.jpg)  
+long
+
+![](images/6eb5166094979d17c7be16571a725ef333c07be4f97c0f8c35d1361d0ff8d59e.jpg)  
+short
+
+![](images/18487dec66ddaa2019bfc213e532588aef073461a9d8d2d11543e80ebfbdbd84.jpg)  
+middle  
+(b)
+
+![](images/865b4f729ea98b545b1620ffe9198a6a878505d1040d35bbaf214b8fe6412abe.jpg)  
+long
+
+![](images/fbb712d19253aafc1fd9d055053cde4360d158fb65c53da6d8203063df92c7ec.jpg)  
+Figure 7. Visual equality comparison of real-synthetic data between the proposed method and the state-of-the-art HDR video reconstruction method: Chen 21 [3]. We present two sets of results in (a) and (b). Please zoom-in electronic versions for better details, and watch the HFR videos on the project page.  
+Figure 8. Validation on the synthetic data.
+
+ample, in the long-exposure frame in the first row of (a), the building marked by a yellow box suffers from severe motion blur and overexposure. Chen21 [3] partially recovers the colors of this building, but it fails to remove the blurry artifacts. In the results generated by our method, the edges are sharp and the colors are vivid. In Fig. 7(b), the motions across RGB frames have a very large span, Chen21 [3] can only recover the corresponding LFR videos, while our method can reconstruct an HFR video with smooth motion.
+
+We evaluate the reconstructed HDR in terms of PSNR, SSIM, HDR-VDP-2 [32], and HDR-VQM [36]. Table 2 clearly shows that our framework outperforms the state-of-the-art method [3] in all the metrics on the real-synthetic data in the condition of 60 FPS. And we achieve excellent performance in the condition of 1000 FPS. We designed ablation experiments and used them to demonstrate the effectiveness of the modules in our framework. For "w/o I", we simply stack the spike trains with a time window, and upsample them using bilinear interpolation; for "w/o PS", we replace PixelShuffle with a convolutional layer. The two groups of experiments verify the effectiveness of spike frame preprocessing in Step ①. For "w/o F1" and "w/o F2", we remove the flow-based interpolation in the deblurring module and the merging module. The two groups of ex
+
+Table 2. Quantitative results and ablation study on our realistic synthetic data. We sample 60 FPS videos from our results for the comparison with Chen21 [3].  $\uparrow (\downarrow)$  indicates larger (smaller) values are better.  
+
+<table><tr><td colspan="6">Comparison with the state-of-th-art method</td></tr><tr><td>Method</td><td>PSNR↑</td><td>SSIM↑</td><td>HDR-VDP2↑</td><td>HDR-VQM↓</td><td>FPS</td></tr><tr><td>Chen21 [3]</td><td>18.46</td><td>0.697</td><td>27.34</td><td>0.536</td><td rowspan="2">60</td></tr><tr><td>Ours</td><td>30.14</td><td>0.921</td><td>60.14</td><td>0.093</td></tr><tr><td>Chen21 [3]</td><td>/</td><td>/</td><td>/</td><td>/</td><td rowspan="2">1000</td></tr><tr><td>Ours</td><td>24.38</td><td>0.903</td><td>47.79</td><td>0.120</td></tr><tr><td colspan="6">Ablation study</td></tr><tr><td>w/o I</td><td>23.15</td><td>0.886</td><td>46.03</td><td>0.143</td><td rowspan="7">1000</td></tr><tr><td>w/o PS</td><td>23.98</td><td>0.881</td><td>46.47</td><td>0.141</td></tr><tr><td>w/o F1</td><td>19.76</td><td>0.723</td><td>38.95</td><td>0.314</td></tr><tr><td>w/o F2</td><td>18.04</td><td>0.716</td><td>35.89</td><td>0.356</td></tr><tr><td>w/ t-loss</td><td>22.41</td><td>0.864</td><td>43.64</td><td>0.142</td></tr><tr><td>w/o DeConv</td><td>24.31</td><td>0.897</td><td>47.66</td><td>0.127</td></tr><tr><td>w/o DM</td><td>19.01</td><td>0.714</td><td>37.97</td><td>0.338</td></tr></table>
+
+periments verify the effectiveness of SC-Flow [16] based interpolation in Steps ② and ③. To further verify the effectiveness of deblurring module, we completely remove it in "w/o DM". For "w/o DeConv", we replace the deformable convolutional layers with traditional convolution layers. For "w/ t-loss", we remove the warping operation on  $\mathbf{C}_{i-1}$  and add the temporal consistent loss that is estimated by a pretrained optical flow model [23], which is widely used in video processing [5, 39]. Since the  $\mathbf{C}_{i-1}$  is warped by accurate optical flow  $\mathbf{F}_{i-1}$  and merged into the current step  $i$ , our method fundamentally has a strong temporal consistent constraint for video processing. Thus, our merging module does not need this loss during training.
+
+# 4.2. Qualitative Evaluation using Real Data
+
+In order to demonstrate the effectiveness of the proposed framework on real-world scenes, we collect 20 sets of real-world data, which are captured by our hybrid camera system shown in Fig. 6. We have compared our slow-motion capability with that of the commercial cameras. As shown in Fig. 9(a), the electric fan is moving at about 40 rounds
+
+![](images/1f268f5b45e6511852f7c10d04b0e95083619bab47aae0ee46893577875ea9d0.jpg)  
+Figure 9. Visual quality comparison of real-world data between the proposed method and commercial cameras with the slow-motion capability. In (a), we show two adjacent frames for the video captured by smartphones that have slow-motion capability. The commercial cameras are not calibrated so their results are not strictly aligned with ours. (b) is the comparison with Phantom camera set to 1000 FPS.
+
+![](images/72f0059269a352e5fae6316d26d6d3997fa3fa7268ce9475787b3e6b04ccd5e3.jpg)  
+(a)
+
+![](images/87e87953be2aadf893e099d367271fb5ced7b1b9999ee6fc17190a8fe64abca6.jpg)
+
+![](images/12ab643dce1827b18edc878212e142f247aa8711e1c782c9617d11b686395bd6.jpg)
+
+![](images/70699cd7e7248946e810a0c7736901cdbac1ebc3551834ffa17d97f4ef9afb79.jpg)
+
+![](images/c3d3ddfd28c99162d50a607d2239a16a351121102d1537088a159bcc3e287777.jpg)  
+(b)
+
+![](images/e93c85761807f3ca93c18962918da723c0e397456cdc1707f1e86ea56554f370.jpg)  
+Figure 10. Qualitative visualization of our method in a super fast scene: a balloon bursting. We select 38 frames from our results for showing.
+
+per second. The short-exposure image is severely underexposed with less blurry artifacts, and the middle- and long-exposure images have severe blurring and oversaturated artifacts. With the accurate motion and texture information captured by the spiking camera, we have recovered temporally smooth video sequences. Four recovered images are shown for the middle- and long-exposure images. For the videos captured by iPhone 13 and Mi 10, the motions between frames are not continuous. And the electric fan captured by Mi 10 is deformed due to the rolling shutter. In Fig. 9(b), we compare our method with the Phantom<sup>7</sup> camera set to 1000 FPS. Since the exposure time of the Phantom camera is extremely short, it fails to capture regions where scene radiance is weak.
+
+# 5. Conclusion
+
+We propose an HFR&HDR video reconstruction method with a hybrid camera that is composed of an alternating-exposure RGB sensor and a spiking sensor. Extensive experiments on synthetic and real-world data demonstrate the superior performance of the proposed method.
+
+Discussion. (i) For super fast scenes, e.g., a balloon bursting, it is difficult to capture clear motions with a conventional RGB camera at 60 FPS. Therefore, the well-exposed color of the bursting balloon is not captured with the short exposure, which brings challenges to our reconstruction of accurate color. In our results, although the colors are somewhat distorted, we can still recover a smooth video sequence. Once the frame rate of the RGB camera is increased, e.g., 120 FPS, temporally smoother video with more accurate color is expected to be more reliably recovered. (ii) Since QIS [1, 29] share the same imaging model with the spiking camera, our method is ready to be applied to it. We show the simulation in supplementary material.
+
+Limitation and future work. Beam splitter is arguable for making a practical system on mobile devices. But when compact design is not a hard constraint, beam splitter has unique advantages in spatial alignment, that is why it is broadly adopted in building a hybrid prototype for HDR [15, 24, 33, 50]. Side-by-side arrangement with parallax unavoidably introduces occlusions and alignment issues, which is a promising direction to explore for our future work. Due to the low spatial resolution  $(250\times 400)$  of the current model we use is, we have to super-resolve the spike frames in feature space. If higher-resolution spike signals can be directly obtained, our method can achieve better visual quality. Besides, there is a domain gap between synthetic spike trains and real-captured spike trains since the noise of the spiking camera is more complex than the simulator. For time complexity, our approach is better suited as a post-processing module. The number of parameters is  $45.7\mathrm{M}$  and the time cost per frame is 0.371s with a single NVIDIA GeForce RTX 3090 graphics card. We hope to tackle these issues in the future work and achieve higher frame rate reconstruction.
+
+# Acknowledgement
+
+This work was supported by National Key R&D Program of China (2021ZD0109803), National Natural Science Foundation of China under Grant No. 62088102, 62136001. Yakun Chang was also supported by China Postdoctoral Science Foundation (8206300710).
+
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+        "text": "2PCNet: Two-Phase Consistency Training for Day-to-Night Unsupervised Domain Adaptive Object Detection",
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+        "text": "Mikhail Kennerley $^{1,2}$ , Jian-Gang Wang $^{2}$ , Bharadwaj Veeravalli $^{1}$ , and Robby T. Tan $^{1}$ $^{1}$ National University of Singapore, Department of Electrical and Computer Engineering  \n $^{2}$ Institute for Infocomm Research, A*STAR  \nmikhailk@u.nus.edu, jgwang@i2r.a-star.edu.sg, elebv@nus.edu.sg, robby.tan@nus.edu.sg",
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+        "text": "Abstract",
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+        "type": "text",
+        "text": "Object detection at night is a challenging problem due to the absence of night image annotations. Despite several domain adaptation methods, achieving high-precision results remains an issue. False-positive error propagation is still observed in methods using the well-established student-teacher framework, particularly for small-scale and low-light objects. This paper proposes a two-phase consistency unsupervised domain adaptation network, 2PCNet, to address these issues. The network employs high-confidence bounding-box predictions from the teacher in the first phase and appends them to the student's region proposals for the teacher to re-evaluate in the second phase, resulting in a combination of high and low confidence pseudo-labels. The night images and pseudo-labels are scaled-down before being used as input to the student, providing stronger small-scale pseudo-labels. To address errors that arise from low-light regions and other night-related attributes in images, we propose a night-specific augmentation pipeline called NightAug. This pipeline involves applying random augmentations, such as glare, blur, and noise, to daytime images. Experiments on publicly available datasets demonstrate that our method achieves superior results to state-of-the-art methods by  $20\\%$ , and to supervised models trained directly on the target data.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
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+    {
+        "type": "text",
+        "text": "Nighttime object detection is critical in many applications. However, the requirement of annotated data by supervised methods is impractical, since night data with annotations is few, and supervised methods are generally prone to overfitting to the training data. Among other reasons, this scarcity is due to poor lighting conditions which makes nighttime images hard to annotate. Hence, methods that",
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+        "image_caption": [
+            "AT",
+            "Figure 1. Qualitative results of state-of-the-art DA methods, DA Faster-RCNN [3], UMT [7], Adaptive Teacher (AT) [15] and our method 2PCNet on the BDD100K [36] dataset. Unlike the SOTA methods, our method is able to detect dark and small scale objects with minimal additional false positive predictions."
+        ],
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+        "image_caption": [
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+    {
+        "type": "text",
+        "text": "do not assume the availability of the annotations are more advantageous. Domain adaptation (DA) is an efficient solution to this problem by allowing the use of readily available annotated source daytime datasets.",
+        "bbox": [
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+    {
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+        "text": "A few domain adaptation methods have been proposed, e.g., adversarial learning which uses image and instance level classifiers [3] and similar concepts [22, 32]. However, these methods isolate the domain adaptation task purely towards the feature extractor, and suppress features of the target data for the sake of domain invariance. Recent unsupervised domain adaptation methods exploit the studentteacher framework (e.g. [1,7,11,15]). Since the student initially learns from the supervised loss, there is a bias towards the source data. Augmentation [7, 11] and adversarial learning [15] have been proposed to address this problem. Unfortunately, particularly for day-to-night unsupervised domain adaptation, these methods suffer from a large num",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_footnote",
+        "text": "1www.github.com/mercarill/2pcnet",
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+    {
+        "type": "text",
+        "text": "ber of inaccurate pseudo-labels produced by the teacher. In our investigation, the problem is notably due to insufficient knowledge of small scale features in the nighttime domain, which are then propagated through the learning process between the teacher and student, resulting in poor object detection performance.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To address the problem, in this paper, we present 2PC-Net, a two-phase consistency unsupervised domain adaptation network for nighttime object detection. Our 2PCNet merges the bounding-boxes of highly-confident pseudolabels, which are predicted in phase one, together with regions proposed by the student's region proposal network (RPN). The merged proposals are then used by the teacher to generate a new set of pseudo-labels in phase two. This provides a combination of high and low confidence pseudolabels. These pseudo-labels are then matched with predictions generated by the student. We can then utilise a weighted consistency loss to ensure that a higher weightage of our unsupervised loss is based on stronger pseudo-labels, yet allow for weaker pseudo-labels to influence the training.",
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+    {
+        "type": "text",
+        "text": "Equipped with this two-phase strategy, we address the problem of errors from small-scale objects. We devise a student-scaling technique, where night images and their pseudo-labels for the student are deliberately scaled down. In order to generate accurate pseudo-labels, images to the teacher remain at their full scale. This results in the pseudolabels of larger objects, which are easier to predict, to be scaled down to smaller objects, allowing for an increase in small scale performance of the student.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Nighttime images suffer from multiple complications not found in daytime scenes such as dark regions, glare, prominent noise, prominent blur, imbalanced lighting, etc. All these cause a problem, since the student, which was trained on daytime images, is much more biased towards the daytime domain's characteristics. To mitigate this problem, we propose NightAug, a set of random nighttime specific augmentations. NightAug includes adding artificial glare, noise, blur, etc. that mimic the night conditions to daytime images. With NightAug we are able to reduce the bias of the student network towards the source data without resulting in adversarial learning or compute-intensive translations. Overall, using 2PCNet, we can see the qualitative improvements of our result in Figure 1. In summary, the contributions of this paper are as follows:",
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+        "list_items": [
+            "- We present 2PCNet, a two-phase consistency approach for student-teacher learning. 2PCNet takes advantage of highly confident teacher labels augmented with less confident regions, which are proposed by the scaled student. This strategy produces a sharp reduction of the error propagation in the learning process.",
+            "- To address the bias of the student towards the source domain, we propose NightAug, a random night spe"
+        ],
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+    {
+        "type": "text",
+        "text": "cific augmentation pipeline to shift the characteristics of daytime images toward nighttime.",
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+    {
+        "type": "text",
+        "text": "- The effectiveness of our approach has been verified by comparing it with the state-of-the-art domain adaptation approaches. An improvement of  $+7.9\\mathrm{AP}(+20\\%)$  and  $+10.2\\mathrm{AP}(26\\%)$  over the SOTA on BDD100K and SHIFT has been achieved, respectively.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Unsupervised Domain Adaptation (UDA) Unsupervised domain adaptation aims to learn transferable features to reduce the discrepancy between a labelled source and unlabelled target domain. Previous works minimised the distance metric (MMD) [16-18] and considered intra-class and inter-class discrepancy [12, 13]. Adversarial feature learning involved adding an adversarial classifier to play the min-max game between the domain discriminator and feature extractors to generate a domain invariant feature map [27, 28, 37]. These methods have been applied to image classification. Our work focuses on object detection, which is more complex as it involves identifying multiple bounding boxes and associated classes in each image.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "UDA for Object Detection Object detection with UDA is a recent challenge due to the complexities of identifying multiple objects in an image. DA-Faster RCNN [3] integrated adversarial learning with image and instance level classifiers, and several approaches have been proposed to improve on this method by introducing scale-awareness [4], class specific discriminators [31], and re-purposing the task-specific classifier as a discriminator [2]. The Mean Teacher (MT) framework [26] has been adopted in semi-supervised methods, such as UMT [7], which incorporates CycleGAN [39] augmented images; AT [15], which combines the student-teacher framework with adversarial learning; and TDD [11], which uses dual student-teacher networks with style transfer.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Nighttime UDA The majority of research on unsupervised domain adaptation (UDA) in nighttime scenarios has focused on semantic segmentation [5, 8, 9, 14, 23, 29, 33]. Translation and style transformation techniques are commonly used to reduce the domain gap between the source and target domains in these methods [8,29,33]. Some UDA-based techniques for nighttime also utilise paired-images to generate a shared feature space [23], while others use an intermediate domain such as twilight to reduce the domain gap during unsupervised learning [5].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Nighttime tracking has also been investigated where adversarial transformers are used to close the domain gap [35]. However, there is a gap in research when it comes to applying UDA techniques in the object detection task for night-",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "11485",
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+        "img_path": "images/d79fc3147efb095c9d9a480464ef2004c703c1cc7d2c0b76ce09ed2f1902d44e.jpg",
+        "image_caption": [
+            "Figure 2. Overview of our proposed framework, 2PCNet. 2PCNet consists of: A student network is trained on both the labelled daytime image, which has been augmented with NightAug, and unlabelled nighttime images. A teacher network which is the exponential moving average (EMA) of the student and provides matched pseudo-labels for unsupervised loss. The match pseudo-labels are the predictions of the teacher (phase two) using the RPN proposals of the student, which in turn was guided by the high confidence pseudo-labels of the teacher (phase one)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "time scenarios. Therefore, we explore the application of UDA techniques in object detection under low-light and nighttime conditions.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Proposed Method",
+        "text_level": 1,
+        "bbox": [
+            76,
+            583,
+            250,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Let  $\\mathbf{D}_s$  be the daytime source data.  $\\mathbf{D}_s = \\{I_s, C_s, B_s\\}$ , where the variables refer to the image, class label and bounding-box label, respectively. Index  $s$  indicates the daytime source. The night target data is represented by  $\\mathbf{D}_t$ , where  $\\mathbf{D}_t = \\{I_t\\}$  as we do not have the target labels available to us. Index  $t$  indicates the nighttime target.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The architecture of our 2PCNet is shown in Figure 2. Our 2PCNet consists of a student and a teacher network. The student is a multi-domain network trained on both labelled daytime images, augmented with NightAug, and unlabelled nighttime images. The teacher focuses on night images to produce pseudo-labels for the student and is the exponential moving average (EMA) of the student. After an initial pretraining phase, the teacher begins producing pseudo-labels, which allows the student to initialise the feature extractor and detector.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "During each iteration, in phase one of 2PCNet, the teacher produces pseudo-labels from the night images. These pseudo-labels are filtered through a confidence",
+        "bbox": [
+            75,
+            854,
+            470,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "threshold. This is to ensure only high-confidence pseudolabels are given to the student. The bounding-boxes from the pseudo-labels are then combined with the region proposals generated by the student's RPN. The merged region proposals are then used to generate predictions from the student's RoI network. In phase two, the teacher utilises the same merged region proposals to generate a matched set of pseudo-labels, where each pseudo-label has its corresponding prediction obtained from the student.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As mentioned earlier, our student network is initialised by pretraining for a set number of iterations. This is done with supervised loss on the augmented daytime images:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\sup } = L _ {\\operatorname {r p n}} \\left(B _ {s}, I _ {s}\\right) + L _ {\\operatorname {r o i}} \\left(B _ {s}, C _ {s}, I _ {s}\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            557,
+            724,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $L_{\\mathrm{rpn}}$  represents the loss from the RPN, which consists of an objectness and bounding-box regression loss.  $L_{\\mathrm{roi}}$  represents the loss from the detector network, consisting of a classification and bounding-box regression loss.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Once the pretraining is completed, the student's weights are then transferred over to the teacher. In the succeeding iterations, the teacher's weights are the exponential moving average (EMA) of the student's. The matched pseudo-labels generated by the teacher,  $\\{C_p^*, B_p^*\\}$ , are then used to guide",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "11486",
+        "bbox": [
+            480,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/c67cd0ceb3844b100df47930828639c1f30a507ba48e45e37211aff677e01841.jpg",
+        "image_caption": [
+            "Figure 3. (Left to Right, Top to Bottom) Ground truth bounding boxes, bounding boxes predicted by the teacher with non-maximal suppression (NMS) and thresholding  $(B_{p})$ , bounding boxes predicted by the student  $(B_{\\mathrm{student}})$  which is guided by  $B_{p}$ , and the bounding boxes predicted by the teacher  $(B_{p}^{*})$  for the consistency loss."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
+            90,
+            282,
+            267
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/19d2798780ffd2eaa87261a168fdf6db1a82fe1e65293999ac403404e0f935dc.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            282,
+            90,
+            482,
+            267
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "the unsupervised loss, defined as:",
+        "bbox": [
+            76,
+            393,
+            299,
+            407
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {u n s u p}} = L _ {\\text {r p n}} ^ {\\text {o b j}} \\left(C _ {p} ^ {*}; I _ {t}\\right) + L _ {\\text {c o n s}} \\left(C _ {p} ^ {*}; I _ {t}\\right), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            135,
+            422,
+            468,
+            441
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $L_{\\mathrm{rpn}}^{\\mathrm{obj}}$  is the objectness loss of the RPN and  $L_{\\mathrm{cons}}$  is the weighted KL-Divergence loss from the predicted outputs which we will further explain in the next section.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.1. Two-Phase Consistency",
+        "text_level": 1,
+        "bbox": [
+            76,
+            512,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Due to the large domain gap between daytime source images and nighttime target images, the teacher is unable to produce high quality pseudo-labels. This generally occurs in the whole scene, but particularly for regions with strong night characteristics, e.g., low-light, glare, uneven lighting, etc. The teacher produces confident pseudo-labels only for regions that share more similarities to the daytime, since it is biased towards the daytime domain. This bias poses a problem for methods that employ a hard-threshold to filter pseudo-labels for categorical cross-entropy loss [7, 15, 26]. The remaining pseudo-labels contain only easy samples with daytime attributes. Consequently, the student does not learn from harder (e.g. darker) areas.",
+        "bbox": [
+            75,
+            537,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As a result of minimal knowledge of the hard samples (i.e., areas with a high level of nighttime attributes), the teacher begins to predict highly confident yet incorrect pseudo-labels. As the teacher provides these incorrect pseudo-labels to the student, a viscous cycle starts where the teacher in turn is updated with incorrect knowledge. Consequently, the error continues to propagate through training. In our case, these errors notably occur in dark/glare regions and as small scale objects.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To address the problem of error propagation, we design a two-phase approach that combines high confidence",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "pseudo-labels together with their less confident counterparts. This combination allows for the high accuracy of confident-labels with the additional knowledge of less confident labels to be distilled onto the student. In phase one, the unlabelled nighttime image,  $I_{t}$ , is used as an input for the teacher to generate pseudo-labels. These pseudo-labels are filtered with a threshold to retain only high-confidence pseudo-labels,  $(C_p, B_p)$ . The bounding-box of the pseudolabels,  $B_{p}$ , is then used as an input to the student.  $B_{p}$  is concatenated to the region proposals generated by the student RPN module:",
+        "bbox": [
+            496,
+            90,
+            890,
+            256
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP ^ {*} = \\operatorname {R P N} _ {\\text {s t u d e n t}} \\left(I _ {t}\\right) \\neq B _ {p}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            602,
+            268,
+            890,
+            285
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $P^{*}$  is the combined region proposals, which are then used as an input to the student's RoI module to predict the classes,  $C_{\\mathrm{student}}$ , and bounding-box,  $B_{\\mathrm{student}}$ , of each region proposal.",
+        "bbox": [
+            496,
+            295,
+            890,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Phase two begins by using the same combined region proposals,  $P^{*}$ , generated in phase one as an input to the teachers RoI module to generate a matched set of pseudolabels:",
+        "bbox": [
+            496,
+            356,
+            890,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\left\\{C _ {p} ^ {*}, B _ {p} ^ {*} \\right\\} = \\operatorname {R o I} _ {\\text {t e a c h e r}} \\left(P ^ {*}\\right). \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            598,
+            428,
+            890,
+            446
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The difference between  $C_p$  and  $C_p^*$  is that  $C_p^*$  is derived from the same region proposals as that of the student predictions  $C_{\\mathrm{student}}$ . This allows us to compare  $C_{\\mathrm{student}}$  and  $C_p^*$  directly:",
+        "bbox": [
+            496,
+            455,
+            890,
+            518
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\left\\{C _ {\\text {s t u d e n t}} (n), B _ {\\text {s t u d e n t}} (n) \\right\\} = \\operatorname {R o I} _ {\\text {s t u d e n t}} \\left(P ^ {*} (n)\\right), \\tag {5} \\\\ \\left\\{C _ {p} ^ {*} (n), B _ {p} ^ {*} (n) \\right\\} = \\operatorname {R o I} _ {\\text {t e a c h e r}} \\left(P ^ {*} (n)\\right), \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            519,
+            527,
+            890,
+            564
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $n = \\{1,2,\\dots,N\\}$  and  $N$  is the number of region proposals in  $P^*$ . This operation ensures that the knowledge of highly confident predictions generated by the teacher is distilled through to the student. In addition, information from less confident predictions can also be learnt. However, we are still required to penalise less confident samples and thus employ weighed KL-Divergence to be used as our consistency loss:",
+        "bbox": [
+            496,
+            571,
+            890,
+            693
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {c o n s}} = \\alpha \\operatorname {K L} \\left(C _ {\\text {s t u d e n t}}, C _ {p} ^ {*}\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            594,
+            705,
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+            722
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\alpha$  is the highest confidence of  $C_p^*$  expressed as  $\\alpha = \\max(C_p^*)$ ; KL() is the KL-divergence function. Note that, pseudo-bounding boxes are not used to generate unsupervised loss, as the confidence score of each pseudo-label represents the class information rather than the bounding box. The outputs of each segment of our two-phase approach are shown in Figure 3.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Student-Scaling",
+        "text_level": 1,
+        "bbox": [
+            500,
+            847,
+            658,
+            863
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In our investigation, we have found that scales of objects have a strong influence on object detection at night. This",
+        "bbox": [
+            496,
+            869,
+            890,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "11487",
+        "bbox": [
+            478,
+            944,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1 Single Augmentation - NightAug"
+        ],
+        "code_body": "imgClean  $\\leftarrow$  img   \nif randFloat  $\\geq 0.5$  then randFloat  $\\leftarrow 0.8*$  randFloat  $+0.2$  img  $\\leftarrow$  augmentation(img, randval) prob  $\\leftarrow 0.4$  while randFloat  $\\geq$  prob do  $x\\gets$  randInt(img.shape[1],2)  $y\\gets$  randInt(img.shape[2],2) img[x,y]  $\\leftarrow$  imgClean[x,y] prob  $\\leftarrow$  prob +0.1 end while   \nend if",
+        "bbox": [
+            91,
+            109,
+            369,
+            291
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "is due to the features of smaller objects being easily overwhelmed by glare or noise. To allow the student to overcome this, we apply scaling augmentation to the student's inputs which includes both the image and the pseudo-labels generated by the teacher. As training proceeds, we follow a schedule to increase the scale of the student augmentation until it equals to that of the original image. By iteratively increasing the scale we allow the student to focus on smaller features earlier in the training process. This process encourages the teacher to make more accurate predictions on smaller scale objects in the later stages of training. In turn, accurate small scale pseudo-labels allow for the increase in the scale of the student's inputs with minimal errors due to scale.",
+        "bbox": [
+            75,
+            320,
+            467,
+            530
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To ensure the knowledge of the previous scales is not forgotten, a gaussian function for the scaling factor is applied. The norm of the Gaussian function is obtained from the schedule values. To prevent additional noise due to pseudo-labels being too small, labels that has an area below a threshold are removed.",
+        "bbox": [
+            75,
+            532,
+            467,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.3. NightAug",
+        "text_level": 1,
+        "bbox": [
+            76,
+            633,
+            187,
+            650
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Night images suffer from a range of complications that are not present in daytime scenes. This causes a problem in the student-teacher framework, where the student would be biased towards the source domain. Previous methods have attempted to address this, but have either required compute-intensive translations [7, 11] or adding additional domain classifiers to the framework [15] which complicates training. We propose NightAug, a nighttime specific augmentation pipeline that is compute-light and does not require training. NightAug consists of a series of augmentations with the aim of steering the characteristics of daytime images to resemble that of a nighttime image.",
+        "bbox": [
+            75,
+            657,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The defining features of nighttime images are that they are darker and have lower contrast than daytime images. In addition the signal-to-night ratio (SNR) could be higher due to the properties of digital cameras such as luminance and",
+        "bbox": [
+            75,
+            839,
+            467,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/44477bcfe46dd0b404ebc19a5eabcfb95708b6ebf6fb6883592a6a5e4c257b7b.jpg",
+        "image_caption": [
+            "Figure 4. NightAug: Original image (top-left) and images with random augmentations from: gaussian blur, gamma correction, brightness, contrast, glare, gaussian noise and random cut-outs."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            89,
+            696,
+            260
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/28b82fb10b3a24991f39d715a100a831e46d1756277035c6f05cde59023c911f.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            697,
+            89,
+            890,
+            260
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "colour noise. Glare and glow from street lamps and headlights are also present in nighttime images. Additionally, images may be out-of-focus due to the cameras inability to detect reference points to focus on in dark environments.",
+        "bbox": [
+            496,
+            349,
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+            411
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Keeping in mind the properties of nighttime images, our NightAug includes random; brightness, contrast, gamma, gaussian noise, gaussian blur augmentations and random glare insertion. The augmentations are randomly applied to the images and are also random in intensity. This randomness results in a wider variance of images that are exposed to the student leading to more robust training [30]. To further increase the variance of the images, at each augmentation step, random segments of the image will ignore the application of that augmentation. This allows for the representation where different areas of nighttime images may be unevenly lighted. This uneven lighting affects the above characteristics of the local region.",
+        "bbox": [
+            496,
+            416,
+            890,
+            612
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "A single augmentation flow of NightAug is demonstrated in Algorithm 1. Samples of an image processed with NightAug are shown in Figure 4. Each augmentation has a set probability of being applied, with the strength of the augmentation being random. Random regions of the augmented image may then be replaced with that of the original image. The probability of this region replacement reduces with each iteration.",
+        "bbox": [
+            496,
+            617,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Overall Loss Our total loss can be represented as:",
+        "bbox": [
+            500,
+            773,
+            843,
+            789
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {\\text {t o t a l}} = L _ {\\sup } + \\lambda L _ {\\text {u n s u p}}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            607,
+            814,
+            890,
+            830
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\lambda$  represents a weight factor for the unsupervised loss, and is set experimentally.  $L_{\\mathrm{sup}}, L_{\\mathrm{unsup}}$  refer to Eq. (1) and Eq. (2), respectively.",
+        "bbox": [
+            496,
+            854,
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+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "11488",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/6ad51ceac8b2659525cb3f8303090968c0631920eb8a8bf84214e9d2a8c2bb84.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>AP</td><td>Pedestrian</td><td>Rider</td><td>Car</td><td>Truck</td><td>Bus</td><td>Motorcycle</td><td>Bicycle</td><td>TrafficLight</td><td>TrafficSign</td></tr><tr><td>Lower-Bound</td><td>41.1</td><td>50.0</td><td>28.9</td><td>66.6</td><td>47.8</td><td>47.5</td><td>32.8</td><td>39.5</td><td>41.0</td><td>56.5</td></tr><tr><td>Upper-Bound</td><td>46.2</td><td>52.1</td><td>35.0</td><td>73.6</td><td>53.5</td><td>54.8</td><td>36.0</td><td>41.8</td><td>52.2</td><td>63.3</td></tr><tr><td>DA F-RCNN [3]</td><td>41.3</td><td>50.4</td><td>30.3</td><td>66.3</td><td>46.8</td><td>48.3</td><td>32.6</td><td>41.4</td><td>41.0</td><td>56.2</td></tr><tr><td>TDD [11]</td><td>34.6</td><td>43.1</td><td>20.7</td><td>68.4</td><td>33.3</td><td>35.6</td><td>16.5</td><td>25.9</td><td>43.1</td><td>59.5</td></tr><tr><td>UMT [7]</td><td>36.2</td><td>46.5</td><td>26.1</td><td>46.8</td><td>44.0</td><td>46.3</td><td>28.2</td><td>40.2</td><td>31.6</td><td>52.7</td></tr><tr><td>AT [15]</td><td>38.5</td><td>42.3</td><td>30.4</td><td>60.8</td><td>48.9</td><td>52.1</td><td>34.5</td><td>42.7</td><td>29.1</td><td>43.9</td></tr><tr><td>2PCNet (Ours)</td><td>46.4</td><td>54.4</td><td>30.8</td><td>73.1</td><td>53.8</td><td>55.2</td><td>37.5</td><td>44.5</td><td>49.4</td><td>65.2</td></tr></table>",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/a67e50c51805e5d3272d20f75a585101e458778aa663a8acedc2e157070dc842.jpg",
+        "table_caption": [
+            "Table 1. Results of day-to-night domain adaptation on the BDD100K dataset, the Average Precision (AP) of all classes are reported. Faster RCNN detector with ResNet-50 feature extractor is used for all experiments to ensure a fair comparison. Faster RCNN is used as the lower-bound and upper-bound and is trained on labelled daytime and nighttime data respectively. The lower-bound provides a baseline without any domain adaptation while the upper-bound is fully supervised, the case where labelled target night data is available."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>APcoco</td><td>Car</td><td>Bus</td><td>Truck</td></tr><tr><td>Lower-Bound</td><td>22.1</td><td>37.5</td><td>29.8</td><td>30.7</td></tr><tr><td>Upper-Bound</td><td>23.9</td><td>42.0</td><td>33.8</td><td>35.0</td></tr><tr><td>FDA [34]</td><td>22.6</td><td>38.5</td><td>37.2</td><td>23.2</td></tr><tr><td>ForkGAN [38]</td><td>22.9</td><td>41.2</td><td>33.3</td><td>32.1</td></tr><tr><td>2PCNet (Ours)</td><td>23.5</td><td>40.7</td><td>38.2</td><td>35.0</td></tr></table>",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Table 2. Comparison of our framework, 2PCNet, with image-to-image (I2I) translation methods. Conducted on the BDD100K dataset. ForkGan and FDA are used for comparison. Reported  $AP_{coco}$  is the averaged AP over IoUs 0.5 to 0.95.",
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+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "4.1. Baselines",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "To evaluate our method, we compare our approach with SOTA methods in domain adaptation for object detection. These include DA-Faster RCNN [3], TDD [11], UMT [7], AT [15] as well as a non-DA baseline Faster-RCNN [21]. Faster-RCNN is used as both our lower and upper-bound, where it is trained on labelled source and target data respectively. We additionally compare our approach with image-to-image translation methods, ForkGAN [38] and FDA [34]. Translation methods are trained on Faster RCNN with both the daytime and translated images.",
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Datasets",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "The majority of existing nighttime datasets either focuses on semantic segmentation which do not provide labels for object detection [5, 23, 24], or contains very few classes [19, 20]. BDD100K [36] was selected as it provides object detection labels which includes a wide range of classes (10). It also has a large number of images compared to other DA datasets covering daytime, nighttime and other adverse conditions.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The SHIFT [25] dataset is a recent simulated driving dataset that contains scenes in various environments. A continuous shift of these environments is available. SHIFT contains 6 class labels that share similarities to the BDD100K classes. For our evaluation, we use images with the 'day' and 'night' label as our source and target data respectively. We further ensure that the weather tag is 'clear' to isolate other weather conditions from the evaluation.",
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+    {
+        "type": "text",
+        "text": "4.3. Implementation",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Following previous SOTA methods, we employ Faster-RCNN [21] as our base detection model and ResNet-50 [10] pretrained on ImageNet [6] as our feature extractor. All images are scaled by resizing its shorter side to 600 pixels. For student-scaling we set a schedule for (0.57, 0.64, 0.71, 0.78, 0.85, 0.92) of the maximum iterations at scales (0.5, 0.6, 0.7, 0.8, 0.9, 1.0). Loss hyperparameters are set at  $\\lambda = 0.3$  and the rate smooth coefficient parameter of the EMA is 0.9996. A confidence threshold of 0.8 for phase one of Two-Phase Consistency. For the initial pretraining of the student model, we train the student for 50k and 20k iterations on the source images, for BDD100K and SHIFT respectively. Supervised inputs are daytime images with and without NightAug. We then copy the weights to the teacher and continue training with the addition of unsupervised loss for an additional 50k iterations. The learning rate is kept at 0.04 throughout training. Our network is trained on 3 RTX3090 GPUs with a batch-size of 6 source and 6 target images.",
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+    {
+        "type": "text",
+        "text": "4.4. Comparison to SOTA",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Comparison on BDD100K We compare our method against the SOTA on real driving scenes and evaluating their domain adaptation performance on nighttime images, the results of this experiment can be seen on Table 1. The results show that our method achieves the highest perfor",
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+    {
+        "type": "page_number",
+        "text": "11489",
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+    {
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+        "img_path": "images/260a68fcdf8a6dfda8ed4d951a9e734559f34114dc70c808af48e92e2eeabd0c.jpg",
+        "image_caption": [
+            "Figure 5. Qualitative results of Faster RCNN, Adaptive Teacher (AT) and our method on the SHIFT dataset with the ground-truth on the far right. We can observe that Faster RCNN is not able to detect objects due to absence of domain adaptation, while AT has a large number of small false positive bounding boxes compared to our method which closely resembles that of the ground-truth."
+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/118d34ec49e84b21fdf24b602e2d317adbad87c2f07af0c8f63bcb2c7fe80499.jpg",
+        "image_caption": [],
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+    },
+    {
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+        "img_path": "images/85899240049ff1fc50d9929c44f154e9f808a51c616d22cd1432f4ba874464f8.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/52216da15ee92e9d03f9f345c2ca5f962ae1e5bd73a17eec5bd7ac074b3d2650.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/826634909662486b1ab343b5849c94145be733bcd7b369139f600ddc99f42a01.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>AP</td><td>Per.</td><td>Car</td><td>Truck</td><td>Bus</td><td>Mcy.</td><td>Bcy.</td></tr><tr><td>Lower-Bound</td><td>41.6</td><td>40.4</td><td>44.5</td><td>49.9</td><td>53.7</td><td>14.3</td><td>46.7</td></tr><tr><td>Upper-Bound</td><td>47.0</td><td>49.7</td><td>51.5</td><td>56.0</td><td>53.6</td><td>19.2</td><td>52.4</td></tr><tr><td>DA FR [3]</td><td>43.7</td><td>43.0</td><td>48.8</td><td>47.8</td><td>52.1</td><td>19.9</td><td>55.8</td></tr><tr><td>UMT [7]</td><td>31.1</td><td>7.7</td><td>47.5</td><td>18.4</td><td>46.8</td><td>16.6</td><td>49.2</td></tr><tr><td>AT [15]</td><td>38.9</td><td>25.8</td><td>33.0</td><td>54.7</td><td>49.5</td><td>20.7</td><td>52.3</td></tr><tr><td>2PCNet (Ours)</td><td>49.1</td><td>51.4</td><td>54.6</td><td>54.8</td><td>56.6</td><td>23.9</td><td>54.2</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Results of Day-to-Night domain adaptation on the SHIFT dataset. The Average Precision (AP) of all classes. Faster RCNN is used as the lower-bound and upper-bound and is trained on labelled daytime and nighttime data respectively.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "mance with an AP of 46.4.  $20.5\\%$  higher than that of the SOTA student-teacher methods and above that of the upper-bound. We have observed in experiments that student-teacher methods underperforms with an AP below that of the lower-bound due to the error-propagation from noisy pseudo-labels. The result of the error is small false positive detections as seen in Figure 1. Our method does not suffer from the same allowing for higher performance. We can also observe that our method performs well across all classes. Even when compared with the upper-bound, 2PC-Net achieves higher AP on the majority of classes. This indicates that our method is able to generalise well across large and small classes.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The comparison with image-to-image translation methods is shown in Table 2. Translation methods do not suffer from the error propagation problem as it is trained on Faster RCNN without a teacher. Even so, we can see that our method outperforms SOTA adverse vision translation",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "methods.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Comparison on SHIFT To further compare our method with SOTA we evaluate on the SHIFT simulation dataset. Due to the nature of the simulated data, many nighttime image characteristics that we have previously mention is not exhibited in this data such as blurriness, noise and glare.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The results of this experiments are shown in Table 3. We can observe that previous SOTA methods that use the student-teacher framework perform worse than the lower-bound. The sub-par performance is again due to the error-propagation problem. AT performs better than UMT due to ATs inclusion of adversarial learning. However, adversarial learning is not enough to mitigate this problem. We can see that the performance of DA FRCNN outperforms both the SOTA student-teacher methods as it would not be affected by error-propagation. It is however, still largely below the upper-bound performance. 2PCNet outperforms these previous methods as well as the upperbound. We achieve an improvement of  $+10.2$  AP over previous SOTA student-teacher methods and  $+2.1$  AP over that of the upper-bound.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.5. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To demonstrate the effectiveness of each of our components, we train several models for 100K iterations and evaluate them on the BDD100K dataset. We present our findings in Table 4.",
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+    {
+        "type": "text",
+        "text": "Two-Phase Consistency We can observe in Table 4 that the addition of Two-Phase Consistency (C) demonstrated a wide performance gap when compared to the Mean-Teacher baseline, +13.5 AP (43%). This improvement in AP ex",
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+    {
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+        "text": "11490",
+        "bbox": [
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+    {
+        "type": "image",
+        "img_path": "images/808250427ec14cf82c8ac96e883ffd23fd2c6af9f58f5aeface3c8be797b87c7.jpg",
+        "image_caption": [
+            "Figure 6. Training curve on BDD100K dataset ablation study. We show the overall AP training curve as well as the AP of large, medium and small objects. MT represents the base Mean Teacher framework. It can be seen that at all scales, the absence of Two-Phase Consistency (C) results in a sharp drop during training. We can also see that with the inclusion of NightAug (NA) and student-scaling (SS) the gradient of the curve increases. We note that the inclusion of a domain classifier (DC) reduces the performance at all scales."
+        ],
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+    {
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+    {
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+        "img_path": "images/35530a358b9d008ad8b061628ac5c0ae9f9d1b58dc0f9a7ef67087c3e74bd327.jpg",
+        "image_caption": [],
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/6e1f6579437a259fb07456dba92adee7672ddce723d1501354e0dc90cdc44b74.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "ists across large, medium and small objects. While the performance of MT is initially strong, it rapidly begins to decline; which can be observed in Figure 6. This drop in performance is due to the error propagation of noisy pseudolabels. The experimental results show that Two-Phase Consistency is able to provide a solution. This ensures that highly confident pseudo-labels are bounded by less confident pseudo-label enabling a balance of knowledge into the student.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "NightAug We benched marked the effectiveness of NightAug in our framework as shown in Table 4. The inclusion of NightAug increases the detection performance of small objects with an increase of  $5\\%$ . Additionally, the gradient of the training performance remains steep as seen in Figure 6. The positive gradient is displayed most strongly for APm and APs where objects are more prone to nighttime specific complications.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Student-Scaling Our final component, student-scaling, is included into the framework and the results can be seen in Table 4. We can observe that student-scaling is able to boost the performance of small object detection by  $6\\%$ . This boost in performance is due to the student network focusing on smaller object earlier in the training process. We note that the performance of large objects have dropped by  $1 - 2\\%$ ; however when referring to the training curves in Figure 6, API remains steep. As the initial focus is on smaller objects, less time is allocated to larger objects during training. This can be mitigated by lengthening training resulting in more iterations for larger objects.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Domain Classifier To conclude our study, we included a domain classifier into our network. Adversarial learning is a widely used DA technique; however when added into 2PCNet, a performance drop across all scales can be seen. This drop is shown in Table 4. The suppression of nighttime features is suspected to be the cause. Suppression is present as the adversarial loss guides the feature extractor to maintain domain invariance. By suppressing nighttime fea",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/4ee03232bc2b517cbeda29e935f6a541aad701501640833e034d50932f217a5a.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"4\">Methods</td><td colspan=\"4\"></td></tr><tr><td>C</td><td>NA</td><td>SS</td><td>DC</td><td>AP</td><td>API</td><td>APm</td><td>APs</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>46.4</td><td>41.7</td><td>25.8</td><td>9.1</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>44.5</td><td>41.6</td><td>25.0</td><td>8.3</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>45.8</td><td>42.2</td><td>25.7</td><td>8.6</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>45.2</td><td>42.9</td><td>25.7</td><td>8.2</td></tr><tr><td></td><td></td><td></td><td></td><td>31.7</td><td>30.4</td><td>16.5</td><td>4.8</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 4. Ablation studies on the BDD100K dataset. The last row represents the base Mean-Teacher network. Methods are referred to as, C: Two-Phase Consistency, NA: NightAug, SS: StudentScaling, DC: Domain Classifier. API, APm, and APs represent the AP of large, medium and small objects respectively.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "tures, the teacher has less information to distil to the student. This is demonstrated in Figure 6 where the domain classifier (dotted purple) initially performs well. But as training continues, our method (solid red) is able to surpass its performance.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our proposed framework, 2PCNet, presents a novel solution to the challenges of day-to-night domain adaptive object detection. With our Two-Phase Consistency approach, we are able to effectively leverage high and low confidence knowledge for the student, while mitigating error propagation commonly present in previous student-teacher methods. We further address issues arising from small scale and dark objects through the use of student-scaling and NightAug, respectively. Experimental results on the e BDD100K [36] and SHIFT [25] datasets demonstrate that 2PCNet outperforms existing state-of-the-art methods. Overall, our proposed framework provides an effective and efficient solution for day-to-night domain adaptive object detection.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements This work is partially supported by MOE2019-T2-1-130.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
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+            104
+        ],
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+    },
+    {
+        "type": "list",
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2023/2PCNet_ Two-Phase Consistency Training for Day-to-Night Unsupervised Domain Adaptive Object Detection/818b1ea7-c7c2-488e-9c91-78c9a94fffa2_model.json

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+            "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+            "content": "2PCNet: Two-Phase Consistency Training for Day-to-Night Unsupervised Domain Adaptive Object Detection"
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+            "content": "Mikhail Kennerley\\(^{1,2}\\), Jian-Gang Wang\\(^{2}\\), Bharadwaj Veeravalli\\(^{1}\\), and Robby T. Tan\\(^{1}\\)  \n\\(^{1}\\)National University of Singapore, Department of Electrical and Computer Engineering  \n\\(^{2}\\)Institute for Infocomm Research, A*STAR  \nmikhailk@u.nus.edu, jgwang@i2r.a-star.edu.sg, elebv@nus.edu.sg, robby.tan@nus.edu.sg"
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+        {
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+            "content": "Object detection at night is a challenging problem due to the absence of night image annotations. Despite several domain adaptation methods, achieving high-precision results remains an issue. False-positive error propagation is still observed in methods using the well-established student-teacher framework, particularly for small-scale and low-light objects. This paper proposes a two-phase consistency unsupervised domain adaptation network, 2PCNet, to address these issues. The network employs high-confidence bounding-box predictions from the teacher in the first phase and appends them to the student's region proposals for the teacher to re-evaluate in the second phase, resulting in a combination of high and low confidence pseudo-labels. The night images and pseudo-labels are scaled-down before being used as input to the student, providing stronger small-scale pseudo-labels. To address errors that arise from low-light regions and other night-related attributes in images, we propose a night-specific augmentation pipeline called NightAug. This pipeline involves applying random augmentations, such as glare, blur, and noise, to daytime images. Experiments on publicly available datasets demonstrate that our method achieves superior results to state-of-the-art methods by \\(20\\%\\), and to supervised models trained directly on the target data."
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+            "content": "1. Introduction"
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+            "angle": 0,
+            "content": "Figure 1. Qualitative results of state-of-the-art DA methods, DA Faster-RCNN [3], UMT [7], Adaptive Teacher (AT) [15] and our method 2PCNet on the BDD100K [36] dataset. Unlike the SOTA methods, our method is able to detect dark and small scale objects with minimal additional false positive predictions."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "do not assume the availability of the annotations are more advantageous. Domain adaptation (DA) is an efficient solution to this problem by allowing the use of readily available annotated source daytime datasets."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "A few domain adaptation methods have been proposed, e.g., adversarial learning which uses image and instance level classifiers [3] and similar concepts [22, 32]. However, these methods isolate the domain adaptation task purely towards the feature extractor, and suppress features of the target data for the sake of domain invariance. Recent unsupervised domain adaptation methods exploit the studentteacher framework (e.g. [1,7,11,15]). Since the student initially learns from the supervised loss, there is a bias towards the source data. Augmentation [7, 11] and adversarial learning [15] have been proposed to address this problem. Unfortunately, particularly for day-to-night unsupervised domain adaptation, these methods suffer from a large num"
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+            "angle": 0,
+            "content": "ber of inaccurate pseudo-labels produced by the teacher. In our investigation, the problem is notably due to insufficient knowledge of small scale features in the nighttime domain, which are then propagated through the learning process between the teacher and student, resulting in poor object detection performance."
+        },
+        {
+            "type": "text",
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+            "content": "To address the problem, in this paper, we present 2PC-Net, a two-phase consistency unsupervised domain adaptation network for nighttime object detection. Our 2PCNet merges the bounding-boxes of highly-confident pseudolabels, which are predicted in phase one, together with regions proposed by the student's region proposal network (RPN). The merged proposals are then used by the teacher to generate a new set of pseudo-labels in phase two. This provides a combination of high and low confidence pseudolabels. These pseudo-labels are then matched with predictions generated by the student. We can then utilise a weighted consistency loss to ensure that a higher weightage of our unsupervised loss is based on stronger pseudo-labels, yet allow for weaker pseudo-labels to influence the training."
+        },
+        {
+            "type": "text",
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+            "angle": 0,
+            "content": "Equipped with this two-phase strategy, we address the problem of errors from small-scale objects. We devise a student-scaling technique, where night images and their pseudo-labels for the student are deliberately scaled down. In order to generate accurate pseudo-labels, images to the teacher remain at their full scale. This results in the pseudolabels of larger objects, which are easier to predict, to be scaled down to smaller objects, allowing for an increase in small scale performance of the student."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Nighttime images suffer from multiple complications not found in daytime scenes such as dark regions, glare, prominent noise, prominent blur, imbalanced lighting, etc. All these cause a problem, since the student, which was trained on daytime images, is much more biased towards the daytime domain's characteristics. To mitigate this problem, we propose NightAug, a set of random nighttime specific augmentations. NightAug includes adding artificial glare, noise, blur, etc. that mimic the night conditions to daytime images. With NightAug we are able to reduce the bias of the student network towards the source data without resulting in adversarial learning or compute-intensive translations. Overall, using 2PCNet, we can see the qualitative improvements of our result in Figure 1. In summary, the contributions of this paper are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "- We present 2PCNet, a two-phase consistency approach for student-teacher learning. 2PCNet takes advantage of highly confident teacher labels augmented with less confident regions, which are proposed by the scaled student. This strategy produces a sharp reduction of the error propagation in the learning process."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.871,
+                0.47,
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+            ],
+            "angle": 0,
+            "content": "- To address the bias of the student towards the source domain, we propose NightAug, a random night spe"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.096,
+                0.772,
+                0.47,
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+            "angle": 0,
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+            "angle": 0,
+            "content": "cific augmentation pipeline to shift the characteristics of daytime images toward nighttime."
+        },
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+            "type": "text",
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+            "content": "- The effectiveness of our approach has been verified by comparing it with the state-of-the-art domain adaptation approaches. An improvement of \\(+7.9\\mathrm{AP}(+20\\%)\\) and \\(+10.2\\mathrm{AP}(26\\%)\\) over the SOTA on BDD100K and SHIFT has been achieved, respectively."
+        },
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+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "Unsupervised Domain Adaptation (UDA) Unsupervised domain adaptation aims to learn transferable features to reduce the discrepancy between a labelled source and unlabelled target domain. Previous works minimised the distance metric (MMD) [16-18] and considered intra-class and inter-class discrepancy [12, 13]. Adversarial feature learning involved adding an adversarial classifier to play the min-max game between the domain discriminator and feature extractors to generate a domain invariant feature map [27, 28, 37]. These methods have been applied to image classification. Our work focuses on object detection, which is more complex as it involves identifying multiple bounding boxes and associated classes in each image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.458,
+                0.892,
+                0.671
+            ],
+            "angle": 0,
+            "content": "UDA for Object Detection Object detection with UDA is a recent challenge due to the complexities of identifying multiple objects in an image. DA-Faster RCNN [3] integrated adversarial learning with image and instance level classifiers, and several approaches have been proposed to improve on this method by introducing scale-awareness [4], class specific discriminators [31], and re-purposing the task-specific classifier as a discriminator [2]. The Mean Teacher (MT) framework [26] has been adopted in semi-supervised methods, such as UMT [7], which incorporates CycleGAN [39] augmented images; AT [15], which combines the student-teacher framework with adversarial learning; and TDD [11], which uses dual student-teacher networks with style transfer."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
+                0.892,
+                0.841
+            ],
+            "angle": 0,
+            "content": "Nighttime UDA The majority of research on unsupervised domain adaptation (UDA) in nighttime scenarios has focused on semantic segmentation [5, 8, 9, 14, 23, 29, 33]. Translation and style transformation techniques are commonly used to reduce the domain gap between the source and target domains in these methods [8,29,33]. Some UDA-based techniques for nighttime also utilise paired-images to generate a shared feature space [23], while others use an intermediate domain such as twilight to reduce the domain gap during unsupervised learning [5]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.841,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Nighttime tracking has also been investigated where adversarial transformers are used to close the domain gap [35]. However, there is a gap in research when it comes to applying UDA techniques in the object detection task for night-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11485"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.089,
+                0.891,
+                0.413
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.075,
+                0.424,
+                0.893,
+                0.496
+            ],
+            "angle": 0,
+            "content": "Figure 2. Overview of our proposed framework, 2PCNet. 2PCNet consists of: A student network is trained on both the labelled daytime image, which has been augmented with NightAug, and unlabelled nighttime images. A teacher network which is the exponential moving average (EMA) of the student and provides matched pseudo-labels for unsupervised loss. The match pseudo-labels are the predictions of the teacher (phase two) using the RPN proposals of the student, which in turn was guided by the high confidence pseudo-labels of the teacher (phase one)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.521,
+                0.471,
+                0.566
+            ],
+            "angle": 0,
+            "content": "time scenarios. Therefore, we explore the application of UDA techniques in object detection under low-light and nighttime conditions."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.584,
+                0.251,
+                0.602
+            ],
+            "angle": 0,
+            "content": "3. Proposed Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.61,
+                0.47,
+                0.702
+            ],
+            "angle": 0,
+            "content": "Let \\(\\mathbf{D}_s\\) be the daytime source data. \\(\\mathbf{D}_s = \\{I_s, C_s, B_s\\}\\), where the variables refer to the image, class label and bounding-box label, respectively. Index \\(s\\) indicates the daytime source. The night target data is represented by \\(\\mathbf{D}_t\\), where \\(\\mathbf{D}_t = \\{I_t\\}\\) as we do not have the target labels available to us. Index \\(t\\) indicates the nighttime target."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.703,
+                0.471,
+                0.853
+            ],
+            "angle": 0,
+            "content": "The architecture of our 2PCNet is shown in Figure 2. Our 2PCNet consists of a student and a teacher network. The student is a multi-domain network trained on both labelled daytime images, augmented with NightAug, and unlabelled nighttime images. The teacher focuses on night images to produce pseudo-labels for the student and is the exponential moving average (EMA) of the student. After an initial pretraining phase, the teacher begins producing pseudo-labels, which allows the student to initialise the feature extractor and detector."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.471,
+                0.901
+            ],
+            "angle": 0,
+            "content": "During each iteration, in phase one of 2PCNet, the teacher produces pseudo-labels from the night images. These pseudo-labels are filtered through a confidence"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.521,
+                0.893,
+                0.656
+            ],
+            "angle": 0,
+            "content": "threshold. This is to ensure only high-confidence pseudolabels are given to the student. The bounding-boxes from the pseudo-labels are then combined with the region proposals generated by the student's RPN. The merged region proposals are then used to generate predictions from the student's RoI network. In phase two, the teacher utilises the same merged region proposals to generate a matched set of pseudo-labels, where each pseudo-label has its corresponding prediction obtained from the student."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.659,
+                0.892,
+                0.706
+            ],
+            "angle": 0,
+            "content": "As mentioned earlier, our student network is initialised by pretraining for a set number of iterations. This is done with supervised loss on the augmented daytime images:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.558,
+                0.726,
+                0.892,
+                0.743
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\sup } = L _ {\\operatorname {r p n}} \\left(B _ {s}, I _ {s}\\right) + L _ {\\operatorname {r o i}} \\left(B _ {s}, C _ {s}, I _ {s}\\right), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.762,
+                0.891,
+                0.823
+            ],
+            "angle": 0,
+            "content": "where \\( L_{\\mathrm{rpn}} \\) represents the loss from the RPN, which consists of an objectness and bounding-box regression loss. \\( L_{\\mathrm{roi}} \\) represents the loss from the detector network, consisting of a classification and bounding-box regression loss."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.826,
+                0.892,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Once the pretraining is completed, the student's weights are then transferred over to the teacher. In the succeeding iterations, the teacher's weights are the exponential moving average (EMA) of the student's. The matched pseudo-labels generated by the teacher, \\(\\{C_p^*, B_p^*\\}\\), are then used to guide"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11486"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.084,
+                0.092,
+                0.283,
+                0.268
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.283,
+                0.092,
+                0.483,
+                0.268
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.282,
+                0.47,
+                0.364
+            ],
+            "angle": 0,
+            "content": "Figure 3. (Left to Right, Top to Bottom) Ground truth bounding boxes, bounding boxes predicted by the teacher with non-maximal suppression (NMS) and thresholding \\((B_{p})\\), bounding boxes predicted by the student \\((B_{\\mathrm{student}})\\) which is guided by \\(B_{p}\\), and the bounding boxes predicted by the teacher \\((B_{p}^{*})\\) for the consistency loss."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.394,
+                0.3,
+                0.409
+            ],
+            "angle": 0,
+            "content": "the unsupervised loss, defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.137,
+                0.424,
+                0.469,
+                0.443
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\text {u n s u p}} = L _ {\\text {r p n}} ^ {\\text {o b j}} \\left(C _ {p} ^ {*}; I _ {t}\\right) + L _ {\\text {c o n s}} \\left(C _ {p} ^ {*}; I _ {t}\\right), \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.455,
+                0.469,
+                0.502
+            ],
+            "angle": 0,
+            "content": "where \\( L_{\\mathrm{rpn}}^{\\mathrm{obj}} \\) is the objectness loss of the RPN and \\( L_{\\mathrm{cons}} \\) is the weighted KL-Divergence loss from the predicted outputs which we will further explain in the next section."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.513,
+                0.294,
+                0.529
+            ],
+            "angle": 0,
+            "content": "3.1. Two-Phase Consistency"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.538,
+                0.47,
+                0.734
+            ],
+            "angle": 0,
+            "content": "Due to the large domain gap between daytime source images and nighttime target images, the teacher is unable to produce high quality pseudo-labels. This generally occurs in the whole scene, but particularly for regions with strong night characteristics, e.g., low-light, glare, uneven lighting, etc. The teacher produces confident pseudo-labels only for regions that share more similarities to the daytime, since it is biased towards the daytime domain. This bias poses a problem for methods that employ a hard-threshold to filter pseudo-labels for categorical cross-entropy loss [7, 15, 26]. The remaining pseudo-labels contain only easy samples with daytime attributes. Consequently, the student does not learn from harder (e.g. darker) areas."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.734,
+                0.469,
+                0.87
+            ],
+            "angle": 0,
+            "content": "As a result of minimal knowledge of the hard samples (i.e., areas with a high level of nighttime attributes), the teacher begins to predict highly confident yet incorrect pseudo-labels. As the teacher provides these incorrect pseudo-labels to the student, a viscous cycle starts where the teacher in turn is updated with incorrect knowledge. Consequently, the error continues to propagate through training. In our case, these errors notably occur in dark/glare regions and as small scale objects."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To address the problem of error propagation, we design a two-phase approach that combines high confidence"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.092,
+                0.892,
+                0.257
+            ],
+            "angle": 0,
+            "content": "pseudo-labels together with their less confident counterparts. This combination allows for the high accuracy of confident-labels with the additional knowledge of less confident labels to be distilled onto the student. In phase one, the unlabelled nighttime image, \\( I_{t} \\), is used as an input for the teacher to generate pseudo-labels. These pseudo-labels are filtered with a threshold to retain only high-confidence pseudo-labels, \\( (C_p, B_p) \\). The bounding-box of the pseudolabels, \\( B_{p} \\), is then used as an input to the student. \\( B_{p} \\) is concatenated to the region proposals generated by the student RPN module:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.603,
+                0.269,
+                0.892,
+                0.286
+            ],
+            "angle": 0,
+            "content": "\\[\nP ^ {*} = \\operatorname {R P N} _ {\\text {s t u d e n t}} \\left(I _ {t}\\right) \\neq B _ {p}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.296,
+                0.891,
+                0.357
+            ],
+            "angle": 0,
+            "content": "where \\( P^{*} \\) is the combined region proposals, which are then used as an input to the student's RoI module to predict the classes, \\( C_{\\mathrm{student}} \\), and bounding-box, \\( B_{\\mathrm{student}} \\), of each region proposal."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.357,
+                0.892,
+                0.416
+            ],
+            "angle": 0,
+            "content": "Phase two begins by using the same combined region proposals, \\( P^{*} \\), generated in phase one as an input to the teachers RoI module to generate a matched set of pseudolabels:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.599,
+                0.429,
+                0.891,
+                0.448
+            ],
+            "angle": 0,
+            "content": "\\[\n\\left\\{C _ {p} ^ {*}, B _ {p} ^ {*} \\right\\} = \\operatorname {R o I} _ {\\text {t e a c h e r}} \\left(P ^ {*}\\right). \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.456,
+                0.892,
+                0.52
+            ],
+            "angle": 0,
+            "content": "The difference between \\( C_p \\) and \\( C_p^* \\) is that \\( C_p^* \\) is derived from the same region proposals as that of the student predictions \\( C_{\\mathrm{student}} \\). This allows us to compare \\( C_{\\mathrm{student}} \\) and \\( C_p^* \\) directly:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.52,
+                0.528,
+                0.892,
+                0.565
+            ],
+            "angle": 0,
+            "content": "\\[\n\\begin{array}{l} \\left\\{C _ {\\text {s t u d e n t}} (n), B _ {\\text {s t u d e n t}} (n) \\right\\} = \\operatorname {R o I} _ {\\text {s t u d e n t}} \\left(P ^ {*} (n)\\right), \\tag {5} \\\\ \\left\\{C _ {p} ^ {*} (n), B _ {p} ^ {*} (n) \\right\\} = \\operatorname {R o I} _ {\\text {t e a c h e r}} \\left(P ^ {*} (n)\\right), \\\\ \\end{array}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.573,
+                0.892,
+                0.694
+            ],
+            "angle": 0,
+            "content": "where \\( n = \\{1,2,\\dots,N\\} \\) and \\( N \\) is the number of region proposals in \\( P^* \\). This operation ensures that the knowledge of highly confident predictions generated by the teacher is distilled through to the student. In addition, information from less confident predictions can also be learnt. However, we are still required to penalise less confident samples and thus employ weighed KL-Divergence to be used as our consistency loss:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.596,
+                0.706,
+                0.891,
+                0.723
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\text {c o n s}} = \\alpha \\operatorname {K L} \\left(C _ {\\text {s t u d e n t}}, C _ {p} ^ {*}\\right), \\tag {6}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.733,
+                0.892,
+                0.84
+            ],
+            "angle": 0,
+            "content": "where \\(\\alpha\\) is the highest confidence of \\(C_p^*\\) expressed as \\(\\alpha = \\max(C_p^*)\\); KL() is the KL-divergence function. Note that, pseudo-bounding boxes are not used to generate unsupervised loss, as the confidence score of each pseudo-label represents the class information rather than the bounding box. The outputs of each segment of our two-phase approach are shown in Figure 3."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.848,
+                0.66,
+                0.864
+            ],
+            "angle": 0,
+            "content": "3.2. Student-Scaling"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.871,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "In our investigation, we have found that scales of objects have a strong influence on object detection at night. This"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11487"
+        }
+    ],
+    [
+        {
+            "type": "code_caption",
+            "bbox": [
+                0.081,
+                0.092,
+                0.388,
+                0.107
+            ],
+            "angle": 0,
+            "content": "Algorithm 1 Single Augmentation - NightAug"
+        },
+        {
+            "type": "algorithm",
+            "bbox": [
+                0.092,
+                0.111,
+                0.37,
+                0.292
+            ],
+            "angle": 0,
+            "content": "imgClean \\(\\leftarrow\\) img   \nif randFloat \\(\\geq 0.5\\) then randFloat \\(\\leftarrow 0.8*\\) randFloat \\(+0.2\\) img \\(\\leftarrow\\) augmentation(img, randval) prob \\(\\leftarrow 0.4\\) while randFloat \\(\\geq\\) prob do \\(x\\gets\\) randInt(img.shape[1],2) \\(y\\gets\\) randInt(img.shape[2],2) img[x,y] \\(\\leftarrow\\) imgClean[x,y] prob \\(\\leftarrow\\) prob +0.1 end while   \nend if"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.321,
+                0.468,
+                0.531
+            ],
+            "angle": 0,
+            "content": "is due to the features of smaller objects being easily overwhelmed by glare or noise. To allow the student to overcome this, we apply scaling augmentation to the student's inputs which includes both the image and the pseudo-labels generated by the teacher. As training proceeds, we follow a schedule to increase the scale of the student augmentation until it equals to that of the original image. By iteratively increasing the scale we allow the student to focus on smaller features earlier in the training process. This process encourages the teacher to make more accurate predictions on smaller scale objects in the later stages of training. In turn, accurate small scale pseudo-labels allow for the increase in the scale of the student's inputs with minimal errors due to scale."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.533,
+                0.468,
+                0.623
+            ],
+            "angle": 0,
+            "content": "To ensure the knowledge of the previous scales is not forgotten, a gaussian function for the scaling factor is applied. The norm of the Gaussian function is obtained from the schedule values. To prevent additional noise due to pseudo-labels being too small, labels that has an area below a threshold are removed."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.635,
+                0.188,
+                0.651
+            ],
+            "angle": 0,
+            "content": "3.3. NightAug"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.659,
+                0.468,
+                0.84
+            ],
+            "angle": 0,
+            "content": "Night images suffer from a range of complications that are not present in daytime scenes. This causes a problem in the student-teacher framework, where the student would be biased towards the source domain. Previous methods have attempted to address this, but have either required compute-intensive translations [7, 11] or adding additional domain classifiers to the framework [15] which complicates training. We propose NightAug, a nighttime specific augmentation pipeline that is compute-light and does not require training. NightAug consists of a series of augmentations with the aim of steering the characteristics of daytime images to resemble that of a nighttime image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.468,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The defining features of nighttime images are that they are darker and have lower contrast than daytime images. In addition the signal-to-night ratio (SNR) could be higher due to the properties of digital cameras such as luminance and"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.09,
+                0.697,
+                0.261
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.698,
+                0.09,
+                0.892,
+                0.261
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.271,
+                0.892,
+                0.314
+            ],
+            "angle": 0,
+            "content": "Figure 4. NightAug: Original image (top-left) and images with random augmentations from: gaussian blur, gamma correction, brightness, contrast, glare, gaussian noise and random cut-outs."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.351,
+                0.892,
+                0.412
+            ],
+            "angle": 0,
+            "content": "colour noise. Glare and glow from street lamps and headlights are also present in nighttime images. Additionally, images may be out-of-focus due to the cameras inability to detect reference points to focus on in dark environments."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.417,
+                0.892,
+                0.613
+            ],
+            "angle": 0,
+            "content": "Keeping in mind the properties of nighttime images, our NightAug includes random; brightness, contrast, gamma, gaussian noise, gaussian blur augmentations and random glare insertion. The augmentations are randomly applied to the images and are also random in intensity. This randomness results in a wider variance of images that are exposed to the student leading to more robust training [30]. To further increase the variance of the images, at each augmentation step, random segments of the image will ignore the application of that augmentation. This allows for the representation where different areas of nighttime images may be unevenly lighted. This uneven lighting affects the above characteristics of the local region."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.618,
+                0.892,
+                0.738
+            ],
+            "angle": 0,
+            "content": "A single augmentation flow of NightAug is demonstrated in Algorithm 1. Samples of an image processed with NightAug are shown in Figure 4. Each augmentation has a set probability of being applied, with the strength of the augmentation being random. Random regions of the augmented image may then be replaced with that of the original image. The probability of this region replacement reduces with each iteration."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.775,
+                0.844,
+                0.79
+            ],
+            "angle": 0,
+            "content": "Overall Loss Our total loss can be represented as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.608,
+                0.815,
+                0.891,
+                0.832
+            ],
+            "angle": 0,
+            "content": "\\[\nL _ {\\text {t o t a l}} = L _ {\\sup } + \\lambda L _ {\\text {u n s u p}}, \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.856,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "where \\(\\lambda\\) represents a weight factor for the unsupervised loss, and is set experimentally. \\(L_{\\mathrm{sup}}, L_{\\mathrm{unsup}}\\) refer to Eq. (1) and Eq. (2), respectively."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.956
+            ],
+            "angle": 0,
+            "content": "11488"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.089,
+                0.894,
+                0.251
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>AP</td><td>Pedestrian</td><td>Rider</td><td>Car</td><td>Truck</td><td>Bus</td><td>Motorcycle</td><td>Bicycle</td><td>TrafficLight</td><td>TrafficSign</td></tr><tr><td>Lower-Bound</td><td>41.1</td><td>50.0</td><td>28.9</td><td>66.6</td><td>47.8</td><td>47.5</td><td>32.8</td><td>39.5</td><td>41.0</td><td>56.5</td></tr><tr><td>Upper-Bound</td><td>46.2</td><td>52.1</td><td>35.0</td><td>73.6</td><td>53.5</td><td>54.8</td><td>36.0</td><td>41.8</td><td>52.2</td><td>63.3</td></tr><tr><td>DA F-RCNN [3]</td><td>41.3</td><td>50.4</td><td>30.3</td><td>66.3</td><td>46.8</td><td>48.3</td><td>32.6</td><td>41.4</td><td>41.0</td><td>56.2</td></tr><tr><td>TDD [11]</td><td>34.6</td><td>43.1</td><td>20.7</td><td>68.4</td><td>33.3</td><td>35.6</td><td>16.5</td><td>25.9</td><td>43.1</td><td>59.5</td></tr><tr><td>UMT [7]</td><td>36.2</td><td>46.5</td><td>26.1</td><td>46.8</td><td>44.0</td><td>46.3</td><td>28.2</td><td>40.2</td><td>31.6</td><td>52.7</td></tr><tr><td>AT [15]</td><td>38.5</td><td>42.3</td><td>30.4</td><td>60.8</td><td>48.9</td><td>52.1</td><td>34.5</td><td>42.7</td><td>29.1</td><td>43.9</td></tr><tr><td>2PCNet (Ours)</td><td>46.4</td><td>54.4</td><td>30.8</td><td>73.1</td><td>53.8</td><td>55.2</td><td>37.5</td><td>44.5</td><td>49.4</td><td>65.2</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.262,
+                0.893,
+                0.318
+            ],
+            "angle": 0,
+            "content": "Table 1. Results of day-to-night domain adaptation on the BDD100K dataset, the Average Precision (AP) of all classes are reported. Faster RCNN detector with ResNet-50 feature extractor is used for all experiments to ensure a fair comparison. Faster RCNN is used as the lower-bound and upper-bound and is trained on labelled daytime and nighttime data respectively. The lower-bound provides a baseline without any domain adaptation while the upper-bound is fully supervised, the case where labelled target night data is available."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.342,
+                0.472,
+                0.455
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>APcoco</td><td>Car</td><td>Bus</td><td>Truck</td></tr><tr><td>Lower-Bound</td><td>22.1</td><td>37.5</td><td>29.8</td><td>30.7</td></tr><tr><td>Upper-Bound</td><td>23.9</td><td>42.0</td><td>33.8</td><td>35.0</td></tr><tr><td>FDA [34]</td><td>22.6</td><td>38.5</td><td>37.2</td><td>23.2</td></tr><tr><td>ForkGAN [38]</td><td>22.9</td><td>41.2</td><td>33.3</td><td>32.1</td></tr><tr><td>2PCNet (Ours)</td><td>23.5</td><td>40.7</td><td>38.2</td><td>35.0</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.467,
+                0.47,
+                0.523
+            ],
+            "angle": 0,
+            "content": "Table 2. Comparison of our framework, 2PCNet, with image-to-image (I2I) translation methods. Conducted on the BDD100K dataset. ForkGan and FDA are used for comparison. Reported \\(AP_{coco}\\) is the averaged AP over IoUs 0.5 to 0.95."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.541,
+                0.21,
+                0.558
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.566,
+                0.186,
+                0.581
+            ],
+            "angle": 0,
+            "content": "4.1. Baselines"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.591,
+                0.47,
+                0.743
+            ],
+            "angle": 0,
+            "content": "To evaluate our method, we compare our approach with SOTA methods in domain adaptation for object detection. These include DA-Faster RCNN [3], TDD [11], UMT [7], AT [15] as well as a non-DA baseline Faster-RCNN [21]. Faster-RCNN is used as both our lower and upper-bound, where it is trained on labelled source and target data respectively. We additionally compare our approach with image-to-image translation methods, ForkGAN [38] and FDA [34]. Translation methods are trained on Faster RCNN with both the daytime and translated images."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.756,
+                0.18,
+                0.77
+            ],
+            "angle": 0,
+            "content": "4.2. Datasets"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The majority of existing nighttime datasets either focuses on semantic segmentation which do not provide labels for object detection [5, 23, 24], or contains very few classes [19, 20]. BDD100K [36] was selected as it provides object detection labels which includes a wide range of classes (10). It also has a large number of images compared to other DA datasets covering daytime, nighttime and other adverse conditions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.344,
+                0.892,
+                0.466
+            ],
+            "angle": 0,
+            "content": "The SHIFT [25] dataset is a recent simulated driving dataset that contains scenes in various environments. A continuous shift of these environments is available. SHIFT contains 6 class labels that share similarities to the BDD100K classes. For our evaluation, we use images with the 'day' and 'night' label as our source and target data respectively. We further ensure that the weather tag is 'clear' to isolate other weather conditions from the evaluation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.478,
+                0.661,
+                0.495
+            ],
+            "angle": 0,
+            "content": "4.3. Implementation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.502,
+                0.893,
+                0.789
+            ],
+            "angle": 0,
+            "content": "Following previous SOTA methods, we employ Faster-RCNN [21] as our base detection model and ResNet-50 [10] pretrained on ImageNet [6] as our feature extractor. All images are scaled by resizing its shorter side to 600 pixels. For student-scaling we set a schedule for (0.57, 0.64, 0.71, 0.78, 0.85, 0.92) of the maximum iterations at scales (0.5, 0.6, 0.7, 0.8, 0.9, 1.0). Loss hyperparameters are set at \\(\\lambda = 0.3\\) and the rate smooth coefficient parameter of the EMA is 0.9996. A confidence threshold of 0.8 for phase one of Two-Phase Consistency. For the initial pretraining of the student model, we train the student for 50k and 20k iterations on the source images, for BDD100K and SHIFT respectively. Supervised inputs are daytime images with and without NightAug. We then copy the weights to the teacher and continue training with the addition of unsupervised loss for an additional 50k iterations. The learning rate is kept at 0.04 throughout training. Our network is trained on 3 RTX3090 GPUs with a batch-size of 6 source and 6 target images."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.801,
+                0.702,
+                0.817
+            ],
+            "angle": 0,
+            "content": "4.4. Comparison to SOTA"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Comparison on BDD100K We compare our method against the SOTA on real driving scenes and evaluating their domain adaptation performance on nighttime images, the results of this experiment can be seen on Table 1. The results show that our method achieves the highest perfor"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11489"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.084,
+                0.092,
+                0.244,
+                0.336
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.246,
+                0.092,
+                0.406,
+                0.337
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.407,
+                0.092,
+                0.566,
+                0.337
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.567,
+                0.092,
+                0.726,
+                0.337
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.727,
+                0.092,
+                0.888,
+                0.337
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.349,
+                0.895,
+                0.392
+            ],
+            "angle": 0,
+            "content": "Figure 5. Qualitative results of Faster RCNN, Adaptive Teacher (AT) and our method on the SHIFT dataset with the ground-truth on the far right. We can observe that Faster RCNN is not able to detect objects due to absence of domain adaptation, while AT has a large number of small false positive bounding boxes compared to our method which closely resembles that of the ground-truth."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.415,
+                0.472,
+                0.535
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>AP</td><td>Per.</td><td>Car</td><td>Truck</td><td>Bus</td><td>Mcy.</td><td>Bcy.</td></tr><tr><td>Lower-Bound</td><td>41.6</td><td>40.4</td><td>44.5</td><td>49.9</td><td>53.7</td><td>14.3</td><td>46.7</td></tr><tr><td>Upper-Bound</td><td>47.0</td><td>49.7</td><td>51.5</td><td>56.0</td><td>53.6</td><td>19.2</td><td>52.4</td></tr><tr><td>DA FR [3]</td><td>43.7</td><td>43.0</td><td>48.8</td><td>47.8</td><td>52.1</td><td>19.9</td><td>55.8</td></tr><tr><td>UMT [7]</td><td>31.1</td><td>7.7</td><td>47.5</td><td>18.4</td><td>46.8</td><td>16.6</td><td>49.2</td></tr><tr><td>AT [15]</td><td>38.9</td><td>25.8</td><td>33.0</td><td>54.7</td><td>49.5</td><td>20.7</td><td>52.3</td></tr><tr><td>2PCNet (Ours)</td><td>49.1</td><td>51.4</td><td>54.6</td><td>54.8</td><td>56.6</td><td>23.9</td><td>54.2</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.547,
+                0.47,
+                0.603
+            ],
+            "angle": 0,
+            "content": "Table 3. Results of Day-to-Night domain adaptation on the SHIFT dataset. The Average Precision (AP) of all classes. Faster RCNN is used as the lower-bound and upper-bound and is trained on labelled daytime and nighttime data respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.626,
+                0.47,
+                0.822
+            ],
+            "angle": 0,
+            "content": "mance with an AP of 46.4. \\(20.5\\%\\) higher than that of the SOTA student-teacher methods and above that of the upper-bound. We have observed in experiments that student-teacher methods underperforms with an AP below that of the lower-bound due to the error-propagation from noisy pseudo-labels. The result of the error is small false positive detections as seen in Figure 1. Our method does not suffer from the same allowing for higher performance. We can also observe that our method performs well across all classes. Even when compared with the upper-bound, 2PC-Net achieves higher AP on the majority of classes. This indicates that our method is able to generalise well across large and small classes."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.826,
+                0.47,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The comparison with image-to-image translation methods is shown in Table 2. Translation methods do not suffer from the error propagation problem as it is trained on Faster RCNN without a teacher. Even so, we can see that our method outperforms SOTA adverse vision translation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.42,
+                0.565,
+                0.433
+            ],
+            "angle": 0,
+            "content": "methods."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.445,
+                0.892,
+                0.521
+            ],
+            "angle": 0,
+            "content": "Comparison on SHIFT To further compare our method with SOTA we evaluate on the SHIFT simulation dataset. Due to the nature of the simulated data, many nighttime image characteristics that we have previously mention is not exhibited in this data such as blurriness, noise and glare."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.521,
+                0.893,
+                0.734
+            ],
+            "angle": 0,
+            "content": "The results of this experiments are shown in Table 3. We can observe that previous SOTA methods that use the student-teacher framework perform worse than the lower-bound. The sub-par performance is again due to the error-propagation problem. AT performs better than UMT due to ATs inclusion of adversarial learning. However, adversarial learning is not enough to mitigate this problem. We can see that the performance of DA FRCNN outperforms both the SOTA student-teacher methods as it would not be affected by error-propagation. It is however, still largely below the upper-bound performance. 2PCNet outperforms these previous methods as well as the upperbound. We achieve an improvement of \\(+10.2\\) AP over previous SOTA student-teacher methods and \\(+2.1\\) AP over that of the upper-bound."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.744,
+                0.665,
+                0.759
+            ],
+            "angle": 0,
+            "content": "4.5. Ablation Studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.769,
+                0.892,
+                0.829
+            ],
+            "angle": 0,
+            "content": "To demonstrate the effectiveness of each of our components, we train several models for 100K iterations and evaluate them on the BDD100K dataset. We present our findings in Table 4."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.84,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Two-Phase Consistency We can observe in Table 4 that the addition of Two-Phase Consistency (C) demonstrated a wide performance gap when compared to the Mean-Teacher baseline, +13.5 AP (43%). This improvement in AP ex"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.48,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "11490"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.082,
+                0.09,
+                0.288,
+                0.216
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.291,
+                0.091,
+                0.487,
+                0.216
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.49,
+                0.091,
+                0.686,
+                0.216
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.688,
+                0.091,
+                0.888,
+                0.216
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.229,
+                0.895,
+                0.286
+            ],
+            "angle": 0,
+            "content": "Figure 6. Training curve on BDD100K dataset ablation study. We show the overall AP training curve as well as the AP of large, medium and small objects. MT represents the base Mean Teacher framework. It can be seen that at all scales, the absence of Two-Phase Consistency (C) results in a sharp drop during training. We can also see that with the inclusion of NightAug (NA) and student-scaling (SS) the gradient of the curve increases. We note that the inclusion of a domain classifier (DC) reduces the performance at all scales."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.311,
+                0.473,
+                0.448
+            ],
+            "angle": 0,
+            "content": "ists across large, medium and small objects. While the performance of MT is initially strong, it rapidly begins to decline; which can be observed in Figure 6. This drop in performance is due to the error propagation of noisy pseudolabels. The experimental results show that Two-Phase Consistency is able to provide a solution. This ensures that highly confident pseudo-labels are bounded by less confident pseudo-label enabling a balance of knowledge into the student."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.457,
+                0.47,
+                0.579
+            ],
+            "angle": 0,
+            "content": "NightAug We benched marked the effectiveness of NightAug in our framework as shown in Table 4. The inclusion of NightAug increases the detection performance of small objects with an increase of \\(5\\%\\). Additionally, the gradient of the training performance remains steep as seen in Figure 6. The positive gradient is displayed most strongly for APm and APs where objects are more prone to nighttime specific complications."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.589,
+                0.471,
+                0.771
+            ],
+            "angle": 0,
+            "content": "Student-Scaling Our final component, student-scaling, is included into the framework and the results can be seen in Table 4. We can observe that student-scaling is able to boost the performance of small object detection by \\(6\\%\\). This boost in performance is due to the student network focusing on smaller object earlier in the training process. We note that the performance of large objects have dropped by \\(1 - 2\\%\\); however when referring to the training curves in Figure 6, API remains steep. As the initial focus is on smaller objects, less time is allocated to larger objects during training. This can be mitigated by lengthening training resulting in more iterations for larger objects."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.471,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Domain Classifier To conclude our study, we included a domain classifier into our network. Adversarial learning is a widely used DA technique; however when added into 2PCNet, a performance drop across all scales can be seen. This drop is shown in Table 4. The suppression of nighttime features is suspected to be the cause. Suppression is present as the adversarial loss guides the feature extractor to maintain domain invariance. By suppressing nighttime fea"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.514,
+                0.309,
+                0.882,
+                0.433
+            ],
+            "angle": 0,
+            "content": "<table><tr><td colspan=\"4\">Methods</td><td colspan=\"4\"></td></tr><tr><td>C</td><td>NA</td><td>SS</td><td>DC</td><td>AP</td><td>API</td><td>APm</td><td>APs</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>46.4</td><td>41.7</td><td>25.8</td><td>9.1</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>44.5</td><td>41.6</td><td>25.0</td><td>8.3</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>45.8</td><td>42.2</td><td>25.7</td><td>8.6</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>45.2</td><td>42.9</td><td>25.7</td><td>8.2</td></tr><tr><td></td><td></td><td></td><td></td><td>31.7</td><td>30.4</td><td>16.5</td><td>4.8</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.498,
+                0.443,
+                0.894,
+                0.514
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablation studies on the BDD100K dataset. The last row represents the base Mean-Teacher network. Methods are referred to as, C: Two-Phase Consistency, NA: NightAug, SS: StudentScaling, DC: Domain Classifier. API, APm, and APs represent the AP of large, medium and small objects respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.531,
+                0.892,
+                0.605
+            ],
+            "angle": 0,
+            "content": "tures, the teacher has less information to distil to the student. This is demonstrated in Figure 6 where the domain classifier (dotted purple) initially performs well. But as training continues, our method (solid red) is able to surpass its performance."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.624,
+                0.619,
+                0.639
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.65,
+                0.892,
+                0.848
+            ],
+            "angle": 0,
+            "content": "Our proposed framework, 2PCNet, presents a novel solution to the challenges of day-to-night domain adaptive object detection. With our Two-Phase Consistency approach, we are able to effectively leverage high and low confidence knowledge for the student, while mitigating error propagation commonly present in previous student-teacher methods. We further address issues arising from small scale and dark objects through the use of student-scaling and NightAug, respectively. Experimental results on the e BDD100K [36] and SHIFT [25] datasets demonstrate that 2PCNet outperforms existing state-of-the-art methods. Overall, our proposed framework provides an effective and efficient solution for day-to-night domain adaptive object detection."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.5,
+                0.871,
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+            ],
+            "angle": 0,
+            "content": "Acknowledgements This work is partially supported by MOE2019-T2-1-130."
+        },
+        {
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2023/2PCNet_ Two-Phase Consistency Training for Day-to-Night Unsupervised Domain Adaptive Object Detection/818b1ea7-c7c2-488e-9c91-78c9a94fffa2_origin.pdf

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2023/2PCNet_ Two-Phase Consistency Training for Day-to-Night Unsupervised Domain Adaptive Object Detection/full.md

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+# 2PCNet: Two-Phase Consistency Training for Day-to-Night Unsupervised Domain Adaptive Object Detection
+
+Mikhail Kennerley $^{1,2}$ , Jian-Gang Wang $^{2}$ , Bharadwaj Veeravalli $^{1}$ , and Robby T. Tan $^{1}$ $^{1}$ National University of Singapore, Department of Electrical and Computer Engineering  
+ $^{2}$ Institute for Infocomm Research, A*STAR  
+mikhailk@u.nus.edu, jgwang@i2r.a-star.edu.sg, elebv@nus.edu.sg, robby.tan@nus.edu.sg
+
+# Abstract
+
+Object detection at night is a challenging problem due to the absence of night image annotations. Despite several domain adaptation methods, achieving high-precision results remains an issue. False-positive error propagation is still observed in methods using the well-established student-teacher framework, particularly for small-scale and low-light objects. This paper proposes a two-phase consistency unsupervised domain adaptation network, 2PCNet, to address these issues. The network employs high-confidence bounding-box predictions from the teacher in the first phase and appends them to the student's region proposals for the teacher to re-evaluate in the second phase, resulting in a combination of high and low confidence pseudo-labels. The night images and pseudo-labels are scaled-down before being used as input to the student, providing stronger small-scale pseudo-labels. To address errors that arise from low-light regions and other night-related attributes in images, we propose a night-specific augmentation pipeline called NightAug. This pipeline involves applying random augmentations, such as glare, blur, and noise, to daytime images. Experiments on publicly available datasets demonstrate that our method achieves superior results to state-of-the-art methods by  $20\%$ , and to supervised models trained directly on the target data.
+
+# 1. Introduction
+
+Nighttime object detection is critical in many applications. However, the requirement of annotated data by supervised methods is impractical, since night data with annotations is few, and supervised methods are generally prone to overfitting to the training data. Among other reasons, this scarcity is due to poor lighting conditions which makes nighttime images hard to annotate. Hence, methods that
+
+![](images/5263fe911ce1f0a867c50db1a23864721ae578206f0864dbf948d76be7debed0.jpg)  
+DA Faster-RCNN
+
+![](images/2e63e3fe63bff5506f7606feab4b1ad88b1cbdc1709be968f5f988018d6f6771.jpg)  
+UMT
+
+![](images/350b7bd91271c7942627218e0872edb02ac1007c41555ba9accbebbb4a8b99d5.jpg)  
+AT  
+Figure 1. Qualitative results of state-of-the-art DA methods, DA Faster-RCNN [3], UMT [7], Adaptive Teacher (AT) [15] and our method 2PCNet on the BDD100K [36] dataset. Unlike the SOTA methods, our method is able to detect dark and small scale objects with minimal additional false positive predictions.
+
+![](images/53f055484860341fb6f8bbfbf09bbdc6bb26422bdf984c4ac17b1fca1945835d.jpg)  
+2PCNet (Ours)
+
+do not assume the availability of the annotations are more advantageous. Domain adaptation (DA) is an efficient solution to this problem by allowing the use of readily available annotated source daytime datasets.
+
+A few domain adaptation methods have been proposed, e.g., adversarial learning which uses image and instance level classifiers [3] and similar concepts [22, 32]. However, these methods isolate the domain adaptation task purely towards the feature extractor, and suppress features of the target data for the sake of domain invariance. Recent unsupervised domain adaptation methods exploit the studentteacher framework (e.g. [1,7,11,15]). Since the student initially learns from the supervised loss, there is a bias towards the source data. Augmentation [7, 11] and adversarial learning [15] have been proposed to address this problem. Unfortunately, particularly for day-to-night unsupervised domain adaptation, these methods suffer from a large num
+
+ber of inaccurate pseudo-labels produced by the teacher. In our investigation, the problem is notably due to insufficient knowledge of small scale features in the nighttime domain, which are then propagated through the learning process between the teacher and student, resulting in poor object detection performance.
+
+To address the problem, in this paper, we present 2PC-Net, a two-phase consistency unsupervised domain adaptation network for nighttime object detection. Our 2PCNet merges the bounding-boxes of highly-confident pseudolabels, which are predicted in phase one, together with regions proposed by the student's region proposal network (RPN). The merged proposals are then used by the teacher to generate a new set of pseudo-labels in phase two. This provides a combination of high and low confidence pseudolabels. These pseudo-labels are then matched with predictions generated by the student. We can then utilise a weighted consistency loss to ensure that a higher weightage of our unsupervised loss is based on stronger pseudo-labels, yet allow for weaker pseudo-labels to influence the training.
+
+Equipped with this two-phase strategy, we address the problem of errors from small-scale objects. We devise a student-scaling technique, where night images and their pseudo-labels for the student are deliberately scaled down. In order to generate accurate pseudo-labels, images to the teacher remain at their full scale. This results in the pseudolabels of larger objects, which are easier to predict, to be scaled down to smaller objects, allowing for an increase in small scale performance of the student.
+
+Nighttime images suffer from multiple complications not found in daytime scenes such as dark regions, glare, prominent noise, prominent blur, imbalanced lighting, etc. All these cause a problem, since the student, which was trained on daytime images, is much more biased towards the daytime domain's characteristics. To mitigate this problem, we propose NightAug, a set of random nighttime specific augmentations. NightAug includes adding artificial glare, noise, blur, etc. that mimic the night conditions to daytime images. With NightAug we are able to reduce the bias of the student network towards the source data without resulting in adversarial learning or compute-intensive translations. Overall, using 2PCNet, we can see the qualitative improvements of our result in Figure 1. In summary, the contributions of this paper are as follows:
+
+- We present 2PCNet, a two-phase consistency approach for student-teacher learning. 2PCNet takes advantage of highly confident teacher labels augmented with less confident regions, which are proposed by the scaled student. This strategy produces a sharp reduction of the error propagation in the learning process.  
+- To address the bias of the student towards the source domain, we propose NightAug, a random night spe
+
+cific augmentation pipeline to shift the characteristics of daytime images toward nighttime.
+
+- The effectiveness of our approach has been verified by comparing it with the state-of-the-art domain adaptation approaches. An improvement of  $+7.9\mathrm{AP}(+20\%)$  and  $+10.2\mathrm{AP}(26\%)$  over the SOTA on BDD100K and SHIFT has been achieved, respectively.
+
+# 2. Related Work
+
+Unsupervised Domain Adaptation (UDA) Unsupervised domain adaptation aims to learn transferable features to reduce the discrepancy between a labelled source and unlabelled target domain. Previous works minimised the distance metric (MMD) [16-18] and considered intra-class and inter-class discrepancy [12, 13]. Adversarial feature learning involved adding an adversarial classifier to play the min-max game between the domain discriminator and feature extractors to generate a domain invariant feature map [27, 28, 37]. These methods have been applied to image classification. Our work focuses on object detection, which is more complex as it involves identifying multiple bounding boxes and associated classes in each image.
+
+UDA for Object Detection Object detection with UDA is a recent challenge due to the complexities of identifying multiple objects in an image. DA-Faster RCNN [3] integrated adversarial learning with image and instance level classifiers, and several approaches have been proposed to improve on this method by introducing scale-awareness [4], class specific discriminators [31], and re-purposing the task-specific classifier as a discriminator [2]. The Mean Teacher (MT) framework [26] has been adopted in semi-supervised methods, such as UMT [7], which incorporates CycleGAN [39] augmented images; AT [15], which combines the student-teacher framework with adversarial learning; and TDD [11], which uses dual student-teacher networks with style transfer.
+
+Nighttime UDA The majority of research on unsupervised domain adaptation (UDA) in nighttime scenarios has focused on semantic segmentation [5, 8, 9, 14, 23, 29, 33]. Translation and style transformation techniques are commonly used to reduce the domain gap between the source and target domains in these methods [8,29,33]. Some UDA-based techniques for nighttime also utilise paired-images to generate a shared feature space [23], while others use an intermediate domain such as twilight to reduce the domain gap during unsupervised learning [5].
+
+Nighttime tracking has also been investigated where adversarial transformers are used to close the domain gap [35]. However, there is a gap in research when it comes to applying UDA techniques in the object detection task for night-
+
+![](images/d79fc3147efb095c9d9a480464ef2004c703c1cc7d2c0b76ce09ed2f1902d44e.jpg)  
+Figure 2. Overview of our proposed framework, 2PCNet. 2PCNet consists of: A student network is trained on both the labelled daytime image, which has been augmented with NightAug, and unlabelled nighttime images. A teacher network which is the exponential moving average (EMA) of the student and provides matched pseudo-labels for unsupervised loss. The match pseudo-labels are the predictions of the teacher (phase two) using the RPN proposals of the student, which in turn was guided by the high confidence pseudo-labels of the teacher (phase one).
+
+time scenarios. Therefore, we explore the application of UDA techniques in object detection under low-light and nighttime conditions.
+
+# 3. Proposed Method
+
+Let  $\mathbf{D}_s$  be the daytime source data.  $\mathbf{D}_s = \{I_s, C_s, B_s\}$ , where the variables refer to the image, class label and bounding-box label, respectively. Index  $s$  indicates the daytime source. The night target data is represented by  $\mathbf{D}_t$ , where  $\mathbf{D}_t = \{I_t\}$  as we do not have the target labels available to us. Index  $t$  indicates the nighttime target.
+
+The architecture of our 2PCNet is shown in Figure 2. Our 2PCNet consists of a student and a teacher network. The student is a multi-domain network trained on both labelled daytime images, augmented with NightAug, and unlabelled nighttime images. The teacher focuses on night images to produce pseudo-labels for the student and is the exponential moving average (EMA) of the student. After an initial pretraining phase, the teacher begins producing pseudo-labels, which allows the student to initialise the feature extractor and detector.
+
+During each iteration, in phase one of 2PCNet, the teacher produces pseudo-labels from the night images. These pseudo-labels are filtered through a confidence
+
+threshold. This is to ensure only high-confidence pseudolabels are given to the student. The bounding-boxes from the pseudo-labels are then combined with the region proposals generated by the student's RPN. The merged region proposals are then used to generate predictions from the student's RoI network. In phase two, the teacher utilises the same merged region proposals to generate a matched set of pseudo-labels, where each pseudo-label has its corresponding prediction obtained from the student.
+
+As mentioned earlier, our student network is initialised by pretraining for a set number of iterations. This is done with supervised loss on the augmented daytime images:
+
+$$
+L _ {\sup } = L _ {\operatorname {r p n}} \left(B _ {s}, I _ {s}\right) + L _ {\operatorname {r o i}} \left(B _ {s}, C _ {s}, I _ {s}\right), \tag {1}
+$$
+
+where  $L_{\mathrm{rpn}}$  represents the loss from the RPN, which consists of an objectness and bounding-box regression loss.  $L_{\mathrm{roi}}$  represents the loss from the detector network, consisting of a classification and bounding-box regression loss.
+
+Once the pretraining is completed, the student's weights are then transferred over to the teacher. In the succeeding iterations, the teacher's weights are the exponential moving average (EMA) of the student's. The matched pseudo-labels generated by the teacher,  $\{C_p^*, B_p^*\}$ , are then used to guide
+
+![](images/c67cd0ceb3844b100df47930828639c1f30a507ba48e45e37211aff677e01841.jpg)  
+Figure 3. (Left to Right, Top to Bottom) Ground truth bounding boxes, bounding boxes predicted by the teacher with non-maximal suppression (NMS) and thresholding  $(B_{p})$ , bounding boxes predicted by the student  $(B_{\mathrm{student}})$  which is guided by  $B_{p}$ , and the bounding boxes predicted by the teacher  $(B_{p}^{*})$  for the consistency loss.
+
+![](images/19d2798780ffd2eaa87261a168fdf6db1a82fe1e65293999ac403404e0f935dc.jpg)
+
+the unsupervised loss, defined as:
+
+$$
+L _ {\text {u n s u p}} = L _ {\text {r p n}} ^ {\text {o b j}} \left(C _ {p} ^ {*}; I _ {t}\right) + L _ {\text {c o n s}} \left(C _ {p} ^ {*}; I _ {t}\right), \tag {2}
+$$
+
+where  $L_{\mathrm{rpn}}^{\mathrm{obj}}$  is the objectness loss of the RPN and  $L_{\mathrm{cons}}$  is the weighted KL-Divergence loss from the predicted outputs which we will further explain in the next section.
+
+# 3.1. Two-Phase Consistency
+
+Due to the large domain gap between daytime source images and nighttime target images, the teacher is unable to produce high quality pseudo-labels. This generally occurs in the whole scene, but particularly for regions with strong night characteristics, e.g., low-light, glare, uneven lighting, etc. The teacher produces confident pseudo-labels only for regions that share more similarities to the daytime, since it is biased towards the daytime domain. This bias poses a problem for methods that employ a hard-threshold to filter pseudo-labels for categorical cross-entropy loss [7, 15, 26]. The remaining pseudo-labels contain only easy samples with daytime attributes. Consequently, the student does not learn from harder (e.g. darker) areas.
+
+As a result of minimal knowledge of the hard samples (i.e., areas with a high level of nighttime attributes), the teacher begins to predict highly confident yet incorrect pseudo-labels. As the teacher provides these incorrect pseudo-labels to the student, a viscous cycle starts where the teacher in turn is updated with incorrect knowledge. Consequently, the error continues to propagate through training. In our case, these errors notably occur in dark/glare regions and as small scale objects.
+
+To address the problem of error propagation, we design a two-phase approach that combines high confidence
+
+pseudo-labels together with their less confident counterparts. This combination allows for the high accuracy of confident-labels with the additional knowledge of less confident labels to be distilled onto the student. In phase one, the unlabelled nighttime image,  $I_{t}$ , is used as an input for the teacher to generate pseudo-labels. These pseudo-labels are filtered with a threshold to retain only high-confidence pseudo-labels,  $(C_p, B_p)$ . The bounding-box of the pseudolabels,  $B_{p}$ , is then used as an input to the student.  $B_{p}$  is concatenated to the region proposals generated by the student RPN module:
+
+$$
+P ^ {*} = \operatorname {R P N} _ {\text {s t u d e n t}} \left(I _ {t}\right) \neq B _ {p}, \tag {3}
+$$
+
+where  $P^{*}$  is the combined region proposals, which are then used as an input to the student's RoI module to predict the classes,  $C_{\mathrm{student}}$ , and bounding-box,  $B_{\mathrm{student}}$ , of each region proposal.
+
+Phase two begins by using the same combined region proposals,  $P^{*}$ , generated in phase one as an input to the teachers RoI module to generate a matched set of pseudolabels:
+
+$$
+\left\{C _ {p} ^ {*}, B _ {p} ^ {*} \right\} = \operatorname {R o I} _ {\text {t e a c h e r}} \left(P ^ {*}\right). \tag {4}
+$$
+
+The difference between  $C_p$  and  $C_p^*$  is that  $C_p^*$  is derived from the same region proposals as that of the student predictions  $C_{\mathrm{student}}$ . This allows us to compare  $C_{\mathrm{student}}$  and  $C_p^*$  directly:
+
+$$
+\begin{array}{l} \left\{C _ {\text {s t u d e n t}} (n), B _ {\text {s t u d e n t}} (n) \right\} = \operatorname {R o I} _ {\text {s t u d e n t}} \left(P ^ {*} (n)\right), \tag {5} \\ \left\{C _ {p} ^ {*} (n), B _ {p} ^ {*} (n) \right\} = \operatorname {R o I} _ {\text {t e a c h e r}} \left(P ^ {*} (n)\right), \\ \end{array}
+$$
+
+where  $n = \{1,2,\dots,N\}$  and  $N$  is the number of region proposals in  $P^*$ . This operation ensures that the knowledge of highly confident predictions generated by the teacher is distilled through to the student. In addition, information from less confident predictions can also be learnt. However, we are still required to penalise less confident samples and thus employ weighed KL-Divergence to be used as our consistency loss:
+
+$$
+L _ {\text {c o n s}} = \alpha \operatorname {K L} \left(C _ {\text {s t u d e n t}}, C _ {p} ^ {*}\right), \tag {6}
+$$
+
+where  $\alpha$  is the highest confidence of  $C_p^*$  expressed as  $\alpha = \max(C_p^*)$ ; KL() is the KL-divergence function. Note that, pseudo-bounding boxes are not used to generate unsupervised loss, as the confidence score of each pseudo-label represents the class information rather than the bounding box. The outputs of each segment of our two-phase approach are shown in Figure 3.
+
+# 3.2. Student-Scaling
+
+In our investigation, we have found that scales of objects have a strong influence on object detection at night. This
+
+Algorithm 1 Single Augmentation - NightAug  
+imgClean  $\leftarrow$  img   
+if randFloat  $\geq 0.5$  then randFloat  $\leftarrow 0.8*$  randFloat  $+0.2$  img  $\leftarrow$  augmentation(img, randval) prob  $\leftarrow 0.4$  while randFloat  $\geq$  prob do  $x\gets$  randInt(img.shape[1],2)  $y\gets$  randInt(img.shape[2],2) img[x,y]  $\leftarrow$  imgClean[x,y] prob  $\leftarrow$  prob +0.1 end while   
+end if
+
+is due to the features of smaller objects being easily overwhelmed by glare or noise. To allow the student to overcome this, we apply scaling augmentation to the student's inputs which includes both the image and the pseudo-labels generated by the teacher. As training proceeds, we follow a schedule to increase the scale of the student augmentation until it equals to that of the original image. By iteratively increasing the scale we allow the student to focus on smaller features earlier in the training process. This process encourages the teacher to make more accurate predictions on smaller scale objects in the later stages of training. In turn, accurate small scale pseudo-labels allow for the increase in the scale of the student's inputs with minimal errors due to scale.
+
+To ensure the knowledge of the previous scales is not forgotten, a gaussian function for the scaling factor is applied. The norm of the Gaussian function is obtained from the schedule values. To prevent additional noise due to pseudo-labels being too small, labels that has an area below a threshold are removed.
+
+# 3.3. NightAug
+
+Night images suffer from a range of complications that are not present in daytime scenes. This causes a problem in the student-teacher framework, where the student would be biased towards the source domain. Previous methods have attempted to address this, but have either required compute-intensive translations [7, 11] or adding additional domain classifiers to the framework [15] which complicates training. We propose NightAug, a nighttime specific augmentation pipeline that is compute-light and does not require training. NightAug consists of a series of augmentations with the aim of steering the characteristics of daytime images to resemble that of a nighttime image.
+
+The defining features of nighttime images are that they are darker and have lower contrast than daytime images. In addition the signal-to-night ratio (SNR) could be higher due to the properties of digital cameras such as luminance and
+
+![](images/44477bcfe46dd0b404ebc19a5eabcfb95708b6ebf6fb6883592a6a5e4c257b7b.jpg)  
+Figure 4. NightAug: Original image (top-left) and images with random augmentations from: gaussian blur, gamma correction, brightness, contrast, glare, gaussian noise and random cut-outs.
+
+![](images/28b82fb10b3a24991f39d715a100a831e46d1756277035c6f05cde59023c911f.jpg)
+
+colour noise. Glare and glow from street lamps and headlights are also present in nighttime images. Additionally, images may be out-of-focus due to the cameras inability to detect reference points to focus on in dark environments.
+
+Keeping in mind the properties of nighttime images, our NightAug includes random; brightness, contrast, gamma, gaussian noise, gaussian blur augmentations and random glare insertion. The augmentations are randomly applied to the images and are also random in intensity. This randomness results in a wider variance of images that are exposed to the student leading to more robust training [30]. To further increase the variance of the images, at each augmentation step, random segments of the image will ignore the application of that augmentation. This allows for the representation where different areas of nighttime images may be unevenly lighted. This uneven lighting affects the above characteristics of the local region.
+
+A single augmentation flow of NightAug is demonstrated in Algorithm 1. Samples of an image processed with NightAug are shown in Figure 4. Each augmentation has a set probability of being applied, with the strength of the augmentation being random. Random regions of the augmented image may then be replaced with that of the original image. The probability of this region replacement reduces with each iteration.
+
+Overall Loss Our total loss can be represented as:
+
+$$
+L _ {\text {t o t a l}} = L _ {\sup } + \lambda L _ {\text {u n s u p}}, \tag {7}
+$$
+
+where  $\lambda$  represents a weight factor for the unsupervised loss, and is set experimentally.  $L_{\mathrm{sup}}, L_{\mathrm{unsup}}$  refer to Eq. (1) and Eq. (2), respectively.
+
+<table><tr><td>Method</td><td>AP</td><td>Pedestrian</td><td>Rider</td><td>Car</td><td>Truck</td><td>Bus</td><td>Motorcycle</td><td>Bicycle</td><td>TrafficLight</td><td>TrafficSign</td></tr><tr><td>Lower-Bound</td><td>41.1</td><td>50.0</td><td>28.9</td><td>66.6</td><td>47.8</td><td>47.5</td><td>32.8</td><td>39.5</td><td>41.0</td><td>56.5</td></tr><tr><td>Upper-Bound</td><td>46.2</td><td>52.1</td><td>35.0</td><td>73.6</td><td>53.5</td><td>54.8</td><td>36.0</td><td>41.8</td><td>52.2</td><td>63.3</td></tr><tr><td>DA F-RCNN [3]</td><td>41.3</td><td>50.4</td><td>30.3</td><td>66.3</td><td>46.8</td><td>48.3</td><td>32.6</td><td>41.4</td><td>41.0</td><td>56.2</td></tr><tr><td>TDD [11]</td><td>34.6</td><td>43.1</td><td>20.7</td><td>68.4</td><td>33.3</td><td>35.6</td><td>16.5</td><td>25.9</td><td>43.1</td><td>59.5</td></tr><tr><td>UMT [7]</td><td>36.2</td><td>46.5</td><td>26.1</td><td>46.8</td><td>44.0</td><td>46.3</td><td>28.2</td><td>40.2</td><td>31.6</td><td>52.7</td></tr><tr><td>AT [15]</td><td>38.5</td><td>42.3</td><td>30.4</td><td>60.8</td><td>48.9</td><td>52.1</td><td>34.5</td><td>42.7</td><td>29.1</td><td>43.9</td></tr><tr><td>2PCNet (Ours)</td><td>46.4</td><td>54.4</td><td>30.8</td><td>73.1</td><td>53.8</td><td>55.2</td><td>37.5</td><td>44.5</td><td>49.4</td><td>65.2</td></tr></table>
+
+Table 1. Results of day-to-night domain adaptation on the BDD100K dataset, the Average Precision (AP) of all classes are reported. Faster RCNN detector with ResNet-50 feature extractor is used for all experiments to ensure a fair comparison. Faster RCNN is used as the lower-bound and upper-bound and is trained on labelled daytime and nighttime data respectively. The lower-bound provides a baseline without any domain adaptation while the upper-bound is fully supervised, the case where labelled target night data is available.  
+
+<table><tr><td>Method</td><td>APcoco</td><td>Car</td><td>Bus</td><td>Truck</td></tr><tr><td>Lower-Bound</td><td>22.1</td><td>37.5</td><td>29.8</td><td>30.7</td></tr><tr><td>Upper-Bound</td><td>23.9</td><td>42.0</td><td>33.8</td><td>35.0</td></tr><tr><td>FDA [34]</td><td>22.6</td><td>38.5</td><td>37.2</td><td>23.2</td></tr><tr><td>ForkGAN [38]</td><td>22.9</td><td>41.2</td><td>33.3</td><td>32.1</td></tr><tr><td>2PCNet (Ours)</td><td>23.5</td><td>40.7</td><td>38.2</td><td>35.0</td></tr></table>
+
+Table 2. Comparison of our framework, 2PCNet, with image-to-image (I2I) translation methods. Conducted on the BDD100K dataset. ForkGan and FDA are used for comparison. Reported  $AP_{coco}$  is the averaged AP over IoUs 0.5 to 0.95.
+
+# 4. Experiments
+
+# 4.1. Baselines
+
+To evaluate our method, we compare our approach with SOTA methods in domain adaptation for object detection. These include DA-Faster RCNN [3], TDD [11], UMT [7], AT [15] as well as a non-DA baseline Faster-RCNN [21]. Faster-RCNN is used as both our lower and upper-bound, where it is trained on labelled source and target data respectively. We additionally compare our approach with image-to-image translation methods, ForkGAN [38] and FDA [34]. Translation methods are trained on Faster RCNN with both the daytime and translated images.
+
+# 4.2. Datasets
+
+The majority of existing nighttime datasets either focuses on semantic segmentation which do not provide labels for object detection [5, 23, 24], or contains very few classes [19, 20]. BDD100K [36] was selected as it provides object detection labels which includes a wide range of classes (10). It also has a large number of images compared to other DA datasets covering daytime, nighttime and other adverse conditions.
+
+The SHIFT [25] dataset is a recent simulated driving dataset that contains scenes in various environments. A continuous shift of these environments is available. SHIFT contains 6 class labels that share similarities to the BDD100K classes. For our evaluation, we use images with the 'day' and 'night' label as our source and target data respectively. We further ensure that the weather tag is 'clear' to isolate other weather conditions from the evaluation.
+
+# 4.3. Implementation
+
+Following previous SOTA methods, we employ Faster-RCNN [21] as our base detection model and ResNet-50 [10] pretrained on ImageNet [6] as our feature extractor. All images are scaled by resizing its shorter side to 600 pixels. For student-scaling we set a schedule for (0.57, 0.64, 0.71, 0.78, 0.85, 0.92) of the maximum iterations at scales (0.5, 0.6, 0.7, 0.8, 0.9, 1.0). Loss hyperparameters are set at  $\lambda = 0.3$  and the rate smooth coefficient parameter of the EMA is 0.9996. A confidence threshold of 0.8 for phase one of Two-Phase Consistency. For the initial pretraining of the student model, we train the student for 50k and 20k iterations on the source images, for BDD100K and SHIFT respectively. Supervised inputs are daytime images with and without NightAug. We then copy the weights to the teacher and continue training with the addition of unsupervised loss for an additional 50k iterations. The learning rate is kept at 0.04 throughout training. Our network is trained on 3 RTX3090 GPUs with a batch-size of 6 source and 6 target images.
+
+# 4.4. Comparison to SOTA
+
+Comparison on BDD100K We compare our method against the SOTA on real driving scenes and evaluating their domain adaptation performance on nighttime images, the results of this experiment can be seen on Table 1. The results show that our method achieves the highest perfor
+
+![](images/260a68fcdf8a6dfda8ed4d951a9e734559f34114dc70c808af48e92e2eeabd0c.jpg)  
+Figure 5. Qualitative results of Faster RCNN, Adaptive Teacher (AT) and our method on the SHIFT dataset with the ground-truth on the far right. We can observe that Faster RCNN is not able to detect objects due to absence of domain adaptation, while AT has a large number of small false positive bounding boxes compared to our method which closely resembles that of the ground-truth.
+
+![](images/fa1c9a5062df328949db62faac6c53ac246b0a74b845931868e4ae6e10da8b1d.jpg)
+
+![](images/118d34ec49e84b21fdf24b602e2d317adbad87c2f07af0c8f63bcb2c7fe80499.jpg)
+
+![](images/85899240049ff1fc50d9929c44f154e9f808a51c616d22cd1432f4ba874464f8.jpg)
+
+![](images/52216da15ee92e9d03f9f345c2ca5f962ae1e5bd73a17eec5bd7ac074b3d2650.jpg)
+
+<table><tr><td>Method</td><td>AP</td><td>Per.</td><td>Car</td><td>Truck</td><td>Bus</td><td>Mcy.</td><td>Bcy.</td></tr><tr><td>Lower-Bound</td><td>41.6</td><td>40.4</td><td>44.5</td><td>49.9</td><td>53.7</td><td>14.3</td><td>46.7</td></tr><tr><td>Upper-Bound</td><td>47.0</td><td>49.7</td><td>51.5</td><td>56.0</td><td>53.6</td><td>19.2</td><td>52.4</td></tr><tr><td>DA FR [3]</td><td>43.7</td><td>43.0</td><td>48.8</td><td>47.8</td><td>52.1</td><td>19.9</td><td>55.8</td></tr><tr><td>UMT [7]</td><td>31.1</td><td>7.7</td><td>47.5</td><td>18.4</td><td>46.8</td><td>16.6</td><td>49.2</td></tr><tr><td>AT [15]</td><td>38.9</td><td>25.8</td><td>33.0</td><td>54.7</td><td>49.5</td><td>20.7</td><td>52.3</td></tr><tr><td>2PCNet (Ours)</td><td>49.1</td><td>51.4</td><td>54.6</td><td>54.8</td><td>56.6</td><td>23.9</td><td>54.2</td></tr></table>
+
+Table 3. Results of Day-to-Night domain adaptation on the SHIFT dataset. The Average Precision (AP) of all classes. Faster RCNN is used as the lower-bound and upper-bound and is trained on labelled daytime and nighttime data respectively.
+
+mance with an AP of 46.4.  $20.5\%$  higher than that of the SOTA student-teacher methods and above that of the upper-bound. We have observed in experiments that student-teacher methods underperforms with an AP below that of the lower-bound due to the error-propagation from noisy pseudo-labels. The result of the error is small false positive detections as seen in Figure 1. Our method does not suffer from the same allowing for higher performance. We can also observe that our method performs well across all classes. Even when compared with the upper-bound, 2PC-Net achieves higher AP on the majority of classes. This indicates that our method is able to generalise well across large and small classes.
+
+The comparison with image-to-image translation methods is shown in Table 2. Translation methods do not suffer from the error propagation problem as it is trained on Faster RCNN without a teacher. Even so, we can see that our method outperforms SOTA adverse vision translation
+
+methods.
+
+Comparison on SHIFT To further compare our method with SOTA we evaluate on the SHIFT simulation dataset. Due to the nature of the simulated data, many nighttime image characteristics that we have previously mention is not exhibited in this data such as blurriness, noise and glare.
+
+The results of this experiments are shown in Table 3. We can observe that previous SOTA methods that use the student-teacher framework perform worse than the lower-bound. The sub-par performance is again due to the error-propagation problem. AT performs better than UMT due to ATs inclusion of adversarial learning. However, adversarial learning is not enough to mitigate this problem. We can see that the performance of DA FRCNN outperforms both the SOTA student-teacher methods as it would not be affected by error-propagation. It is however, still largely below the upper-bound performance. 2PCNet outperforms these previous methods as well as the upperbound. We achieve an improvement of  $+10.2$  AP over previous SOTA student-teacher methods and  $+2.1$  AP over that of the upper-bound.
+
+# 4.5. Ablation Studies
+
+To demonstrate the effectiveness of each of our components, we train several models for 100K iterations and evaluate them on the BDD100K dataset. We present our findings in Table 4.
+
+Two-Phase Consistency We can observe in Table 4 that the addition of Two-Phase Consistency (C) demonstrated a wide performance gap when compared to the Mean-Teacher baseline, +13.5 AP (43%). This improvement in AP ex
+
+![](images/808250427ec14cf82c8ac96e883ffd23fd2c6af9f58f5aeface3c8be797b87c7.jpg)  
+Figure 6. Training curve on BDD100K dataset ablation study. We show the overall AP training curve as well as the AP of large, medium and small objects. MT represents the base Mean Teacher framework. It can be seen that at all scales, the absence of Two-Phase Consistency (C) results in a sharp drop during training. We can also see that with the inclusion of NightAug (NA) and student-scaling (SS) the gradient of the curve increases. We note that the inclusion of a domain classifier (DC) reduces the performance at all scales.
+
+![](images/b6705329c2169a0416d90e84e815498b1f0bfb53c6481a403cfb48ec48081d07.jpg)
+
+![](images/35530a358b9d008ad8b061628ac5c0ae9f9d1b58dc0f9a7ef67087c3e74bd327.jpg)
+
+![](images/6e1f6579437a259fb07456dba92adee7672ddce723d1501354e0dc90cdc44b74.jpg)
+
+ists across large, medium and small objects. While the performance of MT is initially strong, it rapidly begins to decline; which can be observed in Figure 6. This drop in performance is due to the error propagation of noisy pseudolabels. The experimental results show that Two-Phase Consistency is able to provide a solution. This ensures that highly confident pseudo-labels are bounded by less confident pseudo-label enabling a balance of knowledge into the student.
+
+NightAug We benched marked the effectiveness of NightAug in our framework as shown in Table 4. The inclusion of NightAug increases the detection performance of small objects with an increase of  $5\%$ . Additionally, the gradient of the training performance remains steep as seen in Figure 6. The positive gradient is displayed most strongly for APm and APs where objects are more prone to nighttime specific complications.
+
+Student-Scaling Our final component, student-scaling, is included into the framework and the results can be seen in Table 4. We can observe that student-scaling is able to boost the performance of small object detection by  $6\%$ . This boost in performance is due to the student network focusing on smaller object earlier in the training process. We note that the performance of large objects have dropped by  $1 - 2\%$ ; however when referring to the training curves in Figure 6, API remains steep. As the initial focus is on smaller objects, less time is allocated to larger objects during training. This can be mitigated by lengthening training resulting in more iterations for larger objects.
+
+Domain Classifier To conclude our study, we included a domain classifier into our network. Adversarial learning is a widely used DA technique; however when added into 2PCNet, a performance drop across all scales can be seen. This drop is shown in Table 4. The suppression of nighttime features is suspected to be the cause. Suppression is present as the adversarial loss guides the feature extractor to maintain domain invariance. By suppressing nighttime fea
+
+<table><tr><td colspan="4">Methods</td><td colspan="4"></td></tr><tr><td>C</td><td>NA</td><td>SS</td><td>DC</td><td>AP</td><td>API</td><td>APm</td><td>APs</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td></td><td>46.4</td><td>41.7</td><td>25.8</td><td>9.1</td></tr><tr><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>44.5</td><td>41.6</td><td>25.0</td><td>8.3</td></tr><tr><td>✓</td><td>✓</td><td></td><td></td><td>45.8</td><td>42.2</td><td>25.7</td><td>8.6</td></tr><tr><td>✓</td><td></td><td></td><td></td><td>45.2</td><td>42.9</td><td>25.7</td><td>8.2</td></tr><tr><td></td><td></td><td></td><td></td><td>31.7</td><td>30.4</td><td>16.5</td><td>4.8</td></tr></table>
+
+Table 4. Ablation studies on the BDD100K dataset. The last row represents the base Mean-Teacher network. Methods are referred to as, C: Two-Phase Consistency, NA: NightAug, SS: StudentScaling, DC: Domain Classifier. API, APm, and APs represent the AP of large, medium and small objects respectively.
+
+tures, the teacher has less information to distil to the student. This is demonstrated in Figure 6 where the domain classifier (dotted purple) initially performs well. But as training continues, our method (solid red) is able to surpass its performance.
+
+# 5. Conclusion
+
+Our proposed framework, 2PCNet, presents a novel solution to the challenges of day-to-night domain adaptive object detection. With our Two-Phase Consistency approach, we are able to effectively leverage high and low confidence knowledge for the student, while mitigating error propagation commonly present in previous student-teacher methods. We further address issues arising from small scale and dark objects through the use of student-scaling and NightAug, respectively. Experimental results on the e BDD100K [36] and SHIFT [25] datasets demonstrate that 2PCNet outperforms existing state-of-the-art methods. Overall, our proposed framework provides an effective and efficient solution for day-to-night domain adaptive object detection.
+
+Acknowledgements This work is partially supported by MOE2019-T2-1-130.
+
+# References
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+        "type": "text",
+        "text": "3D Cinemagraphy from a Single Image",
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+        "type": "text",
+        "text": "Xingyi Li $^{1,3}$  Zhiguo Cao $^{1}$  Huiqiang Sun $^{1}$  Jianming Zhang $^{2}$  Ke Xian $^{3*}$  Guosheng Lin $^{3}$ $^{1}$ Key Laboratory of Image Processing and Intelligent Control, Ministry of Education School of Artificial Intelligence and Automation, Huazhong University of Science and Technology  \n $^{2}$ Adobe Research  $^{3}$ S-Lab, Nanyang Technological University  \n{xingyi.li, zgcao, shq1031}@hust.edu.cn, jianmzha@adobe.com, {ke.xian, gslin}@ntu.edu.sg  \nhttps://xingyi-li.github.io/3d-cinemagraphy",
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+        "img_path": "images/77e45a8a8ae99f7e5122bf60ba50833109c19c4ad4f2de0de9320aca1eab8f4b.jpg",
+        "image_caption": [
+            "Figure 1. Given a single still image, our method can synthesize videos with plausible animation of the scene while allowing camera movements. Here, we showcase four 3D cinematographs with various camera trajectories. Besides real-world photos (the left two examples), our method can also generalize to paintings (the third one) and synthetic images generated by Stable Diffusion [47] (the rightmost one). To see the effect of 3D cinematography, readers are encouraged to view with Adobe Acrobat or KDE Okular."
+        ],
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "We present 3D Cinemagography, a new technique that marries 2D image animation with 3D photography. Given a single still image as input, our goal is to generate a video that contains both visual content animation and camera motion. We empirically find that naively combining existing 2D image animation and 3D photography methods leads to obvious artifacts or inconsistent animation. Our key insight is that representing and animating the scene in 3D space offers a natural solution to this task. To this end, we first convert the input image into feature-based layered depth images using predicted depth values, followed by unprojecting them to a feature point cloud. To animate the scene, we perform motion estimation and lift the 2D motion into the 3D scene flow. Finally, to resolve the problem of hole emergence as points move forward, we propose to bidirectionally displace the point cloud as per the scene flow and synthesize novel views by separately projecting them into target image planes and blending the results. Extensive experiments demonstrate the effectiveness of our method. A user study is also conducted to validate the compelling rendering results of our method.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+            501,
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Nowadays, since people can easily take images using smartphone cameras, the number of online photos has increased drastically. However, with the rise of online video-sharing platforms such as YouTube and TikTok, people are no longer content with static images as they have grown accustomed to watching videos. It would be great if we could animate those still images and synthesize videos for a better experience. These living images, termed cinematographs, have already been created and gained rapid popularity online [1, 71]. Although cinematographs may engage people with the content for longer than a regular photo, they usually fail to deliver an immersive sense of 3D to audiences. This is because cinematographs are usually based on a static camera and fail to produce parallax effects. We are therefore motivated to explore ways of animating the photos and moving around the cameras at the same time. As shown in Fig. 1, this will bring many still images to life and provide a drastically vivid experience.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we are interested in making the first step towards 3D cinematography that allows both realistic animation of the scene and camera motions with compelling parallax effects from a single image. There are plenty of attempts to tackle either of the two problems. Single-image animation methods [12, 19, 35] manage to produce a real-",
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+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
+            236,
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+    {
+        "type": "page_footnote",
+        "text": "*Corresponding author.",
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+    {
+        "type": "page_number",
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+    {
+        "type": "text",
+        "text": "istic animated video from a single image, but they usually operate in 2D space, and therefore they cannot create camera movement effects. Classic novel view synthesis methods [5, 6, 9, 14, 25] and recent implicit neural representations [37, 40, 58] entail densely captured views as input to render unseen camera perspectives. Single-shot novel view synthesis approaches [21, 39, 52, 66] exhibit the potential for generating novel camera trajectories of the scene from a single image. Nonetheless, these methods usually hypothesize that the observed scene is static without moving elements. Directly combining existing state-of-the-art solutions of single-image animation and novel view synthesis yields visual artifacts or inconsistent animation.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To address the above challenges, we present a novel framework that solves the joint task of image animation and novel view synthesis. This framework can be trained to create 3D cinematographs from a single still image. Our key intuition is that handling this new task in 3D space would naturally enable both animation and moving cameras simultaneously. With this in mind, we first represent the scene as feature-based layered depth images (LDIs) [50] and unproject the feature LDIs into a feature point cloud. To animate the scene, we perform motion estimation and lift the 2D motion to 3D scene flow using depth values predicted by DPT [45]. Next, we animate the point cloud according to the scene flow. To resolve the problem of hole emergence as points move forward, we are inspired by prior works [3, 19, 38] and propose a 3D symmetric animation technique to bidirectionally displace point clouds, which can effectively fill in those unknown regions. Finally, we synthesize novel views at time  $t$  by rendering point clouds into target image planes and blending the results. In this manner, our proposed method can automatically create 3D cinematographs from a single image. Moreover, our framework is highly extensible, e.g., we can augment our motion estimator with user-defined masks and flow hints for accurate flow estimation and controllable animation.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "In summary, our main contributions are:",
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+        "page_idx": 1
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a new task of creating 3D cinematographs from single images. To this end, we propose a novel framework that jointly learns to solve the task of image animation and novel view synthesis in 3D space.",
+            "- We design a 3D symmetric animation technique to address the hole problem as points move forward.",
+            "- Our framework is flexible and customized. We can achieve controllable animation by augmenting our motion estimator with user-defined masks and flow hints."
+        ],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Single-image animation. Different kinds of methods have been explored to animate still images. Some works [8, 22]",
+        "bbox": [
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+            902
+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "focus on animating certain objects via physical simulation but may not be easily applied to more general cases of inthe-wild photos. Given driving videos as guidance, there are plenty of methods that attempt to perform motion transfer on static objects with either a priori knowledge of moving objects [7, 11, 33, 46, 55] or in an unsupervised manner [53, 54, 56]. They entail reference videos to drive the motion of static objects, and thus do not suit our task. Recent advances in generative models have attracted much attention and motivated the community to develop realistic image and video synthesis methods. Many works [31, 32, 34, 51, 69] are based on generative adversarial networks (GANs) and operate transformations in latent space to generate plausible appearance changes and movements. Nonetheless, it is non-trial to allow for explicit control over those latent codes and to animate input imagery in a disentangled manner. As diffusion models [17, 59] improve by leaps and bounds, several diffusion-based works [16, 18, 57] attempt to generate realistic videos from text or images. However, these methods are time-consuming and expensive in terms of computation. Here we focus on methods that utilize learned motion priors to convert a still image into an animated video texture [12, 13, 19, 29, 35]. In particular, Holynski et al. [19] first synthesize the optical flow of the input image via a motion estimation network, then obtain future frames using the estimated flow field. This method renders plausible animation of fluid elements in the input image but suffers from producing camera motions with parallax.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Novel view synthesis from a single image. Novel view synthesis allows for rendering unseen camera perspectives from 2D images and their corresponding camera poses. Recent impressive synthesis results may credit to implicit neural representations [37, 40, 58]. Nevertheless, these methods usually assume dense views as input, which is not always available in most cases. Moreover, they focus on the task of interpolation given multiple views rather than extrapolation. As such, we instead turn to methods aiming at handling single input. Among them, a number of works [15, 26, 28, 62, 63, 70, 72] infer the 3D structure of scenes by learning to predict a scene representation from a single image. These methods are usually trained end-to-end but suffer from generalizing to in-the-wild photos. Most relevant to our work are those approaches [39, 52, 66] that apply depth estimation [45, 65, 67, 68] followed by inpainting occluded regions. For example, 3D Photo [52] estimates monocular depth maps and uses the representation of layered depth images (LDIs) [43, 50], in which context-aware color and depth inpainting are performed. To enable fine-grained detail modeling, SLIDE [21] decomposes the scene into foreground and background via a soft-layering scheme. However, unlike our approach, these methods usually assume the scene is static by default, which largely lessens the sense of reality, especially when some elements such as",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "4596",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/6c4949f4da65374cd84740c97a37b56fee1a8822d40c3c37efaec7f81ec19bb8.jpg",
+        "image_caption": [
+            "Figure 2. An overview of our method. Given a single still image as input, we first predict a dense depth map. To represent the scene in 3D space, we separate the input image into several layers according to depth discontinuities and apply context-aware inpainting, yielding layered depth images (LDIs)  $\\mathcal{L}$ . We then use a 2D feature extractor to encode 2D feature maps for each inpainted LDI color layer, resulting in feature LDIs  $\\mathcal{F}$ . Subsequently, we lift feature LDIs into 3D space using corresponding depth values to obtain a feature point cloud  $\\mathcal{P}$ . To animate the scene, we estimate a 2D motion field from the input image and apply Euler integration to generate forward and backward displacement fields  $F_{0\\rightarrow t}$  and  $F_{0\\rightarrow t - N}$ . We then augment displacement fields with estimated depth values to obtain 3D scene flow fields. Next, we bidirectionally displace the feature point cloud  $\\mathcal{P}$  as per the scene flow and separately project them into target image planes to obtain  $\\mathbf{F}_f$  and  $\\mathbf{F}_b$ . Finally, we blend them together and pass the result through our image decoder to synthesize a novel view at time  $t$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
+            90,
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+            281
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "a creek or smoke are also captured in the input image.",
+        "bbox": [
+            75,
+            433,
+            433,
+            448
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Space-time view synthesis. Space-time view synthesis is the task of rendering novel camera perspectives for dynamic scenes in terms of space and time [30]. Most of the prior works [2, 4, 27] rely on synchronized multi-view videos as input, which prevents their wide applicability. To mitigate this requirement, many neural rendering approaches [30, 41, 44] manage to show promising space-time view synthesis results from monocular videos. They usually train each new scene independently, and thus cannot directly handle in-the-wild inputs. Most related to our work, 3D Moments [64] introduces a novel 3D photography effect where cinematic camera motion and frame interpolation are simultaneously performed. However, this method demands near-duplicate photos as input and is unable to control the animation results. Instead, we show that our method can animate still images while enabling camera motion with 3D parallax. Moreover, we can also extend our system so that users are allowed to interactively control how the photos are animated by providing user-defined masks and flow hints.",
+        "bbox": [
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+            448,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            76,
+            746,
+            169,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Overview",
+        "text_level": 1,
+        "bbox": [
+            76,
+            771,
+            187,
+            786
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Given a single still image, our goal is to synthesize plausible animation of the scene and simultaneously enable camera motion. The output of our method is a realistic cinematograph with compelling parallax effects. Fig. 2 schematically illustrates our pipeline. Our method starts by estimating a motion field and a depth map from the input image. We then separate the RGBD input into several layers",
+        "bbox": [
+            75,
+            794,
+            468,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "as per depth discontinuities and inpaint occluded regions, followed by extracting 2D feature maps for each layer, resulting in feature LDIs [50]. To enable scene animation, we lift the 2D motion to 3D scene flow and unproject feature LDIs into a feature point cloud using their corresponding depth values. Thereafter, we bidirectionally animate the point cloud with scene flow using our 3D symmetric animation technique. We end up rendering them into two animated feature maps and composite the results to synthesize novel views at time  $t$ .",
+        "bbox": [
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+            433,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Motion Estimation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            599,
+            681,
+            616
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To animate a still image, we wish to estimate the corresponding motion field for the observed scene. Generally, the motion we witness in the real world is extremely complicated as it is time-varying and many events such as occlusion and collision could occur. Intuitively, we could directly adopt prior optical flow estimation methods [10, 20, 60, 61] to accomplish this. However, it is not trivial since they usually take a pair of images as input to compute optical flow. Endo et al. [12] instead propose to learn and predict the motion in a recurrent manner, but this kind of approach is prone to large distortions in the long term. To simplify this, we follow Holynski et al. [19] and assume that a time-invariant and constant-velocity motion field, termed Eulerian flow field, can well approximate the bulk of real-world motions, e.g., water, smoke, and clouds. Formally, we denote  $M$  as the Eulerian flow field of the scene, which suggests that",
+        "bbox": [
+            496,
+            626,
+            893,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nF _ {t \\rightarrow t + 1} (\\cdot) = M (\\cdot), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            627,
+            883,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "4597",
+        "bbox": [
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+            944,
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+            957
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $F_{t\\rightarrow t + 1}(\\cdot)$  represents the optical flow map from frame  $t$  to frame  $t + 1$ . This defines how each pixel in the current frame will move in the future. Specifically, we can obtain the next frame via Euler integration:",
+        "bbox": [
+            75,
+            90,
+            468,
+            151
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {x} _ {t + 1} = \\mathbf {x} _ {t} + M (\\mathbf {x} _ {t}), \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            199,
+            166,
+            468,
+            181
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{x}_t$  represents the coordinates of a pixel  $\\mathbf{x}_t$  at time  $t$ . Since the optical flow between consecutive frames is identical, we can easily deduce the displacement field by recursively applying:",
+        "bbox": [
+            75,
+            195,
+            468,
+            255
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nF _ {0 \\rightarrow t} (\\mathbf {x} _ {0}) = F _ {0 \\rightarrow t - 1} (\\mathbf {x} _ {0}) + M (\\mathbf {x} _ {0} + F _ {0 \\rightarrow t - 1} (\\mathbf {x} _ {0})), \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            88,
+            268,
+            468,
+            286
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $F_{0\\rightarrow t}(\\cdot)$  denotes the displacement field from time 0 to time  $t$ , which describes the course of each pixel in the input image across future frames. To estimate the Eulerian flow field, we adopt an image-to-image translation network as our motion estimator, which is able to map an RGB image to the optical flow.",
+        "bbox": [
+            75,
+            297,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. 3D Scene Representation",
+        "text_level": 1,
+        "bbox": [
+            76,
+            401,
+            303,
+            417
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "One common disadvantage of previous single-image animation methods [12, 19, 29] is that they usually operate in 2D space via a deep image warping technique, which prevents them from creating parallax effects. Instead, to enable camera motion, we propose to lift our workspace into 3D and thus resort to 3D scene representation.",
+        "bbox": [
+            75,
+            425,
+            468,
+            516
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We start by estimating the underlying geometry of the scene using the state-of-the-art monocular depth estimator DPT [45], which can predict reasonable dense depth maps for in-the-wild photos. Following Wang et al. [64], we then convert the RGBD input into an LDI representation [50] by separating it into several layers as per depth discontinuities and inpainting occluded regions. Specifically, we first divide the depth range of the source depth map into multiple intervals using agglomerative clustering [36], followed by creating layered depth images  $\\mathcal{L} = \\{\\mathbf{C}_l,\\mathbf{D}_l\\}_{l = 1}^L$ . Next, we inpaint occluded regions of each color and depth layer by applying the pretrained inpainting model from 3D Photo [52]. To improve rendering quality and reduce artifacts, we also introduce a 2D feature extraction network to encode 2D feature maps for each inpainted LDI color layer, resulting in feature LDIs  $\\mathcal{F} = \\{\\mathbf{F}_l,\\mathbf{D}_l\\}_{l = 1}^L$ . Finally, in order to enable animation in 3D space, we unproject feature LDIs into 3D via their corresponding inpainted depth layers, yielding a feature point cloud  $\\mathcal{P} = \\{(\\mathbf{X}_i,\\mathbf{f}_i)\\}$ , where  $\\mathbf{X}_i$  and  $\\mathbf{f}_i$  are 3D coordinates and the feature vector for each 3D point respectively.",
+        "bbox": [
+            75,
+            517,
+            468,
+            834
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4. Point Cloud Animation and Rendering",
+        "text_level": 1,
+        "bbox": [
+            76,
+            845,
+            410,
+            862
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We now have the estimated displacement fields  $F_{0\\rightarrow t}$  and the feature point cloud  $\\mathcal{P}$ . Our next step is to animate this",
+        "bbox": [
+            76,
+            869,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/4420e0d6b8fcb14bf3c3b500c14fac36e9318d4891d4d320681be1555ce24c18.jpg",
+        "image_caption": [
+            "Figure 3. 3D symmetric animation. To address the hole issue, we borrow textural information from the point cloud that moves in the opposite direction and integrate both of the animated point clouds to feasibly fill in the missing regions (the red and blue regions)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            513,
+            90,
+            880,
+            261
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "point cloud over time. To bridge the gap between 2D displacement fields and 3D scene representation, we first augment the displacement fields with estimated depth values to lift them into 3D scene flow. In other words, we now have a function of time  $t$  and the coordinates of a 3D point that returns a corresponding 3D translation vector that can shift this 3D point accordingly. Thus, for time  $t$ , we then move each 3D point by computing its destination as its original position plus a corresponding 3D translation vector, i.e.,  $\\mathcal{P}(t) = \\{(\\mathbf{X}_i(t),\\mathbf{f}_i)\\}$ . Intuitively, this process indeed animates the point cloud from one time to another. However, we empirically find that as points move forward, increasingly large holes emerge. This frequently happens when points leave their original locations without any points filling in those unknown regions.",
+        "bbox": [
+            496,
+            349,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3D symmetric animation. To resolve this, inspired by prior works [3, 19, 38], we propose a 3D symmetric animation technique that leverages bidirectionally displaced point clouds to complement each other. With 3D symmetric animation, we can borrow textural information from point clouds that move in the opposite direction and integrate both of the animated point clouds to feasibly fill in missing regions. Specifically, we directly replace the original Eulerian flow field  $M$  with  $-M$  and recursively apply Eq. (3) to generate a reversed displacement field. Similarly, we then lift this 2D displacement field to obtain inverse scene flow, which is employed to produce point clouds with backward movements. As illustrated in Fig. 3, for time  $t$ , to fill in holes, we respectively apply  $F_{0\\rightarrow t}$  and  $F_{0\\rightarrow t - N}$  to draw associated scene flow fields and use them to move the point cloud, resulting in  $\\mathcal{P}_f(t) = \\{(\\mathbf{X}_i^f (t),\\mathbf{f}_i)\\}$  and  $\\mathcal{P}_b(t) = \\{(\\mathbf{X}_i^b (t),\\mathbf{f}_i)\\}$ , where  $N$  is the number of frames.",
+        "bbox": [
+            496,
+            579,
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+            837
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Neural rendering. We now have two bidirectionally animated feature point clouds. Our final step is to render them into animated feature maps and composite the results for synthesizing novel views at time  $t$ . In particu",
+        "bbox": [
+            496,
+            839,
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+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "4598",
+        "bbox": [
+            480,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "lar, given camera poses and intrinsics, we use a differentiable point-based renderer [66] to splat feature point clouds  $\\mathcal{P}_f(t) = \\{(\\mathbf{X}_i^f (t),\\mathbf{f}_i)\\}$  and  $\\mathcal{P}_b(t) = \\{(\\mathbf{X}_i^b (t),\\mathbf{f}_i)\\}$  separately into the target image plane. This process yields 2D feature maps  $\\mathbf{F}_f$  and  $\\mathbf{F}_b$  along with depth maps  $\\mathbf{D}_f$ ,  $\\mathbf{D}_b$  and alpha maps  $\\alpha_{f},\\alpha_{b}$ . Next, we wish to fuse  $\\mathbf{F}_f$  and  $\\mathbf{F}_b$  into one feature map  $\\mathbf{F}_t$ . Inspired by prior work [64], our intuition is three-fold: 1) to enable endless and seamless looping, we should assign the weight of the two feature maps based on time so as to guarantee that the first and last frame of the synthesized video are identical; 2) the weight map should favor pixel locations with smaller depth values, in the sense that it is impossible to see objects behind those objects closer to the eye; 3) to avoid missing regions as much as possible, we should greatly increase the contribution of those pixel locations that can fill in holes. With this in mind, we formulate the weight map as follows:",
+        "bbox": [
+            76,
+            90,
+            472,
+            349
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {W} _ {t} = \\frac {\\left(1 - \\frac {t}{N}\\right) \\cdot \\boldsymbol {\\alpha} _ {f} \\cdot e ^ {- \\mathbf {D} _ {f}}}{\\left(1 - \\frac {t}{N}\\right) \\cdot \\boldsymbol {\\alpha} _ {f} \\cdot e ^ {- \\mathbf {D} _ {f}} + \\frac {t}{N} \\cdot \\boldsymbol {\\alpha} _ {b} \\cdot e ^ {- \\mathbf {D} _ {b}}}, \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            116,
+            356,
+            468,
+            393
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $N$  is the number of frames. Therefore, we can integrate  $\\mathbf{F}_f$  and  $\\mathbf{F}_b$  via:",
+        "bbox": [
+            76,
+            401,
+            468,
+            433
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {F} _ {t} = \\mathbf {W} _ {t} \\cdot \\mathbf {F} _ {f} + (1 - \\mathbf {W} _ {t}) \\cdot \\mathbf {F} _ {b}. \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            161,
+            441,
+            468,
+            459
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We also obtain the merged depth map  $\\mathbf{D}_t$ :",
+        "bbox": [
+            76,
+            468,
+            356,
+            484
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {D} _ {t} = \\mathbf {W} _ {t} \\cdot \\mathbf {D} _ {f} + (1 - \\mathbf {W} _ {t}) \\cdot \\mathbf {D} _ {b}. \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            156,
+            494,
+            468,
+            511
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Finally, we employ an image decoder network to map the 2D feature map  $\\mathbf{F}_t$  and depth map  $\\mathbf{D}_t$  to a novel view at time  $t$ . Repeating this method, we are able to synthesize a realistic cinematograph with compelling parallax effects.",
+        "bbox": [
+            76,
+            521,
+            468,
+            580
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3.5. Training",
+        "text_level": 1,
+        "bbox": [
+            76,
+            590,
+            181,
+            606
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "This section describes our training scheme. In general, we train our image-to-image translation network, 2D feature extraction network, and image decoder network in a two-stage manner.",
+        "bbox": [
+            76,
+            613,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Training dataset. We use the training set from Holynski et al. [19] as our training dataset. This dataset comprises short video clips of fluid motion that are extracted from longer stock-footage videos. We use the first frames of each video clip and the corresponding ground truth motion fields estimated by a pretrained optical flow network [60] as motion estimation pairs to train our motion estimation network. To develop animation ability, we randomly sample training data from fluid motion video clips. For novel view synthesis training, we require multi-view supervision of the same scene, which is not available in the training set. Instead, we use 3D Photo [52] to generate pseudo ground truth novel views for training.",
+        "bbox": [
+            75,
+            674,
+            468,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Two-stage training. Our model is trained in a two-stage manner. Specifically, we first train our motion estimation",
+        "bbox": [
+            76,
+            869,
+            468,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "network using motion estimation pairs. To train the motion estimation network, we minimize GAN loss, GAN feature matching loss [49], and endpoint error as follows:",
+        "bbox": [
+            498,
+            90,
+            890,
+            137
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {M o t i o n}} = \\mathcal {L} _ {\\text {G A N}} + 1 0 \\mathcal {L} _ {\\text {F M}} + \\mathcal {L} _ {\\text {E P E}}. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            562,
+            143,
+            890,
+            161
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In the second stage, we freeze the motion estimation network and train the feature extraction network and image decoder network. Our model simultaneously learns to render novel views and animate scenes. For novel view synthesis, we set  $t = 0$  and use pseudo ground truth novel views to supervise our model. We randomly sample target viewpoints of scenes and require the model to synthesize them. For animation, we train our model on training triplets (start frame, middle frame, end frame) sampled from fluid motion video clips. In particular, we render the middle frame from both directions using  $F_{0\\rightarrow t}$  and  $F_{0\\rightarrow t - N}$  without changing the camera poses and intrinsics. Besides GAN loss and GAN feature matching loss [49], we also enforce VGG perceptual loss [23, 73] and  $l_{1}$  loss between synthesized and ground truth images. The overall loss is as follows:",
+        "bbox": [
+            496,
+            169,
+            892,
+            395
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {A n i m a t i o n}} = \\mathcal {L} _ {G A N} + 1 0 \\mathcal {L} _ {F M} + \\mathcal {L} _ {l _ {1}} + \\mathcal {L} _ {V G G}. \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            521,
+            404,
+            890,
+            420
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            429,
+            633,
+            445
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our motion estimator is a U-Net [48] based generator with 16 convolutional layers, and we replace Batch Normalization with SPADE [42]. For the feature extraction network and image decoder network, we follow the network architectures from Wang et al. [64]. We adopt the multi-scale discriminator used in SPADE [42] during training.",
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+        "type": "text",
+        "text": "Our model is trained using the Adam optimizer [24]. We conduct all experiments on a single NVIDIA GeForce RTX 3090 GPU. We train the motion estimation network for around  $120k$  iterations with a batch size of 16. We set the generator learning rate to  $5 \\times 10^{-4}$  and the discriminator learning rate to  $2 \\times 10^{-3}$ . For the animation training stage, we train the feature extraction network and image decoder network for around  $250k$  iterations with a learning rate starting at  $1 \\times 10^{-4}$  and then decaying exponentially.",
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+        "type": "text",
+        "text": "4.2. Baselines",
+        "text_level": 1,
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+        "text": "In principle, to evaluate our method, we are required to compare it against current state-of-the-art models. However, to our knowledge, we are the first to tackle the novel task of synthesizing a realistic cinematograph with compelling parallax effects from a single image. As a result, we cannot directly compare to previous works. Instead, we consider forming the following baselines to verify the superiority of our method:",
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+    {
+        "type": "text",
+        "text": "2D animation  $\\rightarrow$  novel view synthesis. One might consider 2D image animation  $\\rightarrow$  single-shot novel view synthesis: first employing a 2D image animation method, then",
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+    {
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+        "text": "4599",
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+        "img_path": "images/c73aa6fbda032b3f48e03479b2b356fc2ed002a2f565478dc012b95cf53ed609.jpg",
+        "table_caption": [
+            "Table 1. Quantitative comparisons against all baselines on the validation set from Holynski et al. [19]. The better approach favors higher PSNR and SSIM but lower LPIPS. The best performance is in bold."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>2D Anim. [19] → NVS [52]</td><td>21.12</td><td>0.633</td><td>0.286</td></tr><tr><td>NV5 [52] → 2D Anim. [19]</td><td>21.97</td><td>0.697</td><td>0.276</td></tr><tr><td>NV5 [52] → 2D Anim. [19] + MA</td><td>22.47</td><td>0.718</td><td>0.261</td></tr><tr><td>Naive PC Anim.</td><td>19.46</td><td>0.647</td><td>0.243</td></tr><tr><td>Naive PC Anim. + 3DSA</td><td>20.49</td><td>0.660</td><td>0.237</td></tr><tr><td>Ours</td><td>23.33</td><td>0.776</td><td>0.197</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "a single-shot novel view synthesis method. Specifically, we first adopt a state-of-the-art image animation method [19] to produce an animated looping video. We then apply DPT [45] to estimate geometry and utilize 3D Photo [52] to generate novel views for each frame.",
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+        "text": "Novel view synthesis  $\\rightarrow$  2D animation. It also appears to be feasible that we first render novel views of scenes by 3D Photo [52] and then use the image animation method [19] to animate each viewpoint. Note that motion estimation should be performed for each frame as viewpoints have changed. However, we empirically find that this usually results in varying motion fields across the video. To mitigate this, we further propose using the moving average technique to smooth estimated motions for each frame. This results in novel view synthesis  $\\rightarrow$  2D animation + MA.",
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+    {
+        "type": "text",
+        "text": "Naive point cloud animation. Intuitively, we may also consider directly unprojecting pixels into 3D space and subsequently moving and rendering the RGB point cloud. Specifically, given a single input image, we first predict the depth map using DPT [45] and estimate 2D optical flow. We then lift the pixels and optical flow into 3D space to form RGB point clouds and scene flow. Finally, we animate RGB point clouds over time according to the scene flow and project these point clouds into target viewpoints. This baseline also faces a similar issue: as time goes by, large holes gradually appear. One might also employ our 3D symmetric animation technique to further enhance this baseline, i.e., naive point cloud animation + 3DSA.",
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+    {
+        "type": "text",
+        "text": "4.3. Results",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Evaluation dataset. Since Holynski et al. [19] only provide a single image for each scene in the test set, we use the validation set from Holynski et al. [19] to evaluate our method and baselines. The validation set consists of 31 unique scenes with 162 samples of ground truth video clips captured by static cameras.",
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+        "text": "Experimental setup. For evaluation, we render novel views of the ground truth videos in 4 different trajectories, resulting in 240 ground truth frames for each sample. This process does not involve inpainting, thus ground truth frames may contain holes. Only considering valid pixels when calculating metrics, we compare the predicted images",
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+        "table_caption": [
+            "Table 2. User study. Pairwise comparison results indicate that users prefer our method as more realistic and immersive."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Comparison</td><td>Human preference</td></tr><tr><td>2D Anim. [19] → NVS [52] / Ours</td><td>12.5% / 87.5%</td></tr><tr><td>NVS [52] → 2D Anim. [19] / Ours</td><td>3.9% / 96.1%</td></tr><tr><td>NVS [52] → 2D Anim. [19] + MA / Ours</td><td>6.1% / 93.9%</td></tr><tr><td>Naive PC Anim. / Ours</td><td>7.6% / 92.4%</td></tr><tr><td>Naive PC Anim. + 3DSA / Ours</td><td>8.6% / 91.4%</td></tr><tr><td>3D Photo [52] / Ours</td><td>10.5% / 89.5%</td></tr><tr><td>Holynski et al. [19] / Ours</td><td>29.9% / 70.1%</td></tr></table>",
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+        "table_caption": [
+            "Table 3. Ablation study on each component of our method."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>w/o features</td><td>21.50</td><td>0.674</td><td>0.228</td></tr><tr><td>w/o inpainting</td><td>22.86</td><td>0.763</td><td>0.216</td></tr><tr><td>w/o 3D symmetric animation</td><td>22.99</td><td>0.768</td><td>0.199</td></tr><tr><td>Full model</td><td>23.33</td><td>0.776</td><td>0.197</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "with the ground truth frames at the same time and viewpoint. For a fair comparison, all methods utilize the depth maps estimated by DPT [45]. Since we focus on comparing rendering quality, all methods use ground truth optical flows, except that NVS  $[52] \\rightarrow 2\\mathrm{D}$  Anim. [19] and NVS  $[52] \\rightarrow 2\\mathrm{D}$  Anim. [19] + MA have to estimate optical flows for each frame apart from the first frame. We adopt PSNR, SSIM, and LPIPS [73] as our evaluation metrics.",
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+        "type": "text",
+        "text": "Quantitative comparisons. As shown in Table 1, our method outperforms all baselines across all metrics by a large margin. This result implies that our method achieves better perceptual quality and produces more realistic renderings, which demonstrates the superiority and effectiveness of our method.",
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+        "text": "Qualitative comparisons. We showcase the visual comparisons in Fig. 4. One can observe that our method presents photorealistic results while other comparative baselines produce more or less visual artifacts. 2D Anim. [19]  $\\rightarrow$  NVS [52] intends to generate stripped flickering artifacts. This is because 2D Anim. [19]  $\\rightarrow$  NVS [52] predicts the depth map for each animated frame, leading to frequent changes in the 3D structure of the scene and inconsistent inpainting. NVS [52]  $\\rightarrow$  2D Anim. [19] and NVS [52]  $\\rightarrow$  2D Anim. [19] + MA show jelly-like effects as optical flow should be estimated for each novel view. This results in varying motion fields across the video and thus inconsistent animation. Although Naive PC Anim. and Naive PC Anim. + 3DSA also lift the workspace into 3D, they are often prone to produce noticeable holes inevitably. One reason for this is that they do not perform inpainting. Note that some artifacts are difficult to observe when only scanning static figures.",
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+        "type": "text",
+        "text": "Controllable animation. Our method is able to create 3D cinematographs from a single image automatically. Further, we show that our framework is also highly extensible. For example, we can involve masks and flow hints as extra in",
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+        "image_caption": [
+            "Figure 4. Qualitative comparisons against all baselines on the validation set from Holynski et al. [19]. Our method produces compelling results while other comparative alternatives suffer from visual artifacts. (a) 2D animation  $[19] \\rightarrow$  novel view synthesis [52], (b) novel view synthesis  $[52] \\rightarrow 2\\mathrm{D}$  animation [19], (c) novel view synthesis  $[52] \\rightarrow 2\\mathrm{D}$  animation  $[19] +$  moving average, (d) naive point cloud animation, (e) naive point cloud animation  $+3\\mathrm{D}$  symmetric animation, (f) our method, and (g) pseudo ground truth."
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+        "image_caption": [
+            "Input",
+            "Figure 5. Controllable animation. By changing the masks and motion hints, our method can interactively control the animation."
+        ],
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+        "image_caption": [
+            "Masks & motion hints"
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+    {
+        "type": "image",
+        "img_path": "images/438519e393db1e5206e2ed44c6a00dce4244e7b410324bda96632ea60ed34f4f.jpg",
+        "image_caption": [
+            "Motion fields"
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "puts to augment our motion estimator. This brings two advantages: (1) more accurate flow estimation; (2) interactive and controllable animation. As shown in Fig. 5, we can control the animation of the scene by providing various masks and motion hints to obtain different motion fields.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Generalizing on in-the-wild photos. To further demonstrate the generalization of our method, we also test our method on in-the-wild photos. We first create hemagraphs with camera motions on the test set from Holynski et al. [19], where, for each scene, only a single image is provided. We then select some online images at random to test our method. To accurately estimate motion fields, we provide masks and flow hints as extra inputs to our motion estimator. As shown in Fig. 6, our method produces reasonable results for in-the-wild inputs while other comparative",
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+    {
+        "type": "text",
+        "text": "alternatives yield visual artifacts or inconsistent animation.",
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+    {
+        "type": "text",
+        "text": "4.4. User Study",
+        "text_level": 1,
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+        "text": "We further conduct a user study to investigate how our method performs in the view of humans when compared with all baselines, 3D Photo [52], and Holynski et al. [19]. Specifically, we collect 50 photos from the test set of Holynski et al. [19] and the Internet. We use different approaches to generate videos with identical settings. During the study, we show each participant an input image and two animated videos generated by our method and a randomly selected approach in random order. 108 volunteers are invited to choose the method with better perceptual quality and realism, or none if it is hard to judge. We report the results in Table 2, which points out that our method surpasses alternative methods by a large margin in terms of the sense of reality and immersion.",
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+        "text": "To validate the effect of each component, we conduct an ablation study on the validation set from Holynski et al. [19] and show the results in Table 3. One can observe: i) 3D symmetric animation technique matters because it allows us to leverage bidirectionally displaced point clouds to complement each other and feasibly fill in missing regions; ii)",
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+            "2D Anim.  $\\rightarrow$  NVS"
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+        "image_caption": [
+            "Naive PC Anim. + 3DSA",
+            "Figure 6. Visual comparisons on the test set from Holynski et al. [19] and in-the-wild photos. Our method consistently produces more realistic rendering with fewer visual artifacts as opposed to other baselines."
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+        "text": "introducing inpainting when constructing 3D geometry can improve the performance as this allows our model to produce plausible structures around depth discontinuities and fill in holes; iii) switching from directly using RGB colors to features in 3D scene representation significantly improves the rendering quality and reduces artifacts.",
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+        "text": "5. Conclusion",
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+        "text": "In this paper, we introduce a novel task of creating 3D cinematographs from single images. To this end, we present a simple yet effective method that makes a connection between image animation and novel view synthesis. We show that our method produces plausible animation of the scene while allowing camera movements. Our framework is flexible and customized. For accurate motion estimation and controllable animation, we can further include masks and flow hints as extra input for the motion estimator. Therefore, users can control how the scene is animated. Furthermore, our method generalizes well to in-the-wild photos, even like paintings or synthetic images generated by diffusion models. We conduct extensive experiments to ver",
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+    {
+        "type": "text",
+        "text": "ify the effectiveness and superiority of our method. A user study also demonstrates that our method generates realistic 3D cinematographs. We hope that our work can bring 3D cinematography into the sight of a broader community and motivate further research.",
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+        "type": "text",
+        "text": "Limitations and future work. Our method may not work well when the depth prediction module estimates erroneous geometry from the input image, e.g., thin structures. In addition, inappropriate motion fields will sometimes lead to undesirable results, e.g., some regions are mistakenly identified as frozen. As we take the first step towards 3D cinematography, in this paper, we focus on handling common moving elements, i.e., fluids. In other words, our method may not apply to more complex motions, e.g., cyclic motion. We leave this for our future work.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements. This study is supported under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s). This work is also supported by Adobe Gift and the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 (MOE-T2EP20220-0007) and Tier 1 (RG14/22).",
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2023/3D Cinemagraphy From a Single Image/822e0c52-d8c7-4a4e-8a84-1a2d57dbe08f_origin.pdf

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2023/3D Cinemagraphy From a Single Image/full.md

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+# 3D Cinemagraphy from a Single Image
+
+Xingyi Li $^{1,3}$  Zhiguo Cao $^{1}$  Huiqiang Sun $^{1}$  Jianming Zhang $^{2}$  Ke Xian $^{3*}$  Guosheng Lin $^{3}$ $^{1}$ Key Laboratory of Image Processing and Intelligent Control, Ministry of Education School of Artificial Intelligence and Automation, Huazhong University of Science and Technology  
+ $^{2}$ Adobe Research  $^{3}$ S-Lab, Nanyang Technological University  
+{xingyi.li, zgcao, shq1031}@hust.edu.cn, jianmzha@adobe.com, {ke.xian, gslin}@ntu.edu.sg  
+https://xingyi-li.github.io/3d-cinemagraphy
+
+![](images/77e45a8a8ae99f7e5122bf60ba50833109c19c4ad4f2de0de9320aca1eab8f4b.jpg)  
+Figure 1. Given a single still image, our method can synthesize videos with plausible animation of the scene while allowing camera movements. Here, we showcase four 3D cinematographs with various camera trajectories. Besides real-world photos (the left two examples), our method can also generalize to paintings (the third one) and synthetic images generated by Stable Diffusion [47] (the rightmost one). To see the effect of 3D cinematography, readers are encouraged to view with Adobe Acrobat or KDE Okular.
+
+![](images/afaecbba82dd6bd57e0f587e50178780a6b79bc215a6dbcec1887dd14bf9fa3b.jpg)
+
+![](images/812c489801e67547cea0e4abdc1db516b991152c6dc20e97d1f533d9d77e7022.jpg)
+
+![](images/9e76c7973b4c0d6ac5f0c7109de2752b00aa644105db1a7c8f97243477dba918.jpg)
+
+# Abstract
+
+We present 3D Cinemagography, a new technique that marries 2D image animation with 3D photography. Given a single still image as input, our goal is to generate a video that contains both visual content animation and camera motion. We empirically find that naively combining existing 2D image animation and 3D photography methods leads to obvious artifacts or inconsistent animation. Our key insight is that representing and animating the scene in 3D space offers a natural solution to this task. To this end, we first convert the input image into feature-based layered depth images using predicted depth values, followed by unprojecting them to a feature point cloud. To animate the scene, we perform motion estimation and lift the 2D motion into the 3D scene flow. Finally, to resolve the problem of hole emergence as points move forward, we propose to bidirectionally displace the point cloud as per the scene flow and synthesize novel views by separately projecting them into target image planes and blending the results. Extensive experiments demonstrate the effectiveness of our method. A user study is also conducted to validate the compelling rendering results of our method.
+
+# 1. Introduction
+
+Nowadays, since people can easily take images using smartphone cameras, the number of online photos has increased drastically. However, with the rise of online video-sharing platforms such as YouTube and TikTok, people are no longer content with static images as they have grown accustomed to watching videos. It would be great if we could animate those still images and synthesize videos for a better experience. These living images, termed cinematographs, have already been created and gained rapid popularity online [1, 71]. Although cinematographs may engage people with the content for longer than a regular photo, they usually fail to deliver an immersive sense of 3D to audiences. This is because cinematographs are usually based on a static camera and fail to produce parallax effects. We are therefore motivated to explore ways of animating the photos and moving around the cameras at the same time. As shown in Fig. 1, this will bring many still images to life and provide a drastically vivid experience.
+
+In this paper, we are interested in making the first step towards 3D cinematography that allows both realistic animation of the scene and camera motions with compelling parallax effects from a single image. There are plenty of attempts to tackle either of the two problems. Single-image animation methods [12, 19, 35] manage to produce a real-
+
+istic animated video from a single image, but they usually operate in 2D space, and therefore they cannot create camera movement effects. Classic novel view synthesis methods [5, 6, 9, 14, 25] and recent implicit neural representations [37, 40, 58] entail densely captured views as input to render unseen camera perspectives. Single-shot novel view synthesis approaches [21, 39, 52, 66] exhibit the potential for generating novel camera trajectories of the scene from a single image. Nonetheless, these methods usually hypothesize that the observed scene is static without moving elements. Directly combining existing state-of-the-art solutions of single-image animation and novel view synthesis yields visual artifacts or inconsistent animation.
+
+To address the above challenges, we present a novel framework that solves the joint task of image animation and novel view synthesis. This framework can be trained to create 3D cinematographs from a single still image. Our key intuition is that handling this new task in 3D space would naturally enable both animation and moving cameras simultaneously. With this in mind, we first represent the scene as feature-based layered depth images (LDIs) [50] and unproject the feature LDIs into a feature point cloud. To animate the scene, we perform motion estimation and lift the 2D motion to 3D scene flow using depth values predicted by DPT [45]. Next, we animate the point cloud according to the scene flow. To resolve the problem of hole emergence as points move forward, we are inspired by prior works [3, 19, 38] and propose a 3D symmetric animation technique to bidirectionally displace point clouds, which can effectively fill in those unknown regions. Finally, we synthesize novel views at time  $t$  by rendering point clouds into target image planes and blending the results. In this manner, our proposed method can automatically create 3D cinematographs from a single image. Moreover, our framework is highly extensible, e.g., we can augment our motion estimator with user-defined masks and flow hints for accurate flow estimation and controllable animation.
+
+In summary, our main contributions are:
+
+- We propose a new task of creating 3D cinematographs from single images. To this end, we propose a novel framework that jointly learns to solve the task of image animation and novel view synthesis in 3D space.  
+- We design a 3D symmetric animation technique to address the hole problem as points move forward.  
+- Our framework is flexible and customized. We can achieve controllable animation by augmenting our motion estimator with user-defined masks and flow hints.
+
+# 2. Related Work
+
+Single-image animation. Different kinds of methods have been explored to animate still images. Some works [8, 22]
+
+focus on animating certain objects via physical simulation but may not be easily applied to more general cases of inthe-wild photos. Given driving videos as guidance, there are plenty of methods that attempt to perform motion transfer on static objects with either a priori knowledge of moving objects [7, 11, 33, 46, 55] or in an unsupervised manner [53, 54, 56]. They entail reference videos to drive the motion of static objects, and thus do not suit our task. Recent advances in generative models have attracted much attention and motivated the community to develop realistic image and video synthesis methods. Many works [31, 32, 34, 51, 69] are based on generative adversarial networks (GANs) and operate transformations in latent space to generate plausible appearance changes and movements. Nonetheless, it is non-trial to allow for explicit control over those latent codes and to animate input imagery in a disentangled manner. As diffusion models [17, 59] improve by leaps and bounds, several diffusion-based works [16, 18, 57] attempt to generate realistic videos from text or images. However, these methods are time-consuming and expensive in terms of computation. Here we focus on methods that utilize learned motion priors to convert a still image into an animated video texture [12, 13, 19, 29, 35]. In particular, Holynski et al. [19] first synthesize the optical flow of the input image via a motion estimation network, then obtain future frames using the estimated flow field. This method renders plausible animation of fluid elements in the input image but suffers from producing camera motions with parallax.
+
+Novel view synthesis from a single image. Novel view synthesis allows for rendering unseen camera perspectives from 2D images and their corresponding camera poses. Recent impressive synthesis results may credit to implicit neural representations [37, 40, 58]. Nevertheless, these methods usually assume dense views as input, which is not always available in most cases. Moreover, they focus on the task of interpolation given multiple views rather than extrapolation. As such, we instead turn to methods aiming at handling single input. Among them, a number of works [15, 26, 28, 62, 63, 70, 72] infer the 3D structure of scenes by learning to predict a scene representation from a single image. These methods are usually trained end-to-end but suffer from generalizing to in-the-wild photos. Most relevant to our work are those approaches [39, 52, 66] that apply depth estimation [45, 65, 67, 68] followed by inpainting occluded regions. For example, 3D Photo [52] estimates monocular depth maps and uses the representation of layered depth images (LDIs) [43, 50], in which context-aware color and depth inpainting are performed. To enable fine-grained detail modeling, SLIDE [21] decomposes the scene into foreground and background via a soft-layering scheme. However, unlike our approach, these methods usually assume the scene is static by default, which largely lessens the sense of reality, especially when some elements such as
+
+![](images/6c4949f4da65374cd84740c97a37b56fee1a8822d40c3c37efaec7f81ec19bb8.jpg)  
+Figure 2. An overview of our method. Given a single still image as input, we first predict a dense depth map. To represent the scene in 3D space, we separate the input image into several layers according to depth discontinuities and apply context-aware inpainting, yielding layered depth images (LDIs)  $\mathcal{L}$ . We then use a 2D feature extractor to encode 2D feature maps for each inpainted LDI color layer, resulting in feature LDIs  $\mathcal{F}$ . Subsequently, we lift feature LDIs into 3D space using corresponding depth values to obtain a feature point cloud  $\mathcal{P}$ . To animate the scene, we estimate a 2D motion field from the input image and apply Euler integration to generate forward and backward displacement fields  $F_{0\rightarrow t}$  and  $F_{0\rightarrow t - N}$ . We then augment displacement fields with estimated depth values to obtain 3D scene flow fields. Next, we bidirectionally displace the feature point cloud  $\mathcal{P}$  as per the scene flow and separately project them into target image planes to obtain  $\mathbf{F}_f$  and  $\mathbf{F}_b$ . Finally, we blend them together and pass the result through our image decoder to synthesize a novel view at time  $t$ .
+
+a creek or smoke are also captured in the input image.
+
+Space-time view synthesis. Space-time view synthesis is the task of rendering novel camera perspectives for dynamic scenes in terms of space and time [30]. Most of the prior works [2, 4, 27] rely on synchronized multi-view videos as input, which prevents their wide applicability. To mitigate this requirement, many neural rendering approaches [30, 41, 44] manage to show promising space-time view synthesis results from monocular videos. They usually train each new scene independently, and thus cannot directly handle in-the-wild inputs. Most related to our work, 3D Moments [64] introduces a novel 3D photography effect where cinematic camera motion and frame interpolation are simultaneously performed. However, this method demands near-duplicate photos as input and is unable to control the animation results. Instead, we show that our method can animate still images while enabling camera motion with 3D parallax. Moreover, we can also extend our system so that users are allowed to interactively control how the photos are animated by providing user-defined masks and flow hints.
+
+# 3. Method
+
+# 3.1. Overview
+
+Given a single still image, our goal is to synthesize plausible animation of the scene and simultaneously enable camera motion. The output of our method is a realistic cinematograph with compelling parallax effects. Fig. 2 schematically illustrates our pipeline. Our method starts by estimating a motion field and a depth map from the input image. We then separate the RGBD input into several layers
+
+as per depth discontinuities and inpaint occluded regions, followed by extracting 2D feature maps for each layer, resulting in feature LDIs [50]. To enable scene animation, we lift the 2D motion to 3D scene flow and unproject feature LDIs into a feature point cloud using their corresponding depth values. Thereafter, we bidirectionally animate the point cloud with scene flow using our 3D symmetric animation technique. We end up rendering them into two animated feature maps and composite the results to synthesize novel views at time  $t$ .
+
+# 3.2. Motion Estimation
+
+To animate a still image, we wish to estimate the corresponding motion field for the observed scene. Generally, the motion we witness in the real world is extremely complicated as it is time-varying and many events such as occlusion and collision could occur. Intuitively, we could directly adopt prior optical flow estimation methods [10, 20, 60, 61] to accomplish this. However, it is not trivial since they usually take a pair of images as input to compute optical flow. Endo et al. [12] instead propose to learn and predict the motion in a recurrent manner, but this kind of approach is prone to large distortions in the long term. To simplify this, we follow Holynski et al. [19] and assume that a time-invariant and constant-velocity motion field, termed Eulerian flow field, can well approximate the bulk of real-world motions, e.g., water, smoke, and clouds. Formally, we denote  $M$  as the Eulerian flow field of the scene, which suggests that
+
+$$
+F _ {t \rightarrow t + 1} (\cdot) = M (\cdot), \tag {1}
+$$
+
+where  $F_{t\rightarrow t + 1}(\cdot)$  represents the optical flow map from frame  $t$  to frame  $t + 1$ . This defines how each pixel in the current frame will move in the future. Specifically, we can obtain the next frame via Euler integration:
+
+$$
+\mathbf {x} _ {t + 1} = \mathbf {x} _ {t} + M (\mathbf {x} _ {t}), \tag {2}
+$$
+
+where  $\mathbf{x}_t$  represents the coordinates of a pixel  $\mathbf{x}_t$  at time  $t$ . Since the optical flow between consecutive frames is identical, we can easily deduce the displacement field by recursively applying:
+
+$$
+F _ {0 \rightarrow t} (\mathbf {x} _ {0}) = F _ {0 \rightarrow t - 1} (\mathbf {x} _ {0}) + M (\mathbf {x} _ {0} + F _ {0 \rightarrow t - 1} (\mathbf {x} _ {0})), \tag {3}
+$$
+
+where  $F_{0\rightarrow t}(\cdot)$  denotes the displacement field from time 0 to time  $t$ , which describes the course of each pixel in the input image across future frames. To estimate the Eulerian flow field, we adopt an image-to-image translation network as our motion estimator, which is able to map an RGB image to the optical flow.
+
+# 3.3. 3D Scene Representation
+
+One common disadvantage of previous single-image animation methods [12, 19, 29] is that they usually operate in 2D space via a deep image warping technique, which prevents them from creating parallax effects. Instead, to enable camera motion, we propose to lift our workspace into 3D and thus resort to 3D scene representation.
+
+We start by estimating the underlying geometry of the scene using the state-of-the-art monocular depth estimator DPT [45], which can predict reasonable dense depth maps for in-the-wild photos. Following Wang et al. [64], we then convert the RGBD input into an LDI representation [50] by separating it into several layers as per depth discontinuities and inpainting occluded regions. Specifically, we first divide the depth range of the source depth map into multiple intervals using agglomerative clustering [36], followed by creating layered depth images  $\mathcal{L} = \{\mathbf{C}_l,\mathbf{D}_l\}_{l = 1}^L$ . Next, we inpaint occluded regions of each color and depth layer by applying the pretrained inpainting model from 3D Photo [52]. To improve rendering quality and reduce artifacts, we also introduce a 2D feature extraction network to encode 2D feature maps for each inpainted LDI color layer, resulting in feature LDIs  $\mathcal{F} = \{\mathbf{F}_l,\mathbf{D}_l\}_{l = 1}^L$ . Finally, in order to enable animation in 3D space, we unproject feature LDIs into 3D via their corresponding inpainted depth layers, yielding a feature point cloud  $\mathcal{P} = \{(\mathbf{X}_i,\mathbf{f}_i)\}$ , where  $\mathbf{X}_i$  and  $\mathbf{f}_i$  are 3D coordinates and the feature vector for each 3D point respectively.
+
+# 3.4. Point Cloud Animation and Rendering
+
+We now have the estimated displacement fields  $F_{0\rightarrow t}$  and the feature point cloud  $\mathcal{P}$ . Our next step is to animate this
+
+![](images/4420e0d6b8fcb14bf3c3b500c14fac36e9318d4891d4d320681be1555ce24c18.jpg)  
+Figure 3. 3D symmetric animation. To address the hole issue, we borrow textural information from the point cloud that moves in the opposite direction and integrate both of the animated point clouds to feasibly fill in the missing regions (the red and blue regions).
+
+point cloud over time. To bridge the gap between 2D displacement fields and 3D scene representation, we first augment the displacement fields with estimated depth values to lift them into 3D scene flow. In other words, we now have a function of time  $t$  and the coordinates of a 3D point that returns a corresponding 3D translation vector that can shift this 3D point accordingly. Thus, for time  $t$ , we then move each 3D point by computing its destination as its original position plus a corresponding 3D translation vector, i.e.,  $\mathcal{P}(t) = \{(\mathbf{X}_i(t),\mathbf{f}_i)\}$ . Intuitively, this process indeed animates the point cloud from one time to another. However, we empirically find that as points move forward, increasingly large holes emerge. This frequently happens when points leave their original locations without any points filling in those unknown regions.
+
+3D symmetric animation. To resolve this, inspired by prior works [3, 19, 38], we propose a 3D symmetric animation technique that leverages bidirectionally displaced point clouds to complement each other. With 3D symmetric animation, we can borrow textural information from point clouds that move in the opposite direction and integrate both of the animated point clouds to feasibly fill in missing regions. Specifically, we directly replace the original Eulerian flow field  $M$  with  $-M$  and recursively apply Eq. (3) to generate a reversed displacement field. Similarly, we then lift this 2D displacement field to obtain inverse scene flow, which is employed to produce point clouds with backward movements. As illustrated in Fig. 3, for time  $t$ , to fill in holes, we respectively apply  $F_{0\rightarrow t}$  and  $F_{0\rightarrow t - N}$  to draw associated scene flow fields and use them to move the point cloud, resulting in  $\mathcal{P}_f(t) = \{(\mathbf{X}_i^f (t),\mathbf{f}_i)\}$  and  $\mathcal{P}_b(t) = \{(\mathbf{X}_i^b (t),\mathbf{f}_i)\}$ , where  $N$  is the number of frames.
+
+Neural rendering. We now have two bidirectionally animated feature point clouds. Our final step is to render them into animated feature maps and composite the results for synthesizing novel views at time  $t$ . In particu
+
+lar, given camera poses and intrinsics, we use a differentiable point-based renderer [66] to splat feature point clouds  $\mathcal{P}_f(t) = \{(\mathbf{X}_i^f (t),\mathbf{f}_i)\}$  and  $\mathcal{P}_b(t) = \{(\mathbf{X}_i^b (t),\mathbf{f}_i)\}$  separately into the target image plane. This process yields 2D feature maps  $\mathbf{F}_f$  and  $\mathbf{F}_b$  along with depth maps  $\mathbf{D}_f$ ,  $\mathbf{D}_b$  and alpha maps  $\alpha_{f},\alpha_{b}$ . Next, we wish to fuse  $\mathbf{F}_f$  and  $\mathbf{F}_b$  into one feature map  $\mathbf{F}_t$ . Inspired by prior work [64], our intuition is three-fold: 1) to enable endless and seamless looping, we should assign the weight of the two feature maps based on time so as to guarantee that the first and last frame of the synthesized video are identical; 2) the weight map should favor pixel locations with smaller depth values, in the sense that it is impossible to see objects behind those objects closer to the eye; 3) to avoid missing regions as much as possible, we should greatly increase the contribution of those pixel locations that can fill in holes. With this in mind, we formulate the weight map as follows:
+
+$$
+\mathbf {W} _ {t} = \frac {\left(1 - \frac {t}{N}\right) \cdot \boldsymbol {\alpha} _ {f} \cdot e ^ {- \mathbf {D} _ {f}}}{\left(1 - \frac {t}{N}\right) \cdot \boldsymbol {\alpha} _ {f} \cdot e ^ {- \mathbf {D} _ {f}} + \frac {t}{N} \cdot \boldsymbol {\alpha} _ {b} \cdot e ^ {- \mathbf {D} _ {b}}}, \tag {4}
+$$
+
+where  $N$  is the number of frames. Therefore, we can integrate  $\mathbf{F}_f$  and  $\mathbf{F}_b$  via:
+
+$$
+\mathbf {F} _ {t} = \mathbf {W} _ {t} \cdot \mathbf {F} _ {f} + (1 - \mathbf {W} _ {t}) \cdot \mathbf {F} _ {b}. \tag {5}
+$$
+
+We also obtain the merged depth map  $\mathbf{D}_t$ :
+
+$$
+\mathbf {D} _ {t} = \mathbf {W} _ {t} \cdot \mathbf {D} _ {f} + (1 - \mathbf {W} _ {t}) \cdot \mathbf {D} _ {b}. \tag {6}
+$$
+
+Finally, we employ an image decoder network to map the 2D feature map  $\mathbf{F}_t$  and depth map  $\mathbf{D}_t$  to a novel view at time  $t$ . Repeating this method, we are able to synthesize a realistic cinematograph with compelling parallax effects.
+
+# 3.5. Training
+
+This section describes our training scheme. In general, we train our image-to-image translation network, 2D feature extraction network, and image decoder network in a two-stage manner.
+
+Training dataset. We use the training set from Holynski et al. [19] as our training dataset. This dataset comprises short video clips of fluid motion that are extracted from longer stock-footage videos. We use the first frames of each video clip and the corresponding ground truth motion fields estimated by a pretrained optical flow network [60] as motion estimation pairs to train our motion estimation network. To develop animation ability, we randomly sample training data from fluid motion video clips. For novel view synthesis training, we require multi-view supervision of the same scene, which is not available in the training set. Instead, we use 3D Photo [52] to generate pseudo ground truth novel views for training.
+
+Two-stage training. Our model is trained in a two-stage manner. Specifically, we first train our motion estimation
+
+network using motion estimation pairs. To train the motion estimation network, we minimize GAN loss, GAN feature matching loss [49], and endpoint error as follows:
+
+$$
+\mathcal {L} _ {\text {M o t i o n}} = \mathcal {L} _ {\text {G A N}} + 1 0 \mathcal {L} _ {\text {F M}} + \mathcal {L} _ {\text {E P E}}. \tag {7}
+$$
+
+In the second stage, we freeze the motion estimation network and train the feature extraction network and image decoder network. Our model simultaneously learns to render novel views and animate scenes. For novel view synthesis, we set  $t = 0$  and use pseudo ground truth novel views to supervise our model. We randomly sample target viewpoints of scenes and require the model to synthesize them. For animation, we train our model on training triplets (start frame, middle frame, end frame) sampled from fluid motion video clips. In particular, we render the middle frame from both directions using  $F_{0\rightarrow t}$  and  $F_{0\rightarrow t - N}$  without changing the camera poses and intrinsics. Besides GAN loss and GAN feature matching loss [49], we also enforce VGG perceptual loss [23, 73] and  $l_{1}$  loss between synthesized and ground truth images. The overall loss is as follows:
+
+$$
+\mathcal {L} _ {\text {A n i m a t i o n}} = \mathcal {L} _ {G A N} + 1 0 \mathcal {L} _ {F M} + \mathcal {L} _ {l _ {1}} + \mathcal {L} _ {V G G}. \tag {8}
+$$
+
+# 4. Experiments
+
+# 4.1. Implementation Details
+
+Our motion estimator is a U-Net [48] based generator with 16 convolutional layers, and we replace Batch Normalization with SPADE [42]. For the feature extraction network and image decoder network, we follow the network architectures from Wang et al. [64]. We adopt the multi-scale discriminator used in SPADE [42] during training.
+
+Our model is trained using the Adam optimizer [24]. We conduct all experiments on a single NVIDIA GeForce RTX 3090 GPU. We train the motion estimation network for around  $120k$  iterations with a batch size of 16. We set the generator learning rate to  $5 \times 10^{-4}$  and the discriminator learning rate to  $2 \times 10^{-3}$ . For the animation training stage, we train the feature extraction network and image decoder network for around  $250k$  iterations with a learning rate starting at  $1 \times 10^{-4}$  and then decaying exponentially.
+
+# 4.2. Baselines
+
+In principle, to evaluate our method, we are required to compare it against current state-of-the-art models. However, to our knowledge, we are the first to tackle the novel task of synthesizing a realistic cinematograph with compelling parallax effects from a single image. As a result, we cannot directly compare to previous works. Instead, we consider forming the following baselines to verify the superiority of our method:
+
+2D animation  $\rightarrow$  novel view synthesis. One might consider 2D image animation  $\rightarrow$  single-shot novel view synthesis: first employing a 2D image animation method, then
+
+Table 1. Quantitative comparisons against all baselines on the validation set from Holynski et al. [19]. The better approach favors higher PSNR and SSIM but lower LPIPS. The best performance is in bold.  
+
+<table><tr><td>Method</td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>2D Anim. [19] → NVS [52]</td><td>21.12</td><td>0.633</td><td>0.286</td></tr><tr><td>NV5 [52] → 2D Anim. [19]</td><td>21.97</td><td>0.697</td><td>0.276</td></tr><tr><td>NV5 [52] → 2D Anim. [19] + MA</td><td>22.47</td><td>0.718</td><td>0.261</td></tr><tr><td>Naive PC Anim.</td><td>19.46</td><td>0.647</td><td>0.243</td></tr><tr><td>Naive PC Anim. + 3DSA</td><td>20.49</td><td>0.660</td><td>0.237</td></tr><tr><td>Ours</td><td>23.33</td><td>0.776</td><td>0.197</td></tr></table>
+
+a single-shot novel view synthesis method. Specifically, we first adopt a state-of-the-art image animation method [19] to produce an animated looping video. We then apply DPT [45] to estimate geometry and utilize 3D Photo [52] to generate novel views for each frame.
+
+Novel view synthesis  $\rightarrow$  2D animation. It also appears to be feasible that we first render novel views of scenes by 3D Photo [52] and then use the image animation method [19] to animate each viewpoint. Note that motion estimation should be performed for each frame as viewpoints have changed. However, we empirically find that this usually results in varying motion fields across the video. To mitigate this, we further propose using the moving average technique to smooth estimated motions for each frame. This results in novel view synthesis  $\rightarrow$  2D animation + MA.
+
+Naive point cloud animation. Intuitively, we may also consider directly unprojecting pixels into 3D space and subsequently moving and rendering the RGB point cloud. Specifically, given a single input image, we first predict the depth map using DPT [45] and estimate 2D optical flow. We then lift the pixels and optical flow into 3D space to form RGB point clouds and scene flow. Finally, we animate RGB point clouds over time according to the scene flow and project these point clouds into target viewpoints. This baseline also faces a similar issue: as time goes by, large holes gradually appear. One might also employ our 3D symmetric animation technique to further enhance this baseline, i.e., naive point cloud animation + 3DSA.
+
+# 4.3. Results
+
+Evaluation dataset. Since Holynski et al. [19] only provide a single image for each scene in the test set, we use the validation set from Holynski et al. [19] to evaluate our method and baselines. The validation set consists of 31 unique scenes with 162 samples of ground truth video clips captured by static cameras.
+
+Experimental setup. For evaluation, we render novel views of the ground truth videos in 4 different trajectories, resulting in 240 ground truth frames for each sample. This process does not involve inpainting, thus ground truth frames may contain holes. Only considering valid pixels when calculating metrics, we compare the predicted images
+
+Table 2. User study. Pairwise comparison results indicate that users prefer our method as more realistic and immersive.  
+
+<table><tr><td>Comparison</td><td>Human preference</td></tr><tr><td>2D Anim. [19] → NVS [52] / Ours</td><td>12.5% / 87.5%</td></tr><tr><td>NVS [52] → 2D Anim. [19] / Ours</td><td>3.9% / 96.1%</td></tr><tr><td>NVS [52] → 2D Anim. [19] + MA / Ours</td><td>6.1% / 93.9%</td></tr><tr><td>Naive PC Anim. / Ours</td><td>7.6% / 92.4%</td></tr><tr><td>Naive PC Anim. + 3DSA / Ours</td><td>8.6% / 91.4%</td></tr><tr><td>3D Photo [52] / Ours</td><td>10.5% / 89.5%</td></tr><tr><td>Holynski et al. [19] / Ours</td><td>29.9% / 70.1%</td></tr></table>
+
+Table 3. Ablation study on each component of our method.  
+
+<table><tr><td></td><td>PSNR↑</td><td>SSIM↑</td><td>LPIPS↓</td></tr><tr><td>w/o features</td><td>21.50</td><td>0.674</td><td>0.228</td></tr><tr><td>w/o inpainting</td><td>22.86</td><td>0.763</td><td>0.216</td></tr><tr><td>w/o 3D symmetric animation</td><td>22.99</td><td>0.768</td><td>0.199</td></tr><tr><td>Full model</td><td>23.33</td><td>0.776</td><td>0.197</td></tr></table>
+
+with the ground truth frames at the same time and viewpoint. For a fair comparison, all methods utilize the depth maps estimated by DPT [45]. Since we focus on comparing rendering quality, all methods use ground truth optical flows, except that NVS  $[52] \rightarrow 2\mathrm{D}$  Anim. [19] and NVS  $[52] \rightarrow 2\mathrm{D}$  Anim. [19] + MA have to estimate optical flows for each frame apart from the first frame. We adopt PSNR, SSIM, and LPIPS [73] as our evaluation metrics.
+
+Quantitative comparisons. As shown in Table 1, our method outperforms all baselines across all metrics by a large margin. This result implies that our method achieves better perceptual quality and produces more realistic renderings, which demonstrates the superiority and effectiveness of our method.
+
+Qualitative comparisons. We showcase the visual comparisons in Fig. 4. One can observe that our method presents photorealistic results while other comparative baselines produce more or less visual artifacts. 2D Anim. [19]  $\rightarrow$  NVS [52] intends to generate stripped flickering artifacts. This is because 2D Anim. [19]  $\rightarrow$  NVS [52] predicts the depth map for each animated frame, leading to frequent changes in the 3D structure of the scene and inconsistent inpainting. NVS [52]  $\rightarrow$  2D Anim. [19] and NVS [52]  $\rightarrow$  2D Anim. [19] + MA show jelly-like effects as optical flow should be estimated for each novel view. This results in varying motion fields across the video and thus inconsistent animation. Although Naive PC Anim. and Naive PC Anim. + 3DSA also lift the workspace into 3D, they are often prone to produce noticeable holes inevitably. One reason for this is that they do not perform inpainting. Note that some artifacts are difficult to observe when only scanning static figures.
+
+Controllable animation. Our method is able to create 3D cinematographs from a single image automatically. Further, we show that our framework is also highly extensible. For example, we can involve masks and flow hints as extra in
+
+![](images/2b9a3b5024c703ad6a3950082d8e7607af5f5941a49d58059b4a31d7dd23adbb.jpg)
+
+![](images/4334070062cd3b6f3f61c4716f983ef356853d2f0c87bbdebda3acd11bb58f24.jpg)
+
+![](images/fa5cce382bbf43a37a88b618101d5ca4327f0c17d97b77d52c1b05d1eb0d96a0.jpg)
+
+![](images/a43c4c8a6d6d40a35c63778061a2597ce60ed6e21c39b83bae9c84489a4a2453.jpg)
+
+![](images/3b3d6ff5aef130dad9ac707fe69750ca678b5d366cde49ca651a5492e0252ded.jpg)
+
+![](images/8629ab41f0c9305323db490922edf6a4e47ba58c4307ccdbbf4ed438de1a7caf.jpg)
+
+![](images/651ff5c4abb3c8701b53eb6ed325a498989ab107ab1f61f94d7dcf2814b29bd4.jpg)  
+Figure 4. Qualitative comparisons against all baselines on the validation set from Holynski et al. [19]. Our method produces compelling results while other comparative alternatives suffer from visual artifacts. (a) 2D animation  $[19] \rightarrow$  novel view synthesis [52], (b) novel view synthesis  $[52] \rightarrow 2\mathrm{D}$  animation [19], (c) novel view synthesis  $[52] \rightarrow 2\mathrm{D}$  animation  $[19] +$  moving average, (d) naive point cloud animation, (e) naive point cloud animation  $+3\mathrm{D}$  symmetric animation, (f) our method, and (g) pseudo ground truth.
+
+![](images/331c677dbb65d9c8fcb4bd343646ea093a83117d483dd86880bdff02a28080be.jpg)
+
+![](images/9bdd6efad93b53201e3059bdb622697f8cdffc9b39353571ef3a60943de609c8.jpg)
+
+![](images/40ee3763d929b45715967b510caf5198dd53ef3dd243ee301bd4af3a6b2dfe69.jpg)
+
+![](images/58cf468364f685b31d3b6dc459e6806ee5bf50a14d606d81ff407aa0e4aa475b.jpg)
+
+![](images/101fdfc66c8e7d9d70c1b1878b53351507d8b82b79bc9d25898fcac07cb054bb.jpg)
+
+![](images/7da3049f12d0abc772d8572f44294c7bb2c968998b0b4142dbcafbfd9e767d1a.jpg)
+
+![](images/e3a2e79cca12412e125ac511395c5ac0c931e84fa031a1b4a2c001f842b53cc3.jpg)
+
+![](images/c7dae67b88b3dd693c188e1d35a4f93844c49e9bfc52632fe5e3999eef2772e4.jpg)
+
+![](images/907677b32cddcac887b489a70cb9d39cdbac34a0f1d53f82b35a8ac9442b405a.jpg)
+
+![](images/384c5b775982f07cf8871ad81a2107da7dc170eacb047dd6a682bca81edff17e.jpg)
+
+![](images/34793c795d25aff587522c040118594855e2b0d7894388abee62f1ff292d4184.jpg)
+
+![](images/802d9c0882d76105fca960886c7495e67b212f93ee128b99e8cf9b908e1cfb0b.jpg)
+
+![](images/2ae7891102eef16b2f71dff01c593fe55bd91fd679a83adce1cb01993d75e9e2.jpg)
+
+![](images/28ace664d6be5ce608c5751704199d8f3a9466423168636eaef72a15f9386770.jpg)
+
+![](images/6171cac29139afec89e9c37141a91e034a08b298fda2f7c0eaed46e54430c695.jpg)  
+Input  
+Figure 5. Controllable animation. By changing the masks and motion hints, our method can interactively control the animation.
+
+![](images/6512544ff9e2a4c89e35e5e0410b46730857ebefa3586d32891f5e604b655193.jpg)  
+Masks & motion hints
+
+![](images/438519e393db1e5206e2ed44c6a00dce4244e7b410324bda96632ea60ed34f4f.jpg)  
+Motion fields
+
+puts to augment our motion estimator. This brings two advantages: (1) more accurate flow estimation; (2) interactive and controllable animation. As shown in Fig. 5, we can control the animation of the scene by providing various masks and motion hints to obtain different motion fields.
+
+Generalizing on in-the-wild photos. To further demonstrate the generalization of our method, we also test our method on in-the-wild photos. We first create hemagraphs with camera motions on the test set from Holynski et al. [19], where, for each scene, only a single image is provided. We then select some online images at random to test our method. To accurately estimate motion fields, we provide masks and flow hints as extra inputs to our motion estimator. As shown in Fig. 6, our method produces reasonable results for in-the-wild inputs while other comparative
+
+alternatives yield visual artifacts or inconsistent animation.
+
+# 4.4. User Study
+
+We further conduct a user study to investigate how our method performs in the view of humans when compared with all baselines, 3D Photo [52], and Holynski et al. [19]. Specifically, we collect 50 photos from the test set of Holynski et al. [19] and the Internet. We use different approaches to generate videos with identical settings. During the study, we show each participant an input image and two animated videos generated by our method and a randomly selected approach in random order. 108 volunteers are invited to choose the method with better perceptual quality and realism, or none if it is hard to judge. We report the results in Table 2, which points out that our method surpasses alternative methods by a large margin in terms of the sense of reality and immersion.
+
+# 4.5. Ablation Study
+
+To validate the effect of each component, we conduct an ablation study on the validation set from Holynski et al. [19] and show the results in Table 3. One can observe: i) 3D symmetric animation technique matters because it allows us to leverage bidirectionally displaced point clouds to complement each other and feasibly fill in missing regions; ii)
+
+![](images/f5a81ab7b712b7b960749e52d83c52d407103fbd4cba6a5547a0585890164b7f.jpg)
+
+![](images/f15f25732e6450fed411f18299fa2ac6ecbc699da2e7d96cfb0faf5db0e8912f.jpg)
+
+![](images/a537a67f5067021e134728ef88014fc757aca63dbd184b9ce803199d7a572b23.jpg)
+
+![](images/f483a064c98f128c705ec1bc2c49ec7771c09ad5d6d3ff2748f7dfdf6c5faac3.jpg)
+
+![](images/1e9333e1c031bf1016858079d90cecb56c3910c4816f1f5dfbadc6eae3e00671.jpg)
+
+![](images/35fe3eb972a1809130e0d10285fae79b16cfae42c84a92aa0e99afc7e9e6d151.jpg)
+
+![](images/686417ad0b34fe4e82290b22a0e1390705cdca8f1343846e18101e735e69e82b.jpg)
+
+![](images/dcf5994d108ca3af8318dd9cc05c36f7662a96438da8eda2332971c021c5c1a5.jpg)
+
+![](images/14082932986a7cd6976251e28ce1a025d3f3ceb34249bedd0533c9af6210f144.jpg)
+
+![](images/775feb0956c44f1ecb7d5ede298bf1672b0ee9545e39db49209de96c71c87d05.jpg)
+
+![](images/4c808cd46b96d136f16ed5f2968847e9994cd67834dccc178c612fc00d07b773.jpg)
+
+![](images/dcfb77c70003a8e89315db6e2dcfb87597df19aba88455302bbe198b0bec233b.jpg)
+
+![](images/6a531b7a7972d6c3ea66dcb96e2e9eae2e9490a239bd9485594f1196377c4c03.jpg)
+
+![](images/bcb1951dc15289fde8623f0ec65bfd45bfa6221e67742d9aa58aea42471f36da.jpg)
+
+![](images/c2570be568c72ca139a833bfa69595dcb84907a38a2e3c8bbcb572f90d24ec02.jpg)
+
+![](images/d4b52e205f17b8e3e3f0f48959728534632f8588920125c9a895982d9acf98b7.jpg)  
+Input
+
+![](images/62b672b63224ab57a02712918e31b9ad7cbf7e898bbf05728e8068d8b69d1f60.jpg)  
+2D Anim.  $\rightarrow$  NVS
+
+![](images/76439cae103eb89c3da25766dd92b3002d79d9ee8b1183b89e558399ea883dcb.jpg)  
+$\mathrm{NVS}\rightarrow 2\mathrm{D}$  Anim.  $^+$  MA
+
+![](images/a0b8de3a8fac3435b38d3675b9502a511377a4f0588daf62921d5ec67ea165a9.jpg)  
+Naive PC Anim. + 3DSA  
+Figure 6. Visual comparisons on the test set from Holynski et al. [19] and in-the-wild photos. Our method consistently produces more realistic rendering with fewer visual artifacts as opposed to other baselines.
+
+![](images/bf29a9be76599a0ec19a90418f4e817bc7da3c7e836f8d67fd5f6c4c015ca424.jpg)  
+Ours
+
+introducing inpainting when constructing 3D geometry can improve the performance as this allows our model to produce plausible structures around depth discontinuities and fill in holes; iii) switching from directly using RGB colors to features in 3D scene representation significantly improves the rendering quality and reduces artifacts.
+
+# 5. Conclusion
+
+In this paper, we introduce a novel task of creating 3D cinematographs from single images. To this end, we present a simple yet effective method that makes a connection between image animation and novel view synthesis. We show that our method produces plausible animation of the scene while allowing camera movements. Our framework is flexible and customized. For accurate motion estimation and controllable animation, we can further include masks and flow hints as extra input for the motion estimator. Therefore, users can control how the scene is animated. Furthermore, our method generalizes well to in-the-wild photos, even like paintings or synthetic images generated by diffusion models. We conduct extensive experiments to ver
+
+ify the effectiveness and superiority of our method. A user study also demonstrates that our method generates realistic 3D cinematographs. We hope that our work can bring 3D cinematography into the sight of a broader community and motivate further research.
+
+Limitations and future work. Our method may not work well when the depth prediction module estimates erroneous geometry from the input image, e.g., thin structures. In addition, inappropriate motion fields will sometimes lead to undesirable results, e.g., some regions are mistakenly identified as frozen. As we take the first step towards 3D cinematography, in this paper, we focus on handling common moving elements, i.e., fluids. In other words, our method may not apply to more complex motions, e.g., cyclic motion. We leave this for our future work.
+
+Acknowledgements. This study is supported under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s). This work is also supported by Adobe Gift and the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 (MOE-T2EP20220-0007) and Tier 1 (RG14/22).
+
+# References
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+[3] Wenbo Bao, Wei-Sheng Lai, Chao Ma, Xiaoyun Zhang, Zhiyong Gao, and Ming-Hsuan Yang. Depth-aware video frame interpolation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 3703-3712, 2019. 2, 4  
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+[9] Paul E Debevec, Camillo J Taylor, and Jitendra Malik. Modeling and rendering architecture from photographs: A hybrid geometry-and image-based approach. In Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, pages 11-20, 1996. 2  
+[10] Alexey Dosovitskiy, Philipp Fischer, Eddy Ilg, Philip Hausser, Caner Hazirbas, Vladimir Golkov, Patrick Van Der Smagt, Daniel Cremers, and Thomas Brox. FlowNet: Learning optical flow with convolutional networks. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 2758-2766, 2015. 3  
+[11] Michail Christos Doukas, Stefanos Zafeiriou, and Viktoriia Sharmanska. HeadGAN: One-shot neural head synthesis and editing. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 14398-14407, 2021. 2  
+[12] Yuki Endo, Yoshihiro Kanamori, and Shigeru Kuriyama. Animating Landscape: Self-supervised learning of decoupled motion and appearance for single-image video synthesis. ACM Transactions on Graphics (Proceedings of ACM
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+SIGGRAPH Asia 2019), 38(6):175:1-175:19, 2019. 1, 2, 3, 4  
+[13] Siming Fan, Jingtan Piao, Chen Qian, Kwan-Yee Lin, and Hongsheng Li. Simulating fluids in real-world still images. arXiv preprint arXiv:2204.11335, 2022. 2  
+[14] Steven J Gortler, Radek Grzeszcuk, Richard Szeliski, and Michael F Cohen. The lumigraph. In Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, pages 43-54, 1996. 2  
+[15] Yuxuan Han, Ruicheng Wang, and Jiaolong Yang. Single-view synthesis in the wild with learned adaptive multiplane images. In ACM SIGGRAPH 2022 Conference Proceedings, pages 1-8, 2022. 2  
+[16] Jonathan Ho, William Chan, Chitwan Saharia, Jay Whang, Ruiqi Gao, Alexey Gritsenko, Diederik P Kingma, Ben Poole, Mohammad Norouzi, David J Fleet, et al. Imagen Video: High definition video generation with diffusion models. arXiv preprint arXiv:2210.02303, 2022. 2  
+[17] Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. In Advances in Neural Information Processing Systems (NeurIPS), 2020. 2  
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+        "text": "Yining Hong $^{1}$ , Chunru Lin $^{2}$ , Yilun Du $^{3}$ , Zhenfang Chen $^{5}$ , Joshua B. Tenenbaum $^{3}$ , Chuang Gan $^{4,5}$ ,  $^{1}$ UCLA,  $^{2}$ Shanghai Jiaotong University,  $^{3}$ MIT CSAIL,  $^{4}$ UMass Amherst,  $^{5}$ MIT-IBM Watson AI Lab https://vis-www.cs.umass.edu/3d-clr/",
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+            "Concept: Q: Are there any televisions? A: Yes",
+            "Counting:  \nQ: How many chairs are close to the table in the room with plant on the cabinet? A: 6",
+            "Q: How many rooms have sofas? A: 1",
+            "Figure 1. An exemplar scene with multi-view images and question-answer pairs of our 3DMV-VQA dataset. 3DMV-VQA contains four question types: concept, counting, relation, comparison. Orange words denote semantic concepts; blue words denote the relations."
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+            "Relation: Q: Facing the computer from the curtain, is there a lamp on the right? A: Yes",
+            "Q: What's on the cabinet in the smaller room? A: Plant"
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+            "Comparison:  \nQ: Are there fewer pictures in the larger room than the other room? A: No  \nQ: Is the computer closer to a printer or a lamp?  \nA: Printer"
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+        "text": "Abstract",
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+        "text": "Humans are able to accurately reason in 3D by gathering multi-view observations of the surrounding world. Inspired by this insight, we introduce a new large-scale benchmark for 3D multi-view visual question answering (3DMV-VQA). This dataset is collected by an embodied agent actively moving and capturing RGB images in an environment using the Habitat simulator. In total, it consists of approximately 5k scenes, 600k images, paired with 50k questions. We evaluate various state-of-the-art models for visual reasoning on our benchmark and find that they all perform poorly. We suggest",
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+        "text": "that a principled approach for 3D reasoning from multi-view images should be to infer a compact 3D representation of the world from the multi-view images, which is further grounded on open-vocabulary semantic concepts, and then to execute reasoning on these 3D representations. As the first step towards this approach, we propose a novel 3D concept learning and reasoning (3D-CLR) framework that seamlessly combines these components via neural fields, 2D pre-trained vision-language models, and neural reasoning operators. Experimental results suggest that our framework outperforms baseline models by a large margin, but the challenge remains largely unsolved. We further perform an in-depth analysis of the challenges and highlight potential future directions.",
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+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "1. Introduction",
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+        "text": "Visual reasoning, the ability to composite rules on internal representations to reason and answer questions about visual scenes, has been a long-standing challenge in the field of artificial intelligence and computer vision. Several datasets [23, 33, 69] have been proposed to tackle this challenge. However, they mainly focus on visual reasoning on 2D single-view images. Since 2D single-view images only cover a limited region of the whole space, such reasoning inevitably has several weaknesses, including occlusion, and failing to answer 3D-related questions about the entire scene that we are interested in. As shown in Fig. 1, it's difficult, even for humans, to count the number of chairs in a scene due to the object occlusion, and it's even harder to infer 3D relations like \"closer\" from a single-view 2D image.",
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+        "text": "On the other hand, there's strong psychological evidence that human beings conduct visual reasoning in the underlying 3D representations [55]. Recently, there have been several works focusing on 3D visual question answering [2,16,62,64]. They mainly use traditional 3D representations (e.g., point clouds) for visual reasoning. This is inconsistent with the way human beings perform 3D reasoning in real life. Instead of being given an entire 3D representation of the scene at once, humans will actively walk around and explore the whole environment, ingesting image observations from different views and converting them into a holistic 3D representation that assists them in understanding and reasoning about the environment. Such abilities are crucial for many embodied AI applications, such as building assistive robots.",
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+        "text": "To this end, we propose the novel task of 3D visual reasoning from multi-view images taken by active exploration of an embodied agent. Specifically, we generate a large-scale benchmark, 3DMV-VQA (3D multi-view visual question answering), that contains approximately 5k scenes and 50k question-answering pairs about these scenes. For each scene, we provide a collection of multi-view image observations. We generate this dataset by placing an embodied agent in the Habitat-Matterport environment [47], which actively explores the environment and takes pictures from different views. We also obtain scene graph annotations from the Habitat-Matterport 3D semantics dataset (HM3DSem) [61], including ground-truth locations, segmentations, semantic information of the objects, as well as relationships among the objects in the environments, for model diagnosis. To evaluate the models' 3D reasoning abilities on the entire environment, we design several 3D-related question types, including concept, counting, relation and comparison.",
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+        "text": "Given this new task, the key challenges we would like to investigate include: 1) how to efficiently obtain the compact visual representation to encode crucial properties (e.g., semantics and relations) by integrating all incomplete observations of the environment in the process of active exploration for 3D visual reasoning? 2) How to ground the semantic con",
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+        "text": "cepts on these 3D representations that could be leveraged for downstream tasks, such as visual reasoning? 3) How to infer the relations among the objects, and perform step-by-step reasoning?",
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+        "text": "As the first step to tackling these challenges, we propose a novel model, 3D-CLR (3D Concept Learning and Reasoning). First, to efficiently obtain a compact 3D representation from multi-view images, we use a neural-field model based on compact voxel grids [57] which is both fast to train and effective at storing scene properties in its voxel grids. As for concept learning, we observe that previous works on 3D scene understanding [1,3] lack the diversity and scale with regard to semantic concepts due to the limited amount of paired 3D-and-language data. Although large-scale vision-language models (VLMs) have achieved impressive performances for zero-shot semantic grounding on 2D images, leveraging these pretrained models for effective open-vocabulary 3D grounding of semantic concepts remains a challenge. To address these challenges, we propose to encode the features of a pre-trained 2D vision-language model (VLM) into the compact 3D representation defined across voxel locations. Specifically, we use the CLIP-LSeg [37] model to obtain features on multi-view images, and propose an alignment loss to map the features in our 3D voxel grid to 2D pixels. By calculating the dot-product attention between the 3D per-point features and CLIP language embeddings, we can ground the semantic concepts in the 3D compact representation. Finally, to answer the questions, we introduce a set of neural reasoning operators, including FILTER, COUNT, RELATION operators and so on, which take the 3D representations of different objects as input and output the predictions.",
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+        "text": "We conduct experiments on our proposed 3DMV-VQA benchmark. Experimental results show that our proposed 3D-CLR outperforms all baseline models a lot. However, failure cases and model diagnosis show that challenges still exist concerning the grounding of small objects and the separation of close object instances. We provide an in-depth analysis of the challenges and discuss potential future directions.",
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+        "text": "To sum up, we have the following contributions in this paper.",
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+            "- We propose the novel task of 3D concept learning and reasoning from multi-view images.",
+            "- By having robots actively explore the embodied environments, we collect a large-scale benchmark on 3D multiview visual question answering (3DMV-VQA).",
+            "- We devise a model that incorporates a neural radiance field, 2D pretrained vision and language model, and neural reasoning operators to ground the concepts and perform 3D reasoning on the multi-view images. We illustrate that our model outperforms all baseline models.",
+            "- We perform an in-depth analysis of the challenges of this new task and highlight potential future directions."
+        ],
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+        "text": "9203",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "text": "Visual Reasoning There have been numerous tasks focusing on learning visual concepts from natural language, including visually-grounded question answering [18, 19], text-image retrieval [59] and so on. Visual reasoning has drawn much attention recently as it requires human-like understanding of the visual scene. A wide variety of benchmarks have been created over the recent years [7, 8, 23, 27, 33, 69]. However, they mainly focus on visual reasoning from 2D single-view images, while there's strong psychological evidence that human beings perform visual reasoning on the underlying 3D representations. In this paper, we propose the novel task of visual reasoning from multi-view images, and collect a large-scale benchmark for this task. In recent years, numerous visual reasoning models have also been proposed, ranging from attention-based methods [5, 30], graph-based methods [28], to models based on large pretrained vision-language model [9, 38]. These methods model the reasoning process implicitly with neural networks. Neural-symbolic methods [6, 40, 65] explicitly perform symbolic reasoning on the objects representations and language representations. They use perception models to extract 2D masks as a first step, and then execute operators and ground concepts on these pre-segmented masks, but are limited to a set of predefined concepts on simple scenes. [26] proposes to use the feature vectors from occupancy networks [42] to do visual reasoning in the 3D space. However, they also use a synthetic dataset, and learn a limited set of semantic concepts from scratch. We propose to learn 3D neural field features from 2D multi-view real-world images, and incorporate a 2D VLM for open-vocabulary reasoning.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "3D Reasoning Understanding and reasoning about 3D scenes has been a long-standing challenge. Recent works focus on leveraging language to explore 3D scenes, such as object captioning [3,4] and object localization from language [1, 17, 29]. Our work is mostly related to 3D Visual Question Answering [2, 16, 62, 64] as we both focus on answering questions and reasoning about 3D scenes. However, these works use point clouds as 3D representations, which diverts from the way human beings perform 3D reasoning. Instead of being given an entire 3D representation all at once, human beings would actively move and explore the environment, integrating multi-view information to get a compact 3D representation. Therefore, we propose 3D reasoning from multi-view images. In addition, since 3D assets paired with natural language descriptions are hard to get in real-life scenarios, previous works struggle to ground open-vocabulary concepts. In our work, we leverage 2D VLMs for zero-shot open-vocabulary concept grounding in the 3D space.",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Embodied Reasoning Our work is also closely related to Embodied Question Answering (EQA) [11, 67] and Interactive Question Answering (IQA) [22, 35], which also involve an embodied agent exploring the environment and answering",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "the question. However, the reasoning mainly focuses on the outcome or the history of the navigation on 2D images and does not require a holistic 3D understanding of the environment. There are also works [12, 20, 51, 54, 56, 68] targeting instruction following in embodied environments, in which an agent is asked to perform a series of tasks based on language instructions. Different from their settings, for our benchmark an embodied agent actively explores the environment and takes multi-view images for 3D-related reasoning.",
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+    {
+        "type": "text",
+        "text": "Neural Fields Our approach utilizes neural fields to parameterize an underlying 3D compact representations of scenes for reasoning. Neural field models (e.g., [43]) have gained much popularity since they can reconstruct a volumetric 3D scene representation from a set of images. Recent works [21, 24, 57, 66] have pushed it further by using classic voxel-grids to explicitly store the scene properties (e.g., density, color and feature) for rendering, which allows for real-time rendering and is utilized by this paper. Neural fields have also been used to represent dynamic scenes [14, 44], appearance [43, 45, 49, 53, 63], physics [34], robotics [32, 52], acoustics [39] and more general multi-modal signals [13]. There are also some works that integrate semantics or language in neural fields [31, 60]. However, they mainly focus on using language for manipulation, editing or generation. [26] leverages neural descriptor field [52] for 3D concept grounding. However, they require ground-truth occupancy values to train the neural field, which can not be applied to real-world scenes. In this paper, we propose to leverage voxel-based neural radiance field [57] to get the compact representations for 3D visual reasoning.",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "3. Dataset Generation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1. Multi-View Images",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Our dataset includes 5k 3D scenes from the Habitat-Matterport 3D Dataset (HM3D) dataset [47], and approximately 600k images rendered from the 3D scenes. The images are rendered via Habitat [50, 58].",
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+        "text": "Scene Generation We build our benchmark on top of the HM3DSem dataset [61], which is a large-scale dataset of 3D real-world indoor scenes with densely annotated semantics. It consists of 142,646 object instance annotations across 216 3D spaces and 3,100 rooms within those spaces. HM3D dataset uses texture information to annotate pixel-accurate object boundaries, which provides large-scale object annotations and ensures the scale, quality, and diversity of 3D visual reasoning questions of our benchmark.",
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+    {
+        "type": "text",
+        "text": "To construct a benchmark that covers questions of different difficulty levels, it's crucial that we include 3D scenes of different scales in our benchmark. We start with single rooms in HM3D scenes, which has an appropriate amount of semantic concepts and relationships to base some simple questions on. To get the scale of single rooms, we calculate bounding",
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+        "page_idx": 2
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+    {
+        "type": "page_number",
+        "text": "9204",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "boxes of rooms according to floor instance segmentations. We then proceed to generate bounding boxes for scenes with multiple adjacent rooms. For more complex holistic scene understanding, we also include whole-house scenes, which may contain tens of rooms. Overall, the 3DMV-VQA benchmark contains three levels of scenes (2000 single-room scenes, 2000 multi-room scenes and 100 whole-house scenes).",
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+    {
+        "type": "text",
+        "text": "Image Rendering After we get the bounding box of each scene, we load the scene into the Habitat simulator. We also put a robot agent with an RGB sensor at a random initial point in the bounding box. The data is collected via exploration of the robot agent. Specifically, at each step of the data collection process, we sample a navigable point and make the agent move to the point along the shortest path. When the agent has arrived at a point, we rotate the agent  $30^{\\circ}$  along z-axis for 12 times so that the agent can observe the  $360^{\\circ}$  view of the scene at the position. It can also look up and down, with a random mild angle from  $[-10^{\\circ}, 10^{\\circ}]$  along the x-axis. A picture is taken each time the agent rotates to a new orientation. In total 12 pictures are taken from each point. While traveling between points, the robot agent further takes pictures. We also exploit a policy such that when the camera is too far from or too close to an object and thus the agent cannot see anything, we discard the bad-view images.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Questions and Answers",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "We pair each scene with machine-generated questions from pre-defined templates. All questions are open-ended and can be answered with a single word (samples in Fig. 1). Concepts and Relationships To generate questions and answers, we utilize the semantic annotations of HM3DSem [61] to get the semantic concepts and their bounding boxes, as well as the bounding boxes of the rooms. We merge semantic concepts with similar meanings (e.g., L-shaped sofa to sofa, desk chair / computer chair e.g. to chair). We also define 11 relationships: inside, above, below, on the top of, close, far, large, small, between, on the left, and on the right. Before generating questions, we first generate a scene graph for each scene containing all concepts and relationships.",
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+        "text": "Question Types We define four types of questions: concept, counting, relation and comparison.",
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+    {
+        "type": "list",
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+        "list_items": [
+            "- Concept. Conceptual questions query if there's an object of a certain semantic concept in the scene, or whether there's a room containing the objects of the semantic concept.",
+            "- Counting. Counting-related questions ask about how many instances of a semantic concept are in the scene, or how many rooms contain objects of the semantic concept.",
+            "- Relation. Relational questions ask about the 11 relationships and their compositions. Based on the number of relations in a question, we have one-hop to three-hop questions for the relation type.",
+            "- Comparison. The comparison question type focuses on the comparison of two objects, two semantic concepts or two"
+        ],
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "rooms. It can be combined with the relational concepts to compare two objects (e.g., larger, closer to, more left etc). It also compares the number of instances of two semantic concepts, or the number of objects of certain concepts in different rooms.",
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+    {
+        "type": "text",
+        "text": "Bias Control. Similar to previous visual reasoning benchmarks [26, 33], we use machine-generated questions since the generation process is fully controllable so that we can avoid dataset bias. Questions are generated from pre-defined templates, and transformed into natural language questions with associated semantic concepts and relationships from the scene. We manually define 41 templates for question generation. We use depth-first search to generate questions. We perform bias control based on three perspectives: template counts, answer counts, and concept counts. For selecting templates, we sort the templates each time we generate a question to ensure a balanced question distribution. We force a flat answer distribution for each template by rejection sampling. Specifically, once we generate a question and an answer, if the number of the questions having the same answer and template is significantly larger than other answers, we discard it and continue searching. Once we find an answer that fits in the ideal answer distribution, we stop the depth-first searching for this question. We also force a flat concept distribution for each template using the same method. In addition to controlling the number of concepts mentioned in the templates, we also control the number of relation tuples consisting of the same concept sets.",
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+    {
+        "type": "text",
+        "text": "4. Method",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Fig. 2 illustrates an overview of our framework. Specifically, our framework consists of three steps. First, we learn a 3D compact representation from multi-view images using neural field. And then we propose to leverage pre-trained 2D vision-and-language model to ground concepts on 3D space. This is achieved by 1) generating 2D pixel features using CLIP-LSeg; 2) aligning the features of 3D voxel grid and 2D pixel features from CLIP-LSeg [37]; 3) dot-product attention between the 3D features and CLIP language features [37]. Finally, to perform visual reasoning, we propose neural reasoning operators, which execute the question step by step on the 3D compact representation and outputs a final answer. For example, we use FILTER operators to ground semantic concepts on the 3D representation, GETINSTANCE to get all instances of a semantic class, and COUNT_RELATION to count how many pairs of the two semantic classes have the queried relation.",
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+    {
+        "type": "text",
+        "text": "4.1. Learning 3D Compact Scene Representations",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Neural radiance fields [43] are capable of learning a 3D representation that can reconstruct a volumetric 3D scene representation from a set of images. Voxel-based meth",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "9205",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/19407b31f659eff8444b6c2a799e47318398d9458986c4f843c53129e65b011a.jpg",
+        "image_caption": [
+            "Figure 2. An overview of our 3D-CLR framework. First, we learn a 3D compact scene representation from multi-view images using neural fields (I). Second, we use CLIP-LSeg model to get per-pixel 2D features (II). We utilize a 3D-2D alignment loss to assign features to the 3D compact representation (III). By calculating the dot-product attention between the 3D per-point features and CLIP language embeddings, we could get the concept grounding in 3D (IV). Finally, the reasoning process is performed via a set of neural reasoning operators, such as FILTER, GET instances and COUNT_RELATION (V). Relation operators are learned via relation networks."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "ods [21, 24, 57, 66] speed up the learning process by explicitly storing the scene properties (e.g., density, color and feature) in its voxel grids. We leverage Direct Voxel Grid Optimization (DVGO) [57] as our backbone for 3D compact representation for its fast speed. DVGO stores the learned density and color properties in its grid cells. The rendering of multi-view images is by interpolating through the voxel grids to get the density and color for each sampled point along each sampled ray, and integrating the colors based on the rendering alpha weights calculated from densities according to quadrature rule [41]. The model is trained by minimizing the L2 loss between the rendered multi-view images and the ground-truth multi-view images. By extracting the density voxel grid, we can get the 3D compact representation (e.g., By visualizing points with density greater than 0.5, we can get the 3D representation as shown in Fig. 2 I.)",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. 3D Semantic Concept Grounding",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Once we extract the 3D compact representation of the scene, we need to ground the semantic concepts for reasoning from language. Recent work from [26] has proposed to ground concepts from paired 3D assets and question-answers. Though promising results have been achieved on synthetic data, it is not feasible for open-vocabulary 3D reasoning in real-world data, since it is hard to collect largescale 3D vision-and-language paired data. To address this challenge, our idea is to leverage pre-trained 2D vision and language model [46, 48] for 3D concept grounding in real-",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "world scenes. But how can we map 2D concepts into 3D neural field representations? Note that 3D compact representations can be learned from 2D multi-view images and that each 2D pixel actually corresponds to several 3D points along the ray. Therefore, it's possible to get 3D features from 2D per-pixel features. Inspired by this, we first add a feature voxel grid representation to DVGO, in addition to density and color, to represent 3D features. We then apply CLIP-LSeg [37] to learn per-pixel 2D features, which can be attended to by CLIP concept embeddings. We use an alignment loss to align 3D features with 2D features so that we can perform concept grounding on the 3D representations.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "2D Feature Extraction. To get per-pixel features that can be attended by concept embeddings, we use the features from language-driven semantic segmentation (CLIP-LSeg) [37], which learns 2D per-pixel features from a pre-trained vision-language model (i.e., [46]). Specifically, it uses the text encoder from CLIP, trains an image encoder to produce an embedding vector for each pixel, and calculates the scores of word-pixel correlation by dot-product. By outputting the semantic class with the maximum score of each pixel, CLIP-LSeg is able to perform zero-shot 2D semantic segmentation.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "3D-2D Alignment. In addition to density and color, we also store a 512-dim feature in each grid cell in the compact representation. To align the 3D per-point features with 2D per-pixel features, we calculate an L1 loss between each pixel and each 3D point sampled on the ray of the pixel. The overall L1 loss along a ray is the weighted sum of all",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "9206",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "the pixel-point alignment losses, with weights same as the rendering weights:  $\\mathcal{L}_{\\mathrm{feature}} = \\sum_{i=1}^{K} w_i (\\| \\pmb{f}_i - F(\\pmb{r}) \\|)$ , where  $\\pmb{r}$  is a ray corresponding to a 2D pixel,  $F(\\pmb{r})$  is the 2D feature from CLIP-LSeg,  $K$  is the total number of sampled points along the ray and  $\\pmb{f}_i$  is the feature of point  $i$  by interpolating through the feature voxel grid,  $w_i$  is the rendering weight.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Concept Grounding through Attention. Since our feature voxel grid representation is learnt from CLIP-LSeg, by calculating the dot-product attention  $< f, v >$  between perpoint 3D feature  $f$  and the CLIP concept embeddings  $v$ , we can get zero-shot view-independent concept grounding and semantic segmentations in the 3D representation, as is presented in Fig. 2 IV.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Neural Reasoning Operators",
+        "text_level": 1,
+        "bbox": [
+            76,
+            297,
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Finally, we use the grounded semantic concepts for 3D reasoning from language. We first transform questions into a sequence of operators that can be executed on the 3D representation for reasoning. We adopt a LSTM-based semantic parser [65] for that. As [26, 40], we further devise a set of operators which can be executed on the 3D representation. Please refer to Appendix for a full list of operators.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Filter Operators. We filter all the grid cells with a certain semantic concept.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Get Instance Operators. We implement this by utilizing DBSCAN [15], an unsupervised algorithm which assigns clusters to a set of points. Specifically, given a set of points in the 3D space, it can group together the points that are closely packed together for instance segmentation.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Relation Operators. We cannot directly execute the relation on the 3D representation as we have not grounded relations. Thus, we represent each relation using a distinct neural module (which is practical as the vocabulary of relations is limited [36]). We first concatenate the voxel grid representations of all the referred objects and feed them into the relation network. The relation network consists of three 3D convolutional layers and then three 3D deconvolutional layers. A score is output by the relation network indicating whether the objects have the relationship or not. Since vanilla 3D CNNs are very slow, we use Sparse Convolution [10] instead. Based on the relations asked in the questions, different relation modules are chosen.",
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "text",
+        "text": "5.1. Experimental Setup",
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+        "type": "text",
+        "text": "Evaluation Metric. We report the visual question answering accuracy on the proposed 3DMV-VQA dataset w.r.t the four types of questions. The train/val/test split is 7:1:2.",
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+        "type": "text",
+        "text": "Implementation Details For 3D compact representations, we adopt the same architectures as DVGO, except skipping the coarse reconstruction phase and directly training the fine reconstruction phase. After that, we freeze the density voxel",
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+        "type": "text",
+        "text": "grid and color voxel grid, for the optimization of the feature voxel grid only. The feature grid has a world size of 100 and feature dim of 512. We train the compact representations for 100,000 iterations and the 3D features for another 20,000 iterations. For LSeg, we use the official demo model, which has the ViT-L/16 image encoder and CLIP's ViT-B/32 text encoder. We follow the official script for inference and use multi-scale inference. For DBSCAN, we use an epsilon value of 1.5, minimum samples of 2, and we use L1 as the clustering method. For the relation networks, each relation is encoded into a three-layer sparse 3D convolution network with hidden size 64. The output is then fed into a one-layer linear network to produce a score, which is normalized by sigmoid function. We use cross-entropy loss to train the relation networks, and we use the one-hop relational questions with \"yes/no\" answers to train the relation networks.",
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+        "text": "5.2. Baselines",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our baselines range from vanilla neural networks, attention-based methods, fine-tuned from large-scale VLM, and graph-based methods, to neural-symbolic methods.",
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+    {
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+        "list_items": [
+            "- LSTM. The question is transferred to word embeddings which are input into a word-level LSTM [25]. The last LSTM hidden state is fed into a multi-layer perceptron (MLP) that outputs a distribution over answers. This method is able to model question-conditional bias since it uses no image information.",
+            "- CNN+LSTM. The question is encoded by the final hidden states from LSTM. We use a resnet-50 to extract frame-level features of images and average them over the time dimension. The features are fed to an MLP to predict the final answer. This is a simple baseline that examines how vanilla neural networks perform on 3DMV-VQA.",
+            "- 3D-Feature+LSTM. We use the 3D features we get from 3D-2D alignment and downsample the voxel grids using 3D-CNN as input, concatenated with language features from LSTM and fed to an MLP.",
+            "- MAC [30]. MAC utilizes a Memory, Attention and Composition cell to perform iterative reasoning process. Like CNN+LSTM, we use the average pooling over multi-view images as the feature map.",
+            "- MAC(V). We treat the multi-view images along a trajectory as a video. We modify the MAC model by applying a temporal attention unit across the video frames to generate a latent encoding for the video.",
+            "- NS-VQA [65]. This is a 2D version of our 3D-CLR model. We use CLIP-LSeg to ground 2D semantic concepts from multi-view images, and the relation network also takes the 2D features as input. We execute the operators on each image and max pool from the answers to get our final predictions."
+        ],
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+    {
+        "type": "page_number",
+        "text": "9207",
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+    {
+        "type": "table",
+        "img_path": "images/23ab7991e1cfd752f1d4a8a42861878aba7055929c68ab960b80aebbac7c7b4f.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Methods</td><td>Concept</td><td>Counting</td><td>Relation</td><td>Comparison</td><td>Overall</td></tr><tr><td>Q-type (rand.)</td><td>49.4</td><td>10.7</td><td>21.6</td><td>49.2</td><td>26.4</td></tr><tr><td>LSTM</td><td>53.4</td><td>15.3</td><td>24.0</td><td>55.2</td><td>29.8</td></tr><tr><td>CNN+LSTM</td><td>57.8</td><td>22.1</td><td>35.2</td><td>59.7</td><td>37.8</td></tr><tr><td>MAC</td><td>62.4</td><td>19.7</td><td>47.8</td><td>62.3</td><td>46.7</td></tr><tr><td>MAC(V)</td><td>60.0</td><td>24.6</td><td>51.6</td><td>65.9</td><td>50.0</td></tr><tr><td>NS-VQA</td><td>59.8</td><td>21.5</td><td>33.4</td><td>61.6</td><td>38.0</td></tr><tr><td>ALPRO</td><td>65.8</td><td>12.7</td><td>42.2</td><td>68.2</td><td>43.3</td></tr><tr><td>LGCN</td><td>56.2</td><td>19.5</td><td>35.5</td><td>66.7</td><td>39.1</td></tr><tr><td>3D-Feature+LSTM</td><td>61.2</td><td>22.4</td><td>49.9</td><td>61.3</td><td>48.2</td></tr><tr><td>3D-CLR (Ours)</td><td>66.1</td><td>41.3</td><td>57.6</td><td>72.3</td><td>57.7</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1. Question-answering accuracy of 3D visual reasoning baselines on different question types.",
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+        "list_items": [
+            "- ALPRO [38]. ALPRO is a video-and-language pre-training framework. A transformer model is pretrained on large webly-source video-text pairs and can be used for downstream tasks like Video Question answering.",
+            "- LGCN [28]. LGCN represents the contents in the video as a location-aware graph by incorporating the location information of an object into the graph construction."
+        ],
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+    {
+        "type": "text",
+        "text": "5.3. Experimental Results",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Result Analysis. We summarize the performances for each question type of baseline models in Table 1. All models are trained on the training set until convergence, tuned on the validation set, and evaluated on the test set. We provide detailed analysis below.",
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+        "text": "First, for the examination of language-bias of the dataset, we find that the performance of LSTM is only slightly higher than random and frequency, and all other baselines outperform LSTM a lot. This suggests that there's little language bias in our dataset. Second, we observe that encoding temporal information in MAC (i.e., MAC(V)) is better than average-pooling of the features, especially in counting and relation. This suggests that average-pooling of the features may cause the model to lose information from multi-view images, while attention on multi-view images helps boost the 3D reasoning performances. Third, we also find that fine-tuning on large-scale pretrained model (i.e., ALPRO) has relatively high accuracies in concept-related questions, but for counting it's only slightly higher than the random baseline, suggesting that pretraining on large-scale video-language dataset may improve the model's perception ability, but does not provide the model with the ability to tackle with more difficult reasoning types such as counting. Next, we find that LGCN has poor performances on the relational questions, indicating that building a location-aware graph over 2D objects still doesn't equip the model with 3D location reasoning abilities. Last but not least, we find that 3D-based baselines are better than their 2D counterparts. 3D-Feature+LSTM performs well on the 3D-related questions, such as counting and relation, than most of the image-based",
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+    {
+        "type": "text",
+        "text": "basielines. Compared with 3D-CLR, NS-VQA can perform well in the conceptual questions. However, it underperforms 3D-CLR a lot in counting and relation, suggesting that these two types of questions require the holistic 3D understanding of the entire 3D scenes. Our 3D-CLR outperforms other baselines by a large margin, but is still far from satisfying. From the accuracy of the conceptual question, we can see that it can only ground approximately  $66\\%$  of the semantic concepts. This indicates that our 3DMV-VQA dataset is indeed very challenging.",
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+    {
+        "type": "text",
+        "text": "Qualitative Examples. In Fig. 3, we show four qualitative examples. From the examples, we show that our 3D-CLR can infer an accurate 3D representation from multi-view images, as well as ground semantic concepts on the 3D representations to get the semantic segmentations of the entire scene. Our 3D-CLR can also learn 3D relationships such as \"close\", \"largest\", \"on top of\" and so on. However, 3D-CLR also fails on some questions. For the third scene in the qualitative examples, it fails to ground the concepts \"mouse\" and \"printer\". Also, it cannot accurately count the instances sometimes. We give detailed discussions below.",
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+    {
+        "type": "text",
+        "text": "5.4. Discussions",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We perform an in-depth analysis to understand the challenge of this dataset. We leverage the modular design of our 3D-CLR, replacing individual components of the framework with ground-truth annotations for model diagnosis. The result is shown in Fig 4. 3D-CLR w/ Semantic denotes our model with ground-truth semantic concepts from HM3DSem annotations. 3D-CLR w/ Instance denotes that we have ground-truth instance segmentations of semantic concepts. From Fig. 3 and Fig. 4, we summarize several key challenges of our benchmark:",
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+    {
+        "type": "text",
+        "text": "Very close object instances From Fig. 4, we can see that even with ground-truth semantic labeling of the 3D points, 3D-CLR still has unsatisfying results on counting questions. This suggests that the instance segmentations provided by DBSCAN are not accurate enough. From the top two qualitative examples in Fig. 3, we can also see that if two chairs",
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+    {
+        "type": "page_number",
+        "text": "9208",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/e5f9988ee998345087af1d898b960d9fdfd34ec0911c04da788d53c90dc149f8.jpg",
+        "image_caption": [
+            "Figure 3. Qualitative examples of our 3D-CLR. We can see that 3D-CLR can ground most of the concepts and answer most questions correctly. However, it still fails sometimes, mainly because it cannot separate close object instances and ground small objects."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/5ce1c4d9a9daa672b4fac5b8b44d25fd911caa8af39a62561b7b2db9edf488ea.jpg",
+        "image_caption": [
+            "Figure 4. Model diagnosis of our 3D-CLR."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "contact each other, DBSCAN will not tell them apart and thus have poor performance on counting. One crucial future direction is to improve unsupervised instance segmentations on very close object instances.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Grounding small objects Fig. 4 suggests that 3D-CLR fails to ground a large portion of the semantic concepts, which hinders the performance. From the last example in Fig. 3, we can see that 3D-CLR fails to ground small objects like \"computer mouse\". Further examination indicates there are two possible reasons: 1) CLIP-LSeg fails to assign the right features to objects with limited pixels; 2) The resolution of feature voxel grid is not high enough and therefore small objects cannot be represented in the compact representation. An interesting future direction would be learning exploration policies that enable the agents to get closer to uncertain objects that cannot be grounded.",
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+    {
+        "type": "text",
+        "text": "Ambiguity on 3D relations Even with ground-truth seman",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "tic and instance segmentations, the performance of the relation network still needs to be improved. We find that most of the failure cases are correlated to the \"inside\" relation. From the segmentations in Fig. 3, we can see that 3D-CLR is unable to ground the objects in the cabinets. A potential solution can be joint depth and segmentation predictions.",
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+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this paper, we introduce the novel task of 3D reasoning from multi-view images. By placing embodied robot that actively explores indoor environments, we collect a large-scale benchmark named 3DMV-VQA. We also propose a new 3D-CLR model that incorporates neural field, 2D VLM, as well as reasoning operators for this task and illustrate its effectiveness. Finally, we perform an in-depth analysis to understand the challenges of this dataset and also point out potential future directions. We hope that 3DMV-VQA can be used to push the frontiers of 3D reasoning.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements. This work was supported by the MIT-IBM Watson AI Lab, DARPA MCS, DSO grant DSOCO21072, and gift funding from MERL, Cisco, Sony, and Amazon. We would also like to thank the computation support from AiMOS, a server cluster for the IBM Research AI Hardware Center.",
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+    {
+        "type": "page_number",
+        "text": "9209",
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+    },
+    {
+        "type": "text",
+        "text": "References",
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+        "page_idx": 8
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2023/3D Concept Learning and Reasoning From Multi-View Images/6720ecfb-203e-4307-9b9b-8d1051d4343b_origin.pdf

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2023/3D Concept Learning and Reasoning From Multi-View Images/full.md

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+# 3D Concept Learning and Reasoning from Multi-View Images
+
+Yining Hong $^{1}$ , Chunru Lin $^{2}$ , Yilun Du $^{3}$ , Zhenfang Chen $^{5}$ , Joshua B. Tenenbaum $^{3}$ , Chuang Gan $^{4,5}$ ,  $^{1}$ UCLA,  $^{2}$ Shanghai Jiaotong University,  $^{3}$ MIT CSAIL,  $^{4}$ UMass Amherst,  $^{5}$ MIT-IBM Watson AI Lab https://vis-www.cs.umass.edu/3d-clr/
+
+![](images/0139c5dde162a2aa92dcfb3c8dcbb7922e85a282412b0fa7132181e9fb7d8996.jpg)  
+Concept: Q: Are there any televisions? A: Yes  
+Counting:  
+Q: How many chairs are close to the table in the room with plant on the cabinet? A: 6  
+Q: How many rooms have sofas? A: 1  
+Figure 1. An exemplar scene with multi-view images and question-answer pairs of our 3DMV-VQA dataset. 3DMV-VQA contains four question types: concept, counting, relation, comparison. Orange words denote semantic concepts; blue words denote the relations.
+
+![](images/9c2499a72b5232613521f83970886d73892accd35822abbe76380eef8f2aa6d4.jpg)
+
+![](images/bcdc54a8ca47ecfc2e80d202e50dbd8f6ca69bcd75c2d68e299c3a97942513b0.jpg)
+
+![](images/adb9c46914582c93ffb458cac411cec963fc04c004c0d353d24ebdb993d37a5a.jpg)
+
+![](images/8b29d6f5ef01af8dd76de5ff59d2297cdec550b6c7ae842222df4b69bb5b62d8.jpg)  
+Relation: Q: Facing the computer from the curtain, is there a lamp on the right? A: Yes  
+Q: What's on the cabinet in the smaller room? A: Plant
+
+![](images/49645c25bde17b0db6d9b773fde5388ec829dbf8fc93453c2f9d34d1a84bd58e.jpg)
+
+![](images/533b12da53016d7d003d444faa1199643658affa31d497d3c6002146c1f27325.jpg)  
+Comparison:  
+Q: Are there fewer pictures in the larger room than the other room? A: No  
+Q: Is the computer closer to a printer or a lamp?  
+A: Printer
+
+![](images/874bbee417fccf7c5a5cbc21ef58df9624603c16927e8facc7e608b9c78004c5.jpg)
+
+![](images/8c5023c7c3bb44a5cbe06b847a2eb0751a7ff0bfc87e1dd62dc7e15795a12609.jpg)
+
+# Abstract
+
+Humans are able to accurately reason in 3D by gathering multi-view observations of the surrounding world. Inspired by this insight, we introduce a new large-scale benchmark for 3D multi-view visual question answering (3DMV-VQA). This dataset is collected by an embodied agent actively moving and capturing RGB images in an environment using the Habitat simulator. In total, it consists of approximately 5k scenes, 600k images, paired with 50k questions. We evaluate various state-of-the-art models for visual reasoning on our benchmark and find that they all perform poorly. We suggest
+
+that a principled approach for 3D reasoning from multi-view images should be to infer a compact 3D representation of the world from the multi-view images, which is further grounded on open-vocabulary semantic concepts, and then to execute reasoning on these 3D representations. As the first step towards this approach, we propose a novel 3D concept learning and reasoning (3D-CLR) framework that seamlessly combines these components via neural fields, 2D pre-trained vision-language models, and neural reasoning operators. Experimental results suggest that our framework outperforms baseline models by a large margin, but the challenge remains largely unsolved. We further perform an in-depth analysis of the challenges and highlight potential future directions.
+
+# 1. Introduction
+
+Visual reasoning, the ability to composite rules on internal representations to reason and answer questions about visual scenes, has been a long-standing challenge in the field of artificial intelligence and computer vision. Several datasets [23, 33, 69] have been proposed to tackle this challenge. However, they mainly focus on visual reasoning on 2D single-view images. Since 2D single-view images only cover a limited region of the whole space, such reasoning inevitably has several weaknesses, including occlusion, and failing to answer 3D-related questions about the entire scene that we are interested in. As shown in Fig. 1, it's difficult, even for humans, to count the number of chairs in a scene due to the object occlusion, and it's even harder to infer 3D relations like "closer" from a single-view 2D image.
+
+On the other hand, there's strong psychological evidence that human beings conduct visual reasoning in the underlying 3D representations [55]. Recently, there have been several works focusing on 3D visual question answering [2,16,62,64]. They mainly use traditional 3D representations (e.g., point clouds) for visual reasoning. This is inconsistent with the way human beings perform 3D reasoning in real life. Instead of being given an entire 3D representation of the scene at once, humans will actively walk around and explore the whole environment, ingesting image observations from different views and converting them into a holistic 3D representation that assists them in understanding and reasoning about the environment. Such abilities are crucial for many embodied AI applications, such as building assistive robots.
+
+To this end, we propose the novel task of 3D visual reasoning from multi-view images taken by active exploration of an embodied agent. Specifically, we generate a large-scale benchmark, 3DMV-VQA (3D multi-view visual question answering), that contains approximately 5k scenes and 50k question-answering pairs about these scenes. For each scene, we provide a collection of multi-view image observations. We generate this dataset by placing an embodied agent in the Habitat-Matterport environment [47], which actively explores the environment and takes pictures from different views. We also obtain scene graph annotations from the Habitat-Matterport 3D semantics dataset (HM3DSem) [61], including ground-truth locations, segmentations, semantic information of the objects, as well as relationships among the objects in the environments, for model diagnosis. To evaluate the models' 3D reasoning abilities on the entire environment, we design several 3D-related question types, including concept, counting, relation and comparison.
+
+Given this new task, the key challenges we would like to investigate include: 1) how to efficiently obtain the compact visual representation to encode crucial properties (e.g., semantics and relations) by integrating all incomplete observations of the environment in the process of active exploration for 3D visual reasoning? 2) How to ground the semantic con
+
+cepts on these 3D representations that could be leveraged for downstream tasks, such as visual reasoning? 3) How to infer the relations among the objects, and perform step-by-step reasoning?
+
+As the first step to tackling these challenges, we propose a novel model, 3D-CLR (3D Concept Learning and Reasoning). First, to efficiently obtain a compact 3D representation from multi-view images, we use a neural-field model based on compact voxel grids [57] which is both fast to train and effective at storing scene properties in its voxel grids. As for concept learning, we observe that previous works on 3D scene understanding [1,3] lack the diversity and scale with regard to semantic concepts due to the limited amount of paired 3D-and-language data. Although large-scale vision-language models (VLMs) have achieved impressive performances for zero-shot semantic grounding on 2D images, leveraging these pretrained models for effective open-vocabulary 3D grounding of semantic concepts remains a challenge. To address these challenges, we propose to encode the features of a pre-trained 2D vision-language model (VLM) into the compact 3D representation defined across voxel locations. Specifically, we use the CLIP-LSeg [37] model to obtain features on multi-view images, and propose an alignment loss to map the features in our 3D voxel grid to 2D pixels. By calculating the dot-product attention between the 3D per-point features and CLIP language embeddings, we can ground the semantic concepts in the 3D compact representation. Finally, to answer the questions, we introduce a set of neural reasoning operators, including FILTER, COUNT, RELATION operators and so on, which take the 3D representations of different objects as input and output the predictions.
+
+We conduct experiments on our proposed 3DMV-VQA benchmark. Experimental results show that our proposed 3D-CLR outperforms all baseline models a lot. However, failure cases and model diagnosis show that challenges still exist concerning the grounding of small objects and the separation of close object instances. We provide an in-depth analysis of the challenges and discuss potential future directions.
+
+To sum up, we have the following contributions in this paper.
+
+- We propose the novel task of 3D concept learning and reasoning from multi-view images.  
+- By having robots actively explore the embodied environments, we collect a large-scale benchmark on 3D multiview visual question answering (3DMV-VQA).  
+- We devise a model that incorporates a neural radiance field, 2D pretrained vision and language model, and neural reasoning operators to ground the concepts and perform 3D reasoning on the multi-view images. We illustrate that our model outperforms all baseline models.  
+- We perform an in-depth analysis of the challenges of this new task and highlight potential future directions.
+
+# 2. Related Work
+
+Visual Reasoning There have been numerous tasks focusing on learning visual concepts from natural language, including visually-grounded question answering [18, 19], text-image retrieval [59] and so on. Visual reasoning has drawn much attention recently as it requires human-like understanding of the visual scene. A wide variety of benchmarks have been created over the recent years [7, 8, 23, 27, 33, 69]. However, they mainly focus on visual reasoning from 2D single-view images, while there's strong psychological evidence that human beings perform visual reasoning on the underlying 3D representations. In this paper, we propose the novel task of visual reasoning from multi-view images, and collect a large-scale benchmark for this task. In recent years, numerous visual reasoning models have also been proposed, ranging from attention-based methods [5, 30], graph-based methods [28], to models based on large pretrained vision-language model [9, 38]. These methods model the reasoning process implicitly with neural networks. Neural-symbolic methods [6, 40, 65] explicitly perform symbolic reasoning on the objects representations and language representations. They use perception models to extract 2D masks as a first step, and then execute operators and ground concepts on these pre-segmented masks, but are limited to a set of predefined concepts on simple scenes. [26] proposes to use the feature vectors from occupancy networks [42] to do visual reasoning in the 3D space. However, they also use a synthetic dataset, and learn a limited set of semantic concepts from scratch. We propose to learn 3D neural field features from 2D multi-view real-world images, and incorporate a 2D VLM for open-vocabulary reasoning.
+
+3D Reasoning Understanding and reasoning about 3D scenes has been a long-standing challenge. Recent works focus on leveraging language to explore 3D scenes, such as object captioning [3,4] and object localization from language [1, 17, 29]. Our work is mostly related to 3D Visual Question Answering [2, 16, 62, 64] as we both focus on answering questions and reasoning about 3D scenes. However, these works use point clouds as 3D representations, which diverts from the way human beings perform 3D reasoning. Instead of being given an entire 3D representation all at once, human beings would actively move and explore the environment, integrating multi-view information to get a compact 3D representation. Therefore, we propose 3D reasoning from multi-view images. In addition, since 3D assets paired with natural language descriptions are hard to get in real-life scenarios, previous works struggle to ground open-vocabulary concepts. In our work, we leverage 2D VLMs for zero-shot open-vocabulary concept grounding in the 3D space.
+
+Embodied Reasoning Our work is also closely related to Embodied Question Answering (EQA) [11, 67] and Interactive Question Answering (IQA) [22, 35], which also involve an embodied agent exploring the environment and answering
+
+the question. However, the reasoning mainly focuses on the outcome or the history of the navigation on 2D images and does not require a holistic 3D understanding of the environment. There are also works [12, 20, 51, 54, 56, 68] targeting instruction following in embodied environments, in which an agent is asked to perform a series of tasks based on language instructions. Different from their settings, for our benchmark an embodied agent actively explores the environment and takes multi-view images for 3D-related reasoning.
+
+Neural Fields Our approach utilizes neural fields to parameterize an underlying 3D compact representations of scenes for reasoning. Neural field models (e.g., [43]) have gained much popularity since they can reconstruct a volumetric 3D scene representation from a set of images. Recent works [21, 24, 57, 66] have pushed it further by using classic voxel-grids to explicitly store the scene properties (e.g., density, color and feature) for rendering, which allows for real-time rendering and is utilized by this paper. Neural fields have also been used to represent dynamic scenes [14, 44], appearance [43, 45, 49, 53, 63], physics [34], robotics [32, 52], acoustics [39] and more general multi-modal signals [13]. There are also some works that integrate semantics or language in neural fields [31, 60]. However, they mainly focus on using language for manipulation, editing or generation. [26] leverages neural descriptor field [52] for 3D concept grounding. However, they require ground-truth occupancy values to train the neural field, which can not be applied to real-world scenes. In this paper, we propose to leverage voxel-based neural radiance field [57] to get the compact representations for 3D visual reasoning.
+
+# 3. Dataset Generation
+
+# 3.1. Multi-View Images
+
+Our dataset includes 5k 3D scenes from the Habitat-Matterport 3D Dataset (HM3D) dataset [47], and approximately 600k images rendered from the 3D scenes. The images are rendered via Habitat [50, 58].
+
+Scene Generation We build our benchmark on top of the HM3DSem dataset [61], which is a large-scale dataset of 3D real-world indoor scenes with densely annotated semantics. It consists of 142,646 object instance annotations across 216 3D spaces and 3,100 rooms within those spaces. HM3D dataset uses texture information to annotate pixel-accurate object boundaries, which provides large-scale object annotations and ensures the scale, quality, and diversity of 3D visual reasoning questions of our benchmark.
+
+To construct a benchmark that covers questions of different difficulty levels, it's crucial that we include 3D scenes of different scales in our benchmark. We start with single rooms in HM3D scenes, which has an appropriate amount of semantic concepts and relationships to base some simple questions on. To get the scale of single rooms, we calculate bounding
+
+boxes of rooms according to floor instance segmentations. We then proceed to generate bounding boxes for scenes with multiple adjacent rooms. For more complex holistic scene understanding, we also include whole-house scenes, which may contain tens of rooms. Overall, the 3DMV-VQA benchmark contains three levels of scenes (2000 single-room scenes, 2000 multi-room scenes and 100 whole-house scenes).
+
+Image Rendering After we get the bounding box of each scene, we load the scene into the Habitat simulator. We also put a robot agent with an RGB sensor at a random initial point in the bounding box. The data is collected via exploration of the robot agent. Specifically, at each step of the data collection process, we sample a navigable point and make the agent move to the point along the shortest path. When the agent has arrived at a point, we rotate the agent  $30^{\circ}$  along z-axis for 12 times so that the agent can observe the  $360^{\circ}$  view of the scene at the position. It can also look up and down, with a random mild angle from  $[-10^{\circ}, 10^{\circ}]$  along the x-axis. A picture is taken each time the agent rotates to a new orientation. In total 12 pictures are taken from each point. While traveling between points, the robot agent further takes pictures. We also exploit a policy such that when the camera is too far from or too close to an object and thus the agent cannot see anything, we discard the bad-view images.
+
+# 3.2. Questions and Answers
+
+We pair each scene with machine-generated questions from pre-defined templates. All questions are open-ended and can be answered with a single word (samples in Fig. 1). Concepts and Relationships To generate questions and answers, we utilize the semantic annotations of HM3DSem [61] to get the semantic concepts and their bounding boxes, as well as the bounding boxes of the rooms. We merge semantic concepts with similar meanings (e.g., L-shaped sofa to sofa, desk chair / computer chair e.g. to chair). We also define 11 relationships: inside, above, below, on the top of, close, far, large, small, between, on the left, and on the right. Before generating questions, we first generate a scene graph for each scene containing all concepts and relationships.
+
+Question Types We define four types of questions: concept, counting, relation and comparison.
+
+- Concept. Conceptual questions query if there's an object of a certain semantic concept in the scene, or whether there's a room containing the objects of the semantic concept.  
+- Counting. Counting-related questions ask about how many instances of a semantic concept are in the scene, or how many rooms contain objects of the semantic concept.  
+- Relation. Relational questions ask about the 11 relationships and their compositions. Based on the number of relations in a question, we have one-hop to three-hop questions for the relation type.  
+- Comparison. The comparison question type focuses on the comparison of two objects, two semantic concepts or two
+
+rooms. It can be combined with the relational concepts to compare two objects (e.g., larger, closer to, more left etc). It also compares the number of instances of two semantic concepts, or the number of objects of certain concepts in different rooms.
+
+Bias Control. Similar to previous visual reasoning benchmarks [26, 33], we use machine-generated questions since the generation process is fully controllable so that we can avoid dataset bias. Questions are generated from pre-defined templates, and transformed into natural language questions with associated semantic concepts and relationships from the scene. We manually define 41 templates for question generation. We use depth-first search to generate questions. We perform bias control based on three perspectives: template counts, answer counts, and concept counts. For selecting templates, we sort the templates each time we generate a question to ensure a balanced question distribution. We force a flat answer distribution for each template by rejection sampling. Specifically, once we generate a question and an answer, if the number of the questions having the same answer and template is significantly larger than other answers, we discard it and continue searching. Once we find an answer that fits in the ideal answer distribution, we stop the depth-first searching for this question. We also force a flat concept distribution for each template using the same method. In addition to controlling the number of concepts mentioned in the templates, we also control the number of relation tuples consisting of the same concept sets.
+
+# 4. Method
+
+Fig. 2 illustrates an overview of our framework. Specifically, our framework consists of three steps. First, we learn a 3D compact representation from multi-view images using neural field. And then we propose to leverage pre-trained 2D vision-and-language model to ground concepts on 3D space. This is achieved by 1) generating 2D pixel features using CLIP-LSeg; 2) aligning the features of 3D voxel grid and 2D pixel features from CLIP-LSeg [37]; 3) dot-product attention between the 3D features and CLIP language features [37]. Finally, to perform visual reasoning, we propose neural reasoning operators, which execute the question step by step on the 3D compact representation and outputs a final answer. For example, we use FILTER operators to ground semantic concepts on the 3D representation, GETINSTANCE to get all instances of a semantic class, and COUNT_RELATION to count how many pairs of the two semantic classes have the queried relation.
+
+# 4.1. Learning 3D Compact Scene Representations
+
+Neural radiance fields [43] are capable of learning a 3D representation that can reconstruct a volumetric 3D scene representation from a set of images. Voxel-based meth
+
+![](images/19407b31f659eff8444b6c2a799e47318398d9458986c4f843c53129e65b011a.jpg)  
+Figure 2. An overview of our 3D-CLR framework. First, we learn a 3D compact scene representation from multi-view images using neural fields (I). Second, we use CLIP-LSeg model to get per-pixel 2D features (II). We utilize a 3D-2D alignment loss to assign features to the 3D compact representation (III). By calculating the dot-product attention between the 3D per-point features and CLIP language embeddings, we could get the concept grounding in 3D (IV). Finally, the reasoning process is performed via a set of neural reasoning operators, such as FILTER, GET instances and COUNT_RELATION (V). Relation operators are learned via relation networks.
+
+ods [21, 24, 57, 66] speed up the learning process by explicitly storing the scene properties (e.g., density, color and feature) in its voxel grids. We leverage Direct Voxel Grid Optimization (DVGO) [57] as our backbone for 3D compact representation for its fast speed. DVGO stores the learned density and color properties in its grid cells. The rendering of multi-view images is by interpolating through the voxel grids to get the density and color for each sampled point along each sampled ray, and integrating the colors based on the rendering alpha weights calculated from densities according to quadrature rule [41]. The model is trained by minimizing the L2 loss between the rendered multi-view images and the ground-truth multi-view images. By extracting the density voxel grid, we can get the 3D compact representation (e.g., By visualizing points with density greater than 0.5, we can get the 3D representation as shown in Fig. 2 I.)
+
+# 4.2. 3D Semantic Concept Grounding
+
+Once we extract the 3D compact representation of the scene, we need to ground the semantic concepts for reasoning from language. Recent work from [26] has proposed to ground concepts from paired 3D assets and question-answers. Though promising results have been achieved on synthetic data, it is not feasible for open-vocabulary 3D reasoning in real-world data, since it is hard to collect largescale 3D vision-and-language paired data. To address this challenge, our idea is to leverage pre-trained 2D vision and language model [46, 48] for 3D concept grounding in real-
+
+world scenes. But how can we map 2D concepts into 3D neural field representations? Note that 3D compact representations can be learned from 2D multi-view images and that each 2D pixel actually corresponds to several 3D points along the ray. Therefore, it's possible to get 3D features from 2D per-pixel features. Inspired by this, we first add a feature voxel grid representation to DVGO, in addition to density and color, to represent 3D features. We then apply CLIP-LSeg [37] to learn per-pixel 2D features, which can be attended to by CLIP concept embeddings. We use an alignment loss to align 3D features with 2D features so that we can perform concept grounding on the 3D representations.
+
+2D Feature Extraction. To get per-pixel features that can be attended by concept embeddings, we use the features from language-driven semantic segmentation (CLIP-LSeg) [37], which learns 2D per-pixel features from a pre-trained vision-language model (i.e., [46]). Specifically, it uses the text encoder from CLIP, trains an image encoder to produce an embedding vector for each pixel, and calculates the scores of word-pixel correlation by dot-product. By outputting the semantic class with the maximum score of each pixel, CLIP-LSeg is able to perform zero-shot 2D semantic segmentation.
+
+3D-2D Alignment. In addition to density and color, we also store a 512-dim feature in each grid cell in the compact representation. To align the 3D per-point features with 2D per-pixel features, we calculate an L1 loss between each pixel and each 3D point sampled on the ray of the pixel. The overall L1 loss along a ray is the weighted sum of all
+
+the pixel-point alignment losses, with weights same as the rendering weights:  $\mathcal{L}_{\mathrm{feature}} = \sum_{i=1}^{K} w_i (\| \pmb{f}_i - F(\pmb{r}) \|)$ , where  $\pmb{r}$  is a ray corresponding to a 2D pixel,  $F(\pmb{r})$  is the 2D feature from CLIP-LSeg,  $K$  is the total number of sampled points along the ray and  $\pmb{f}_i$  is the feature of point  $i$  by interpolating through the feature voxel grid,  $w_i$  is the rendering weight.
+
+Concept Grounding through Attention. Since our feature voxel grid representation is learnt from CLIP-LSeg, by calculating the dot-product attention  $< f, v >$  between perpoint 3D feature  $f$  and the CLIP concept embeddings  $v$ , we can get zero-shot view-independent concept grounding and semantic segmentations in the 3D representation, as is presented in Fig. 2 IV.
+
+# 4.3. Neural Reasoning Operators
+
+Finally, we use the grounded semantic concepts for 3D reasoning from language. We first transform questions into a sequence of operators that can be executed on the 3D representation for reasoning. We adopt a LSTM-based semantic parser [65] for that. As [26, 40], we further devise a set of operators which can be executed on the 3D representation. Please refer to Appendix for a full list of operators.
+
+Filter Operators. We filter all the grid cells with a certain semantic concept.
+
+Get Instance Operators. We implement this by utilizing DBSCAN [15], an unsupervised algorithm which assigns clusters to a set of points. Specifically, given a set of points in the 3D space, it can group together the points that are closely packed together for instance segmentation.
+
+Relation Operators. We cannot directly execute the relation on the 3D representation as we have not grounded relations. Thus, we represent each relation using a distinct neural module (which is practical as the vocabulary of relations is limited [36]). We first concatenate the voxel grid representations of all the referred objects and feed them into the relation network. The relation network consists of three 3D convolutional layers and then three 3D deconvolutional layers. A score is output by the relation network indicating whether the objects have the relationship or not. Since vanilla 3D CNNs are very slow, we use Sparse Convolution [10] instead. Based on the relations asked in the questions, different relation modules are chosen.
+
+# 5. Experiments
+
+# 5.1. Experimental Setup
+
+Evaluation Metric. We report the visual question answering accuracy on the proposed 3DMV-VQA dataset w.r.t the four types of questions. The train/val/test split is 7:1:2.
+
+Implementation Details For 3D compact representations, we adopt the same architectures as DVGO, except skipping the coarse reconstruction phase and directly training the fine reconstruction phase. After that, we freeze the density voxel
+
+grid and color voxel grid, for the optimization of the feature voxel grid only. The feature grid has a world size of 100 and feature dim of 512. We train the compact representations for 100,000 iterations and the 3D features for another 20,000 iterations. For LSeg, we use the official demo model, which has the ViT-L/16 image encoder and CLIP's ViT-B/32 text encoder. We follow the official script for inference and use multi-scale inference. For DBSCAN, we use an epsilon value of 1.5, minimum samples of 2, and we use L1 as the clustering method. For the relation networks, each relation is encoded into a three-layer sparse 3D convolution network with hidden size 64. The output is then fed into a one-layer linear network to produce a score, which is normalized by sigmoid function. We use cross-entropy loss to train the relation networks, and we use the one-hop relational questions with "yes/no" answers to train the relation networks.
+
+# 5.2. Baselines
+
+Our baselines range from vanilla neural networks, attention-based methods, fine-tuned from large-scale VLM, and graph-based methods, to neural-symbolic methods.
+
+- LSTM. The question is transferred to word embeddings which are input into a word-level LSTM [25]. The last LSTM hidden state is fed into a multi-layer perceptron (MLP) that outputs a distribution over answers. This method is able to model question-conditional bias since it uses no image information.  
+- CNN+LSTM. The question is encoded by the final hidden states from LSTM. We use a resnet-50 to extract frame-level features of images and average them over the time dimension. The features are fed to an MLP to predict the final answer. This is a simple baseline that examines how vanilla neural networks perform on 3DMV-VQA.  
+- 3D-Feature+LSTM. We use the 3D features we get from 3D-2D alignment and downsample the voxel grids using 3D-CNN as input, concatenated with language features from LSTM and fed to an MLP.  
+- MAC [30]. MAC utilizes a Memory, Attention and Composition cell to perform iterative reasoning process. Like CNN+LSTM, we use the average pooling over multi-view images as the feature map.  
+- MAC(V). We treat the multi-view images along a trajectory as a video. We modify the MAC model by applying a temporal attention unit across the video frames to generate a latent encoding for the video.  
+- NS-VQA [65]. This is a 2D version of our 3D-CLR model. We use CLIP-LSeg to ground 2D semantic concepts from multi-view images, and the relation network also takes the 2D features as input. We execute the operators on each image and max pool from the answers to get our final predictions.
+
+<table><tr><td>Methods</td><td>Concept</td><td>Counting</td><td>Relation</td><td>Comparison</td><td>Overall</td></tr><tr><td>Q-type (rand.)</td><td>49.4</td><td>10.7</td><td>21.6</td><td>49.2</td><td>26.4</td></tr><tr><td>LSTM</td><td>53.4</td><td>15.3</td><td>24.0</td><td>55.2</td><td>29.8</td></tr><tr><td>CNN+LSTM</td><td>57.8</td><td>22.1</td><td>35.2</td><td>59.7</td><td>37.8</td></tr><tr><td>MAC</td><td>62.4</td><td>19.7</td><td>47.8</td><td>62.3</td><td>46.7</td></tr><tr><td>MAC(V)</td><td>60.0</td><td>24.6</td><td>51.6</td><td>65.9</td><td>50.0</td></tr><tr><td>NS-VQA</td><td>59.8</td><td>21.5</td><td>33.4</td><td>61.6</td><td>38.0</td></tr><tr><td>ALPRO</td><td>65.8</td><td>12.7</td><td>42.2</td><td>68.2</td><td>43.3</td></tr><tr><td>LGCN</td><td>56.2</td><td>19.5</td><td>35.5</td><td>66.7</td><td>39.1</td></tr><tr><td>3D-Feature+LSTM</td><td>61.2</td><td>22.4</td><td>49.9</td><td>61.3</td><td>48.2</td></tr><tr><td>3D-CLR (Ours)</td><td>66.1</td><td>41.3</td><td>57.6</td><td>72.3</td><td>57.7</td></tr></table>
+
+Table 1. Question-answering accuracy of 3D visual reasoning baselines on different question types.
+
+- ALPRO [38]. ALPRO is a video-and-language pre-training framework. A transformer model is pretrained on large webly-source video-text pairs and can be used for downstream tasks like Video Question answering.  
+- LGCN [28]. LGCN represents the contents in the video as a location-aware graph by incorporating the location information of an object into the graph construction.
+
+# 5.3. Experimental Results
+
+Result Analysis. We summarize the performances for each question type of baseline models in Table 1. All models are trained on the training set until convergence, tuned on the validation set, and evaluated on the test set. We provide detailed analysis below.
+
+First, for the examination of language-bias of the dataset, we find that the performance of LSTM is only slightly higher than random and frequency, and all other baselines outperform LSTM a lot. This suggests that there's little language bias in our dataset. Second, we observe that encoding temporal information in MAC (i.e., MAC(V)) is better than average-pooling of the features, especially in counting and relation. This suggests that average-pooling of the features may cause the model to lose information from multi-view images, while attention on multi-view images helps boost the 3D reasoning performances. Third, we also find that fine-tuning on large-scale pretrained model (i.e., ALPRO) has relatively high accuracies in concept-related questions, but for counting it's only slightly higher than the random baseline, suggesting that pretraining on large-scale video-language dataset may improve the model's perception ability, but does not provide the model with the ability to tackle with more difficult reasoning types such as counting. Next, we find that LGCN has poor performances on the relational questions, indicating that building a location-aware graph over 2D objects still doesn't equip the model with 3D location reasoning abilities. Last but not least, we find that 3D-based baselines are better than their 2D counterparts. 3D-Feature+LSTM performs well on the 3D-related questions, such as counting and relation, than most of the image-based
+
+basielines. Compared with 3D-CLR, NS-VQA can perform well in the conceptual questions. However, it underperforms 3D-CLR a lot in counting and relation, suggesting that these two types of questions require the holistic 3D understanding of the entire 3D scenes. Our 3D-CLR outperforms other baselines by a large margin, but is still far from satisfying. From the accuracy of the conceptual question, we can see that it can only ground approximately  $66\%$  of the semantic concepts. This indicates that our 3DMV-VQA dataset is indeed very challenging.
+
+Qualitative Examples. In Fig. 3, we show four qualitative examples. From the examples, we show that our 3D-CLR can infer an accurate 3D representation from multi-view images, as well as ground semantic concepts on the 3D representations to get the semantic segmentations of the entire scene. Our 3D-CLR can also learn 3D relationships such as "close", "largest", "on top of" and so on. However, 3D-CLR also fails on some questions. For the third scene in the qualitative examples, it fails to ground the concepts "mouse" and "printer". Also, it cannot accurately count the instances sometimes. We give detailed discussions below.
+
+# 5.4. Discussions
+
+We perform an in-depth analysis to understand the challenge of this dataset. We leverage the modular design of our 3D-CLR, replacing individual components of the framework with ground-truth annotations for model diagnosis. The result is shown in Fig 4. 3D-CLR w/ Semantic denotes our model with ground-truth semantic concepts from HM3DSem annotations. 3D-CLR w/ Instance denotes that we have ground-truth instance segmentations of semantic concepts. From Fig. 3 and Fig. 4, we summarize several key challenges of our benchmark:
+
+Very close object instances From Fig. 4, we can see that even with ground-truth semantic labeling of the 3D points, 3D-CLR still has unsatisfying results on counting questions. This suggests that the instance segmentations provided by DBSCAN are not accurate enough. From the top two qualitative examples in Fig. 3, we can also see that if two chairs
+
+![](images/e5f9988ee998345087af1d898b960d9fdfd34ec0911c04da788d53c90dc149f8.jpg)  
+Figure 3. Qualitative examples of our 3D-CLR. We can see that 3D-CLR can ground most of the concepts and answer most questions correctly. However, it still fails sometimes, mainly because it cannot separate close object instances and ground small objects.
+
+![](images/5ce1c4d9a9daa672b4fac5b8b44d25fd911caa8af39a62561b7b2db9edf488ea.jpg)  
+Figure 4. Model diagnosis of our 3D-CLR.
+
+contact each other, DBSCAN will not tell them apart and thus have poor performance on counting. One crucial future direction is to improve unsupervised instance segmentations on very close object instances.
+
+Grounding small objects Fig. 4 suggests that 3D-CLR fails to ground a large portion of the semantic concepts, which hinders the performance. From the last example in Fig. 3, we can see that 3D-CLR fails to ground small objects like "computer mouse". Further examination indicates there are two possible reasons: 1) CLIP-LSeg fails to assign the right features to objects with limited pixels; 2) The resolution of feature voxel grid is not high enough and therefore small objects cannot be represented in the compact representation. An interesting future direction would be learning exploration policies that enable the agents to get closer to uncertain objects that cannot be grounded.
+
+Ambiguity on 3D relations Even with ground-truth seman
+
+tic and instance segmentations, the performance of the relation network still needs to be improved. We find that most of the failure cases are correlated to the "inside" relation. From the segmentations in Fig. 3, we can see that 3D-CLR is unable to ground the objects in the cabinets. A potential solution can be joint depth and segmentation predictions.
+
+# 6. Conclusion
+
+In this paper, we introduce the novel task of 3D reasoning from multi-view images. By placing embodied robot that actively explores indoor environments, we collect a large-scale benchmark named 3DMV-VQA. We also propose a new 3D-CLR model that incorporates neural field, 2D VLM, as well as reasoning operators for this task and illustrate its effectiveness. Finally, we perform an in-depth analysis to understand the challenges of this dataset and also point out potential future directions. We hope that 3DMV-VQA can be used to push the frontiers of 3D reasoning.
+
+Acknowledgements. This work was supported by the MIT-IBM Watson AI Lab, DARPA MCS, DSO grant DSOCO21072, and gift funding from MERL, Cisco, Sony, and Amazon. We would also like to thank the computation support from AiMOS, a server cluster for the IBM Research AI Hardware Center.
+
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2023/3D GAN Inversion With Facial Symmetry Prior/02a489c6-c89c-4dc3-afcb-600bfa013373_content_list.json

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+    {
+        "type": "text",
+        "text": "3D GAN Inversion with Facial Symmetry Prior",
+        "text_level": 1,
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+        "text": "Fei Yin $^{1}$ , Yong Zhang $^{2\\dagger}$ , Xuan Wang $^{3}$ , Tengfei Wang $^{4}$ , Xiaoyu Li $^{2}$ , Yuan Gong $^{1}$ , Yanbo Fan $^{2}$ , Xiaodong Cun $^{2}$ , Ying Shan $^{2}$ , Cengiz Öztireli $^{5}$ , Yujiu Yang $^{1\\dagger}$ , Shenzhen International Graduate School, Tsinghua University  \n $^{2}$ Tencent AI Lab  $^{3}$ Ant Group  $^{4}$ HKUST  $^{5}$ University of Cambridge",
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+        "type": "text",
+        "text": "Abstract",
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+    {
+        "type": "text",
+        "text": "Recently, a surge of high-quality 3D-aware GANs have been proposed, which leverage the generative power of neural rendering. It is natural to associate 3D GANs with GAN inversion methods to project a real image into the generator's latent space, allowing free-view consistent synthesis and editing, referred as 3D GAN inversion. Although with the facial prior preserved in pre-trained 3D GANs, reconstructing a 3D portrait with only one monocular image is still an ill-posed problem. The straightforward application of 2D GAN inversion methods focuses on texture similarity only while ignoring the correctness of 3D geometry shapes. It may raise geometry collapse effects, especially when reconstructing a side face under an extreme pose. Besides, the synthetic results in novel views are prone to be blurry. In this work, we propose a novel method to promote 3D GAN inversion by introducing facial symmetry prior. We design a pipeline and constraints to make full use of the pseudo auxiliary view obtained via image flipping, which helps obtain a view-consistent and well-structured geometry shape during the inversion process. To enhance texture fidelity in unobserved viewpoints, pseudo labels from depth-guided 3D warping can provide extra supervision. We design constraints to filter out conflict areas for optimization in asymmetric situations. Comprehensive quantitative and qualitative evaluations on image reconstruction and editing demonstrate the superiority of our method.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Recent 3D-aware generative adversarial networks (3D GANs) have seen immense progress. By incorporating a neural rendering engine into the generator network architecture, 3D GANs can synthesize view-consistent images. To increase the generation resolution, existing methods [5,12,25,30,31,36-38,41] boost the 3D inductive bias",
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+        "img_path": "images/9260a43193a7b1a051371d2fff12dabdcb84fd7ca87930b2bc075b9a6bd50a9b.jpg",
+        "image_caption": [
+            "Figure 1. Visual examples of our inversion method. Direct applying 2D GAN inversion methods (PTI [28]) to the 3D GAN suffers from inaccurate geometry in novel views. Our method excels in synthesizing consistent geometry and high-fidelity texture in different views, even reconstructing a face under an extreme pose."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "with an additional 2D CNN-based upsampler or an efficient 3D representation modeling method. With tremendous effort, 3D GANs can produce photorealistic images while enforcing strong 3D consistency across different views.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We are interested in the task of reconstructing a human face with 3D geometry and texture given only one monocular image. It is an ill-posed problem and close to the harsh condition of real scenarios. With the power of 3D GANs, it seems achievable via projecting a target image onto the manifold of a pre-trained generator. The process is referred as 3D GAN inversion. A straightforward path is to follow the 2D GAN inversion method [28], i.e., optimizing the latent code and the network parameters of the generator to overfit the specific portrait.",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "Work done during an internship at Tencent AI Lab.",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "† Corresponding Author.",
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+    {
+        "type": "page_number",
+        "text": "342",
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+    {
+        "type": "text",
+        "text": "However, since the ground truth 3D geometry is absent given one monocular image, the inversion result is far from satisfactory. The process of fitting a 3D GAN to one image would sacrifice geometric correctness in order to make the synthetic texture as close as possible to the input, even destroying the original semantic-rich latent space. As the optimization process goes, the face geometry tends to degenerate into a flattened shape, due to the absence of geometry supervision, e.g., images from other views. Besides, there exist quality issues in texture synthesis under novel views. The rendered images of unseen views tend to be blurry and inconsistent with the original image, especially when reconstructing a side face under an extreme pose. Because there is no texture supervision for unseen views given only one monocular image. The failure cases of directly applying [28] are illustrated in Fig. 1.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In this work, to alleviate the issue caused by missing geometry and texture supervision under multiple views, we propose a novel 3D GAN inversion approach by taking full advantage of facial symmetry prior to construct pseudo supervision of different views. Intuitively, we note that human faces are almost symmetric. Assuming the given portrait is symmetric, we can obtain an additional perspective of the portrait by simply mirroring the image. The images of two distinct views can provide geometric relations between the 3D points and their 2D projections based on epipolar geometry. Motivated by this, we seek to leverage facial symmetry as the geometric prior constraining the inversion. The symmetry prior is also employed in a traditional 3D reconstruction work [35]. We leverage the mirrored image as extra supervision of another view when performing the inversion, which prevents the geometry collapse. A rough geometry can be obtained by the inversion with the original and mirror images.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To further enhance texture quality and geometry in novel views, we employ depth-guided 3D warping to generate the pseudo images of the views surrounding the input and symmetric camera pose. The depth is inferred from the rough 3D volume. The original image along with the pseudo images are used to fine-tune the generator's parameters for the joint promotion of texture and geometry. To prevent the optimized geometry from deviating too much from the rough geometry, we design a geometry regularization term as a constraint. However, human faces are never fully symmetric in practice, neither in shape nor appearance. Therefore, we design several constraints to extract meaningful information adaptively from the mirror image without compromising the original reconstruction quality.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our main contributions are as follows:",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "- We propose a novel 3D GAN inversion method by incorporating facial symmetry prior. It enables a high-quality reconstruction while preserving the multi-view consistency in geometry and texture.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "- We conduct comprehensive experiments to demonstrate the effectiveness of our method and compare it with many state-of-the-art inversion methods. We also apply our method to various downstream applications.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. 3D-Aware GANs",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Recently, neural scene representations have incorporated 3D prior into image synthesis with explicit camera control. Inspired by the success of Neural Radiance Fields (NeRF) [22], [6,24] employ implicit volumetric neural rendering structure for consistent novel view synthesis, required only unconstrained monocular images training. To overcome the computational cost and lift the generation resolution, the following methods adopt a two-stage rendering process [5, 12, 21, 25, 30, 31, 37, 38, 41, 42]. Since 2D upsamplers may introduce view-inconsistent artifacts, NeRF path regularization [12] and dual discriminators [5] are proposed. Different 3D modeling representations are further designed for scalable and fast rendering. EG3D [5] introduces tri-plane representation, and GRAM-HD [36] proposes to render radiance manifolds first for efficient sampling. Boosting with the powerful high-fidelity unconditioned 3D GANs, we can achieve real image 3D reconstruction and editing. Specifically, we select the state-of-the-art EG3D [5] as our backbone.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. GAN Inversion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            550,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To edit a real image [29, 39], GAN inversion is applied first to discover a corresponding latent code from which the generator can synthesize the real image. Existing 2D GAN inversion approaches can be categorized into optimization-based, learning-based, and hybrid methods. [1, 16] directly minimize the reconstruction distance via optimizing the latent codes. Learning-based methods [2, 3, 32, 34] exploit a general encoder network to map the input image into latent space in real-time. Hybrid methods would apply the latent code predicted from the encoder as initialization in the later optimization process. Beyond the original inversion latent space, PTI [28] further optimizes the parameters of the generator to enhance the visual fidelity.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "As for the 3D GAN inversion task, most methods directly transfer the 2D methods, e.g., PTI [28] and e4e [32], which may suffer from the poor results in novel views. Pix2NeRF [4] introduced a joint distillation strategy for training a 3D inversion encoder. A concurrent work [18] proposes to perform camera pose optimization simultaneously to ensure view consistency. However, none of the above methods take geometry shape into consideration.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "343",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/d75a1f0e84d6476ff667bcfbebf14831b191b283b1dc5e67fdd592cbabc96bd2.jpg",
+        "image_caption": [
+            "Figure 2. The proposed framework. A) Our method first performs inversion with the help of the symmetry view to achieve the latent code  $w^{+}$  with a roughly correct geometry. B) The original image and the mirror one, along with adjacent warping pseudos, are used for joint optimization to enhance the geometry and texture of rendered images in novel views. C) Depth-guided 3D warping are used to generate pseudo images in novel views to provide extra supervision. Unfaithful regions are filtered out with the authentic mask."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
+            88,
+            321,
+            275
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/962dca2b8aea70d9409e2bf2c19d3023a6a0d158b6e429885d6d85077916bff9.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            323,
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+            275
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/617c2fdcc313ba70621dcd2ad8b8b0e39aaf1a3d8a6e574efb070d9c5e7b9ead.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            632,
+            88,
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+            273
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2.3. Few-shot NeRF",
+        "text_level": 1,
+        "bbox": [
+            76,
+            356,
+            230,
+            372
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Few-shot NeRF aims at reconstructing general 3D scenarios where only a few observed views are available, which shares a similar setting with 3D GAN inversion. MVS-NeRF [7] leverages plane-swept cost volumes in multi-view stereo for geometry-aware scene reasoning to improve performance. DietNeRF [13] enforces semantic consistency between rendered images from unseen view and seen images via a CLIP encoder [27]. RegNeRF [23] regularizes the texture of patches rendered from unobserved viewpoints without relying on additional training modules. Since it is hard to find a common prior for general scenes, these methods investigate how to ensure the geometry consistency of different views, which gives us inspiration.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Definition of 3D GAN Inversion",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Similar to 2D GAN inversion, 3D GAN inversion aims to project an input image  $I$  onto the manifold of a pretrained unconditional 3D GAN model  $G_{\\mathrm{3D}}(\\cdot ;\\theta)$  parameterized by weight  $\\theta$ . After inversion,  $G_{\\mathrm{3D}}$  can reconstruct the image faithfully given the corresponding camera pose, synthesize content-consistent images in novel views, and facilitate downstream tasks like face editing. One formulation of the 3D GAN inversion problem is defined as follows:",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw ^ {*} = \\underset {w} {\\arg \\max } = \\mathcal {L} \\left(G _ {3 D} (w, \\pi ; \\theta), I\\right), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            143,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $w$  is the latent representation in  $\\mathcal{W}^+$  space and  $\\pi$  is the corresponding camera matrix of input image. The loss function  $\\mathcal{L}(\\cdot, \\cdot)$  is usually defined as pixel-wise reconstruction loss or perceptual loss. In our settings, camera matrix  $\\pi$  is known, which is extracted by a pre-trained detector [9]. This formulation cares about the  $\\mathcal{W}^+$  space. However, the inversion in the  $\\mathcal{W}^+$  space is always not enough to capture local facial details, resulting in inaccurate reconstruction.",
+        "bbox": [
+            75,
+            779,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Following the recent optimization-based 2D GAN inversion method [28], we perform the inversion in the extended latent space for more accurate reconstruction, i.e., the combination of the  $\\mathcal{W}^{+}$  space and the parameter space. The formulation is defined as:",
+        "bbox": [
+            496,
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nw ^ {*}, \\theta^ {*} = \\underset {w, \\theta} {\\arg \\max } = \\mathcal {L} \\left(G _ {3 D} (w, \\pi ; \\theta), I\\right). \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            555,
+            439,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Note that  $w$  and  $\\theta$  are optimized alternatively, i.e.,  $w$  is optimized using Eq. (1) first and then  $\\theta$  is optimized with the fixed  $w^{*}$ .",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4. The Proposed Approach",
+        "text_level": 1,
+        "bbox": [
+            498,
+            527,
+            728,
+            545
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Our goal is to reconstruct a human face through a pretrained 3D GAN given a single monocular image. The reconstruction is supposed to preserve authentic appearance texture and geometry shape in novel views. Due to the limited information about geometry and texture from a single image, overfitting a single view tends to be trapped in geometry collapse, get the blurry texture and miss details in unseen views, especially when reconstructing a side face under an extreme pose. To overcome the issue of lacking information about other views, we introduce facial symmetry prior to promote inversion. We propose a two-stage inversion pipeline, i.e., inversion for rough geometry and joint optimization of geometry and texture. In the first stage, we obtain a rough geometry by optimizing the latent code  $w$  using the original and mirror images in Sec. 4.1. In the second stage, we refine the geometry and texture by optimizing the parameter  $\\theta$  with the depth-guided 3D warping and a set of designed constraints in Sec 4.2. An overview of our method is shown in Fig. 2.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "4.1. Inversion with Symmetry for Rough Geometry",
+        "text_level": 1,
+        "bbox": [
+            498,
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "The purpose of this stage is to learn a rough geometry as a pivot for further tuning. To compensate for the missing",
+        "bbox": [
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+        "text": "344",
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+        "type": "image",
+        "img_path": "images/0f5db3830d58f25681435aa4f8ed08732d28a412480e407a1a989c5cef01d562.jpg",
+        "image_caption": [
+            "Figure 3. Visualization of warped pseudos. The red bounding box contains the range of employed pseudos, depending on the yaw angle of the input image. A frontal face can be warped by a wider range of yaw angles than a side face to get authentic pseudos."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            89,
+            890,
+            186
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/42c87874b858d5fe2f82d16dea9111ba8e70fe1b34c608585d3396830611401c.jpg",
+        "image_caption": [
+            "Source Image",
+            "Figure 4. Visualization of authentic mask and warped pseudo."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            239,
+            176,
+            315
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/be838299f22ea3da41917e8e21bad9d732202582cb08a69961d057302938841a.jpg",
+        "image_caption": [
+            "Warped Image"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            176,
+            239,
+            272,
+            315
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/32e55225f4c19c8ebfad56bc936e8466d3b4936d4665531f0c1b819be3ca68f4.jpg",
+        "image_caption": [
+            "Authentic Mask"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            274,
+            239,
+            370,
+            315
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/c00774424ba472ae986435bbc55c6eddacfd8e638237193878207153cf037ce7.jpg",
+        "image_caption": [
+            "Pseudo"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            372,
+            239,
+            467,
+            315
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "information of unseen views, we resort to facial symmetry prior, i.e., the left face is almost the same as the right one. We simply flip the input image  $I_{s}$  horizontally to get the mirror image  $I_{m}$  whose corresponding camera pose  $\\pi_{m}$  can be calculated by multiplying a fixed matrix by the camera extrinsic parameters of  $\\pi_{s}$ . The intrinsic parameters are unchanged. The mirror image serves as the pseudo-projected image under a novel view.",
+        "bbox": [
+            75,
+            372,
+            467,
+            492
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Since human faces are not always perfectly symmetric, the mirror image is just an approximation under the novel view. There exists inconsistent content between the original image and the mirror one if they have an overlapping face region, i.e., different colors in the position, referred as conflict content. The inversion should depend more on the original image and take partial useful information from the mirror one. Furthermore, we observe that a frontal face can provide more effective information than a side face. A nearly frontal face provides plenty of facial information, and we should trust less on its mirror image to avoid conflict in the overlapping region. While a side face provides information for only half one face, it has only a small overlapping conflict region with its mirror image. Hence, we should trust more on the mirror image. We exploit an adaptive weighting strategy for the importance of the mirror image according to its yaw angle  $\\alpha_{\\mathrm{yaw}}$ . We use a Gaussian function with respect to  $\\alpha_{\\mathrm{yaw}}$  to approximate the importance of different views. The weight  $\\lambda_{m}$  of the mirror image is defined as:",
+        "bbox": [
+            75,
+            493,
+            468,
+            781
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {E} (x) = \\frac {1}{\\sigma \\sqrt {2 \\pi}} e ^ {- \\frac {(x - \\mu) ^ {2}}{2 \\sigma^ {2}}}, \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            187,
+            801,
+            468,
+            834
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\lambda_ {m} = \\left\\{ \\begin{array}{l l} 1 - \\mathcal {E} \\left(\\alpha_ {\\text {y a w}}\\right), & \\text {i f} \\mathcal {E} \\left(\\alpha_ {\\text {y a w}}\\right) \\leq k; \\\\ 0, & \\text {i f} \\mathcal {E} \\left(\\alpha_ {\\text {y a w}}\\right) > k; \\end{array} \\right. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            138,
+            835,
+            468,
+            876
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\sigma, \\mu$  and  $k$  are hyper-parameters. As a nearly frontal",
+        "bbox": [
+            76,
+            885,
+            468,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "mirror face can compensate for very limited extra information for the original image, its weight  $\\lambda_{m}$  is clamped to 0.",
+        "bbox": [
+            498,
+            243,
+            890,
+            273
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To optimize the latent code in  $\\mathcal{W}^+$  space, the Perceptual loss [40] is used to minimize the distance between the generated results and the original and mirror images. Following [17, 28], a noise regularization term  $\\mathcal{L}_n(n)$  is employed to prevent the noise vector from containing vital information. The objective in this stage is defined as follows:",
+        "bbox": [
+            496,
+            273,
+            890,
+            364
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {i n v}} = \\mathcal {L} _ {\\mathrm {L P I P S}} \\left(G _ {3 \\mathrm {D}} \\left(w, \\pi_ {s}; \\theta\\right), I _ {s}\\right) + \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            527,
+            369,
+            890,
+            393
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\lambda_ {m} \\mathcal {L} _ {\\text {L P I P S}} \\left(G _ {3 \\mathrm {D}} \\left(w, \\pi_ {m}; \\theta\\right), I _ {m}\\right) + \\lambda_ {n} \\mathcal {L} _ {n} (n),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            555,
+            390,
+            841,
+            405
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $n$  is the noise vector and  $\\lambda_{n}$  is a trade-off parameter. The generator is kept frozen at this stage. Visual illustrations in Fig. 8 show that the geometry can be greatly improved with the facial symmetry prior.",
+        "bbox": [
+            496,
+            410,
+            890,
+            470
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4.2. Joint Optimization of Geometry and Texture",
+        "text_level": 1,
+        "bbox": [
+            498,
+            478,
+            879,
+            494
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Though we obtain the rough geometry via the optimization of  $w$  in the first stage, there is a distinct gap between the texture of the rendered face and that of the original one, even under the same camera pose. The rendered face shares a similar face geometry with the original one, but it becomes a different identity. In this stage, we optimize the generator's parameters  $\\theta$  to bridge the texture gap for identity preservation and refine the rough geometry as well. We design a geometry regularization constraint to avoid the model degrading to generate flattened geometry. Moreover, we construct a set of pseudo images in different views to provide supervision via depth-guided 3D warping.",
+        "bbox": [
+            496,
+            501,
+            890,
+            681
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Geometry Regularization. We observe that optimizing the generator without any constraint on the geometry will cause the deviation of the geometry from the rough one, resulting in a flattened geometry similar to the case of inversion with a single image. To avoid the geometry drift during overfitting the texture, we regularize the optimized density obtained from the 3D volume of 3D GAN to be similar to that from the rough volume obtained in the first stage. Specifically, with the fixed  $w$ , we generate depth maps  $D$  from 3D GAN under different sampled views and calculate  $\\mathcal{L}_2$  distance between them with the corresponding depth maps  $D_0$  generated from the un-tuned generator in the first stage:",
+        "bbox": [
+            496,
+            685,
+            890,
+            866
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {d e p t h}} = \\sum_ {i \\in \\mathbb {S}} \\| D ^ {i} - D _ {0} ^ {i} \\| _ {2}, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            604,
+            871,
+            890,
+            902
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "345",
+        "bbox": [
+            485,
+            945,
+            509,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbb{S}$  is the sampled camera pose set.",
+        "bbox": [
+            76,
+            90,
+            344,
+            104
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Depth-guided 3D Warping for Pseudo Supervision. Optimizing the generator with only two images is still not enough to capture the facial details, resulting in blurry effects around facial components such as eyes (see Fig. 11). Hence, we propose to construct pseudo images of different views for extra supervision using the rough geometry and the original and mirror images. Specifically, given the original image (source view) and the rough geometry, we can synthesize an image under a novel view (target view) by warping with 3D guidance. A coordinate pixel  $p_t$  of the synthesized image in the target view can be obtained by projecting back onto the source view with the relative camera pose  $\\pi_{t\\rightarrow s}$  and the camera intrinsic parameters  $K$ :",
+        "bbox": [
+            75,
+            108,
+            468,
+            305
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\np _ {t \\rightarrow s} = K \\pi_ {t \\rightarrow s} D _ {t} \\left(p _ {t}\\right) K ^ {- 1} p _ {t}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            168,
+            313,
+            468,
+            329
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $D_{t}(\\cdot)$  is the depth map of the target view. Since the projected coordinate  $p_{t\\rightarrow s}$  are continuous values, we can extract the color values from the original image with a differentiable bilinear sampling mechanism, i.e.,  $I_{s\\rightarrow t} = I_s(p_{t\\rightarrow s})$ . The low-resolution depth map will be upsampled to match the dimension of the image.",
+        "bbox": [
+            76,
+            335,
+            468,
+            426
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Authentic Mask. Without distinguishing the foreground pixels from the background, the background pixels in the original image may be projected onto the foreground plane, leading to erroneous results. To overcome this issue, we form a mask to indicate the visibility of pixels to filter invisible areas using the rendered depth values. Specifically, we can get the projected depth value  $D_{s}(p_{t\\rightarrow s})$  via sampling from the depth map in the source view. Here we employ the euclidean distance between  $D_{s}(p_{t\\rightarrow s})$  and the depth map  $D_{t}(p_{t})$  in the target view to calculate the mask. A large distance indicates the pixel  $p_t$  is invisible. To ensure the projected pixels are located on the front visible surface, we only preserve the area where the distance is under a threshold  $\\tau$ :",
+        "bbox": [
+            75,
+            428,
+            468,
+            637
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nM \\left(p _ {t}\\right) = \\left\\| D _ {t} \\left(p _ {t}\\right) - D _ {s} \\left(p _ {t \\rightarrow s}\\right)\\right\\| <   \\tau . \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            145,
+            647,
+            468,
+            664
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, due to the poor depth estimation of the background, only the facial part would be warped. We warp the facial mask of the source view to the target view and multiply it with the visibility mask  $M(p_{t})$  to get the authentic mask  $M_{t}$ . An example is shown in Fig. 4. After multiplying the mask  $M_{t}$  with the warped image  $I_{s\\rightarrow t}$ , the resulting image can be used for supervision.",
+        "bbox": [
+            75,
+            671,
+            468,
+            777
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Adjacent View Warping. Fig. 3 illustrates the warping results of two examples. When the yaw angle between the source and target views increases, the warping results have more distortions and become less authentic. Therefore, it is intuitive to abandon the pseudo images of the target views that deviate a lot from the source view. Empirically, a frontal face can be warped by a wider range of yaw angles than a side face to get authentic pseudo images. The",
+        "bbox": [
+            75,
+            779,
+            468,
+            900
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "variance of sampling yaw angles for constructing pseudo images is set to a fixed ratio of  $\\lambda_{m}$  that depends on the viewpoint mentioned in Sec. 4.1. The LPIPS loss [14] is used to compute the multi-view pixel-wise distance as follows:",
+        "bbox": [
+            498,
+            90,
+            890,
+            151
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {a d j}} = \\mathcal {L} _ {\\mathrm {L P I P S}} \\left(M _ {t} \\cdot G _ {\\mathrm {3 D}} (w, \\pi_ {t}; \\theta), M _ {t} \\cdot I _ {s \\rightarrow t}\\right). \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            540,
+            164,
+            890,
+            181
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Although the pseudo images of several unseen adjacent views around the source view have been constructed, it brings marginal improvements on remote views. Especially for a side face, the pseudo images of the remote views are blurry and have incomplete texture (see Fig. 3). Therefore, we also construct pseudo images of the adjacent views around the view of the mirror image.",
+        "bbox": [
+            496,
+            194,
+            890,
+            299
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Since the conflict region between the original and mirror images has a side effect on the generator optimization process, resulting in blurry effects on rendered images, even reconstructing the source view (see Fig. 9), we propose to take partial meaningful information from the symmetric views without harming the original inversion quality. We compute the similarities only for facial components, rather than the whole face region. Besides, instead of using a pixelwise loss, we exploit the contextual loss [20] to improve the texture quality. The loss for symmetric views is defined as:",
+        "bbox": [
+            496,
+            300,
+            890,
+            450
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s y m}} = \\sum_ {\\mathrm {c} \\in \\mathbb {F}} \\mathcal {L} _ {\\mathrm {C X}} \\left(\\operatorname {R O I} ^ {c} \\left(G _ {3 \\mathrm {D}} \\left(w, \\pi_ {t}; \\theta\\right)\\right), \\operatorname {R O I} ^ {c} \\left(I _ {m \\rightarrow t}\\right)\\right), \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            514,
+            463,
+            890,
+            507
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $I_{m\\rightarrow t}$  is the pseudo image of the viewpoint  $\\pi_t$  warped from the mirror image  $I_{m}$ .  $\\mathrm{ROI}^c (\\cdot)$  refers to the region of interest component  $c$  from the collection  $\\mathbb{F} = \\{\\text{eyes, nose, mouth}\\}$ .",
+        "bbox": [
+            496,
+            508,
+            890,
+            568
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The reconstruction loss between the original image and its corresponding rendered image is still in use to ensure the quality of the initial perspective, which is defined as:",
+        "bbox": [
+            496,
+            569,
+            890,
+            614
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {o r i}} = \\mathcal {L} _ {2} \\left(G _ {\\mathrm {3 D}} \\left(w, \\pi_ {s}; \\theta\\right), I _ {s}\\right) + \\mathcal {L} _ {\\mathrm {L P I P S}} \\left(G _ {\\mathrm {3 D}} \\left(w, \\pi_ {s}; \\theta\\right), I _ {s}\\right). \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            501,
+            627,
+            890,
+            657
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The overall objective of optimizing the generator's parameters is defined as:",
+        "bbox": [
+            496,
+            657,
+            890,
+            686
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {o p t}} = \\mathcal {L} _ {\\text {o r i}} + \\lambda_ {\\text {a d j}} \\mathcal {L} _ {\\text {a d j}} + \\lambda_ {\\text {s y m}} \\mathcal {L} _ {\\text {s y m}} + \\lambda_ {\\text {d e p t h}} \\mathcal {L} _ {\\text {d e p t h}}. \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            519,
+            700,
+            890,
+            718
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The trade-off hyper-parameters are set as follows:  $\\lambda_{\\mathrm{adj}} = 0.1$ ,  $\\lambda_{\\mathrm{sym}} = 0.05$ , and  $\\lambda_{\\mathrm{depth}} = 1$ .",
+        "bbox": [
+            496,
+            729,
+            890,
+            762
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            776,
+            633,
+            792
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5.1. Experimental Settings",
+        "text_level": 1,
+        "bbox": [
+            500,
+            801,
+            705,
+            816
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We conduct the experiments on human faces datasets. For all experiments, we select EG3D [5] as our 3D GAN prior, which is pre-trained on FFHQ dataset [15]. We verified quantitative metrics on CelebA-HQ test dataset [19]. We further evaluated on MEAD [33], a",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "346",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/1470c26a073523eeed04b623eec00b3a4506c2f62ea9d69dad6437cf3de65479.jpg",
+        "image_caption": [
+            "SG2"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            78,
+            87,
+            166,
+            358
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/6f39e9d126fa143ebda910254e2cd452fc4782e5fb5112c75a624b98dfc3f054.jpg",
+        "image_caption": [
+            "SG2  $W^{+}$"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            166,
+            88,
+            253,
+            358
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/8dae65f2f2a02f5c53ea8ac3cb13de8615d53ec51bbdd1fecc7008652fa909a6.jpg",
+        "image_caption": [
+            "PTI"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            253,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/33e8f1cb68534e6bd42f66de2805b7e39eb7c0c210af7c41ec2c04d775f800dd.jpg",
+        "image_caption": [
+            "Ours"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/8212cc13a848a7c393a0b90e1ac2e011acd090eac9c9eb3f7d04f9c59d2a0e00.jpg",
+        "image_caption": [
+            "Source Image"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            426,
+            123,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/635c354de2acf40041996d77ca926dcf9f864cce12a4dfd408101568c6f69d9b.jpg",
+        "image_caption": [
+            "Source Image"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
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+    {
+        "type": "image",
+        "img_path": "images/a109649a33cb0f0a26d936e4cc64438d53480ab09ccd92b9a91660b7acce29d3.jpg",
+        "image_caption": [
+            "SG2"
+        ],
+        "image_footnote": [],
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+        "page_idx": 5
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+    {
+        "type": "image",
+        "img_path": "images/2e65c836a8e794365c38d4e39c1ff2acc56f59cc49fece8bcd124bcbb4a5c1ca.jpg",
+        "image_caption": [
+            "SG2  $W^{+}$"
+        ],
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+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/f29b17df448d553e0cb66f8bdd7006215fcd2889a15267c75bc1c83c65980209.jpg",
+        "image_caption": [
+            "PTI"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/b40919e94b2a054a78398d3044dd4babad9cd9fbde75bff6fed0dc54feafafb6.jpg",
+        "image_caption": [
+            "Ours"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/f39ad32e77ec31c76de8c5434bd4e2ffa93755129aa0f84a7efcfdc3337892c1.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>MSE ↓</td><td>LPIPS ↓</td><td>MS-SSIM ↓</td><td>ID ↑</td><td>Pose ↓</td><td>Depth ↓</td></tr><tr><td>SG2 [16]</td><td>0.0881</td><td>0.3231</td><td>0.3557</td><td>0.8209</td><td>0.043</td><td>0.0505</td></tr><tr><td>SG2 W+ [1]</td><td>0.0439</td><td>0.2261</td><td>0.2483</td><td>0.8735</td><td>0.040</td><td>0.0500</td></tr><tr><td>PTI [28]</td><td>0.0084</td><td>0.0920</td><td>0.0980</td><td>0.9432</td><td>0.037</td><td>0.0510</td></tr><tr><td>SPI (Ours)</td><td>0.0082</td><td>0.0865</td><td>0.0991</td><td>0.9470</td><td>0.036</td><td>0.0476</td></tr></table>",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 1. Quantitative comparison on CelebA-HQ [19].",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "multi-view high-quality video dataset. The first frame from each viewpoint video of 10 identities is extracted for testing.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Metrics. We evaluate image reconstruction quality and similarity with the following metrics: mean squared error (MSE), perceptual similarity loss (LPIPS) [40], structural similarity (MS-SSIM), and identity similarity (ID) by employing a pre-trained face recognition network [8].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Baselines. We mainly compare our methods with optimization-based 2D GAN inversion methods. SG2 [16] directly inverts real images into  $\\mathcal{W}$  space with an optimization scheme. [1] extends the inversion into  $\\mathcal{W}^+$  space, denoted by SG2  $\\mathcal{W}^+$ . PTI [28] would further tune generator parameters in a second stage. For a fair comparison, both PTI and ours first optimize the latent for 500 steps and then fine-tune the generator for 1,000 steps, while SG2 and SG2  $\\mathcal{W}^+$  optimize the latent for 1,500 steps.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "5.2. Reconstruction and Novel View Synthesis",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Qualitative Evaluation. Fig. 5 presents a qualitative comparison of texture and geometry quality of different views. As for the original view, our method is able to inverse challenging details such as earrings, make-up, and wrinkles, which demonstrates that we do not sacrifice the original reconstruction performance. When the camera rotates to",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/9290fe419202b1600b795c1a2479733fc03d03e00ef18faa70abd8d60f7cfc82.jpg",
+        "image_caption": [
+            "Figure 5. Qualitative comparisons with state-of-the-art methods on novel view synthesis. The reconstruction quality of the original view is presented in the first row. The texture and geometry in novel views are shown in the rest rows.",
+            "Figure 6. Comparison of identity preservation in novel views. The x-axis represents the yaw angle of the input image. '0' indicates the frontal face."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "novel views, images generated from 2D inversion methods present a twisted appearance, due to the nearly flattened geometry shape. Since SG2 does not deviate too far from the initial GAN space, it can generate a portrait with a structured geometry, but fails to preserve the identity. Our method is capable of maintaining authentic and consistent geometry in novel views along with a sharp appearance, even when rotated to an extreme pose.",
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+    },
+    {
+        "type": "text",
+        "text": "Quantitative Evaluation. The reconstruction metrics of the original view are shown in Table 1. As can be seen, the results align with our qualitative evaluation as we achieved comparable scores to the current 2D state-of-the-art inversion methods [28]. The MSE, LPIPS, and ID similarities of ours are further improved, which can be attributed to the employment of  $\\mathcal{W}^+$  latent space. Following EG3D, we",
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "347",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/549688891ff4cf7f4ccba5d7fa7eb4ab784a254da5e92e34c81f613878d4c6be.jpg",
+        "image_caption": [
+            "Figure 7. Qualitative comparisons with PTI [28] on MEAD [33]."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/864a823edc119faabd82356225added9e0c199703a73b28abb93a46873430445.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>View</td><td>MSE ↓</td><td>LPIPS ↓</td><td>MS-SSIM ↓</td><td>ID ↑</td></tr><tr><td>PTI</td><td rowspan=\"2\">F</td><td>0.03204</td><td>0.2971</td><td>0.2070</td><td>0.8445</td></tr><tr><td>Ours</td><td>0.03296</td><td>0.3088</td><td>0.2135</td><td>0.8388</td></tr><tr><td>PTI</td><td rowspan=\"2\">L30</td><td>0.04355</td><td>0.2992</td><td>0.2274</td><td>0.8446</td></tr><tr><td>Ours</td><td>0.03399</td><td>0.2796</td><td>0.2025</td><td>0.8469</td></tr><tr><td>PTI</td><td rowspan=\"2\">L60</td><td>0.08255</td><td>0.3902</td><td>0.3143</td><td>0.7568</td></tr><tr><td>Ours</td><td>0.04069</td><td>0.3113</td><td>0.2379</td><td>0.8272</td></tr><tr><td>PTI</td><td rowspan=\"2\">R30</td><td>0.04574</td><td>0.3110</td><td>0.2393</td><td>0.8383</td></tr><tr><td>Ours</td><td>0.03203</td><td>0.2807</td><td>0.2057</td><td>0.8529</td></tr><tr><td>PTI</td><td rowspan=\"2\">R60</td><td>0.07865</td><td>0.3829</td><td>0.3106</td><td>0.7995</td></tr><tr><td>Ours</td><td>0.04541</td><td>0.3160</td><td>0.2400</td><td>0.8335</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Quantitative comparison on MEAD [33]. View denotes the yaw angle of the input image. F is frontal, L is left side, and R is right side. 30 and 60 are the rotation degrees. Each time we use one view as the inversion input and use all 5 views as ground truth for evaluation. The average performance of 4 unseen views and 1 seen view is reported.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "evaluate shape quality by calculating  $\\mathcal{L}_2$  for pseudo-ground-truth depth-maps (Depth) generated from DECA [10], and poses (Pose) estimated from synthesized images.",
+        "bbox": [
+            75,
+            564,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We also use identity similarity to evaluate the identity preservation of the synthesized novel views. Given a portrait, we synthesize a novel view image under the symmetric camera pose of the portrait. The similarity between the synthesized image and the flipped image portrait is calculated. The results are shown in Fig. 6. It can be observed that when the yaw angle of a portrait is small, all methods can perform well with a high similarity score. But when the yaw angle is large, only our method can maintain a high score, while other methods encounter a sharp performance drop due to the inaccurate geometry. As we employ the symmetry prior and the adjacent pseudo supervision, the rendered faces can better preserve the texture and geometry. These results demonstrate that we can achieve an identity-consistent 3D inversion.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Evaluation on MEAD. To get a comprehensive understanding of the performance of our method, we evaluate on MEAD, a multi-view dataset. The quantitative comparison between the reconstruction portraits and the ground truth in",
+        "bbox": [
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+            839,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/01f64dbb372a527572505301802d38858746ef8b6cc0e5f875f43db08a93c32b.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            87,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/81a45e6fe76e4e1ef8dde0a83a39460da3d2eed14819a8f3290a238cff396eee.jpg",
+        "image_caption": [
+            "Figure 8. Ablation study of facial symmetry prior.",
+            "Figure 9. Ablation study of authentic mask. Vanilla denotes simply using the full mirror image for supervision. While Ours filters out conflict areas with the designed constraints."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            214,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "different views is shown in Tab. 2. PTI [28] and our method achieve comparable performance when given a frontal portrait. When the view of the input face has an offset from the canonical one, our method surpasses PTI distinctly. Our metrics remain stable as the yaw angle becomes larger while the performance of PTI degrades significantly. The qualitative results are shown in Fig. 7. The geometry shape of PTI suffers from the flattening phenomenon. In contrast, our method can generate a consistent geometry and texture in novel views.",
+        "bbox": [
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+            438,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3. Evaluation of Symmetry Prior",
+        "text_level": 1,
+        "bbox": [
+            500,
+            603,
+            767,
+            619
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To understand the importance of the symmetry prior, we perform an ablation study by conducting the inversion with or without using the prior. The visual results are shown in Fig. 8. Both approaches can obtain good geometries in the original view. However, in the first row, the geometry of the woman with a thin face turns to be obese as the camera gradually rotates, which aligns with its rendered image. The second row shows that the geometry and the rendered image maintain a better view consistency. We even find that, with the auxiliary view, some expression details can be strengthened, such as the slightly opened mouth.",
+        "bbox": [
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+            628,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The symmetry prior cannot be directly employed in the optimization stage because there exist asymmetric areas in a human face. Optimizing the conflict areas will lead to poor results. As shown in Fig. 9, the slanted hair and the single earring in the source image mismatch those in the mirror one. In the first row, when simply using both two images to optimize the generator, the reconstruction quality suffers",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "348",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/7c547f6157cd26838a1220a87b88dc74faa9bf4c29c6f4faa564171b3ded4081.jpg",
+        "image_caption": [
+            "Figure 10. Editing results incorporated with [26] and [11]."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
+            87,
+            468,
+            333
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "from degradation. Novel views synthesized by the vanilla version will encounter incorrect texture and blurry results in the conflict areas. Our method can handle such asymmetric cases without the quality worsening by filtering out conflict areas with the designed constraints. Hair, teeth, and other details are consistent in different views, which validates the effectiveness of the proposed constraints.",
+        "bbox": [
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+            373,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.4. View-consistent Face Editing",
+        "text_level": 1,
+        "bbox": [
+            76,
+            489,
+            334,
+            506
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Editing a facial image should preserve the original identity while performing a meaningful and visually plausible modification. We extend our methods to downstream editing tasks to validate that the 3D GAN inversion process does not degrade the editability of the original generator. We follow StyleCLIP [26] to achieve text-guided semantic editing and StyleGAN-NADA [11] for stylization, shown in Fig. 10. The editing operation not only influences the original view but also changes the novel view's appearance consistently. It demonstrates that our inversion solution retains the properties in the original space of the generator and can be associated with other editing methods flexibly.",
+        "bbox": [
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+            513,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.5. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            76,
+            705,
+            228,
+            720
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Adjacent Warping. Recall that we employ depth-guided warping to create pseudo supervision to improve the texture quality of novel views. In Fig. 11, we can find that this operation can enhance facial component details such as eyelashes and teeth, improving the overall visual quality.",
+        "bbox": [
+            75,
+            729,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Depth Regularization. Since supervision signals all come from RGB images, there is no explicit geometry supervision to ensure shape correctness. The shape is prone to drift to overfit the single image. Unnatural distortions will appear in novel views with the drifted shape. In the third column of Fig. 11, the jaw and nose are elongated with no con",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/335f4b7c612ab4dd30d80990b3c3e7550938932cfdca8dfed32fdddceb463838.jpg",
+        "image_caption": [
+            "Figure 11. Ablation study of different designed modules."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            87,
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+            325
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "straints. With depth regularization, geometry will be calibrated within reasonable limits.",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Two-stage Optimization. The joint optimization stage via utilizing a large parameter space can further improve texture, allowing to reconstruct the out-of-domain details, e.g., auspicious mole, as shown in the last column of Fig. 11.",
+        "bbox": [
+            498,
+            412,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            505,
+            617,
+            520
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We propose a novel 3D GAN inversion method with facial symmetry prior. As demonstrated in massive experiments, our method can support 3D reconstruction at extreme angles with robust geometry. With the designed constraints on texture and geometry, the reconstructed portraits are high-fidelity and possess consistent identity across different views. Besides, the proposed method enables various downstream applications without compromising faithfulness and photorealism.",
+        "bbox": [
+            496,
+            536,
+            890,
+            672
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Limitation and Future Works. Since the effect of illumination is ignored in our assumption, the illumination is modeled implicitly. During the fitting process of the given image with symmetry prior, light sources sometimes become perfectly symmetrical and distorted. We will attempt to settle the problem via modeling illumination explicitly with albedo and normal in future work.",
+        "bbox": [
+            496,
+            680,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement. This work was partly supported by the National Natural Science Foundation of China (Grant No. U1903213) and the Shenzhen Science and Technology Program (JCYJ20220818101014030, ZDSYS20200811142605016). This work was partly supported by a UKRI Future Leaders Fellowship [grant number G104084].",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "349",
+        "bbox": [
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+            945,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
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+        "sub_type": "ref_text",
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2023/3D GAN Inversion With Facial Symmetry Prior/02a489c6-c89c-4dc3-afcb-600bfa013373_model.json

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+            "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "content": "3D GAN Inversion with Facial Symmetry Prior"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "content": "Fei Yin\\(^{1}\\), Yong Zhang\\(^{2\\dagger}\\), Xuan Wang\\(^{3}\\), Tengfei Wang\\(^{4}\\), Xiaoyu Li\\(^{2}\\), Yuan Gong\\(^{1}\\), Yanbo Fan\\(^{2}\\), Xiaodong Cun\\(^{2}\\), Ying Shan\\(^{2}\\), Cengiz Öztireli\\(^{5}\\), Yujiu Yang\\(^{1\\dagger}\\), Shenzhen International Graduate School, Tsinghua University  \n\\(^{2}\\)Tencent AI Lab \\(^{3}\\)Ant Group \\(^{4}\\)HKUST \\(^{5}\\)University of Cambridge"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.235,
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+            "angle": 0,
+            "content": "Abstract"
+        },
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+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "Recently, a surge of high-quality 3D-aware GANs have been proposed, which leverage the generative power of neural rendering. It is natural to associate 3D GANs with GAN inversion methods to project a real image into the generator's latent space, allowing free-view consistent synthesis and editing, referred as 3D GAN inversion. Although with the facial prior preserved in pre-trained 3D GANs, reconstructing a 3D portrait with only one monocular image is still an ill-posed problem. The straightforward application of 2D GAN inversion methods focuses on texture similarity only while ignoring the correctness of 3D geometry shapes. It may raise geometry collapse effects, especially when reconstructing a side face under an extreme pose. Besides, the synthetic results in novel views are prone to be blurry. In this work, we propose a novel method to promote 3D GAN inversion by introducing facial symmetry prior. We design a pipeline and constraints to make full use of the pseudo auxiliary view obtained via image flipping, which helps obtain a view-consistent and well-structured geometry shape during the inversion process. To enhance texture fidelity in unobserved viewpoints, pseudo labels from depth-guided 3D warping can provide extra supervision. We design constraints to filter out conflict areas for optimization in asymmetric situations. Comprehensive quantitative and qualitative evaluations on image reconstruction and editing demonstrate the superiority of our method."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.079,
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+            "angle": 0,
+            "content": "1. Introduction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
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+            "angle": 0,
+            "content": "Recent 3D-aware generative adversarial networks (3D GANs) have seen immense progress. By incorporating a neural rendering engine into the generator network architecture, 3D GANs can synthesize view-consistent images. To increase the generation resolution, existing methods [5,12,25,30,31,36-38,41] boost the 3D inductive bias"
+        },
+        {
+            "type": "image",
+            "bbox": [
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+            "content": null
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+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
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+            "angle": 0,
+            "content": "Figure 1. Visual examples of our inversion method. Direct applying 2D GAN inversion methods (PTI [28]) to the 3D GAN suffers from inaccurate geometry in novel views. Our method excels in synthesizing consistent geometry and high-fidelity texture in different views, even reconstructing a face under an extreme pose."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.689,
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+            "angle": 0,
+            "content": "with an additional 2D CNN-based upsampler or an efficient 3D representation modeling method. With tremendous effort, 3D GANs can produce photorealistic images while enforcing strong 3D consistency across different views."
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "We are interested in the task of reconstructing a human face with 3D geometry and texture given only one monocular image. It is an ill-posed problem and close to the harsh condition of real scenarios. With the power of 3D GANs, it seems achievable via projecting a target image onto the manifold of a pre-trained generator. The process is referred as 3D GAN inversion. A straightforward path is to follow the 2D GAN inversion method [28], i.e., optimizing the latent code and the network parameters of the generator to overfit the specific portrait."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
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+            "angle": 0,
+            "content": "Work done during an internship at Tencent AI Lab."
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+        {
+            "type": "page_footnote",
+            "bbox": [
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+            "angle": 0,
+            "content": "† Corresponding Author."
+        },
+        {
+            "type": "list",
+            "bbox": [
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+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+            "angle": 0,
+            "content": "342"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
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+                0.092,
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+            ],
+            "angle": 0,
+            "content": "However, since the ground truth 3D geometry is absent given one monocular image, the inversion result is far from satisfactory. The process of fitting a 3D GAN to one image would sacrifice geometric correctness in order to make the synthetic texture as close as possible to the input, even destroying the original semantic-rich latent space. As the optimization process goes, the face geometry tends to degenerate into a flattened shape, due to the absence of geometry supervision, e.g., images from other views. Besides, there exist quality issues in texture synthesis under novel views. The rendered images of unseen views tend to be blurry and inconsistent with the original image, especially when reconstructing a side face under an extreme pose. Because there is no texture supervision for unseen views given only one monocular image. The failure cases of directly applying [28] are illustrated in Fig. 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.333,
+                0.473,
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+            ],
+            "angle": 0,
+            "content": "In this work, to alleviate the issue caused by missing geometry and texture supervision under multiple views, we propose a novel 3D GAN inversion approach by taking full advantage of facial symmetry prior to construct pseudo supervision of different views. Intuitively, we note that human faces are almost symmetric. Assuming the given portrait is symmetric, we can obtain an additional perspective of the portrait by simply mirroring the image. The images of two distinct views can provide geometric relations between the 3D points and their 2D projections based on epipolar geometry. Motivated by this, we seek to leverage facial symmetry as the geometric prior constraining the inversion. The symmetry prior is also employed in a traditional 3D reconstruction work [35]. We leverage the mirrored image as extra supervision of another view when performing the inversion, which prevents the geometry collapse. A rough geometry can be obtained by the inversion with the original and mirror images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.606,
+                0.473,
+                0.816
+            ],
+            "angle": 0,
+            "content": "To further enhance texture quality and geometry in novel views, we employ depth-guided 3D warping to generate the pseudo images of the views surrounding the input and symmetric camera pose. The depth is inferred from the rough 3D volume. The original image along with the pseudo images are used to fine-tune the generator's parameters for the joint promotion of texture and geometry. To prevent the optimized geometry from deviating too much from the rough geometry, we design a geometry regularization term as a constraint. However, human faces are never fully symmetric in practice, neither in shape nor appearance. Therefore, we design several constraints to extract meaningful information adaptively from the mirror image without compromising the original reconstruction quality."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.097,
+                0.817,
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+                0.831
+            ],
+            "angle": 0,
+            "content": "Our main contributions are as follows:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.096,
+                0.84,
+                0.47,
+                0.903
+            ],
+            "angle": 0,
+            "content": "- We propose a novel 3D GAN inversion method by incorporating facial symmetry prior. It enables a high-quality reconstruction while preserving the multi-view consistency in geometry and texture."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.519,
+                0.092,
+                0.892,
+                0.153
+            ],
+            "angle": 0,
+            "content": "- We conduct comprehensive experiments to demonstrate the effectiveness of our method and compare it with many state-of-the-art inversion methods. We also apply our method to various downstream applications."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.184,
+                0.642,
+                0.2
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.213,
+                0.666,
+                0.228
+            ],
+            "angle": 0,
+            "content": "2.1. 3D-Aware GANs"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.242,
+                0.895,
+                0.529
+            ],
+            "angle": 0,
+            "content": "Recently, neural scene representations have incorporated 3D prior into image synthesis with explicit camera control. Inspired by the success of Neural Radiance Fields (NeRF) [22], [6,24] employ implicit volumetric neural rendering structure for consistent novel view synthesis, required only unconstrained monocular images training. To overcome the computational cost and lift the generation resolution, the following methods adopt a two-stage rendering process [5, 12, 21, 25, 30, 31, 37, 38, 41, 42]. Since 2D upsamplers may introduce view-inconsistent artifacts, NeRF path regularization [12] and dual discriminators [5] are proposed. Different 3D modeling representations are further designed for scalable and fast rendering. EG3D [5] introduces tri-plane representation, and GRAM-HD [36] proposes to render radiance manifolds first for efficient sampling. Boosting with the powerful high-fidelity unconditioned 3D GANs, we can achieve real image 3D reconstruction and editing. Specifically, we select the state-of-the-art EG3D [5] as our backbone."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.551,
+                0.655,
+                0.567
+            ],
+            "angle": 0,
+            "content": "2.2. GAN Inversion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.579,
+                0.895,
+                0.777
+            ],
+            "angle": 0,
+            "content": "To edit a real image [29, 39], GAN inversion is applied first to discover a corresponding latent code from which the generator can synthesize the real image. Existing 2D GAN inversion approaches can be categorized into optimization-based, learning-based, and hybrid methods. [1, 16] directly minimize the reconstruction distance via optimizing the latent codes. Learning-based methods [2, 3, 32, 34] exploit a general encoder network to map the input image into latent space in real-time. Hybrid methods would apply the latent code predicted from the encoder as initialization in the later optimization process. Beyond the original inversion latent space, PTI [28] further optimizes the parameters of the generator to enhance the visual fidelity."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.78,
+                0.895,
+                0.903
+            ],
+            "angle": 0,
+            "content": "As for the 3D GAN inversion task, most methods directly transfer the 2D methods, e.g., PTI [28] and e4e [32], which may suffer from the poor results in novel views. Pix2NeRF [4] introduced a joint distillation strategy for training a 3D inversion encoder. A concurrent work [18] proposes to perform camera pose optimization simultaneously to ensure view consistency. However, none of the above methods take geometry shape into consideration."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.957
+            ],
+            "angle": 0,
+            "content": "343"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.089,
+                0.322,
+                0.276
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.325,
+                0.089,
+                0.631,
+                0.276
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.633,
+                0.089,
+                0.888,
+                0.275
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.288,
+                0.895,
+                0.346
+            ],
+            "angle": 0,
+            "content": "Figure 2. The proposed framework. A) Our method first performs inversion with the help of the symmetry view to achieve the latent code \\( w^{+} \\) with a roughly correct geometry. B) The original image and the mirror one, along with adjacent warping pseudos, are used for joint optimization to enhance the geometry and texture of rendered images in novel views. C) Depth-guided 3D warping are used to generate pseudo images in novel views to provide extra supervision. Unfaithful regions are filtered out with the authentic mask."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.357,
+                0.232,
+                0.373
+            ],
+            "angle": 0,
+            "content": "2.3. Few-shot NeRF"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.381,
+                0.474,
+                0.579
+            ],
+            "angle": 0,
+            "content": "Few-shot NeRF aims at reconstructing general 3D scenarios where only a few observed views are available, which shares a similar setting with 3D GAN inversion. MVS-NeRF [7] leverages plane-swept cost volumes in multi-view stereo for geometry-aware scene reasoning to improve performance. DietNeRF [13] enforces semantic consistency between rendered images from unseen view and seen images via a CLIP encoder [27]. RegNeRF [23] regularizes the texture of patches rendered from unobserved viewpoints without relying on additional training modules. Since it is hard to find a common prior for general scenes, these methods investigate how to ensure the geometry consistency of different views, which gives us inspiration."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.59,
+                0.367,
+                0.607
+            ],
+            "angle": 0,
+            "content": "3. Definition of 3D GAN Inversion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.615,
+                0.47,
+                0.738
+            ],
+            "angle": 0,
+            "content": "Similar to 2D GAN inversion, 3D GAN inversion aims to project an input image \\(I\\) onto the manifold of a pretrained unconditional 3D GAN model \\(G_{\\mathrm{3D}}(\\cdot ;\\theta)\\) parameterized by weight \\(\\theta\\). After inversion, \\(G_{\\mathrm{3D}}\\) can reconstruct the image faithfully given the corresponding camera pose, synthesize content-consistent images in novel views, and facilitate downstream tasks like face editing. One formulation of the 3D GAN inversion problem is defined as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.145,
+                0.751,
+                0.47,
+                0.775
+            ],
+            "angle": 0,
+            "content": "\\[\nw ^ {*} = \\underset {w} {\\arg \\max } = \\mathcal {L} \\left(G _ {3 D} (w, \\pi ; \\theta), I\\right), \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.471,
+                0.902
+            ],
+            "angle": 0,
+            "content": "where \\( w \\) is the latent representation in \\( \\mathcal{W}^+ \\) space and \\( \\pi \\) is the corresponding camera matrix of input image. The loss function \\( \\mathcal{L}(\\cdot, \\cdot) \\) is usually defined as pixel-wise reconstruction loss or perceptual loss. In our settings, camera matrix \\( \\pi \\) is known, which is extracted by a pre-trained detector [9]. This formulation cares about the \\( \\mathcal{W}^+ \\) space. However, the inversion in the \\( \\mathcal{W}^+ \\) space is always not enough to capture local facial details, resulting in inaccurate reconstruction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.358,
+                0.892,
+                0.434
+            ],
+            "angle": 0,
+            "content": "Following the recent optimization-based 2D GAN inversion method [28], we perform the inversion in the extended latent space for more accurate reconstruction, i.e., the combination of the \\(\\mathcal{W}^{+}\\) space and the parameter space. The formulation is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.556,
+                0.44,
+                0.892,
+                0.466
+            ],
+            "angle": 0,
+            "content": "\\[\nw ^ {*}, \\theta^ {*} = \\underset {w, \\theta} {\\arg \\max } = \\mathcal {L} \\left(G _ {3 D} (w, \\pi ; \\theta), I\\right). \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.471,
+                0.892,
+                0.516
+            ],
+            "angle": 0,
+            "content": "Note that \\( w \\) and \\( \\theta \\) are optimized alternatively, i.e., \\( w \\) is optimized using Eq. (1) first and then \\( \\theta \\) is optimized with the fixed \\( w^{*} \\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.528,
+                0.729,
+                0.546
+            ],
+            "angle": 0,
+            "content": "4. The Proposed Approach"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.554,
+                0.893,
+                0.842
+            ],
+            "angle": 0,
+            "content": "Our goal is to reconstruct a human face through a pretrained 3D GAN given a single monocular image. The reconstruction is supposed to preserve authentic appearance texture and geometry shape in novel views. Due to the limited information about geometry and texture from a single image, overfitting a single view tends to be trapped in geometry collapse, get the blurry texture and miss details in unseen views, especially when reconstructing a side face under an extreme pose. To overcome the issue of lacking information about other views, we introduce facial symmetry prior to promote inversion. We propose a two-stage inversion pipeline, i.e., inversion for rough geometry and joint optimization of geometry and texture. In the first stage, we obtain a rough geometry by optimizing the latent code \\( w \\) using the original and mirror images in Sec. 4.1. In the second stage, we refine the geometry and texture by optimizing the parameter \\( \\theta \\) with the depth-guided 3D warping and a set of designed constraints in Sec 4.2. An overview of our method is shown in Fig. 2."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.848,
+                0.892,
+                0.865
+            ],
+            "angle": 0,
+            "content": "4.1. Inversion with Symmetry for Rough Geometry"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.871,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "The purpose of this stage is to learn a rough geometry as a pivot for further tuning. To compensate for the missing"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.957
+            ],
+            "angle": 0,
+            "content": "344"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.09,
+                0.891,
+                0.188
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.202,
+                0.893,
+                0.23
+            ],
+            "angle": 0,
+            "content": "Figure 3. Visualization of warped pseudos. The red bounding box contains the range of employed pseudos, depending on the yaw angle of the input image. A frontal face can be warped by a wider range of yaw angles than a side face to get authentic pseudos."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.08,
+                0.241,
+                0.177,
+                0.316
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.111,
+                0.316,
+                0.145,
+                0.335
+            ],
+            "angle": 0,
+            "content": "Source Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.178,
+                0.241,
+                0.274,
+                0.316
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.207,
+                0.316,
+                0.245,
+                0.335
+            ],
+            "angle": 0,
+            "content": "Warped Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.275,
+                0.241,
+                0.371,
+                0.316
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.302,
+                0.316,
+                0.351,
+                0.334
+            ],
+            "angle": 0,
+            "content": "Authentic Mask"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.373,
+                0.241,
+                0.468,
+                0.316
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.402,
+                0.316,
+                0.439,
+                0.325
+            ],
+            "angle": 0,
+            "content": "Pseudo"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.088,
+                0.346,
+                0.457,
+                0.361
+            ],
+            "angle": 0,
+            "content": "Figure 4. Visualization of authentic mask and warped pseudo."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.373,
+                0.468,
+                0.493
+            ],
+            "angle": 0,
+            "content": "information of unseen views, we resort to facial symmetry prior, i.e., the left face is almost the same as the right one. We simply flip the input image \\( I_{s} \\) horizontally to get the mirror image \\( I_{m} \\) whose corresponding camera pose \\( \\pi_{m} \\) can be calculated by multiplying a fixed matrix by the camera extrinsic parameters of \\( \\pi_{s} \\). The intrinsic parameters are unchanged. The mirror image serves as the pseudo-projected image under a novel view."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.494,
+                0.47,
+                0.782
+            ],
+            "angle": 0,
+            "content": "Since human faces are not always perfectly symmetric, the mirror image is just an approximation under the novel view. There exists inconsistent content between the original image and the mirror one if they have an overlapping face region, i.e., different colors in the position, referred as conflict content. The inversion should depend more on the original image and take partial useful information from the mirror one. Furthermore, we observe that a frontal face can provide more effective information than a side face. A nearly frontal face provides plenty of facial information, and we should trust less on its mirror image to avoid conflict in the overlapping region. While a side face provides information for only half one face, it has only a small overlapping conflict region with its mirror image. Hence, we should trust more on the mirror image. We exploit an adaptive weighting strategy for the importance of the mirror image according to its yaw angle \\(\\alpha_{\\mathrm{yaw}}\\). We use a Gaussian function with respect to \\(\\alpha_{\\mathrm{yaw}}\\) to approximate the importance of different views. The weight \\(\\lambda_{m}\\) of the mirror image is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.188,
+                0.802,
+                0.469,
+                0.835
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {E} (x) = \\frac {1}{\\sigma \\sqrt {2 \\pi}} e ^ {- \\frac {(x - \\mu) ^ {2}}{2 \\sigma^ {2}}}, \\tag {3}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.14,
+                0.837,
+                0.469,
+                0.877
+            ],
+            "angle": 0,
+            "content": "\\[\n\\lambda_ {m} = \\left\\{ \\begin{array}{l l} 1 - \\mathcal {E} \\left(\\alpha_ {\\text {y a w}}\\right), & \\text {i f} \\mathcal {E} \\left(\\alpha_ {\\text {y a w}}\\right) \\leq k; \\\\ 0, & \\text {i f} \\mathcal {E} \\left(\\alpha_ {\\text {y a w}}\\right) > k; \\end{array} \\right. \\tag {4}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.886,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "where \\(\\sigma, \\mu\\) and \\(k\\) are hyper-parameters. As a nearly frontal"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.244,
+                0.892,
+                0.274
+            ],
+            "angle": 0,
+            "content": "mirror face can compensate for very limited extra information for the original image, its weight \\(\\lambda_{m}\\) is clamped to 0."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.275,
+                0.892,
+                0.365
+            ],
+            "angle": 0,
+            "content": "To optimize the latent code in \\(\\mathcal{W}^+\\) space, the Perceptual loss [40] is used to minimize the distance between the generated results and the original and mirror images. Following [17, 28], a noise regularization term \\(\\mathcal{L}_n(n)\\) is employed to prevent the noise vector from containing vital information. The objective in this stage is defined as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.528,
+                0.37,
+                0.891,
+                0.395
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {i n v}} = \\mathcal {L} _ {\\mathrm {L P I P S}} \\left(G _ {3 \\mathrm {D}} \\left(w, \\pi_ {s}; \\theta\\right), I _ {s}\\right) + \\tag {5}\n\\]"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.556,
+                0.391,
+                0.843,
+                0.406
+            ],
+            "angle": 0,
+            "content": "\\[\n\\lambda_ {m} \\mathcal {L} _ {\\text {L P I P S}} \\left(G _ {3 \\mathrm {D}} \\left(w, \\pi_ {m}; \\theta\\right), I _ {m}\\right) + \\lambda_ {n} \\mathcal {L} _ {n} (n),\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.411,
+                0.892,
+                0.472
+            ],
+            "angle": 0,
+            "content": "where \\( n \\) is the noise vector and \\( \\lambda_{n} \\) is a trade-off parameter. The generator is kept frozen at this stage. Visual illustrations in Fig. 8 show that the geometry can be greatly improved with the facial symmetry prior."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.499,
+                0.479,
+                0.88,
+                0.495
+            ],
+            "angle": 0,
+            "content": "4.2. Joint Optimization of Geometry and Texture"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.502,
+                0.892,
+                0.683
+            ],
+            "angle": 0,
+            "content": "Though we obtain the rough geometry via the optimization of \\( w \\) in the first stage, there is a distinct gap between the texture of the rendered face and that of the original one, even under the same camera pose. The rendered face shares a similar face geometry with the original one, but it becomes a different identity. In this stage, we optimize the generator's parameters \\( \\theta \\) to bridge the texture gap for identity preservation and refine the rough geometry as well. We design a geometry regularization constraint to avoid the model degrading to generate flattened geometry. Moreover, we construct a set of pseudo images in different views to provide supervision via depth-guided 3D warping."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.686,
+                0.892,
+                0.867
+            ],
+            "angle": 0,
+            "content": "Geometry Regularization. We observe that optimizing the generator without any constraint on the geometry will cause the deviation of the geometry from the rough one, resulting in a flattened geometry similar to the case of inversion with a single image. To avoid the geometry drift during overfitting the texture, we regularize the optimized density obtained from the 3D volume of 3D GAN to be similar to that from the rough volume obtained in the first stage. Specifically, with the fixed \\( w \\), we generate depth maps \\( D \\) from 3D GAN under different sampled views and calculate \\( \\mathcal{L}_2 \\) distance between them with the corresponding depth maps \\( D_0 \\) generated from the un-tuned generator in the first stage:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.606,
+                0.872,
+                0.891,
+                0.904
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {d e p t h}} = \\sum_ {i \\in \\mathbb {S}} \\| D ^ {i} - D _ {0} ^ {i} \\| _ {2}, \\tag {6}\n\\]"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.957
+            ],
+            "angle": 0,
+            "content": "345"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.092,
+                0.345,
+                0.106
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathbb{S}\\) is the sampled camera pose set."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.109,
+                0.47,
+                0.306
+            ],
+            "angle": 0,
+            "content": "Depth-guided 3D Warping for Pseudo Supervision. Optimizing the generator with only two images is still not enough to capture the facial details, resulting in blurry effects around facial components such as eyes (see Fig. 11). Hence, we propose to construct pseudo images of different views for extra supervision using the rough geometry and the original and mirror images. Specifically, given the original image (source view) and the rough geometry, we can synthesize an image under a novel view (target view) by warping with 3D guidance. A coordinate pixel \\( p_t \\) of the synthesized image in the target view can be obtained by projecting back onto the source view with the relative camera pose \\( \\pi_{t\\rightarrow s} \\) and the camera intrinsic parameters \\( K \\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.169,
+                0.314,
+                0.469,
+                0.33
+            ],
+            "angle": 0,
+            "content": "\\[\np _ {t \\rightarrow s} = K \\pi_ {t \\rightarrow s} D _ {t} \\left(p _ {t}\\right) K ^ {- 1} p _ {t}, \\tag {7}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.337,
+                0.469,
+                0.428
+            ],
+            "angle": 0,
+            "content": "where \\( D_{t}(\\cdot) \\) is the depth map of the target view. Since the projected coordinate \\( p_{t\\rightarrow s} \\) are continuous values, we can extract the color values from the original image with a differentiable bilinear sampling mechanism, i.e., \\( I_{s\\rightarrow t} = I_s(p_{t\\rightarrow s}) \\). The low-resolution depth map will be upsampled to match the dimension of the image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.429,
+                0.47,
+                0.638
+            ],
+            "angle": 0,
+            "content": "Authentic Mask. Without distinguishing the foreground pixels from the background, the background pixels in the original image may be projected onto the foreground plane, leading to erroneous results. To overcome this issue, we form a mask to indicate the visibility of pixels to filter invisible areas using the rendered depth values. Specifically, we can get the projected depth value \\( D_{s}(p_{t\\rightarrow s}) \\) via sampling from the depth map in the source view. Here we employ the euclidean distance between \\( D_{s}(p_{t\\rightarrow s}) \\) and the depth map \\( D_{t}(p_{t}) \\) in the target view to calculate the mask. A large distance indicates the pixel \\( p_t \\) is invisible. To ensure the projected pixels are located on the front visible surface, we only preserve the area where the distance is under a threshold \\( \\tau \\):"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.147,
+                0.648,
+                0.469,
+                0.665
+            ],
+            "angle": 0,
+            "content": "\\[\nM \\left(p _ {t}\\right) = \\left\\| D _ {t} \\left(p _ {t}\\right) - D _ {s} \\left(p _ {t \\rightarrow s}\\right)\\right\\| <   \\tau . \\tag {8}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.672,
+                0.469,
+                0.778
+            ],
+            "angle": 0,
+            "content": "Furthermore, due to the poor depth estimation of the background, only the facial part would be warped. We warp the facial mask of the source view to the target view and multiply it with the visibility mask \\( M(p_{t}) \\) to get the authentic mask \\( M_{t} \\). An example is shown in Fig. 4. After multiplying the mask \\( M_{t} \\) with the warped image \\( I_{s\\rightarrow t} \\), the resulting image can be used for supervision."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.78,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Adjacent View Warping. Fig. 3 illustrates the warping results of two examples. When the yaw angle between the source and target views increases, the warping results have more distortions and become less authentic. Therefore, it is intuitive to abandon the pseudo images of the target views that deviate a lot from the source view. Empirically, a frontal face can be warped by a wider range of yaw angles than a side face to get authentic pseudo images. The"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.092,
+                0.892,
+                0.152
+            ],
+            "angle": 0,
+            "content": "variance of sampling yaw angles for constructing pseudo images is set to a fixed ratio of \\(\\lambda_{m}\\) that depends on the viewpoint mentioned in Sec. 4.1. The LPIPS loss [14] is used to compute the multi-view pixel-wise distance as follows:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.542,
+                0.165,
+                0.892,
+                0.182
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {a d j}} = \\mathcal {L} _ {\\mathrm {L P I P S}} \\left(M _ {t} \\cdot G _ {\\mathrm {3 D}} (w, \\pi_ {t}; \\theta), M _ {t} \\cdot I _ {s \\rightarrow t}\\right). \\tag {9}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.195,
+                0.892,
+                0.3
+            ],
+            "angle": 0,
+            "content": "Although the pseudo images of several unseen adjacent views around the source view have been constructed, it brings marginal improvements on remote views. Especially for a side face, the pseudo images of the remote views are blurry and have incomplete texture (see Fig. 3). Therefore, we also construct pseudo images of the adjacent views around the view of the mirror image."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.301,
+                0.892,
+                0.452
+            ],
+            "angle": 0,
+            "content": "Since the conflict region between the original and mirror images has a side effect on the generator optimization process, resulting in blurry effects on rendered images, even reconstructing the source view (see Fig. 9), we propose to take partial meaningful information from the symmetric views without harming the original inversion quality. We compute the similarities only for facial components, rather than the whole face region. Besides, instead of using a pixelwise loss, we exploit the contextual loss [20] to improve the texture quality. The loss for symmetric views is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.516,
+                0.464,
+                0.891,
+                0.508
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {s y m}} = \\sum_ {\\mathrm {c} \\in \\mathbb {F}} \\mathcal {L} _ {\\mathrm {C X}} \\left(\\operatorname {R O I} ^ {c} \\left(G _ {3 \\mathrm {D}} \\left(w, \\pi_ {t}; \\theta\\right)\\right), \\operatorname {R O I} ^ {c} \\left(I _ {m \\rightarrow t}\\right)\\right), \\tag {10}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.509,
+                0.892,
+                0.569
+            ],
+            "angle": 0,
+            "content": "where \\(I_{m\\rightarrow t}\\) is the pseudo image of the viewpoint \\(\\pi_t\\) warped from the mirror image \\(I_{m}\\). \\(\\mathrm{ROI}^c (\\cdot)\\) refers to the region of interest component \\(c\\) from the collection \\(\\mathbb{F} = \\{\\text{eyes, nose, mouth}\\}\\)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.57,
+                0.892,
+                0.616
+            ],
+            "angle": 0,
+            "content": "The reconstruction loss between the original image and its corresponding rendered image is still in use to ensure the quality of the initial perspective, which is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.502,
+                0.628,
+                0.891,
+                0.658
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\mathrm {o r i}} = \\mathcal {L} _ {2} \\left(G _ {\\mathrm {3 D}} \\left(w, \\pi_ {s}; \\theta\\right), I _ {s}\\right) + \\mathcal {L} _ {\\mathrm {L P I P S}} \\left(G _ {\\mathrm {3 D}} \\left(w, \\pi_ {s}; \\theta\\right), I _ {s}\\right). \\tag {11}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.659,
+                0.891,
+                0.688
+            ],
+            "angle": 0,
+            "content": "The overall objective of optimizing the generator's parameters is defined as:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.52,
+                0.702,
+                0.891,
+                0.719
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {o p t}} = \\mathcal {L} _ {\\text {o r i}} + \\lambda_ {\\text {a d j}} \\mathcal {L} _ {\\text {a d j}} + \\lambda_ {\\text {s y m}} \\mathcal {L} _ {\\text {s y m}} + \\lambda_ {\\text {d e p t h}} \\mathcal {L} _ {\\text {d e p t h}}. \\tag {12}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.731,
+                0.892,
+                0.763
+            ],
+            "angle": 0,
+            "content": "The trade-off hyper-parameters are set as follows: \\(\\lambda_{\\mathrm{adj}} = 0.1\\), \\(\\lambda_{\\mathrm{sym}} = 0.05\\), and \\(\\lambda_{\\mathrm{depth}} = 1\\)."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.777,
+                0.634,
+                0.794
+            ],
+            "angle": 0,
+            "content": "5. Experiments"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.802,
+                0.707,
+                0.818
+            ],
+            "angle": 0,
+            "content": "5.1. Experimental Settings"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.825,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Datasets. We conduct the experiments on human faces datasets. For all experiments, we select EG3D [5] as our 3D GAN prior, which is pre-trained on FFHQ dataset [15]. We verified quantitative metrics on CelebA-HQ test dataset [19]. We further evaluated on MEAD [33], a"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
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+                0.512,
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+            "angle": 0,
+            "content": "346"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
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+                0.088,
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+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.11,
+                0.359,
+                0.137,
+                0.368
+            ],
+            "angle": 0,
+            "content": "SG2"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.168,
+                0.089,
+                0.254,
+                0.359
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.187,
+                0.359,
+                0.236,
+                0.368
+            ],
+            "angle": 0,
+            "content": "SG2 \\(W^{+}\\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.254,
+                0.089,
+                0.339,
+                0.359
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.284,
+                0.359,
+                0.305,
+                0.368
+            ],
+            "angle": 0,
+            "content": "PTI"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.341,
+                0.089,
+                0.426,
+                0.359
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.368,
+                0.36,
+                0.396,
+                0.369
+            ],
+            "angle": 0,
+            "content": "Ours"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.427,
+                0.124,
+                0.543,
+                0.214
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.451,
+                0.215,
+                0.519,
+                0.224
+            ],
+            "angle": 0,
+            "content": "Source Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.427,
+                0.248,
+                0.543,
+                0.339
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.451,
+                0.339,
+                0.518,
+                0.348
+            ],
+            "angle": 0,
+            "content": "Source Image"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.543,
+                0.089,
+                0.63,
+                0.359
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.574,
+                0.359,
+                0.599,
+                0.369
+            ],
+            "angle": 0,
+            "content": "SG2"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.63,
+                0.09,
+                0.716,
+                0.359
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.652,
+                0.359,
+                0.699,
+                0.368
+            ],
+            "angle": 0,
+            "content": "SG2 \\(W^{+}\\)"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.718,
+                0.09,
+                0.804,
+                0.359
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.75,
+                0.359,
+                0.771,
+                0.368
+            ],
+            "angle": 0,
+            "content": "PTI"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.804,
+                0.09,
+                0.891,
+                0.359
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.83,
+                0.359,
+                0.857,
+                0.368
+            ],
+            "angle": 0,
+            "content": "Ours"
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.381,
+                0.893,
+                0.41
+            ],
+            "angle": 0,
+            "content": "Figure 5. Qualitative comparisons with state-of-the-art methods on novel view synthesis. The reconstruction quality of the original view is presented in the first row. The texture and geometry in novel views are shown in the rest rows."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.421,
+                0.466,
+                0.486
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>MSE ↓</td><td>LPIPS ↓</td><td>MS-SSIM ↓</td><td>ID ↑</td><td>Pose ↓</td><td>Depth ↓</td></tr><tr><td>SG2 [16]</td><td>0.0881</td><td>0.3231</td><td>0.3557</td><td>0.8209</td><td>0.043</td><td>0.0505</td></tr><tr><td>SG2 W+ [1]</td><td>0.0439</td><td>0.2261</td><td>0.2483</td><td>0.8735</td><td>0.040</td><td>0.0500</td></tr><tr><td>PTI [28]</td><td>0.0084</td><td>0.0920</td><td>0.0980</td><td>0.9432</td><td>0.037</td><td>0.0510</td></tr><tr><td>SPI (Ours)</td><td>0.0082</td><td>0.0865</td><td>0.0991</td><td>0.9470</td><td>0.036</td><td>0.0476</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.11,
+                0.495,
+                0.435,
+                0.51
+            ],
+            "angle": 0,
+            "content": "Table 1. Quantitative comparison on CelebA-HQ [19]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.527,
+                0.469,
+                0.557
+            ],
+            "angle": 0,
+            "content": "multi-view high-quality video dataset. The first frame from each viewpoint video of 10 identities is extracted for testing."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.56,
+                0.469,
+                0.636
+            ],
+            "angle": 0,
+            "content": "Metrics. We evaluate image reconstruction quality and similarity with the following metrics: mean squared error (MSE), perceptual similarity loss (LPIPS) [40], structural similarity (MS-SSIM), and identity similarity (ID) by employing a pre-trained face recognition network [8]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.639,
+                0.47,
+                0.775
+            ],
+            "angle": 0,
+            "content": "Baselines. We mainly compare our methods with optimization-based 2D GAN inversion methods. SG2 [16] directly inverts real images into \\(\\mathcal{W}\\) space with an optimization scheme. [1] extends the inversion into \\(\\mathcal{W}^+\\) space, denoted by SG2 \\(\\mathcal{W}^+\\). PTI [28] would further tune generator parameters in a second stage. For a fair comparison, both PTI and ours first optimize the latent for 500 steps and then fine-tune the generator for 1,000 steps, while SG2 and SG2 \\(\\mathcal{W}^+\\) optimize the latent for 1,500 steps."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.786,
+                0.431,
+                0.803
+            ],
+            "angle": 0,
+            "content": "5.2. Reconstruction and Novel View Synthesis"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.81,
+                0.469,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Qualitative Evaluation. Fig. 5 presents a qualitative comparison of texture and geometry quality of different views. As for the original view, our method is able to inverse challenging details such as earrings, make-up, and wrinkles, which demonstrates that we do not sacrifice the original reconstruction performance. When the camera rotates to"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.499,
+                0.42,
+                0.895,
+                0.606
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.499,
+                0.614,
+                0.893,
+                0.656
+            ],
+            "angle": 0,
+            "content": "Figure 6. Comparison of identity preservation in novel views. The x-axis represents the yaw angle of the input image. '0' indicates the frontal face."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.672,
+                0.892,
+                0.793
+            ],
+            "angle": 0,
+            "content": "novel views, images generated from 2D inversion methods present a twisted appearance, due to the nearly flattened geometry shape. Since SG2 does not deviate too far from the initial GAN space, it can generate a portrait with a structured geometry, but fails to preserve the identity. Our method is capable of maintaining authentic and consistent geometry in novel views along with a sharp appearance, even when rotated to an extreme pose."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.893,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Quantitative Evaluation. The reconstruction metrics of the original view are shown in Table 1. As can be seen, the results align with our qualitative evaluation as we achieved comparable scores to the current 2D state-of-the-art inversion methods [28]. The MSE, LPIPS, and ID similarities of ours are further improved, which can be attributed to the employment of \\(\\mathcal{W}^+\\) latent space. Following EG3D, we"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.945,
+                0.511,
+                0.956
+            ],
+            "angle": 0,
+            "content": "347"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.079,
+                0.089,
+                0.468,
+                0.226
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.08,
+                0.237,
+                0.466,
+                0.251
+            ],
+            "angle": 0,
+            "content": "Figure 7. Qualitative comparisons with PTI [28] on MEAD [33]."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.079,
+                0.255,
+                0.476,
+                0.446
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Method</td><td>View</td><td>MSE ↓</td><td>LPIPS ↓</td><td>MS-SSIM ↓</td><td>ID ↑</td></tr><tr><td>PTI</td><td rowspan=\"2\">F</td><td>0.03204</td><td>0.2971</td><td>0.2070</td><td>0.8445</td></tr><tr><td>Ours</td><td>0.03296</td><td>0.3088</td><td>0.2135</td><td>0.8388</td></tr><tr><td>PTI</td><td rowspan=\"2\">L30</td><td>0.04355</td><td>0.2992</td><td>0.2274</td><td>0.8446</td></tr><tr><td>Ours</td><td>0.03399</td><td>0.2796</td><td>0.2025</td><td>0.8469</td></tr><tr><td>PTI</td><td rowspan=\"2\">L60</td><td>0.08255</td><td>0.3902</td><td>0.3143</td><td>0.7568</td></tr><tr><td>Ours</td><td>0.04069</td><td>0.3113</td><td>0.2379</td><td>0.8272</td></tr><tr><td>PTI</td><td rowspan=\"2\">R30</td><td>0.04574</td><td>0.3110</td><td>0.2393</td><td>0.8383</td></tr><tr><td>Ours</td><td>0.03203</td><td>0.2807</td><td>0.2057</td><td>0.8529</td></tr><tr><td>PTI</td><td rowspan=\"2\">R60</td><td>0.07865</td><td>0.3829</td><td>0.3106</td><td>0.7995</td></tr><tr><td>Ours</td><td>0.04541</td><td>0.3160</td><td>0.2400</td><td>0.8335</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.457,
+                0.47,
+                0.542
+            ],
+            "angle": 0,
+            "content": "Table 2. Quantitative comparison on MEAD [33]. View denotes the yaw angle of the input image. F is frontal, L is left side, and R is right side. 30 and 60 are the rotation degrees. Each time we use one view as the inversion input and use all 5 views as ground truth for evaluation. The average performance of 4 unseen views and 1 seen view is reported."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.565,
+                0.469,
+                0.611
+            ],
+            "angle": 0,
+            "content": "evaluate shape quality by calculating \\(\\mathcal{L}_2\\) for pseudo-ground-truth depth-maps (Depth) generated from DECA [10], and poses (Pose) estimated from synthesized images."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.612,
+                0.469,
+                0.837
+            ],
+            "angle": 0,
+            "content": "We also use identity similarity to evaluate the identity preservation of the synthesized novel views. Given a portrait, we synthesize a novel view image under the symmetric camera pose of the portrait. The similarity between the synthesized image and the flipped image portrait is calculated. The results are shown in Fig. 6. It can be observed that when the yaw angle of a portrait is small, all methods can perform well with a high similarity score. But when the yaw angle is large, only our method can maintain a high score, while other methods encounter a sharp performance drop due to the inaccurate geometry. As we employ the symmetry prior and the adjacent pseudo supervision, the rendered faces can better preserve the texture and geometry. These results demonstrate that we can achieve an identity-consistent 3D inversion."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.84,
+                0.47,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Evaluation on MEAD. To get a comprehensive understanding of the performance of our method, we evaluate on MEAD, a multi-view dataset. The quantitative comparison between the reconstruction portraits and the ground truth in"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.501,
+                0.088,
+                0.892,
+                0.19
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.546,
+                0.2,
+                0.845,
+                0.215
+            ],
+            "angle": 0,
+            "content": "Figure 8. Ablation study of facial symmetry prior."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.502,
+                0.215,
+                0.892,
+                0.371
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.498,
+                0.381,
+                0.892,
+                0.424
+            ],
+            "angle": 0,
+            "content": "Figure 9. Ablation study of authentic mask. Vanilla denotes simply using the full mirror image for supervision. While Ours filters out conflict areas with the designed constraints."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.439,
+                0.893,
+                0.59
+            ],
+            "angle": 0,
+            "content": "different views is shown in Tab. 2. PTI [28] and our method achieve comparable performance when given a frontal portrait. When the view of the input face has an offset from the canonical one, our method surpasses PTI distinctly. Our metrics remain stable as the yaw angle becomes larger while the performance of PTI degrades significantly. The qualitative results are shown in Fig. 7. The geometry shape of PTI suffers from the flattening phenomenon. In contrast, our method can generate a consistent geometry and texture in novel views."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.604,
+                0.769,
+                0.62
+            ],
+            "angle": 0,
+            "content": "5.3. Evaluation of Symmetry Prior"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.629,
+                0.892,
+                0.794
+            ],
+            "angle": 0,
+            "content": "To understand the importance of the symmetry prior, we perform an ablation study by conducting the inversion with or without using the prior. The visual results are shown in Fig. 8. Both approaches can obtain good geometries in the original view. However, in the first row, the geometry of the woman with a thin face turns to be obese as the camera gradually rotates, which aligns with its rendered image. The second row shows that the geometry and the rendered image maintain a better view consistency. We even find that, with the auxiliary view, some expression details can be strengthened, such as the slightly opened mouth."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "The symmetry prior cannot be directly employed in the optimization stage because there exist asymmetric areas in a human face. Optimizing the conflict areas will lead to poor results. As shown in Fig. 9, the slanted hair and the single earring in the source image mismatch those in the mirror one. In the first row, when simply using both two images to optimize the generator, the reconstruction quality suffers"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.486,
+                0.946,
+                0.511,
+                0.956
+            ],
+            "angle": 0,
+            "content": "348"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.078,
+                0.088,
+                0.47,
+                0.334
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.099,
+                0.345,
+                0.446,
+                0.358
+            ],
+            "angle": 0,
+            "content": "Figure 10. Editing results incorporated with [26] and [11]."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.374,
+                0.47,
+                0.48
+            ],
+            "angle": 0,
+            "content": "from degradation. Novel views synthesized by the vanilla version will encounter incorrect texture and blurry results in the conflict areas. Our method can handle such asymmetric cases without the quality worsening by filtering out conflict areas with the designed constraints. Hair, teeth, and other details are consistent in different views, which validates the effectiveness of the proposed constraints."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.49,
+                0.336,
+                0.507
+            ],
+            "angle": 0,
+            "content": "5.4. View-consistent Face Editing"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.514,
+                0.47,
+                0.696
+            ],
+            "angle": 0,
+            "content": "Editing a facial image should preserve the original identity while performing a meaningful and visually plausible modification. We extend our methods to downstream editing tasks to validate that the 3D GAN inversion process does not degrade the editability of the original generator. We follow StyleCLIP [26] to achieve text-guided semantic editing and StyleGAN-NADA [11] for stylization, shown in Fig. 10. The editing operation not only influences the original view but also changes the novel view's appearance consistently. It demonstrates that our inversion solution retains the properties in the original space of the generator and can be associated with other editing methods flexibly."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.706,
+                0.23,
+                0.722
+            ],
+            "angle": 0,
+            "content": "5.5. Ablation Study"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.731,
+                0.469,
+                0.809
+            ],
+            "angle": 0,
+            "content": "Adjacent Warping. Recall that we employ depth-guided warping to create pseudo supervision to improve the texture quality of novel views. In Fig. 11, we can find that this operation can enhance facial component details such as eyelashes and teeth, improving the overall visual quality."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.811,
+                0.469,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Depth Regularization. Since supervision signals all come from RGB images, there is no explicit geometry supervision to ensure shape correctness. The shape is prone to drift to overfit the single image. Unnatural distortions will appear in novel views with the drifted shape. In the third column of Fig. 11, the jaw and nose are elongated with no con"
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.503,
+                0.088,
+                0.891,
+                0.326
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.526,
+                0.334,
+                0.866,
+                0.35
+            ],
+            "angle": 0,
+            "content": "Figure 11. Ablation study of different designed modules."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.375,
+                0.891,
+                0.404
+            ],
+            "angle": 0,
+            "content": "straints. With depth regularization, geometry will be calibrated within reasonable limits."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.499,
+                0.414,
+                0.892,
+                0.475
+            ],
+            "angle": 0,
+            "content": "Two-stage Optimization. The joint optimization stage via utilizing a large parameter space can further improve texture, allowing to reconstruct the out-of-domain details, e.g., auspicious mole, as shown in the last column of Fig. 11."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.5,
+                0.506,
+                0.619,
+                0.521
+            ],
+            "angle": 0,
+            "content": "6. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.537,
+                0.892,
+                0.673
+            ],
+            "angle": 0,
+            "content": "We propose a novel 3D GAN inversion method with facial symmetry prior. As demonstrated in massive experiments, our method can support 3D reconstruction at extreme angles with robust geometry. With the designed constraints on texture and geometry, the reconstructed portraits are high-fidelity and possess consistent identity across different views. Besides, the proposed method enables various downstream applications without compromising faithfulness and photorealism."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.681,
+                0.892,
+                0.786
+            ],
+            "angle": 0,
+            "content": "Limitation and Future Works. Since the effect of illumination is ignored in our assumption, the illumination is modeled implicitly. During the fitting process of the given image with symmetry prior, light sources sometimes become perfectly symmetrical and distorted. We will attempt to settle the problem via modeling illumination explicitly with albedo and normal in future work."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.498,
+                0.796,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Acknowledgement. This work was partly supported by the National Natural Science Foundation of China (Grant No. U1903213) and the Shenzhen Science and Technology Program (JCYJ20220818101014030, ZDSYS20200811142605016). This work was partly supported by a UKRI Future Leaders Fellowship [grant number G104084]."
+        },
+        {
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+        }
+    ],
+    [
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2023/3D GAN Inversion With Facial Symmetry Prior/02a489c6-c89c-4dc3-afcb-600bfa013373_origin.pdf

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2023/3D GAN Inversion With Facial Symmetry Prior/full.md

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+# 3D GAN Inversion with Facial Symmetry Prior
+
+Fei Yin $^{1}$ , Yong Zhang $^{2\dagger}$ , Xuan Wang $^{3}$ , Tengfei Wang $^{4}$ , Xiaoyu Li $^{2}$ , Yuan Gong $^{1}$ , Yanbo Fan $^{2}$ , Xiaodong Cun $^{2}$ , Ying Shan $^{2}$ , Cengiz Öztireli $^{5}$ , Yujiu Yang $^{1\dagger}$ , Shenzhen International Graduate School, Tsinghua University  
+ $^{2}$ Tencent AI Lab  $^{3}$ Ant Group  $^{4}$ HKUST  $^{5}$ University of Cambridge
+
+# Abstract
+
+Recently, a surge of high-quality 3D-aware GANs have been proposed, which leverage the generative power of neural rendering. It is natural to associate 3D GANs with GAN inversion methods to project a real image into the generator's latent space, allowing free-view consistent synthesis and editing, referred as 3D GAN inversion. Although with the facial prior preserved in pre-trained 3D GANs, reconstructing a 3D portrait with only one monocular image is still an ill-posed problem. The straightforward application of 2D GAN inversion methods focuses on texture similarity only while ignoring the correctness of 3D geometry shapes. It may raise geometry collapse effects, especially when reconstructing a side face under an extreme pose. Besides, the synthetic results in novel views are prone to be blurry. In this work, we propose a novel method to promote 3D GAN inversion by introducing facial symmetry prior. We design a pipeline and constraints to make full use of the pseudo auxiliary view obtained via image flipping, which helps obtain a view-consistent and well-structured geometry shape during the inversion process. To enhance texture fidelity in unobserved viewpoints, pseudo labels from depth-guided 3D warping can provide extra supervision. We design constraints to filter out conflict areas for optimization in asymmetric situations. Comprehensive quantitative and qualitative evaluations on image reconstruction and editing demonstrate the superiority of our method.
+
+# 1. Introduction
+
+Recent 3D-aware generative adversarial networks (3D GANs) have seen immense progress. By incorporating a neural rendering engine into the generator network architecture, 3D GANs can synthesize view-consistent images. To increase the generation resolution, existing methods [5,12,25,30,31,36-38,41] boost the 3D inductive bias
+
+![](images/9260a43193a7b1a051371d2fff12dabdcb84fd7ca87930b2bc075b9a6bd50a9b.jpg)  
+Figure 1. Visual examples of our inversion method. Direct applying 2D GAN inversion methods (PTI [28]) to the 3D GAN suffers from inaccurate geometry in novel views. Our method excels in synthesizing consistent geometry and high-fidelity texture in different views, even reconstructing a face under an extreme pose.
+
+with an additional 2D CNN-based upsampler or an efficient 3D representation modeling method. With tremendous effort, 3D GANs can produce photorealistic images while enforcing strong 3D consistency across different views.
+
+We are interested in the task of reconstructing a human face with 3D geometry and texture given only one monocular image. It is an ill-posed problem and close to the harsh condition of real scenarios. With the power of 3D GANs, it seems achievable via projecting a target image onto the manifold of a pre-trained generator. The process is referred as 3D GAN inversion. A straightforward path is to follow the 2D GAN inversion method [28], i.e., optimizing the latent code and the network parameters of the generator to overfit the specific portrait.
+
+However, since the ground truth 3D geometry is absent given one monocular image, the inversion result is far from satisfactory. The process of fitting a 3D GAN to one image would sacrifice geometric correctness in order to make the synthetic texture as close as possible to the input, even destroying the original semantic-rich latent space. As the optimization process goes, the face geometry tends to degenerate into a flattened shape, due to the absence of geometry supervision, e.g., images from other views. Besides, there exist quality issues in texture synthesis under novel views. The rendered images of unseen views tend to be blurry and inconsistent with the original image, especially when reconstructing a side face under an extreme pose. Because there is no texture supervision for unseen views given only one monocular image. The failure cases of directly applying [28] are illustrated in Fig. 1.
+
+In this work, to alleviate the issue caused by missing geometry and texture supervision under multiple views, we propose a novel 3D GAN inversion approach by taking full advantage of facial symmetry prior to construct pseudo supervision of different views. Intuitively, we note that human faces are almost symmetric. Assuming the given portrait is symmetric, we can obtain an additional perspective of the portrait by simply mirroring the image. The images of two distinct views can provide geometric relations between the 3D points and their 2D projections based on epipolar geometry. Motivated by this, we seek to leverage facial symmetry as the geometric prior constraining the inversion. The symmetry prior is also employed in a traditional 3D reconstruction work [35]. We leverage the mirrored image as extra supervision of another view when performing the inversion, which prevents the geometry collapse. A rough geometry can be obtained by the inversion with the original and mirror images.
+
+To further enhance texture quality and geometry in novel views, we employ depth-guided 3D warping to generate the pseudo images of the views surrounding the input and symmetric camera pose. The depth is inferred from the rough 3D volume. The original image along with the pseudo images are used to fine-tune the generator's parameters for the joint promotion of texture and geometry. To prevent the optimized geometry from deviating too much from the rough geometry, we design a geometry regularization term as a constraint. However, human faces are never fully symmetric in practice, neither in shape nor appearance. Therefore, we design several constraints to extract meaningful information adaptively from the mirror image without compromising the original reconstruction quality.
+
+Our main contributions are as follows:
+
+- We propose a novel 3D GAN inversion method by incorporating facial symmetry prior. It enables a high-quality reconstruction while preserving the multi-view consistency in geometry and texture.
+
+- We conduct comprehensive experiments to demonstrate the effectiveness of our method and compare it with many state-of-the-art inversion methods. We also apply our method to various downstream applications.
+
+# 2. Related Work
+
+# 2.1. 3D-Aware GANs
+
+Recently, neural scene representations have incorporated 3D prior into image synthesis with explicit camera control. Inspired by the success of Neural Radiance Fields (NeRF) [22], [6,24] employ implicit volumetric neural rendering structure for consistent novel view synthesis, required only unconstrained monocular images training. To overcome the computational cost and lift the generation resolution, the following methods adopt a two-stage rendering process [5, 12, 21, 25, 30, 31, 37, 38, 41, 42]. Since 2D upsamplers may introduce view-inconsistent artifacts, NeRF path regularization [12] and dual discriminators [5] are proposed. Different 3D modeling representations are further designed for scalable and fast rendering. EG3D [5] introduces tri-plane representation, and GRAM-HD [36] proposes to render radiance manifolds first for efficient sampling. Boosting with the powerful high-fidelity unconditioned 3D GANs, we can achieve real image 3D reconstruction and editing. Specifically, we select the state-of-the-art EG3D [5] as our backbone.
+
+# 2.2. GAN Inversion
+
+To edit a real image [29, 39], GAN inversion is applied first to discover a corresponding latent code from which the generator can synthesize the real image. Existing 2D GAN inversion approaches can be categorized into optimization-based, learning-based, and hybrid methods. [1, 16] directly minimize the reconstruction distance via optimizing the latent codes. Learning-based methods [2, 3, 32, 34] exploit a general encoder network to map the input image into latent space in real-time. Hybrid methods would apply the latent code predicted from the encoder as initialization in the later optimization process. Beyond the original inversion latent space, PTI [28] further optimizes the parameters of the generator to enhance the visual fidelity.
+
+As for the 3D GAN inversion task, most methods directly transfer the 2D methods, e.g., PTI [28] and e4e [32], which may suffer from the poor results in novel views. Pix2NeRF [4] introduced a joint distillation strategy for training a 3D inversion encoder. A concurrent work [18] proposes to perform camera pose optimization simultaneously to ensure view consistency. However, none of the above methods take geometry shape into consideration.
+
+![](images/d75a1f0e84d6476ff667bcfbebf14831b191b283b1dc5e67fdd592cbabc96bd2.jpg)  
+Figure 2. The proposed framework. A) Our method first performs inversion with the help of the symmetry view to achieve the latent code  $w^{+}$  with a roughly correct geometry. B) The original image and the mirror one, along with adjacent warping pseudos, are used for joint optimization to enhance the geometry and texture of rendered images in novel views. C) Depth-guided 3D warping are used to generate pseudo images in novel views to provide extra supervision. Unfaithful regions are filtered out with the authentic mask.
+
+![](images/962dca2b8aea70d9409e2bf2c19d3023a6a0d158b6e429885d6d85077916bff9.jpg)
+
+![](images/617c2fdcc313ba70621dcd2ad8b8b0e39aaf1a3d8a6e574efb070d9c5e7b9ead.jpg)
+
+# 2.3. Few-shot NeRF
+
+Few-shot NeRF aims at reconstructing general 3D scenarios where only a few observed views are available, which shares a similar setting with 3D GAN inversion. MVS-NeRF [7] leverages plane-swept cost volumes in multi-view stereo for geometry-aware scene reasoning to improve performance. DietNeRF [13] enforces semantic consistency between rendered images from unseen view and seen images via a CLIP encoder [27]. RegNeRF [23] regularizes the texture of patches rendered from unobserved viewpoints without relying on additional training modules. Since it is hard to find a common prior for general scenes, these methods investigate how to ensure the geometry consistency of different views, which gives us inspiration.
+
+# 3. Definition of 3D GAN Inversion
+
+Similar to 2D GAN inversion, 3D GAN inversion aims to project an input image  $I$  onto the manifold of a pretrained unconditional 3D GAN model  $G_{\mathrm{3D}}(\cdot ;\theta)$  parameterized by weight  $\theta$ . After inversion,  $G_{\mathrm{3D}}$  can reconstruct the image faithfully given the corresponding camera pose, synthesize content-consistent images in novel views, and facilitate downstream tasks like face editing. One formulation of the 3D GAN inversion problem is defined as follows:
+
+$$
+w ^ {*} = \underset {w} {\arg \max } = \mathcal {L} \left(G _ {3 D} (w, \pi ; \theta), I\right), \tag {1}
+$$
+
+where  $w$  is the latent representation in  $\mathcal{W}^+$  space and  $\pi$  is the corresponding camera matrix of input image. The loss function  $\mathcal{L}(\cdot, \cdot)$  is usually defined as pixel-wise reconstruction loss or perceptual loss. In our settings, camera matrix  $\pi$  is known, which is extracted by a pre-trained detector [9]. This formulation cares about the  $\mathcal{W}^+$  space. However, the inversion in the  $\mathcal{W}^+$  space is always not enough to capture local facial details, resulting in inaccurate reconstruction.
+
+Following the recent optimization-based 2D GAN inversion method [28], we perform the inversion in the extended latent space for more accurate reconstruction, i.e., the combination of the  $\mathcal{W}^{+}$  space and the parameter space. The formulation is defined as:
+
+$$
+w ^ {*}, \theta^ {*} = \underset {w, \theta} {\arg \max } = \mathcal {L} \left(G _ {3 D} (w, \pi ; \theta), I\right). \tag {2}
+$$
+
+Note that  $w$  and  $\theta$  are optimized alternatively, i.e.,  $w$  is optimized using Eq. (1) first and then  $\theta$  is optimized with the fixed  $w^{*}$ .
+
+# 4. The Proposed Approach
+
+Our goal is to reconstruct a human face through a pretrained 3D GAN given a single monocular image. The reconstruction is supposed to preserve authentic appearance texture and geometry shape in novel views. Due to the limited information about geometry and texture from a single image, overfitting a single view tends to be trapped in geometry collapse, get the blurry texture and miss details in unseen views, especially when reconstructing a side face under an extreme pose. To overcome the issue of lacking information about other views, we introduce facial symmetry prior to promote inversion. We propose a two-stage inversion pipeline, i.e., inversion for rough geometry and joint optimization of geometry and texture. In the first stage, we obtain a rough geometry by optimizing the latent code  $w$  using the original and mirror images in Sec. 4.1. In the second stage, we refine the geometry and texture by optimizing the parameter  $\theta$  with the depth-guided 3D warping and a set of designed constraints in Sec 4.2. An overview of our method is shown in Fig. 2.
+
+# 4.1. Inversion with Symmetry for Rough Geometry
+
+The purpose of this stage is to learn a rough geometry as a pivot for further tuning. To compensate for the missing
+
+![](images/0f5db3830d58f25681435aa4f8ed08732d28a412480e407a1a989c5cef01d562.jpg)  
+Figure 3. Visualization of warped pseudos. The red bounding box contains the range of employed pseudos, depending on the yaw angle of the input image. A frontal face can be warped by a wider range of yaw angles than a side face to get authentic pseudos.
+
+![](images/42c87874b858d5fe2f82d16dea9111ba8e70fe1b34c608585d3396830611401c.jpg)  
+Source Image  
+Figure 4. Visualization of authentic mask and warped pseudo.
+
+![](images/be838299f22ea3da41917e8e21bad9d732202582cb08a69961d057302938841a.jpg)  
+Warped Image
+
+![](images/32e55225f4c19c8ebfad56bc936e8466d3b4936d4665531f0c1b819be3ca68f4.jpg)  
+Authentic Mask
+
+![](images/c00774424ba472ae986435bbc55c6eddacfd8e638237193878207153cf037ce7.jpg)  
+Pseudo
+
+information of unseen views, we resort to facial symmetry prior, i.e., the left face is almost the same as the right one. We simply flip the input image  $I_{s}$  horizontally to get the mirror image  $I_{m}$  whose corresponding camera pose  $\pi_{m}$  can be calculated by multiplying a fixed matrix by the camera extrinsic parameters of  $\pi_{s}$ . The intrinsic parameters are unchanged. The mirror image serves as the pseudo-projected image under a novel view.
+
+Since human faces are not always perfectly symmetric, the mirror image is just an approximation under the novel view. There exists inconsistent content between the original image and the mirror one if they have an overlapping face region, i.e., different colors in the position, referred as conflict content. The inversion should depend more on the original image and take partial useful information from the mirror one. Furthermore, we observe that a frontal face can provide more effective information than a side face. A nearly frontal face provides plenty of facial information, and we should trust less on its mirror image to avoid conflict in the overlapping region. While a side face provides information for only half one face, it has only a small overlapping conflict region with its mirror image. Hence, we should trust more on the mirror image. We exploit an adaptive weighting strategy for the importance of the mirror image according to its yaw angle  $\alpha_{\mathrm{yaw}}$ . We use a Gaussian function with respect to  $\alpha_{\mathrm{yaw}}$  to approximate the importance of different views. The weight  $\lambda_{m}$  of the mirror image is defined as:
+
+$$
+\mathcal {E} (x) = \frac {1}{\sigma \sqrt {2 \pi}} e ^ {- \frac {(x - \mu) ^ {2}}{2 \sigma^ {2}}}, \tag {3}
+$$
+
+$$
+\lambda_ {m} = \left\{ \begin{array}{l l} 1 - \mathcal {E} \left(\alpha_ {\text {y a w}}\right), & \text {i f} \mathcal {E} \left(\alpha_ {\text {y a w}}\right) \leq k; \\ 0, & \text {i f} \mathcal {E} \left(\alpha_ {\text {y a w}}\right) > k; \end{array} \right. \tag {4}
+$$
+
+where  $\sigma, \mu$  and  $k$  are hyper-parameters. As a nearly frontal
+
+mirror face can compensate for very limited extra information for the original image, its weight  $\lambda_{m}$  is clamped to 0.
+
+To optimize the latent code in  $\mathcal{W}^+$  space, the Perceptual loss [40] is used to minimize the distance between the generated results and the original and mirror images. Following [17, 28], a noise regularization term  $\mathcal{L}_n(n)$  is employed to prevent the noise vector from containing vital information. The objective in this stage is defined as follows:
+
+$$
+\mathcal {L} _ {\text {i n v}} = \mathcal {L} _ {\mathrm {L P I P S}} \left(G _ {3 \mathrm {D}} \left(w, \pi_ {s}; \theta\right), I _ {s}\right) + \tag {5}
+$$
+
+$$
+\lambda_ {m} \mathcal {L} _ {\text {L P I P S}} \left(G _ {3 \mathrm {D}} \left(w, \pi_ {m}; \theta\right), I _ {m}\right) + \lambda_ {n} \mathcal {L} _ {n} (n),
+$$
+
+where  $n$  is the noise vector and  $\lambda_{n}$  is a trade-off parameter. The generator is kept frozen at this stage. Visual illustrations in Fig. 8 show that the geometry can be greatly improved with the facial symmetry prior.
+
+# 4.2. Joint Optimization of Geometry and Texture
+
+Though we obtain the rough geometry via the optimization of  $w$  in the first stage, there is a distinct gap between the texture of the rendered face and that of the original one, even under the same camera pose. The rendered face shares a similar face geometry with the original one, but it becomes a different identity. In this stage, we optimize the generator's parameters  $\theta$  to bridge the texture gap for identity preservation and refine the rough geometry as well. We design a geometry regularization constraint to avoid the model degrading to generate flattened geometry. Moreover, we construct a set of pseudo images in different views to provide supervision via depth-guided 3D warping.
+
+Geometry Regularization. We observe that optimizing the generator without any constraint on the geometry will cause the deviation of the geometry from the rough one, resulting in a flattened geometry similar to the case of inversion with a single image. To avoid the geometry drift during overfitting the texture, we regularize the optimized density obtained from the 3D volume of 3D GAN to be similar to that from the rough volume obtained in the first stage. Specifically, with the fixed  $w$ , we generate depth maps  $D$  from 3D GAN under different sampled views and calculate  $\mathcal{L}_2$  distance between them with the corresponding depth maps  $D_0$  generated from the un-tuned generator in the first stage:
+
+$$
+\mathcal {L} _ {\text {d e p t h}} = \sum_ {i \in \mathbb {S}} \| D ^ {i} - D _ {0} ^ {i} \| _ {2}, \tag {6}
+$$
+
+where  $\mathbb{S}$  is the sampled camera pose set.
+
+Depth-guided 3D Warping for Pseudo Supervision. Optimizing the generator with only two images is still not enough to capture the facial details, resulting in blurry effects around facial components such as eyes (see Fig. 11). Hence, we propose to construct pseudo images of different views for extra supervision using the rough geometry and the original and mirror images. Specifically, given the original image (source view) and the rough geometry, we can synthesize an image under a novel view (target view) by warping with 3D guidance. A coordinate pixel  $p_t$  of the synthesized image in the target view can be obtained by projecting back onto the source view with the relative camera pose  $\pi_{t\rightarrow s}$  and the camera intrinsic parameters  $K$ :
+
+$$
+p _ {t \rightarrow s} = K \pi_ {t \rightarrow s} D _ {t} \left(p _ {t}\right) K ^ {- 1} p _ {t}, \tag {7}
+$$
+
+where  $D_{t}(\cdot)$  is the depth map of the target view. Since the projected coordinate  $p_{t\rightarrow s}$  are continuous values, we can extract the color values from the original image with a differentiable bilinear sampling mechanism, i.e.,  $I_{s\rightarrow t} = I_s(p_{t\rightarrow s})$ . The low-resolution depth map will be upsampled to match the dimension of the image.
+
+Authentic Mask. Without distinguishing the foreground pixels from the background, the background pixels in the original image may be projected onto the foreground plane, leading to erroneous results. To overcome this issue, we form a mask to indicate the visibility of pixels to filter invisible areas using the rendered depth values. Specifically, we can get the projected depth value  $D_{s}(p_{t\rightarrow s})$  via sampling from the depth map in the source view. Here we employ the euclidean distance between  $D_{s}(p_{t\rightarrow s})$  and the depth map  $D_{t}(p_{t})$  in the target view to calculate the mask. A large distance indicates the pixel  $p_t$  is invisible. To ensure the projected pixels are located on the front visible surface, we only preserve the area where the distance is under a threshold  $\tau$ :
+
+$$
+M \left(p _ {t}\right) = \left\| D _ {t} \left(p _ {t}\right) - D _ {s} \left(p _ {t \rightarrow s}\right)\right\| <   \tau . \tag {8}
+$$
+
+Furthermore, due to the poor depth estimation of the background, only the facial part would be warped. We warp the facial mask of the source view to the target view and multiply it with the visibility mask  $M(p_{t})$  to get the authentic mask  $M_{t}$ . An example is shown in Fig. 4. After multiplying the mask  $M_{t}$  with the warped image  $I_{s\rightarrow t}$ , the resulting image can be used for supervision.
+
+Adjacent View Warping. Fig. 3 illustrates the warping results of two examples. When the yaw angle between the source and target views increases, the warping results have more distortions and become less authentic. Therefore, it is intuitive to abandon the pseudo images of the target views that deviate a lot from the source view. Empirically, a frontal face can be warped by a wider range of yaw angles than a side face to get authentic pseudo images. The
+
+variance of sampling yaw angles for constructing pseudo images is set to a fixed ratio of  $\lambda_{m}$  that depends on the viewpoint mentioned in Sec. 4.1. The LPIPS loss [14] is used to compute the multi-view pixel-wise distance as follows:
+
+$$
+\mathcal {L} _ {\mathrm {a d j}} = \mathcal {L} _ {\mathrm {L P I P S}} \left(M _ {t} \cdot G _ {\mathrm {3 D}} (w, \pi_ {t}; \theta), M _ {t} \cdot I _ {s \rightarrow t}\right). \tag {9}
+$$
+
+Although the pseudo images of several unseen adjacent views around the source view have been constructed, it brings marginal improvements on remote views. Especially for a side face, the pseudo images of the remote views are blurry and have incomplete texture (see Fig. 3). Therefore, we also construct pseudo images of the adjacent views around the view of the mirror image.
+
+Since the conflict region between the original and mirror images has a side effect on the generator optimization process, resulting in blurry effects on rendered images, even reconstructing the source view (see Fig. 9), we propose to take partial meaningful information from the symmetric views without harming the original inversion quality. We compute the similarities only for facial components, rather than the whole face region. Besides, instead of using a pixelwise loss, we exploit the contextual loss [20] to improve the texture quality. The loss for symmetric views is defined as:
+
+$$
+\mathcal {L} _ {\mathrm {s y m}} = \sum_ {\mathrm {c} \in \mathbb {F}} \mathcal {L} _ {\mathrm {C X}} \left(\operatorname {R O I} ^ {c} \left(G _ {3 \mathrm {D}} \left(w, \pi_ {t}; \theta\right)\right), \operatorname {R O I} ^ {c} \left(I _ {m \rightarrow t}\right)\right), \tag {10}
+$$
+
+where  $I_{m\rightarrow t}$  is the pseudo image of the viewpoint  $\pi_t$  warped from the mirror image  $I_{m}$ .  $\mathrm{ROI}^c (\cdot)$  refers to the region of interest component  $c$  from the collection  $\mathbb{F} = \{\text{eyes, nose, mouth}\}$ .
+
+The reconstruction loss between the original image and its corresponding rendered image is still in use to ensure the quality of the initial perspective, which is defined as:
+
+$$
+\mathcal {L} _ {\mathrm {o r i}} = \mathcal {L} _ {2} \left(G _ {\mathrm {3 D}} \left(w, \pi_ {s}; \theta\right), I _ {s}\right) + \mathcal {L} _ {\mathrm {L P I P S}} \left(G _ {\mathrm {3 D}} \left(w, \pi_ {s}; \theta\right), I _ {s}\right). \tag {11}
+$$
+
+The overall objective of optimizing the generator's parameters is defined as:
+
+$$
+\mathcal {L} _ {\text {o p t}} = \mathcal {L} _ {\text {o r i}} + \lambda_ {\text {a d j}} \mathcal {L} _ {\text {a d j}} + \lambda_ {\text {s y m}} \mathcal {L} _ {\text {s y m}} + \lambda_ {\text {d e p t h}} \mathcal {L} _ {\text {d e p t h}}. \tag {12}
+$$
+
+The trade-off hyper-parameters are set as follows:  $\lambda_{\mathrm{adj}} = 0.1$ ,  $\lambda_{\mathrm{sym}} = 0.05$ , and  $\lambda_{\mathrm{depth}} = 1$ .
+
+# 5. Experiments
+
+# 5.1. Experimental Settings
+
+Datasets. We conduct the experiments on human faces datasets. For all experiments, we select EG3D [5] as our 3D GAN prior, which is pre-trained on FFHQ dataset [15]. We verified quantitative metrics on CelebA-HQ test dataset [19]. We further evaluated on MEAD [33], a
+
+![](images/1470c26a073523eeed04b623eec00b3a4506c2f62ea9d69dad6437cf3de65479.jpg)  
+SG2
+
+![](images/6f39e9d126fa143ebda910254e2cd452fc4782e5fb5112c75a624b98dfc3f054.jpg)  
+SG2  $W^{+}$
+
+![](images/8dae65f2f2a02f5c53ea8ac3cb13de8615d53ec51bbdd1fecc7008652fa909a6.jpg)  
+PTI
+
+![](images/33e8f1cb68534e6bd42f66de2805b7e39eb7c0c210af7c41ec2c04d775f800dd.jpg)  
+Ours
+
+![](images/8212cc13a848a7c393a0b90e1ac2e011acd090eac9c9eb3f7d04f9c59d2a0e00.jpg)  
+Source Image
+
+![](images/635c354de2acf40041996d77ca926dcf9f864cce12a4dfd408101568c6f69d9b.jpg)  
+Source Image
+
+![](images/a109649a33cb0f0a26d936e4cc64438d53480ab09ccd92b9a91660b7acce29d3.jpg)  
+SG2
+
+![](images/2e65c836a8e794365c38d4e39c1ff2acc56f59cc49fece8bcd124bcbb4a5c1ca.jpg)  
+SG2  $W^{+}$
+
+![](images/f29b17df448d553e0cb66f8bdd7006215fcd2889a15267c75bc1c83c65980209.jpg)  
+PTI
+
+![](images/b40919e94b2a054a78398d3044dd4babad9cd9fbde75bff6fed0dc54feafafb6.jpg)  
+Ours
+
+<table><tr><td>Method</td><td>MSE ↓</td><td>LPIPS ↓</td><td>MS-SSIM ↓</td><td>ID ↑</td><td>Pose ↓</td><td>Depth ↓</td></tr><tr><td>SG2 [16]</td><td>0.0881</td><td>0.3231</td><td>0.3557</td><td>0.8209</td><td>0.043</td><td>0.0505</td></tr><tr><td>SG2 W+ [1]</td><td>0.0439</td><td>0.2261</td><td>0.2483</td><td>0.8735</td><td>0.040</td><td>0.0500</td></tr><tr><td>PTI [28]</td><td>0.0084</td><td>0.0920</td><td>0.0980</td><td>0.9432</td><td>0.037</td><td>0.0510</td></tr><tr><td>SPI (Ours)</td><td>0.0082</td><td>0.0865</td><td>0.0991</td><td>0.9470</td><td>0.036</td><td>0.0476</td></tr></table>
+
+Table 1. Quantitative comparison on CelebA-HQ [19].
+
+multi-view high-quality video dataset. The first frame from each viewpoint video of 10 identities is extracted for testing.
+
+Metrics. We evaluate image reconstruction quality and similarity with the following metrics: mean squared error (MSE), perceptual similarity loss (LPIPS) [40], structural similarity (MS-SSIM), and identity similarity (ID) by employing a pre-trained face recognition network [8].
+
+Baselines. We mainly compare our methods with optimization-based 2D GAN inversion methods. SG2 [16] directly inverts real images into  $\mathcal{W}$  space with an optimization scheme. [1] extends the inversion into  $\mathcal{W}^+$  space, denoted by SG2  $\mathcal{W}^+$ . PTI [28] would further tune generator parameters in a second stage. For a fair comparison, both PTI and ours first optimize the latent for 500 steps and then fine-tune the generator for 1,000 steps, while SG2 and SG2  $\mathcal{W}^+$  optimize the latent for 1,500 steps.
+
+# 5.2. Reconstruction and Novel View Synthesis
+
+Qualitative Evaluation. Fig. 5 presents a qualitative comparison of texture and geometry quality of different views. As for the original view, our method is able to inverse challenging details such as earrings, make-up, and wrinkles, which demonstrates that we do not sacrifice the original reconstruction performance. When the camera rotates to
+
+![](images/9290fe419202b1600b795c1a2479733fc03d03e00ef18faa70abd8d60f7cfc82.jpg)  
+Figure 5. Qualitative comparisons with state-of-the-art methods on novel view synthesis. The reconstruction quality of the original view is presented in the first row. The texture and geometry in novel views are shown in the rest rows.  
+Figure 6. Comparison of identity preservation in novel views. The x-axis represents the yaw angle of the input image. '0' indicates the frontal face.
+
+novel views, images generated from 2D inversion methods present a twisted appearance, due to the nearly flattened geometry shape. Since SG2 does not deviate too far from the initial GAN space, it can generate a portrait with a structured geometry, but fails to preserve the identity. Our method is capable of maintaining authentic and consistent geometry in novel views along with a sharp appearance, even when rotated to an extreme pose.
+
+Quantitative Evaluation. The reconstruction metrics of the original view are shown in Table 1. As can be seen, the results align with our qualitative evaluation as we achieved comparable scores to the current 2D state-of-the-art inversion methods [28]. The MSE, LPIPS, and ID similarities of ours are further improved, which can be attributed to the employment of  $\mathcal{W}^+$  latent space. Following EG3D, we
+
+![](images/549688891ff4cf7f4ccba5d7fa7eb4ab784a254da5e92e34c81f613878d4c6be.jpg)  
+Figure 7. Qualitative comparisons with PTI [28] on MEAD [33].
+
+<table><tr><td>Method</td><td>View</td><td>MSE ↓</td><td>LPIPS ↓</td><td>MS-SSIM ↓</td><td>ID ↑</td></tr><tr><td>PTI</td><td rowspan="2">F</td><td>0.03204</td><td>0.2971</td><td>0.2070</td><td>0.8445</td></tr><tr><td>Ours</td><td>0.03296</td><td>0.3088</td><td>0.2135</td><td>0.8388</td></tr><tr><td>PTI</td><td rowspan="2">L30</td><td>0.04355</td><td>0.2992</td><td>0.2274</td><td>0.8446</td></tr><tr><td>Ours</td><td>0.03399</td><td>0.2796</td><td>0.2025</td><td>0.8469</td></tr><tr><td>PTI</td><td rowspan="2">L60</td><td>0.08255</td><td>0.3902</td><td>0.3143</td><td>0.7568</td></tr><tr><td>Ours</td><td>0.04069</td><td>0.3113</td><td>0.2379</td><td>0.8272</td></tr><tr><td>PTI</td><td rowspan="2">R30</td><td>0.04574</td><td>0.3110</td><td>0.2393</td><td>0.8383</td></tr><tr><td>Ours</td><td>0.03203</td><td>0.2807</td><td>0.2057</td><td>0.8529</td></tr><tr><td>PTI</td><td rowspan="2">R60</td><td>0.07865</td><td>0.3829</td><td>0.3106</td><td>0.7995</td></tr><tr><td>Ours</td><td>0.04541</td><td>0.3160</td><td>0.2400</td><td>0.8335</td></tr></table>
+
+Table 2. Quantitative comparison on MEAD [33]. View denotes the yaw angle of the input image. F is frontal, L is left side, and R is right side. 30 and 60 are the rotation degrees. Each time we use one view as the inversion input and use all 5 views as ground truth for evaluation. The average performance of 4 unseen views and 1 seen view is reported.
+
+evaluate shape quality by calculating  $\mathcal{L}_2$  for pseudo-ground-truth depth-maps (Depth) generated from DECA [10], and poses (Pose) estimated from synthesized images.
+
+We also use identity similarity to evaluate the identity preservation of the synthesized novel views. Given a portrait, we synthesize a novel view image under the symmetric camera pose of the portrait. The similarity between the synthesized image and the flipped image portrait is calculated. The results are shown in Fig. 6. It can be observed that when the yaw angle of a portrait is small, all methods can perform well with a high similarity score. But when the yaw angle is large, only our method can maintain a high score, while other methods encounter a sharp performance drop due to the inaccurate geometry. As we employ the symmetry prior and the adjacent pseudo supervision, the rendered faces can better preserve the texture and geometry. These results demonstrate that we can achieve an identity-consistent 3D inversion.
+
+Evaluation on MEAD. To get a comprehensive understanding of the performance of our method, we evaluate on MEAD, a multi-view dataset. The quantitative comparison between the reconstruction portraits and the ground truth in
+
+![](images/01f64dbb372a527572505301802d38858746ef8b6cc0e5f875f43db08a93c32b.jpg)
+
+![](images/81a45e6fe76e4e1ef8dde0a83a39460da3d2eed14819a8f3290a238cff396eee.jpg)  
+Figure 8. Ablation study of facial symmetry prior.  
+Figure 9. Ablation study of authentic mask. Vanilla denotes simply using the full mirror image for supervision. While Ours filters out conflict areas with the designed constraints.
+
+different views is shown in Tab. 2. PTI [28] and our method achieve comparable performance when given a frontal portrait. When the view of the input face has an offset from the canonical one, our method surpasses PTI distinctly. Our metrics remain stable as the yaw angle becomes larger while the performance of PTI degrades significantly. The qualitative results are shown in Fig. 7. The geometry shape of PTI suffers from the flattening phenomenon. In contrast, our method can generate a consistent geometry and texture in novel views.
+
+# 5.3. Evaluation of Symmetry Prior
+
+To understand the importance of the symmetry prior, we perform an ablation study by conducting the inversion with or without using the prior. The visual results are shown in Fig. 8. Both approaches can obtain good geometries in the original view. However, in the first row, the geometry of the woman with a thin face turns to be obese as the camera gradually rotates, which aligns with its rendered image. The second row shows that the geometry and the rendered image maintain a better view consistency. We even find that, with the auxiliary view, some expression details can be strengthened, such as the slightly opened mouth.
+
+The symmetry prior cannot be directly employed in the optimization stage because there exist asymmetric areas in a human face. Optimizing the conflict areas will lead to poor results. As shown in Fig. 9, the slanted hair and the single earring in the source image mismatch those in the mirror one. In the first row, when simply using both two images to optimize the generator, the reconstruction quality suffers
+
+![](images/7c547f6157cd26838a1220a87b88dc74faa9bf4c29c6f4faa564171b3ded4081.jpg)  
+Figure 10. Editing results incorporated with [26] and [11].
+
+from degradation. Novel views synthesized by the vanilla version will encounter incorrect texture and blurry results in the conflict areas. Our method can handle such asymmetric cases without the quality worsening by filtering out conflict areas with the designed constraints. Hair, teeth, and other details are consistent in different views, which validates the effectiveness of the proposed constraints.
+
+# 5.4. View-consistent Face Editing
+
+Editing a facial image should preserve the original identity while performing a meaningful and visually plausible modification. We extend our methods to downstream editing tasks to validate that the 3D GAN inversion process does not degrade the editability of the original generator. We follow StyleCLIP [26] to achieve text-guided semantic editing and StyleGAN-NADA [11] for stylization, shown in Fig. 10. The editing operation not only influences the original view but also changes the novel view's appearance consistently. It demonstrates that our inversion solution retains the properties in the original space of the generator and can be associated with other editing methods flexibly.
+
+# 5.5. Ablation Study
+
+Adjacent Warping. Recall that we employ depth-guided warping to create pseudo supervision to improve the texture quality of novel views. In Fig. 11, we can find that this operation can enhance facial component details such as eyelashes and teeth, improving the overall visual quality.
+
+Depth Regularization. Since supervision signals all come from RGB images, there is no explicit geometry supervision to ensure shape correctness. The shape is prone to drift to overfit the single image. Unnatural distortions will appear in novel views with the drifted shape. In the third column of Fig. 11, the jaw and nose are elongated with no con
+
+![](images/335f4b7c612ab4dd30d80990b3c3e7550938932cfdca8dfed32fdddceb463838.jpg)  
+Figure 11. Ablation study of different designed modules.
+
+straints. With depth regularization, geometry will be calibrated within reasonable limits.
+
+Two-stage Optimization. The joint optimization stage via utilizing a large parameter space can further improve texture, allowing to reconstruct the out-of-domain details, e.g., auspicious mole, as shown in the last column of Fig. 11.
+
+# 6. Conclusion
+
+We propose a novel 3D GAN inversion method with facial symmetry prior. As demonstrated in massive experiments, our method can support 3D reconstruction at extreme angles with robust geometry. With the designed constraints on texture and geometry, the reconstructed portraits are high-fidelity and possess consistent identity across different views. Besides, the proposed method enables various downstream applications without compromising faithfulness and photorealism.
+
+Limitation and Future Works. Since the effect of illumination is ignored in our assumption, the illumination is modeled implicitly. During the fitting process of the given image with symmetry prior, light sources sometimes become perfectly symmetrical and distorted. We will attempt to settle the problem via modeling illumination explicitly with albedo and normal in future work.
+
+Acknowledgement. This work was partly supported by the National Natural Science Foundation of China (Grant No. U1903213) and the Shenzhen Science and Technology Program (JCYJ20220818101014030, ZDSYS20200811142605016). This work was partly supported by a UKRI Future Leaders Fellowship [grant number G104084].
+
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+            "Figure 1. 3D Highlighter localizes semantic regions on a shape using text as input. Our technique reasons about where to place seemingly unrelated concepts in semantically meaningful locations on the 3D shape, such as a 'necklace' on a horse or 'shoes' on an alien."
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+        "text": "We present 3D Highlighter, a technique for localizing semantic regions on a mesh using text as input. A key feature of our system is the ability to interpret \"out-of-domain\" localizations. Our system demonstrates the ability to reason about where to place non-obviously related concepts on an input 3D shape, such as adding clothing to a bare 3D animal model. Our method contextualizes the text description using a neural field and colors the corresponding region of the shape using a probability-weighted blend. Our neural optimization is guided by a pre-trained CLIP encoder, which bypasses the need for any 3D datasets or 3D annotations. Thus, 3D Highlighter is highly flexible, general, and capable of producing localizations on a myriad of input shapes. Our code is publicly available at https://github.com/threedle/3DHighlighter.",
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+        "text": "Semantic localization of regions on 3D meshes is an important problem in computer graphics and vision with broad applications. One such application is the incorporation of semantic information into the 3D modeling process. A particularly challenging aspect of this task emerges when 3D geometric signals are insufficient for performing segmentation, e.g. where to add a shirt to a bare 3D human model.",
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+        "text": "We propose 3D Highlighter, a method for automatically localizing fine-grained semantic regions on a shape based",
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+        "text": "on only a text description. Our system contextualizes the text prompt and highlights the corresponding shape region using the network-predicted probabilities. Using only text, users are able to semantically identify regions on a shape. Our system takes meshes as input, making it compatible with 3D modeling workflows and tools.",
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+        "type": "text",
+        "text": "This highlighting task requires both object-level and part-level understanding. 3D Highlighter demonstrates the ability to reason about where to place seemingly unrelated concepts on the 3D shape, such as a hat on a candle (Fig. 1). Our system localizes attributes that are geometrically absent from a shape, which we refer to as hallucinated highlighting. Understanding a part's global shape context is challenging even when relying on salient geometric features [17,27], let alone without them.",
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+        "type": "text",
+        "text": "We optimize the weights of a neural network to produce probabilities that are used to color a given 3D shape in accordance with the specified text. We leverage a pre-trained vision-language model (CLIP [31]) to guide the neural optimization towards the text-specified region. This neural optimization formulation is flexible, bypassing the need for any 3D datasets, 3D annotations, or 3D pre-training. Our system is not bound to a specific set of classes, and, as shown in Fig. 2, is not limited to object parts defined by salient geometric features.",
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+    {
+        "type": "text",
+        "text": "We encode the part selection as a neural field [44] over the mesh surface. Our network learns to map each point on the surface to a probability of belonging to the text-specified region. We translate the inferred probabilities to a visual at-",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "20930",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/017b26d3608a89b48df7256a49f16654424c0c1d823dddfbe5754975975d1db4.jpg",
+        "image_caption": [
+            "Figure 2. Hallucinated part highlighting. Our system is able to reason about where to highlight a geometrically-absent region on shapes. The resulting localizations demonstrate global understanding and localized part-awareness."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "tribute on the mesh surface, which can be rendered and visually understood. The network-predicted probabilities act as a soft-selection operator which blends the highlighter color onto the mesh. The network weights are updated by encouraging the CLIP [31] embedding of the 2D renders of the highlighted mesh to adhere to the specified text. As a result, the network implicitly learns to segment the object to adhere to the text prompt.",
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+        "type": "text",
+        "text": "We make several design choices that are key to the success of 3D Highlighter. Our network does not directly color the mesh. Rather, we predict a probability of being inside the text-specified highlight, which is used to blend colors on the mesh. The network is initialized such that points have roughly a  $50\\%$  probability of being highlighted, resulting in a mesh with albedo halfway between the highlight and background color. During optimization, the relative blend weight of the highlight color directly corresponds to the highlight probability. This blending enables the network to naturally and smoothly increase or decrease the segmenta",
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+    {
+        "type": "text",
+        "text": "tion probability in accordance with the text specification of the target region.",
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+    {
+        "type": "text",
+        "text": "In summary, we present a method for localizing semantic regions on 3D shapes. The localization is specified by a textual description, which is intuitive, flexible, and not limited to a specific training dataset. We demonstrate applications of our method to shape editing and stylization. Furthermore, our field formulation enables the 3D Highlighter to work with different mesh resolutions and triangulations. A key feature of our system is the ability to interpret out-of-domain localizations. For example, 3D Highlighter is able to figure out where to place a 'hat' on a candle as seen in Fig. 1, demonstrating the ability to reason about where to place seemingly unrelated concepts on the 3D shape.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "text": "Geometry-driven segmentation. Traditional works in geometry processing use low-level geometric features (such as surface area, curvature, or geodesic distance) in or-",
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+        "text": "20931",
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+    {
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+        "img_path": "images/9766ef4a11261cc1f15997de6dd888eb8713529b811146c3bb3ee2bfeb3e8788.jpg",
+        "image_caption": [
+            "Headphones"
+        ],
+        "image_footnote": [],
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+        "page_idx": 2
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+        "img_path": "images/81cd7b51d2cfd8d78a71821d36fd79da22a5b7a19117eff2d1f513b1af286837.jpg",
+        "image_caption": [
+            "Shoes"
+        ],
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+        "bbox": [
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+        "img_path": "images/294bd74ac95b194ac50b261400ea011e725354d47acbb368eeae197473ee4fbe.jpg",
+        "image_caption": [
+            "Hat"
+        ],
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+    {
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+        "img_path": "images/959b668781fd20b838201489cefa175f07a439dd1efd9bafbc25d1795cc64b51.jpg",
+        "image_caption": [
+            "Shoes"
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+        "image_caption": [
+            "Necklace"
+        ],
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+        "img_path": "images/77c4c76920741c24fa86ab07bfca602d48b239ea9ec27eea54eea9565ea4204c.jpg",
+        "image_caption": [
+            "Glasses"
+        ],
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+        "img_path": "images/2019c1bb121776727762325c858011eb3ff3e6de4ad7452ff2614f5f21bf286c.jpg",
+        "image_caption": [
+            "Belt"
+        ],
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+        "img_path": "images/770a8424474d00430078d9ff43613e1f1d548b70b88925618a0696fb033d8dc8.jpg",
+        "image_caption": [
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+        "img_path": "images/57decd69583ee7eab9d4754d219932c4bfbc74046be0677bb3003a98f148289a.jpg",
+        "image_caption": [
+            "Necklace"
+        ],
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+        "bbox": [
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+    {
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+        "img_path": "images/78d80f0d2b6d1a2c6fcc7194230b72a5c46477d56b3699b6d6aa54ef4b3657cc.jpg",
+        "image_caption": [
+            "Necklace",
+            "Figure 3. Our method is able to highlight different parts on the same object. For target selections that correspond to distinct regions, 3D Highlighter produces selections that are semantically meaningful and spatially separated without signal from underlying geometry."
+        ],
+        "image_footnote": [],
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+        "image_caption": [
+            "Roof"
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+    {
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+        "img_path": "images/7c5d9feaaeb944ad53557f28a02665cc718c380495e4710928de625be0f015b7.jpg",
+        "image_caption": [
+            "Arms"
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "der to infer high-level semantic attributes for segmenting shapes [35]. In particular, decomposing shapes into smaller parts or segments often corresponds with physical 3D semantic parts [13, 35]. One approach is to partition shapes based on convexity, or an approximation of convexity [1, 23]. The medial axis carries topological information, which may also be used as a guideline for segmentation [6,8,35,47].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The underlying assumption in these works is that processing the local geometry can be used to understand the semantics for segmentation. By contrast, a key aspect of our work is the ability to perform hallucinated highlights: segmentations that can not necessarily be inferred by geometry alone. See example highlights in Fig. 2 (e.g., localizing a heart on a goat).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Data-driven segmentation. In the deep learning era, the 3D part segmentation task has been widely tackled by neural network models [11, 15, 20, 26, 36, 45]. Training such a model is typically done in a fully-supervised manner on a large dataset of shapes annotated with a given set of part classes. For example, MeshCNN [11] was trained on a",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "human-body segmentation dataset [24] for learning semantic part segmentation. To alleviate the need for 3D annotations, unsupervised learning schemes utilize large collections of unlabelled data [5,7,14,37,49]. For example, Hong et al. [14] inferred part-segmentation through question answering on rendered images from PartNet [46].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In contrast to existing deep learning approaches for shape segmentation, we do not rely on any 3D dataset, nor are we bounded to a specific shape category or set of parts. Instead, we specify the desired localization using text and a pre-trained CLIP model which encompasses rich semantic object understanding. Thus, our 3D Highlighter is capable of localizing various semantic regions on a wide variety of 3D shapes.",
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+    {
+        "type": "text",
+        "text": "Text-guidance. Recent works have leveraged pre-trained vision-language embedding spaces, such as CLIP [31], for analysis, synthesis, and editing. Some techniques leverage pre-trained image encoders for achieving semantic segmentation in images and neural radiance fields [2, 19, 21]. Such techniques are capable of segmenting entire objects within a scene based on text, e.g., a chair inside a room. However, they may struggle to segment parts within an object; e.g., failing to distinguish a window (part) from a house (object) [21].",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our work is inspired by the emergent analysis in text-driven synthesis techniques for 3D data [10, 16, 18, 25, 30, 42]. Specifically, Text2Mesh [25] devised a framework for text-driven stylization of 3D meshes, observing that the resulting textures consider part-aware semantics. Yet, since Text2Mesh directly synthesizes stylizations, there is no obvious way to extract any underlying semantic analysis. To address this, we opt to use a highlighter color only as a means for visualizing the network-predicted segmentations.",
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+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "An illustration of our method is shown in Fig. 5. The inputs to our system are a mesh  $M$ , represented by vertices  $V \\in \\mathbb{R}^{n \\times 3}$  and faces  $F \\in \\{1, \\dots, n\\}^{m \\times 3}$ , and a text description  $T$ . Our neural network, referred to as neural highlighter, is optimized to map vertex positions  $v \\in V$  to a",
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+        "img_path": "images/ea684b3ec72b0b19c97fc2fdb468f84d805f3b34d80640e79d6e262bad979e7b.jpg",
+        "image_caption": [
+            "Figure 4. Localized editing. We incorporate textures and displacements to a region highlighted with 3D Highlighter. Used styles: Brick (left), Colorful Crochet (middle), Cactus (right)."
+        ],
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+    {
+        "type": "page_number",
+        "text": "20932",
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+    {
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+        "img_path": "images/37f87f8d97108d41f0f6ba47ae01309f80e0de863dac84e8359d80d6fcc580bd.jpg",
+        "image_caption": [
+            "Figure 5. Overview of 3D Highlighter. The Neural Highlighter maps each point on the input mesh to a probability. The mesh is colored using a probability-weighted blend and then rendered from multiple views. The neural highlighter weights are guided by the similarity between the CLIP embeddings of the 2D augmented images and the input text."
+        ],
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+    {
+        "type": "text",
+        "text": "probability  $p$  of belonging to the text-specified region. Each vertex on the mesh is colored according to a probability-weighted blend between the highlighter color and a gray background color. The resulting highlighted mesh  $M'$  is rendered from multiple views, and we apply 2D augmentations to obtain a set of images. We supervise the network optimization by comparing the CLIP-embedded images to the CLIP embedding of the desired text.",
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+    {
+        "type": "text",
+        "text": "3.1. Neural Highlighter",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our neural highlighter is a neural field [44] mapping coordinates  $\\mathbf{x} \\in \\mathbb{R}^3$  to  $p \\in [0,1]$ , where  $p$  is the probability that  $\\mathbf{x}$  belongs to the text-specified region. The neural highlighter is represented as a multi-layer perceptron (MLP)  $\\mathcal{F}_{\\theta}$  that takes an input vertex  $v$  in the form of a 3D coordinate  $\\mathbf{x}_v = (x,y,z)$  and predicts a highlight probability  $p_v$ ,  $\\mathcal{F}_{\\theta}(\\mathbf{x}_v) = p_v$ . This formulation allows us to query the neural field to obtain meaningful highlight probabilities for any 3D point on (or near) the mesh surface. Thus, once optimized, the network weights conveniently transfer the localization to different meshes of the same object without requiring further optimization (Fig. 9).",
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "Representing our neural highlighter as an MLP produces contiguous localizations and reduces artifacts. MLPs have been shown to exhibit a spectral bias towards smooth solutions [32], especially on low-dimensional inputs such as 3D coordinates [38]. The bias towards low-frequency outputs encourages our 3D Highlighter to predict contiguous localizations with sharp boundaries and discourages noisy highlights (Fig. 7). For this reason, our approach does not utilize positional encoding. See supplemental material for",
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+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/00d170565c319d089b1f02247d1441eae50c822102195bd45107ab7ca0b587ad.jpg",
+        "image_caption": [
+            "Figure 6. Viewpoint robustness. Our system produces consistent results even when using different primary viewpoints. Results for three different primary viewpoints for the target text 'necklace'."
+        ],
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+    {
+        "type": "text",
+        "text": "additional details.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.2. Mesh Color Blending",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We leverage the per-point highlight probability to color the mesh in a continuous, differentiable manner, generating semantically meaningful renders for CLIP supervision. We use a probability-weighted blend, where each vertex color  $C_v$  is a linear combination of the highlight color  $H$  and gray color  $G$  weighted by the network-predicted highlight probability  $C_v = p_v \\cdot H + (1 - p_v) \\cdot G$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "At the start of the optimization process, all vertex probabilities are initialized near 0.5 and thus the entire mesh is half-lighted. As the optimization progresses, vertices smoothly transition towards gray or highlighter color (based on the network predictions) such that vertices predicted to be highlighted adhere to the text-specified region. This formulation translates each step of the optimization to a colored mesh that is semantically meaningful to CLIP. Our method provides continuous gradients, in contrast to coloring vertices according to the argmax of the highlight probability. Our blending scheme results in a smoother optimization landscape and reduces highlight artifacts (Fig. 7).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This formulation is also important for downstream applications that wish to use the localizations, e.g. editing and stylization. Predicting per-point highlight probabilities provides an explicit representation of the highlight region on the mesh surface. An alternative approach, optimizing the surface color directly, would only provide a visual result without explicit information about which vertices belong to the localization.",
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+    {
+        "type": "text",
+        "text": "3.3. Unsupervised Guidance",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "We guide our neural optimization using the joint vision-language embedding space of CLIP [31]. We formulate the desired highlight by describing the association between the input mesh [object] and target localization [region]. Specifically, we design our target text  $T$  to be: \"a gray [object] with highlighted [region].\" We render the highlighted geometry from multiple views using differentiable rendering [4]. At each optimization step, we randomly sample  $n$  views from a Gaussian distribution centered around a primary view. This",
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+    {
+        "type": "page_number",
+        "text": "20933",
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+    {
+        "type": "text",
+        "text": "ensures that the underlying object is recognizable in the majority of views shown to CLIP.",
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "In a preliminary viewpoint prediction stage, we render  $360^{\\circ}$  views of the mesh and measure the CLIP similarity to the target text prompt. We select the primary view to be the render with the highest CLIP similarity. We found that there exist many possible viewpoints which produce desirable highlighter results (see Fig. 6). More details about how the primary view is selected can be found in the supplemental material.",
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+    {
+        "type": "text",
+        "text": "For each view  $\\psi$ , we render a 2D image  $I_{\\psi}$  and apply a random perspective 2D augmentation  $\\phi$ , as done in previous works [9, 25]. We then encode each of the augmented images into the CLIP embedding space (in  $\\mathbb{R}^{768}$ ) using CLIP's image encoder, denoted as  $E_I$ . Our final aggregate image representation  $\\mathsf{e}_I$  is the average CLIP encoding over all views:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathsf {e} _ {I} = \\frac {1}{n} \\sum_ {\\psi} E _ {I} \\left(\\phi \\left(I _ {\\psi}\\right)\\right) \\in \\mathbb {R} ^ {7 6 8}. \\tag {1}\n$$\n",
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+        "text": "Similarly, we encode the target selection text  $T$  with CLIP's text encoder  $E_{T}$  to get the encoded target representation  $\\mathsf{e}_T = E_T(T)\\in \\mathbb{R}^{768}$ . Our loss  $\\mathcal{L}$  for optimizing the neural highlighter parameters  $\\theta$  is formulated as the negative cosine similarity between the aggregate image embedding and the text embedding:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\underset {\\theta} {\\operatorname {a r g m i n}} \\mathcal {L} (\\theta) = - \\frac {\\mathrm {e} _ {I} \\cdot \\mathrm {e} _ {T}}{\\left| \\mathrm {e} _ {I} \\right| \\cdot \\left| \\mathrm {e} _ {T} \\right|}. \\tag {2}\n$$\n",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "When the loss is minimized, the CLIP embedding of the rendered highlighted mesh becomes similar to the target text embedding. Thus, the localized region will reflect the target text region.",
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+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this section we examine various capabilities of 3D Highlighter. First, we demonstrate the fidelity of our highlighter localization in Sec. 4.1, including qualitative and quantitative evaluations. As far as we can ascertain, our method is the first technique to perform text-driven localization on 3D shapes without pre-training on 3D data. Thus, we adapt an existing language-guided segmentation technique for 2D images to serve as a baseline [21]. Moreover, we demonstrate the robustness of 3D Highlighter in Sec. 4.2. Then we explore several applications of our method in Sec. 4.3, such as selective editing, localized manipulation, and segmentation. Finally, in Sec. 4.4 we evaluate the influence of key components of 3D Highlighter and discuss its limitations in Sec. 4.5.",
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+    {
+        "type": "text",
+        "text": "We apply our method to a large variety of meshes from different sources: COSEG [41], Turbo Squid [40], Thingi10K [48], Toys4k [34], ModelNet [43], and",
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+        "type": "text",
+        "text": "ShapeNet [3]. 3D Highlighter does not impose any restrictions on the mesh quality; many of the meshes used contain artifacts, such as elements that are non-manifold, unoriented, and contain boundaries or self-intersections. Our PyTorch [29] implementation optimization takes around 5 minutes to run on an Nvidia A40 GPU. In our experiments, we used CLIP ViT-L/14 at  $224 \\times 224$  resolution.",
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+    {
+        "type": "text",
+        "text": "4.1. Generality and Fidelity of 3D Highlighter",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Highlight generality. 3D Highlighter is not restricted to any particular category for either the input mesh or the text-specified localization, since it does not rely on a 3D dataset or 3D pre-training. In Fig. 2, we see our method achieves accurate localization for a diverse collection of meshes from various domains such as humanoids, animals, and manufactured objects. 3D Highlighter is capable of localizing a wide variety of diverse attributes even when the context of these target attributes is entirely unrelated to the input mesh. Moreover, 3D Highlighter demonstrates that it can perform hallucinated highlighting, where it selects regions on meshes with no underlying geometric signal (such as a bow tie on a camel or a hat on a pig).",
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+        "type": "text",
+        "text": "Highlight specificity. In Fig. 3, we observe that semantic differences are reflected in the network-predicted highlight. 3D Highlighter is able to successfully localize different text-specified regions on the same mesh. Our framework demonstrates the nuanced understanding required to disambiguate different target regions, such as headphones and hat on the rabbit. Finally, the ability to identify many different regions on a single mesh allows users intuitive, comprehensive, and fine-grained control over part localization.",
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+        "type": "text",
+        "text": "Quantitative evaluation. 3D Highlighter is the first system to select semantic regions on 3D shapes using text guidance, without any 3D datasets. Since there are no quantitative benchmarks to evaluate the quality of our highlights, we do so with a perceptual user study.",
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+        "type": "text",
+        "text": "Moreover, since there are no existing approaches for text-based segmentation in 3D, we create two baselines by",
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+        "image_caption": [
+            "full 0.332",
+            "Figure 7. Ablation experiments. We present ablation results for target text 'shoes' using our system (full), direct optimization (direct), without probability-weighted blending (no blend), and without 2D augmentations (no augs). Resulting CLIP scores shown below each image."
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+            "no augs 0.287"
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+    {
+        "type": "page_number",
+        "text": "20934",
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+    {
+        "type": "table",
+        "img_path": "images/b3be0d0e666ca5f462af074cce672d8c2cae5aff8a5262c1ee93e5c9b349656c.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Control</td><td>LSeg</td><td>Text2LIVE</td><td>Ours</td></tr><tr><td>Average Score ↑</td><td>1.00</td><td>1.26</td><td>2.23</td><td>4.38</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1. Perceptual study. We extend two image-based approaches LSeg [21] (segmentation) and Text2LIVE [2] (localized editing) to the highlighting task and report mean user rating.",
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+    {
+        "type": "text",
+        "text": "extending two different 2D image-based approaches. The first baseline extends LSeg [21] which directly predicts a segmentation in 2D, while the second baseline extends Text2LIVE [2] which infers an edit mask for 2D image manipulation. To evaluate these baselines, we render a bare mesh from a view where the target localization region is clearly visible. We extract the 2D segmentation produced by the image baselines and use it to color the rendered image. Then we ask users to rate the highlight quality of both baselines and our 3D Highlighter result rendered from the same view in our perceptual study.",
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+    {
+        "type": "text",
+        "text": "Our perceptual study reports quantitative results on the quality of highlights from both 3D Highlighter and baselines. Users were asked to rate each result from 1-5 on how effectively the highlight represents \"an [object] with a region corresponding to a [region] highlighted.\" Visual examples from our study are shown in the supplemental material (Fig. 21). In total, 33 users evaluated each method on 5 mesh and region combinations.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Our 3D Highlighter achieved the highest ratings compared to the baselines (Tab. 1). LSeg is built for text-driven semantic segmentation and excels at segmenting entire objects within a scene. However, LSeg struggles to identify parts within a single object, leading to subpar performance on our highlighting task. Text2LIVE was not explicitly built for segmentation, however it does rely on inferring a continuously-valued edit mask (i.e. a soft-segmentation) when performing localized image editing. The edit mask is designed to produce high-quality image manipulations; however, it is not directly suitable for identifying the sharp segmentation boundaries required for our highlighting task. Qualitative comparisons and an additional quantitative comparison using a modified CLIP R-Precision metric are discussed in the supplemental material.",
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+    {
+        "type": "text",
+        "text": "4.2. Robustness of 3D Highlighter",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Localization transfer. An important benefit of formulating 3D Highlighter as a neural field optimization is the ability to trivially transfer localization results between different meshings. This ability is useful for many tasks in geometry processing which require an object to be re-triangulated, simplified, subdivided, or otherwise remeshed. Localization transfer is possible since our neural highlighter is represented as a field over the shape and is independent of any",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/966054bc4a85eb1b71c9edcf7fe929a75c3553c5be242fe48ac20cedf257a5fb.jpg",
+        "image_caption": [
+            "Figure 8. Controlled stylization. Given three different stylizations of the same object, we use 3D Highlighter to select different regions and combine them together (Ours). Attempting to achieve this composition with a holistic approach leads to an undesirable result (Text2Mesh [25])."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "specific meshing. Although the neural highlighter is trained on mesh vertices, the resulting network encodes a smooth field and produces meaningful outputs for any 3D point on (or near) the mesh surface.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In Fig. 9, we show an optimization of the 3D Highlighter on a single mesh triangulation (original) for the prompt 'shoes'. We then apply the already-optimized neural highlighter to remeshed (middle) and subdivided (right) versions of the original mesh, showing the transferability of the selected region to different triangulations. This result demonstrates how 3D Highlighter is independent of the input mesh and that, once we have a localization for one mesh, we can trivially transfer it to any other meshing of the same object.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Viewpoint robustness. Our method is robust to the primary view choice. This property is important for our localization task, as we may not know a priori which view is ideal. In Fig. 6, we perform our optimization using three different primary viewpoints:  $0^{\\circ}$ ,  $90^{\\circ}$ , and  $-90^{\\circ}$  (viewpoints shown in blue). We then present predicted localizations, showing that for all three views, 3D Highlighter is able to accurately identify the target localization region, regardless of whether that region is visible from the primary view.",
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+    {
+        "type": "text",
+        "text": "From the  $-90^{\\circ}$  primary view, the target region (the neck) is not visible. However, is still visible with a low probability for views sampled from the Gaussian distribution",
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+    {
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+        "img_path": "images/f018918fbaf8736ed616c12a107abff622ccc97a3598f00583aa31289e4ad0d6.jpg",
+        "image_caption": [
+            "Figure 9. Localization transfer. We optimize our neural highlighter on one mesh (original) for the prompt 'shoes'. Once optimized, the network weights transfer the localization to different meshings of the same object (remeshed and subdivided)."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "page_number",
+        "text": "20935",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "around the primary view. This means that over the course of optimization, regions other than the neck are mostly seen while the target region is rarely visible. Nonetheless, our method manages to highlight the desired region, which implies its robustness to how frequently the target region for localization is seen. Furthermore, it shows that oversampling views where the target region is not visible does not negatively influence the optimization.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.3. Applications of 3D Highlighter",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Selective editing. In Fig. 4, we show that it is possible to use 3D Highlighter to selectively edit a 3D object within a semantic region. This is applicable to techniques which incorporate global texture or material properties over the entire shape, such as in Text2Mesh [25] or MatCap [39]. Starting with different bare input meshes, we edit the entire shape using a global stylization technique [25]. Then, we use 3D Highlighter to select a text-specified region and incorporate the modifications only in the selected area. Thus 3D Highlighter provides direct control over where to stylize shapes, enabling users to obtain localized stylizations based on semantic cues.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Controlled stylization via composition. Achieving compositionality with language models is a challenging task [33]. For example, starting with a human mesh and using Text2Mesh [25] to stylize 'Iron Man with the head of Steve Jobs and Yeti legs', leads to muddled and undesirable results (Fig. 8, rightmost). Our method enables compositionality between different shape modifications by chaining simple concepts together (Fig. 8). Specifically, we decompose the desired modification into three separate attainable targets ('Iron Man', 'Steve Jobs', and 'Yeti'), which we stylize individually with Text2Mesh. We then utilize our 3D Highlighter to localize the text-specified regions. We achieve the desired composition by combining the highlighted regions together, obtaining clear boundaries between stylizations.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Semantic segmentation. In Fig. 10, we show that our technique is not restricted to hallucinated highlighting and is capable of localizing semantically-specified geometric regions. These text-driven localizations identify unique geometric parts without utilizing any 3D datasets or part labels.",
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "4.4. Components of 3D Highlighter",
+        "text_level": 1,
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+        "page_idx": 6
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+    {
+        "type": "text",
+        "text": "Ablation study. Several components are key for facilitating 3D Highlighter. We provide ablation results in Fig. 7 to demonstrate the effect of our design choices. First, using a direct optimization of the vertex color (direct) instead of optimizing a neural field results in splotchy highlight artifacts. Since the neural field has a spectral bias towards smooth solutions [32], omitting it leads to an undesired noisy output. Second, removing the probability weighted blending (no blend) and instead coloring vertices using only",
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+    {
+        "type": "image",
+        "img_path": "images/5f07d2dbe7886e50bd891038211e2c20cd2aa37502ddaa9905c6454b084a0a90.jpg",
+        "image_caption": [
+            "Arm"
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+        "image_caption": [
+            "Slide"
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+    {
+        "type": "image",
+        "img_path": "images/68ef7f752136e4660dafb1582c8a971b0bd35ab5640a501d31930cc7a2fb506d.jpg",
+        "image_caption": [
+            "Propeller",
+            "Figure 10. Semantic Segmentation. 3D Highlighter produces semantic segmentations for unique geometric parts without any 3D dataset or annotations."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "two distinct values also produces a noisy highlight pattern. Without a continuous color blend, the gradients become ill-conditioned and unstable, leading to highlight artifacts and irregular localization boundaries. Lastly, similar to previous works [9, 25], we observe that without 2D perspective augmentations (no augs), 3D Highlighter outputs degenerate solutions. The ablation study emphasizes the importance of our key design choices in 3D Highlighter for its ability to highlight a coherent and localized region on the input shape.",
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+    {
+        "type": "text",
+        "text": "Prompt formulation and CLIP understanding. Our prompt formulation combined with our coloring scheme results in the correct association between objects and their properties, a known challenge when using CLIP [33]. In Fig. 12, we analyze the CLIP score for two different prompts: 'gray chair with highlighted back' (left) and 'blue chair with red back' (right). For each prompt, we measure the CLIP similarity to renders of both the correct assignment and flipped assignment.",
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+    {
+        "type": "text",
+        "text": "We observe that our prompt formulation ('gray chair with highlighted back') results in a higher average CLIP score for the correct assignment. In contrast, when specifying colors in the prompt ('blue chair with red back') and styling the mesh accordingly, we see higher CLIP scores for the flipped association. Using the same gray and yellow renders (left), we also compare to a prompt specifying colors ('gray chair with yellow back') and find that the higher",
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+        "image_caption": [
+            "Figure 11. Network initialization. We optimize 3D Highlighter for the text prompt 'belt' using different initialization methods: using a default initialization where all output probabilities are near 0.5 (middle) or altering the final layer so that all outputs are 0 (left) or 1 (right). Initializing with 0 or 1 leads to an undesirable result."
+        ],
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+    {
+        "type": "page_number",
+        "text": "20936",
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/46a442d6d6c2c3000f719cefdc0f5284a2910bc7d071a06bbdd8e125c11897ff.jpg",
+        "image_caption": [
+            "Figure 12. CLIP understanding. We examine CLIP similarity scores for several prompt formulations targeting the 'back' of the chair while using the correct color assignment and where the coloring is flipped. For the prompt 'gray chair with highlighted back' (left) we observe that the CLIP score is higher for the correct assignment. For the prompt 'blue chair with red back' (right) the CLIP score is higher for the flipped (incorrect) assignment."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "CLIP score corresponds to the flipped selection (data not shown).",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We also measure the CLIP scores for our standard prompt formulation: 'gray chair with highlighted back', replacing the yellow color in the rendering with other colors, such as red and blue, and find that the correct selection has a higher CLIP score (data not shown). To conclude, our prompt formulation (i.e., the use of the term 'highlighted') coincides with CLIP's understanding and 3D Highlighter is robust to the highlight color.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Network initialization. Initializing the network such that the object is partially highlighted (i.e., with highlight probability equal to 0.5) is important for obtaining desirable results. In Fig. 11, we show the optimization of our method for the target text prompt 'belt' using three different initializations. Our method (middle) initializes all output probabilities near 0.5 by random weight initialization of the network. We compare to initializing the output probabilities to 0 (left) or 1 (right), in which we set the weights of the last layer to 0, and the bias to 0 or 1, respectively.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "For the initialization to both 0.5 and 1, a highlight color is uniformly present on the styled mesh, whereas with 0, the mesh is gray with no highlight. Consequently, we hypothesize that the presence of highlight color at initialization is important for CLIP's supervision.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "4.5. Limitations",
+        "text_level": 1,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "3D Highlighter is robust to variations of the object specification in the target prompt. However, there should still be a logical connection between the 3D shape and its description. Fig. 13 shows results for a camel mesh and the target highlight 'shinguards'. For each optimization, we use a slightly different target prompt by varying the object specification. The prompts are of the form \"[object] with highlighted shinguards\", where [object] is replaced with camel, pig, animal, or chair.",
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+    {
+        "type": "text",
+        "text": "In Fig. 13, we observe that with object specifications",
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+    },
+    {
+        "type": "text",
+        "text": "that resemble the geometry of camel, such as pig and animal, 3D Highlighter accurately localizes the desired region. However, for a description that is incompatible with the object's geometry (i.e., referring to a camel as a chair), our method does not produce meaningful results. This result sheds light on 3D Highlighter's robustness to text descriptions: 3D Highlighter is able to reason about a mesh even when its description is not perfectly accurate, provided that it is sufficiently similar to the true description (i.e., referring to a camel mesh as a pig).",
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+    },
+    {
+        "type": "text",
+        "text": "5. Conclusions",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We present a technique for highlighting semantic regions on meshes using text as input, without any 3D datasets or 3D pre-training. 3D Highlighter can reason about where to place a non-obviously related part on a 3D object (i.e. a hat on a candle). The ability to combine unconnected parts and objects together is reminiscent of ideas from image analogies [12, 22]. In this work, we show that we can identify part-concepts that are geometrically absent from a shape, giving rise to our hallucinated highlighting capability.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "During neural optimization, our neural network infers a probability which we use to blend the highlight color onto the mesh. The network-predicted probabilities are general, and provide a soft-segmentation which we show can be used for a variety of different applications (Figs. 4 and 8). In the future, we are interested in extending our framework to obtain part correspondence between shapes that differ topologically but are semantically related.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Acknowledgments",
+        "text_level": 1,
+        "bbox": [
+            500,
+            565,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "We thank the University of Chicago for providing the AI cluster resources, services, and the professional support of the technical staff. This work was also supported in part by gifts from Adobe Research. Finally, we would like to thank Richard Liu, Avery Zhou, and the members of 3DL for their thorough and insightful feedback on our work.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/d466cfa6af2a35e8ea84c273f2ed61469a2e59581258127dfb4738c887104207.jpg",
+        "image_caption": [
+            "Figure 13. Prompt generality. Our system is robust to certain variations in object specifications. We achieve desirable results for the text input 'camel with highlighted shinguards' (left), as well as for other variations ('pig' and 'animal'). If the object specification, such as 'chair', is incompatible with the input geometry, 3D Highlighter no longer produces meaningful results."
+        ],
+        "image_footnote": [],
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+        "text": "20937",
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+    },
+    {
+        "type": "text",
+        "text": "References",
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2023/3D Highlighter_ Localizing Regions on 3D Shapes via Text Descriptions/40cb675d-902c-46da-982e-90a4332ad0f2_origin.pdf

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2023/3D Highlighter_ Localizing Regions on 3D Shapes via Text Descriptions/full.md

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+# 3D Highlighter: Localizing Regions on 3D Shapes via Text Descriptions
+
+Dale Decatur
+
+University of Chicago
+
+ddecatur@uchicago.edu
+
+Itai Lang
+
+University of Chicago
+
+itailang@uchicago.edu
+
+Rana Hanocka
+
+University of Chicago
+
+ranahanocka@uchicago.edu
+
+![](images/3ce3a39f1eb0d64ad65575fb6db76724d3770833ec5661ef4d5b62770f653931.jpg)  
+Hat
+
+![](images/60c4879aeb4ae28ea5aa5ff682daf21552ad4ac22b576e77b4c48bb58976f923.jpg)  
+Necklace
+
+![](images/fe90a136ea0f9260c9f288ed71d72975217f89971a6a4916f93a99516821e195.jpg)  
+Headlights  
+Figure 1. 3D Highlighter localizes semantic regions on a shape using text as input. Our technique reasons about where to place seemingly unrelated concepts in semantically meaningful locations on the 3D shape, such as a 'necklace' on a horse or 'shoes' on an alien.
+
+![](images/5fb07b1e0540704ea8d02f727270040e868b72855b1128eb69cfd2362028f4f0.jpg)  
+Shoes
+
+![](images/4ae578474bf040ed0bec23be64939a47d3ec22c8b57557e5f3c545daefabbbef.jpg)  
+Eyeglasses
+
+# Abstract
+
+We present 3D Highlighter, a technique for localizing semantic regions on a mesh using text as input. A key feature of our system is the ability to interpret "out-of-domain" localizations. Our system demonstrates the ability to reason about where to place non-obviously related concepts on an input 3D shape, such as adding clothing to a bare 3D animal model. Our method contextualizes the text description using a neural field and colors the corresponding region of the shape using a probability-weighted blend. Our neural optimization is guided by a pre-trained CLIP encoder, which bypasses the need for any 3D datasets or 3D annotations. Thus, 3D Highlighter is highly flexible, general, and capable of producing localizations on a myriad of input shapes. Our code is publicly available at https://github.com/threedle/3DHighlighter.
+
+# 1. Introduction
+
+Semantic localization of regions on 3D meshes is an important problem in computer graphics and vision with broad applications. One such application is the incorporation of semantic information into the 3D modeling process. A particularly challenging aspect of this task emerges when 3D geometric signals are insufficient for performing segmentation, e.g. where to add a shirt to a bare 3D human model.
+
+We propose 3D Highlighter, a method for automatically localizing fine-grained semantic regions on a shape based
+
+on only a text description. Our system contextualizes the text prompt and highlights the corresponding shape region using the network-predicted probabilities. Using only text, users are able to semantically identify regions on a shape. Our system takes meshes as input, making it compatible with 3D modeling workflows and tools.
+
+This highlighting task requires both object-level and part-level understanding. 3D Highlighter demonstrates the ability to reason about where to place seemingly unrelated concepts on the 3D shape, such as a hat on a candle (Fig. 1). Our system localizes attributes that are geometrically absent from a shape, which we refer to as hallucinated highlighting. Understanding a part's global shape context is challenging even when relying on salient geometric features [17,27], let alone without them.
+
+We optimize the weights of a neural network to produce probabilities that are used to color a given 3D shape in accordance with the specified text. We leverage a pre-trained vision-language model (CLIP [31]) to guide the neural optimization towards the text-specified region. This neural optimization formulation is flexible, bypassing the need for any 3D datasets, 3D annotations, or 3D pre-training. Our system is not bound to a specific set of classes, and, as shown in Fig. 2, is not limited to object parts defined by salient geometric features.
+
+We encode the part selection as a neural field [44] over the mesh surface. Our network learns to map each point on the surface to a probability of belonging to the text-specified region. We translate the inferred probabilities to a visual at-
+
+![](images/017b26d3608a89b48df7256a49f16654424c0c1d823dddfbe5754975975d1db4.jpg)  
+Figure 2. Hallucinated part highlighting. Our system is able to reason about where to highlight a geometrically-absent region on shapes. The resulting localizations demonstrate global understanding and localized part-awareness.
+
+tribute on the mesh surface, which can be rendered and visually understood. The network-predicted probabilities act as a soft-selection operator which blends the highlighter color onto the mesh. The network weights are updated by encouraging the CLIP [31] embedding of the 2D renders of the highlighted mesh to adhere to the specified text. As a result, the network implicitly learns to segment the object to adhere to the text prompt.
+
+We make several design choices that are key to the success of 3D Highlighter. Our network does not directly color the mesh. Rather, we predict a probability of being inside the text-specified highlight, which is used to blend colors on the mesh. The network is initialized such that points have roughly a  $50\%$  probability of being highlighted, resulting in a mesh with albedo halfway between the highlight and background color. During optimization, the relative blend weight of the highlight color directly corresponds to the highlight probability. This blending enables the network to naturally and smoothly increase or decrease the segmenta
+
+tion probability in accordance with the text specification of the target region.
+
+In summary, we present a method for localizing semantic regions on 3D shapes. The localization is specified by a textual description, which is intuitive, flexible, and not limited to a specific training dataset. We demonstrate applications of our method to shape editing and stylization. Furthermore, our field formulation enables the 3D Highlighter to work with different mesh resolutions and triangulations. A key feature of our system is the ability to interpret out-of-domain localizations. For example, 3D Highlighter is able to figure out where to place a 'hat' on a candle as seen in Fig. 1, demonstrating the ability to reason about where to place seemingly unrelated concepts on the 3D shape.
+
+# 2. Related Work
+
+Geometry-driven segmentation. Traditional works in geometry processing use low-level geometric features (such as surface area, curvature, or geodesic distance) in or-
+
+![](images/9766ef4a11261cc1f15997de6dd888eb8713529b811146c3bb3ee2bfeb3e8788.jpg)  
+Headphones
+
+![](images/81cd7b51d2cfd8d78a71821d36fd79da22a5b7a19117eff2d1f513b1af286837.jpg)  
+Shoes
+
+![](images/294bd74ac95b194ac50b261400ea011e725354d47acbb368eeae197473ee4fbe.jpg)  
+Hat
+
+![](images/959b668781fd20b838201489cefa175f07a439dd1efd9bafbc25d1795cc64b51.jpg)  
+Shoes
+
+![](images/7c59cf4c4e5b68a607234db82cf9d6bcbab0a29c916e3e3e1d450e3ec7c0381d.jpg)  
+Necklace
+
+![](images/77c4c76920741c24fa86ab07bfca602d48b239ea9ec27eea54eea9565ea4204c.jpg)  
+Glasses
+
+![](images/2019c1bb121776727762325c858011eb3ff3e6de4ad7452ff2614f5f21bf286c.jpg)  
+Belt
+
+![](images/770a8424474d00430078d9ff43613e1f1d548b70b88925618a0696fb033d8dc8.jpg)  
+Hat
+
+![](images/57decd69583ee7eab9d4754d219932c4bfbc74046be0677bb3003a98f148289a.jpg)  
+Necklace
+
+![](images/78d80f0d2b6d1a2c6fcc7194230b72a5c46477d56b3699b6d6aa54ef4b3657cc.jpg)  
+Necklace  
+Figure 3. Our method is able to highlight different parts on the same object. For target selections that correspond to distinct regions, 3D Highlighter produces selections that are semantically meaningful and spatially separated without signal from underlying geometry.
+
+![](images/ad0b618d045f1d549053c56f8bda5ecb063249ae42b25d58f0f874c73ea53607.jpg)  
+Roof
+
+![](images/7c5d9feaaeb944ad53557f28a02665cc718c380495e4710928de625be0f015b7.jpg)  
+Arms
+
+der to infer high-level semantic attributes for segmenting shapes [35]. In particular, decomposing shapes into smaller parts or segments often corresponds with physical 3D semantic parts [13, 35]. One approach is to partition shapes based on convexity, or an approximation of convexity [1, 23]. The medial axis carries topological information, which may also be used as a guideline for segmentation [6,8,35,47].
+
+The underlying assumption in these works is that processing the local geometry can be used to understand the semantics for segmentation. By contrast, a key aspect of our work is the ability to perform hallucinated highlights: segmentations that can not necessarily be inferred by geometry alone. See example highlights in Fig. 2 (e.g., localizing a heart on a goat).
+
+Data-driven segmentation. In the deep learning era, the 3D part segmentation task has been widely tackled by neural network models [11, 15, 20, 26, 36, 45]. Training such a model is typically done in a fully-supervised manner on a large dataset of shapes annotated with a given set of part classes. For example, MeshCNN [11] was trained on a
+
+human-body segmentation dataset [24] for learning semantic part segmentation. To alleviate the need for 3D annotations, unsupervised learning schemes utilize large collections of unlabelled data [5,7,14,37,49]. For example, Hong et al. [14] inferred part-segmentation through question answering on rendered images from PartNet [46].
+
+In contrast to existing deep learning approaches for shape segmentation, we do not rely on any 3D dataset, nor are we bounded to a specific shape category or set of parts. Instead, we specify the desired localization using text and a pre-trained CLIP model which encompasses rich semantic object understanding. Thus, our 3D Highlighter is capable of localizing various semantic regions on a wide variety of 3D shapes.
+
+Text-guidance. Recent works have leveraged pre-trained vision-language embedding spaces, such as CLIP [31], for analysis, synthesis, and editing. Some techniques leverage pre-trained image encoders for achieving semantic segmentation in images and neural radiance fields [2, 19, 21]. Such techniques are capable of segmenting entire objects within a scene based on text, e.g., a chair inside a room. However, they may struggle to segment parts within an object; e.g., failing to distinguish a window (part) from a house (object) [21].
+
+Our work is inspired by the emergent analysis in text-driven synthesis techniques for 3D data [10, 16, 18, 25, 30, 42]. Specifically, Text2Mesh [25] devised a framework for text-driven stylization of 3D meshes, observing that the resulting textures consider part-aware semantics. Yet, since Text2Mesh directly synthesizes stylizations, there is no obvious way to extract any underlying semantic analysis. To address this, we opt to use a highlighter color only as a means for visualizing the network-predicted segmentations.
+
+# 3. Method
+
+An illustration of our method is shown in Fig. 5. The inputs to our system are a mesh  $M$ , represented by vertices  $V \in \mathbb{R}^{n \times 3}$  and faces  $F \in \{1, \dots, n\}^{m \times 3}$ , and a text description  $T$ . Our neural network, referred to as neural highlighter, is optimized to map vertex positions  $v \in V$  to a
+
+![](images/ea684b3ec72b0b19c97fc2fdb468f84d805f3b34d80640e79d6e262bad979e7b.jpg)  
+Figure 4. Localized editing. We incorporate textures and displacements to a region highlighted with 3D Highlighter. Used styles: Brick (left), Colorful Crochet (middle), Cactus (right).
+
+![](images/37f87f8d97108d41f0f6ba47ae01309f80e0de863dac84e8359d80d6fcc580bd.jpg)  
+Figure 5. Overview of 3D Highlighter. The Neural Highlighter maps each point on the input mesh to a probability. The mesh is colored using a probability-weighted blend and then rendered from multiple views. The neural highlighter weights are guided by the similarity between the CLIP embeddings of the 2D augmented images and the input text.
+
+probability  $p$  of belonging to the text-specified region. Each vertex on the mesh is colored according to a probability-weighted blend between the highlighter color and a gray background color. The resulting highlighted mesh  $M'$  is rendered from multiple views, and we apply 2D augmentations to obtain a set of images. We supervise the network optimization by comparing the CLIP-embedded images to the CLIP embedding of the desired text.
+
+# 3.1. Neural Highlighter
+
+Our neural highlighter is a neural field [44] mapping coordinates  $\mathbf{x} \in \mathbb{R}^3$  to  $p \in [0,1]$ , where  $p$  is the probability that  $\mathbf{x}$  belongs to the text-specified region. The neural highlighter is represented as a multi-layer perceptron (MLP)  $\mathcal{F}_{\theta}$  that takes an input vertex  $v$  in the form of a 3D coordinate  $\mathbf{x}_v = (x,y,z)$  and predicts a highlight probability  $p_v$ ,  $\mathcal{F}_{\theta}(\mathbf{x}_v) = p_v$ . This formulation allows us to query the neural field to obtain meaningful highlight probabilities for any 3D point on (or near) the mesh surface. Thus, once optimized, the network weights conveniently transfer the localization to different meshes of the same object without requiring further optimization (Fig. 9).
+
+Representing our neural highlighter as an MLP produces contiguous localizations and reduces artifacts. MLPs have been shown to exhibit a spectral bias towards smooth solutions [32], especially on low-dimensional inputs such as 3D coordinates [38]. The bias towards low-frequency outputs encourages our 3D Highlighter to predict contiguous localizations with sharp boundaries and discourages noisy highlights (Fig. 7). For this reason, our approach does not utilize positional encoding. See supplemental material for
+
+![](images/00d170565c319d089b1f02247d1441eae50c822102195bd45107ab7ca0b587ad.jpg)  
+Figure 6. Viewpoint robustness. Our system produces consistent results even when using different primary viewpoints. Results for three different primary viewpoints for the target text 'necklace'.
+
+additional details.
+
+# 3.2. Mesh Color Blending
+
+We leverage the per-point highlight probability to color the mesh in a continuous, differentiable manner, generating semantically meaningful renders for CLIP supervision. We use a probability-weighted blend, where each vertex color  $C_v$  is a linear combination of the highlight color  $H$  and gray color  $G$  weighted by the network-predicted highlight probability  $C_v = p_v \cdot H + (1 - p_v) \cdot G$ .
+
+At the start of the optimization process, all vertex probabilities are initialized near 0.5 and thus the entire mesh is half-lighted. As the optimization progresses, vertices smoothly transition towards gray or highlighter color (based on the network predictions) such that vertices predicted to be highlighted adhere to the text-specified region. This formulation translates each step of the optimization to a colored mesh that is semantically meaningful to CLIP. Our method provides continuous gradients, in contrast to coloring vertices according to the argmax of the highlight probability. Our blending scheme results in a smoother optimization landscape and reduces highlight artifacts (Fig. 7).
+
+This formulation is also important for downstream applications that wish to use the localizations, e.g. editing and stylization. Predicting per-point highlight probabilities provides an explicit representation of the highlight region on the mesh surface. An alternative approach, optimizing the surface color directly, would only provide a visual result without explicit information about which vertices belong to the localization.
+
+# 3.3. Unsupervised Guidance
+
+We guide our neural optimization using the joint vision-language embedding space of CLIP [31]. We formulate the desired highlight by describing the association between the input mesh [object] and target localization [region]. Specifically, we design our target text  $T$  to be: "a gray [object] with highlighted [region]." We render the highlighted geometry from multiple views using differentiable rendering [4]. At each optimization step, we randomly sample  $n$  views from a Gaussian distribution centered around a primary view. This
+
+ensures that the underlying object is recognizable in the majority of views shown to CLIP.
+
+In a preliminary viewpoint prediction stage, we render  $360^{\circ}$  views of the mesh and measure the CLIP similarity to the target text prompt. We select the primary view to be the render with the highest CLIP similarity. We found that there exist many possible viewpoints which produce desirable highlighter results (see Fig. 6). More details about how the primary view is selected can be found in the supplemental material.
+
+For each view  $\psi$ , we render a 2D image  $I_{\psi}$  and apply a random perspective 2D augmentation  $\phi$ , as done in previous works [9, 25]. We then encode each of the augmented images into the CLIP embedding space (in  $\mathbb{R}^{768}$ ) using CLIP's image encoder, denoted as  $E_I$ . Our final aggregate image representation  $\mathsf{e}_I$  is the average CLIP encoding over all views:
+
+$$
+\mathsf {e} _ {I} = \frac {1}{n} \sum_ {\psi} E _ {I} \left(\phi \left(I _ {\psi}\right)\right) \in \mathbb {R} ^ {7 6 8}. \tag {1}
+$$
+
+Similarly, we encode the target selection text  $T$  with CLIP's text encoder  $E_{T}$  to get the encoded target representation  $\mathsf{e}_T = E_T(T)\in \mathbb{R}^{768}$ . Our loss  $\mathcal{L}$  for optimizing the neural highlighter parameters  $\theta$  is formulated as the negative cosine similarity between the aggregate image embedding and the text embedding:
+
+$$
+\underset {\theta} {\operatorname {a r g m i n}} \mathcal {L} (\theta) = - \frac {\mathrm {e} _ {I} \cdot \mathrm {e} _ {T}}{\left| \mathrm {e} _ {I} \right| \cdot \left| \mathrm {e} _ {T} \right|}. \tag {2}
+$$
+
+When the loss is minimized, the CLIP embedding of the rendered highlighted mesh becomes similar to the target text embedding. Thus, the localized region will reflect the target text region.
+
+# 4. Experiments
+
+In this section we examine various capabilities of 3D Highlighter. First, we demonstrate the fidelity of our highlighter localization in Sec. 4.1, including qualitative and quantitative evaluations. As far as we can ascertain, our method is the first technique to perform text-driven localization on 3D shapes without pre-training on 3D data. Thus, we adapt an existing language-guided segmentation technique for 2D images to serve as a baseline [21]. Moreover, we demonstrate the robustness of 3D Highlighter in Sec. 4.2. Then we explore several applications of our method in Sec. 4.3, such as selective editing, localized manipulation, and segmentation. Finally, in Sec. 4.4 we evaluate the influence of key components of 3D Highlighter and discuss its limitations in Sec. 4.5.
+
+We apply our method to a large variety of meshes from different sources: COSEG [41], Turbo Squid [40], Thingi10K [48], Toys4k [34], ModelNet [43], and
+
+ShapeNet [3]. 3D Highlighter does not impose any restrictions on the mesh quality; many of the meshes used contain artifacts, such as elements that are non-manifold, unoriented, and contain boundaries or self-intersections. Our PyTorch [29] implementation optimization takes around 5 minutes to run on an Nvidia A40 GPU. In our experiments, we used CLIP ViT-L/14 at  $224 \times 224$  resolution.
+
+# 4.1. Generality and Fidelity of 3D Highlighter
+
+Highlight generality. 3D Highlighter is not restricted to any particular category for either the input mesh or the text-specified localization, since it does not rely on a 3D dataset or 3D pre-training. In Fig. 2, we see our method achieves accurate localization for a diverse collection of meshes from various domains such as humanoids, animals, and manufactured objects. 3D Highlighter is capable of localizing a wide variety of diverse attributes even when the context of these target attributes is entirely unrelated to the input mesh. Moreover, 3D Highlighter demonstrates that it can perform hallucinated highlighting, where it selects regions on meshes with no underlying geometric signal (such as a bow tie on a camel or a hat on a pig).
+
+Highlight specificity. In Fig. 3, we observe that semantic differences are reflected in the network-predicted highlight. 3D Highlighter is able to successfully localize different text-specified regions on the same mesh. Our framework demonstrates the nuanced understanding required to disambiguate different target regions, such as headphones and hat on the rabbit. Finally, the ability to identify many different regions on a single mesh allows users intuitive, comprehensive, and fine-grained control over part localization.
+
+Quantitative evaluation. 3D Highlighter is the first system to select semantic regions on 3D shapes using text guidance, without any 3D datasets. Since there are no quantitative benchmarks to evaluate the quality of our highlights, we do so with a perceptual user study.
+
+Moreover, since there are no existing approaches for text-based segmentation in 3D, we create two baselines by
+
+![](images/bc15b6e2fd97a1bca99a84cbc1cc4d816c22f4721d8c569ef7f947c5c65b0fdf.jpg)  
+full 0.332  
+Figure 7. Ablation experiments. We present ablation results for target text 'shoes' using our system (full), direct optimization (direct), without probability-weighted blending (no blend), and without 2D augmentations (no augs). Resulting CLIP scores shown below each image.
+
+![](images/52a2f7096b5ab00c340d7d071fed787c78435618dc985fa5fa6b478c27ed7455.jpg)  
+direct 0.319
+
+![](images/6b07bb4a37b67c5f9e25a7fb0f25dd1d8c1db0da75ff7c2ab87ecddb8d4b90de.jpg)  
+no blend 0.297
+
+![](images/8670507fec27605e15a778c258920e876d7976893e58d1abc1a1f06678d85e08.jpg)  
+no augs 0.287
+
+<table><tr><td>Method</td><td>Control</td><td>LSeg</td><td>Text2LIVE</td><td>Ours</td></tr><tr><td>Average Score ↑</td><td>1.00</td><td>1.26</td><td>2.23</td><td>4.38</td></tr></table>
+
+Table 1. Perceptual study. We extend two image-based approaches LSeg [21] (segmentation) and Text2LIVE [2] (localized editing) to the highlighting task and report mean user rating.
+
+extending two different 2D image-based approaches. The first baseline extends LSeg [21] which directly predicts a segmentation in 2D, while the second baseline extends Text2LIVE [2] which infers an edit mask for 2D image manipulation. To evaluate these baselines, we render a bare mesh from a view where the target localization region is clearly visible. We extract the 2D segmentation produced by the image baselines and use it to color the rendered image. Then we ask users to rate the highlight quality of both baselines and our 3D Highlighter result rendered from the same view in our perceptual study.
+
+Our perceptual study reports quantitative results on the quality of highlights from both 3D Highlighter and baselines. Users were asked to rate each result from 1-5 on how effectively the highlight represents "an [object] with a region corresponding to a [region] highlighted." Visual examples from our study are shown in the supplemental material (Fig. 21). In total, 33 users evaluated each method on 5 mesh and region combinations.
+
+Our 3D Highlighter achieved the highest ratings compared to the baselines (Tab. 1). LSeg is built for text-driven semantic segmentation and excels at segmenting entire objects within a scene. However, LSeg struggles to identify parts within a single object, leading to subpar performance on our highlighting task. Text2LIVE was not explicitly built for segmentation, however it does rely on inferring a continuously-valued edit mask (i.e. a soft-segmentation) when performing localized image editing. The edit mask is designed to produce high-quality image manipulations; however, it is not directly suitable for identifying the sharp segmentation boundaries required for our highlighting task. Qualitative comparisons and an additional quantitative comparison using a modified CLIP R-Precision metric are discussed in the supplemental material.
+
+# 4.2. Robustness of 3D Highlighter
+
+Localization transfer. An important benefit of formulating 3D Highlighter as a neural field optimization is the ability to trivially transfer localization results between different meshings. This ability is useful for many tasks in geometry processing which require an object to be re-triangulated, simplified, subdivided, or otherwise remeshed. Localization transfer is possible since our neural highlighter is represented as a field over the shape and is independent of any
+
+![](images/966054bc4a85eb1b71c9edcf7fe929a75c3553c5be242fe48ac20cedf257a5fb.jpg)  
+Figure 8. Controlled stylization. Given three different stylizations of the same object, we use 3D Highlighter to select different regions and combine them together (Ours). Attempting to achieve this composition with a holistic approach leads to an undesirable result (Text2Mesh [25]).
+
+specific meshing. Although the neural highlighter is trained on mesh vertices, the resulting network encodes a smooth field and produces meaningful outputs for any 3D point on (or near) the mesh surface.
+
+In Fig. 9, we show an optimization of the 3D Highlighter on a single mesh triangulation (original) for the prompt 'shoes'. We then apply the already-optimized neural highlighter to remeshed (middle) and subdivided (right) versions of the original mesh, showing the transferability of the selected region to different triangulations. This result demonstrates how 3D Highlighter is independent of the input mesh and that, once we have a localization for one mesh, we can trivially transfer it to any other meshing of the same object.
+
+Viewpoint robustness. Our method is robust to the primary view choice. This property is important for our localization task, as we may not know a priori which view is ideal. In Fig. 6, we perform our optimization using three different primary viewpoints:  $0^{\circ}$ ,  $90^{\circ}$ , and  $-90^{\circ}$  (viewpoints shown in blue). We then present predicted localizations, showing that for all three views, 3D Highlighter is able to accurately identify the target localization region, regardless of whether that region is visible from the primary view.
+
+From the  $-90^{\circ}$  primary view, the target region (the neck) is not visible. However, is still visible with a low probability for views sampled from the Gaussian distribution
+
+![](images/f018918fbaf8736ed616c12a107abff622ccc97a3598f00583aa31289e4ad0d6.jpg)  
+Figure 9. Localization transfer. We optimize our neural highlighter on one mesh (original) for the prompt 'shoes'. Once optimized, the network weights transfer the localization to different meshings of the same object (remeshed and subdivided).
+
+around the primary view. This means that over the course of optimization, regions other than the neck are mostly seen while the target region is rarely visible. Nonetheless, our method manages to highlight the desired region, which implies its robustness to how frequently the target region for localization is seen. Furthermore, it shows that oversampling views where the target region is not visible does not negatively influence the optimization.
+
+# 4.3. Applications of 3D Highlighter
+
+Selective editing. In Fig. 4, we show that it is possible to use 3D Highlighter to selectively edit a 3D object within a semantic region. This is applicable to techniques which incorporate global texture or material properties over the entire shape, such as in Text2Mesh [25] or MatCap [39]. Starting with different bare input meshes, we edit the entire shape using a global stylization technique [25]. Then, we use 3D Highlighter to select a text-specified region and incorporate the modifications only in the selected area. Thus 3D Highlighter provides direct control over where to stylize shapes, enabling users to obtain localized stylizations based on semantic cues.
+
+Controlled stylization via composition. Achieving compositionality with language models is a challenging task [33]. For example, starting with a human mesh and using Text2Mesh [25] to stylize 'Iron Man with the head of Steve Jobs and Yeti legs', leads to muddled and undesirable results (Fig. 8, rightmost). Our method enables compositionality between different shape modifications by chaining simple concepts together (Fig. 8). Specifically, we decompose the desired modification into three separate attainable targets ('Iron Man', 'Steve Jobs', and 'Yeti'), which we stylize individually with Text2Mesh. We then utilize our 3D Highlighter to localize the text-specified regions. We achieve the desired composition by combining the highlighted regions together, obtaining clear boundaries between stylizations.
+
+Semantic segmentation. In Fig. 10, we show that our technique is not restricted to hallucinated highlighting and is capable of localizing semantically-specified geometric regions. These text-driven localizations identify unique geometric parts without utilizing any 3D datasets or part labels.
+
+# 4.4. Components of 3D Highlighter
+
+Ablation study. Several components are key for facilitating 3D Highlighter. We provide ablation results in Fig. 7 to demonstrate the effect of our design choices. First, using a direct optimization of the vertex color (direct) instead of optimizing a neural field results in splotchy highlight artifacts. Since the neural field has a spectral bias towards smooth solutions [32], omitting it leads to an undesired noisy output. Second, removing the probability weighted blending (no blend) and instead coloring vertices using only
+
+![](images/5f07d2dbe7886e50bd891038211e2c20cd2aa37502ddaa9905c6454b084a0a90.jpg)  
+Arm
+
+![](images/6b22d823e0eed84c95e938a67070eeed0862e956e2f688fba10eb3562f8f2beb.jpg)  
+Slide
+
+![](images/68ef7f752136e4660dafb1582c8a971b0bd35ab5640a501d31930cc7a2fb506d.jpg)  
+Propeller  
+Figure 10. Semantic Segmentation. 3D Highlighter produces semantic segmentations for unique geometric parts without any 3D dataset or annotations.
+
+two distinct values also produces a noisy highlight pattern. Without a continuous color blend, the gradients become ill-conditioned and unstable, leading to highlight artifacts and irregular localization boundaries. Lastly, similar to previous works [9, 25], we observe that without 2D perspective augmentations (no augs), 3D Highlighter outputs degenerate solutions. The ablation study emphasizes the importance of our key design choices in 3D Highlighter for its ability to highlight a coherent and localized region on the input shape.
+
+Prompt formulation and CLIP understanding. Our prompt formulation combined with our coloring scheme results in the correct association between objects and their properties, a known challenge when using CLIP [33]. In Fig. 12, we analyze the CLIP score for two different prompts: 'gray chair with highlighted back' (left) and 'blue chair with red back' (right). For each prompt, we measure the CLIP similarity to renders of both the correct assignment and flipped assignment.
+
+We observe that our prompt formulation ('gray chair with highlighted back') results in a higher average CLIP score for the correct assignment. In contrast, when specifying colors in the prompt ('blue chair with red back') and styling the mesh accordingly, we see higher CLIP scores for the flipped association. Using the same gray and yellow renders (left), we also compare to a prompt specifying colors ('gray chair with yellow back') and find that the higher
+
+![](images/97dddc40b0091821cfab65ba2c7e2cfb43f71a6956850708ff94d0d1f24f3e7e.jpg)  
+Figure 11. Network initialization. We optimize 3D Highlighter for the text prompt 'belt' using different initialization methods: using a default initialization where all output probabilities are near 0.5 (middle) or altering the final layer so that all outputs are 0 (left) or 1 (right). Initializing with 0 or 1 leads to an undesirable result.
+
+![](images/46a442d6d6c2c3000f719cefdc0f5284a2910bc7d071a06bbdd8e125c11897ff.jpg)  
+Figure 12. CLIP understanding. We examine CLIP similarity scores for several prompt formulations targeting the 'back' of the chair while using the correct color assignment and where the coloring is flipped. For the prompt 'gray chair with highlighted back' (left) we observe that the CLIP score is higher for the correct assignment. For the prompt 'blue chair with red back' (right) the CLIP score is higher for the flipped (incorrect) assignment.
+
+CLIP score corresponds to the flipped selection (data not shown).
+
+We also measure the CLIP scores for our standard prompt formulation: 'gray chair with highlighted back', replacing the yellow color in the rendering with other colors, such as red and blue, and find that the correct selection has a higher CLIP score (data not shown). To conclude, our prompt formulation (i.e., the use of the term 'highlighted') coincides with CLIP's understanding and 3D Highlighter is robust to the highlight color.
+
+Network initialization. Initializing the network such that the object is partially highlighted (i.e., with highlight probability equal to 0.5) is important for obtaining desirable results. In Fig. 11, we show the optimization of our method for the target text prompt 'belt' using three different initializations. Our method (middle) initializes all output probabilities near 0.5 by random weight initialization of the network. We compare to initializing the output probabilities to 0 (left) or 1 (right), in which we set the weights of the last layer to 0, and the bias to 0 or 1, respectively.
+
+For the initialization to both 0.5 and 1, a highlight color is uniformly present on the styled mesh, whereas with 0, the mesh is gray with no highlight. Consequently, we hypothesize that the presence of highlight color at initialization is important for CLIP's supervision.
+
+# 4.5. Limitations
+
+3D Highlighter is robust to variations of the object specification in the target prompt. However, there should still be a logical connection between the 3D shape and its description. Fig. 13 shows results for a camel mesh and the target highlight 'shinguards'. For each optimization, we use a slightly different target prompt by varying the object specification. The prompts are of the form "[object] with highlighted shinguards", where [object] is replaced with camel, pig, animal, or chair.
+
+In Fig. 13, we observe that with object specifications
+
+that resemble the geometry of camel, such as pig and animal, 3D Highlighter accurately localizes the desired region. However, for a description that is incompatible with the object's geometry (i.e., referring to a camel as a chair), our method does not produce meaningful results. This result sheds light on 3D Highlighter's robustness to text descriptions: 3D Highlighter is able to reason about a mesh even when its description is not perfectly accurate, provided that it is sufficiently similar to the true description (i.e., referring to a camel mesh as a pig).
+
+# 5. Conclusions
+
+We present a technique for highlighting semantic regions on meshes using text as input, without any 3D datasets or 3D pre-training. 3D Highlighter can reason about where to place a non-obviously related part on a 3D object (i.e. a hat on a candle). The ability to combine unconnected parts and objects together is reminiscent of ideas from image analogies [12, 22]. In this work, we show that we can identify part-concepts that are geometrically absent from a shape, giving rise to our hallucinated highlighting capability.
+
+During neural optimization, our neural network infers a probability which we use to blend the highlight color onto the mesh. The network-predicted probabilities are general, and provide a soft-segmentation which we show can be used for a variety of different applications (Figs. 4 and 8). In the future, we are interested in extending our framework to obtain part correspondence between shapes that differ topologically but are semantically related.
+
+# 6. Acknowledgments
+
+We thank the University of Chicago for providing the AI cluster resources, services, and the professional support of the technical staff. This work was also supported in part by gifts from Adobe Research. Finally, we would like to thank Richard Liu, Avery Zhou, and the members of 3DL for their thorough and insightful feedback on our work.
+
+![](images/d466cfa6af2a35e8ea84c273f2ed61469a2e59581258127dfb4738c887104207.jpg)  
+Figure 13. Prompt generality. Our system is robust to certain variations in object specifications. We achieve desirable results for the text input 'camel with highlighted shinguards' (left), as well as for other variations ('pig' and 'animal'). If the object specification, such as 'chair', is incompatible with the input geometry, 3D Highlighter no longer produces meaningful results.
+
+# References
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+        "text": "3D Human Keypoints Estimation from Point Clouds in the Wild without Human Labels",
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+        "text": "Zhenzhen Weng $^{1*}$  Alexander S. Gorban $^{2}$  Jingwei Ji $^{2}$  Mahyar Najibi $^{2}$  Yin Zhou $^{2}$  Dragomir Anguelov $^{2}$",
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+        "text": "$^{1}$ Stanford University  $^{2}$ Waymo",
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+        "text": "Abstract",
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+        "type": "text",
+        "text": "Training a 3D human keypoint detector from point clouds in a supervised manner requires large volumes of high quality labels. While it is relatively easy to capture large amounts of human point clouds, annotating 3D keypoints is expensive, subjective, error prone and especially difficult for long-tail cases (pedestrians with rare poses, scooterists, etc.). In this work, we propose GC-KPL - Geometry Consistency inspired Key Point Leaning, an approach for learning 3D human joint locations from point clouds without human labels. We achieve this by our novel unsupervised loss formulations that account for the structure and movement of the human body. We show that by training on a large training set from Waymo Open Dataset [21] without any human annotated keypoints, we are able to achieve reasonable performance as compared to the fully supervised approach. Further, the backbone benefits from the unsupervised training and is useful in downstream few-shot learning of keypoints, where fine-tuning on only 10 percent of the labeled training data gives comparable performance to fine-tuning on the entire set. We demonstrated that GC-KPL outperforms by a large margin over SoTA when trained on entire dataset and efficiently leverages large volumes of unlabeled data.",
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+        "text": "1. Introduction",
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+        "type": "text",
+        "text": "Estimation of human pose in 3D is an important problem in computer vision and it has a wide range of applications including AR/VR, AI-assisted healthcare, and autonomous driving [4,29,32]. For autonomous systems, being able to perceive human poses from sensor data (e.g. Li-DAR point clouds) is particularly essential to reason about the surrounding environment and make safe maneuvers.",
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+        "text": "Despite the high level of interest in human pose estimation in the wild, only few papers approached outdoor 3D keypoint detection using point cloud. A main reason is that",
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+        "image_caption": [
+            "Figure 1. We present GC-KPL, a novel method for learning 3D human keypoints from in-the-wild point clouds without any human labels. We propose to learn keypoint locations using unsupervised losses that account for the structure and movement of the human body. The backbone learns useful semantics from unsupervised learning and can be used in downstream fine-tuning tasks to boost the performance of 3D keypoint estimation."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "training a pedestrian pose estimation model requires large amount of high quality in-the-wild data with ground truth labels. Annotating 3D human keypoints on point cloud data is expensive, time consuming and error prone. Although there are a few existing point cloud datasets with ground truth human poses [11, 13, 21], they are limited in terms of the quantity of the 3D annotations and diversity of the data. Therefore, fully-supervised human keypoint detectors trained on such datasets do not generalize well for long tail cases. For this reason, previous approaches on pedestrian 3D keypoint estimation have mainly focused on utilizing 2D weak supervision [4, 32] which is easier to obtain, or leveraging signals from others modalities (e.g. RGB, depth) [29]. Nonetheless, there is a lot of useful information in the large amount of unlabeled LiDAR data that previous works on human pose estimation have not made an effort to utilize.",
+        "bbox": [
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+    {
+        "type": "header",
+        "text": "CVF",
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+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_footnote",
+        "text": "*Work done as an intern at Waymo.",
+        "bbox": [
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+    },
+    {
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+        "text": "1158",
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+    {
+        "type": "text",
+        "text": "In this work, we propose a novel and effective method for learning 3D human keypoints from in-the-wild point clouds without using any manual labeled 3D keypoints. Our approach is built on top of the key observation that human skeletons are roughly centered within approximately rigid body parts and that the location and movement of the surface points should explain the movement of the skeleton and vice versa. To that end, we design novel unsupervised loss terms for learning locations of the 3D keypoints/skeleton within human point clouds which correspond to 3D locations of major joints of human body.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In the proposed method, we first train a transformer-based regression model for predicting keypoints and a semantic segmentation model for localizing body parts on a synthetic data constructed from randomly posed SMPL human body model [15]. Then, we train on the entire Waymo Open Dataset [21] without using any 3D ground-truth annotation of human keypoints. Through unsupervised training, keypoint predictions are refined and the backbone learns useful information from large amount of unannotated data.",
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+    {
+        "type": "text",
+        "text": "In summary, we make the following contributions:",
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+    {
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+        "list_items": [
+            "- We present GC-KPL, a method for learning human 3D keypoints for in-the-wild point clouds without any manual keypoint annotations.",
+            "- Drawing insight from the structure and movement of the human body, we propose three effective and novel unsupervised losses for refining keypoints. We show that the proposed losses are effective for unsupervised keypoint learning on Waymo Open Dataset.",
+            "- Through downstream fine-tuning/few-shot experiments, we demonstrate that GC-KPL can be used as unsupervised representation learning for human point clouds, which opens up the possibility to utilize a practically infinite amounts of sensor data to improve human pose understanding in autonomous driving."
+        ],
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.1. 3D Human Keypoint Estimation from Points Clouds",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "There have been a few works [19, 31, 34] about estimating 3D keypoints from clean and carefully-curated point clouds [6], but 3D keypoint estimation from in-the-wild point clouds is a much less studied problem. Due to the lack of ground-truth 3D human pose annotations paired with Li-DAR data, there has not been a lot of works on 3d human keypoint estimation from LiDAR information. Among the few point cloud datasets with 3D keypoint annotations, Li-DARHuman26M [13] captures long-range human motions with ground truth motion acquired by the IMU system and pose information derived from SMPL models fitted into point clouds. It is among the first few datasets which have",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "LiDAR point clouds synchronized with RGB images, but SMPL shape parameters are same for all 13 subjects and it does not feature in-the-wild pedestrians where there could be much more background noise and occlusion. PedX [11] offers 3D automatic pedestrian annotations obtained using model fitting on different modalities, gathered effectively from a single intersection with only 75 pedestrians (the second intersection has only 218 frames, labels for the third scene were not released). Waymo Open Dataset [21] has more than 3,500 subjects from over 1,000 different in-the-wild scenes with high-quality 2D and 3D manual annotations. Despite the existence of these datasets, the few works on 3D pose estimation from point clouds mostly rely on weak supervision. HPERL model [4] trains on 2D ground-truth pose annotations and uses a reprojection loss for the 3D pose regression task. Multi-modal model in [32] uses 2D labels on RGB images as weak supervision, and creates pseudo ground-truth 3D joint positions from the projection of annotated 2D joints. HUM3DIL [29] leverages RGB information with LiDAR points, by computing pixel-aligned multi-modal features with the 3D positions of the LiDAR signal. In contrast, our method does not use any RGB information or weak supervision.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.2. Unsupervised Keypoint Localization",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "There are a number of works that aim to recover 3D keypoints using self-supervised geometric reasoning [12, 22], but they are limited to rigid objects. More recent unsupervised methods work for articulated objects from monocular RGB data [9, 10, 10, 18, 20, 24], multi-view data [16], or point clouds [27], where authors suggest to condition on the predicted keypoints and train a conditional generative model to supervise the keypoints through reconstruction losses. We propose a simpler pipeline where we apply our novel unsupervised losses to the predicted keypoints directly and do not require additional models besides the keypoint predictor itself.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2.3. Self-supervised Learning for Point Clouds",
+        "text_level": 1,
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Self-supervised representation learning has proven to be remarkably useful in language [3, 17] and 2D vision tasks [2, 7]. As LiDAR sensors become more affordable and common, there has been an increasing amount of research interest in self-supervised learning on 3D point clouds. Previous works proposed to learn representations of object or scene level point clouds through contrastive learning [8, 25, 30] or reconstruction [23, 26, 28, 33], which is useful in downstream classification or segmentation tasks. In contrast, our supervision signals come from the unique structure of the human body and our learned backbone is particularly useful in downstream human keypoint estimation tasks.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "1159",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
+        "bbox": [
+            76,
+            89,
+            169,
+            104
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this section, we describe our complete training pipeline which contains two stages. In the first stage, we initialize the model parameters on a synthetic dataset (Sec. 3.1). The purpose of Stage I is to warm-up the model with reasonable semantics. The second stage generalizes the model to the real-world data. In this stage, we use our unsupervised losses to refine the keypoint predictions on in-the-wild point clouds (Sec. 3.2). An overview of our pipeline is in Fig. 2.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Stage I: Initialization on Synthetic Data",
+        "text_level": 1,
+        "bbox": [
+            76,
+            257,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this stage, we initialize the model on a synthetic dataset that is constructed by ray casting onto randomly posed human mesh models (SMPL [15]). We describe details of synthetic data generation in Supplementary.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The goal of this stage is to train a model  $f$  that takes a point cloud of a human  $\\mathbf{P} \\in \\mathbb{R}^{N \\times 3}$  and outputs 3D locations of keypoints  $\\hat{\\mathbf{Y}} \\in \\mathbb{R}^{(J + 1) \\times 3}$ , as well as soft body part assignments (or part segmentation)  $\\hat{\\mathbf{W}} \\in \\mathbb{R}^{N \\times (J + 1)}$  that contains the probability of each point  $i$  belonging to body part  $j \\in [J]$  or the background.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\{\\hat {\\mathbf {Y}}, \\hat {\\mathbf {W}} \\} = f (\\mathbf {P}) \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\forall i \\in [ N ], \\sum_ {j = 1} ^ {J + 1} \\hat {\\mathbf {W}} _ {i, j} = 1 \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Ground truth information about part segmentation  $\\mathbf{W}$  and keypoint locations  $\\mathbf{Y}$  are readily available for synthetic data. Hence, we can train the model by directly supervising the predicted keypoint through L2 loss,",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {k p} = \\left\\| \\hat {\\mathbf {Y}} - \\mathbf {Y} \\right\\| _ {2} \\tag {3}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "and predicted segmentation through cross entropy loss,",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {s e g}} = - \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {J + 1} \\mathbf {W} _ {i, j} \\log \\left(\\hat {\\mathbf {W}} _ {i, j}\\right) \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            163,
+            633,
+            468,
+            669
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Overall, we minimize",
+        "bbox": [
+            76,
+            681,
+            223,
+            694
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {s y n}} = \\lambda_ {k p} \\mathcal {L} _ {\\mathrm {k p}} + \\lambda_ {\\text {s e g}} \\mathcal {L} _ {\\text {s e g}} \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            707,
+            468,
+            724
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Notably, in Sec. 4.6 we show that supervision in this stage is not required - ground truth  $\\mathbf{W}$  and  $\\mathbf{Y}$  can be replaced by surrogate ground truths to achieve comparable results.",
+        "bbox": [
+            75,
+            734,
+            468,
+            780
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Stage II: Self-Supervised Learning on In-the-Wild Data",
+        "text_level": 1,
+        "bbox": [
+            76,
+            787,
+            468,
+            816
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "In this stage, we further refine the network using unsupervised losses. The key insight behind the design of the losses is that the human body is composed of limbs, each of which is a rigid part. Therefore, points on a limb move with the limb and should stay roughly at the same location",
+        "bbox": [
+            75,
+            825,
+            468,
+            900
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "in each limb's local coordinate system. To account for this, we propose flow loss that encourages the points to stay in the same location (despite rotation around the limb) within each limb's local cylindrical coordinate.",
+        "bbox": [
+            496,
+            90,
+            890,
+            150
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We start by formally defining the key ingredients in the following formulations. In our setup, a human skeleton  $L$  is composed of limbs, each of which is connecting two keypoints. A limb  $l = (y_{a}, y_{b}) \\in L$  is a line segment connecting the parent  $y_{a}$  and child keypoints  $y_{b}$  on this limb, and all surface points on this limb have segmentation label  $a$ .",
+        "bbox": [
+            496,
+            150,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "All three proposed losses are in terms of surface points in each predicted limb's local coordinate system. Therefore, we first convert all input points to each limbs' local cylindrical coordinate and compute the radial and axial coordinates. Specifically, we project point  $p \\in \\mathbf{P}$  in global coordinate on to vector  $\\overrightarrow{\\hat{y}_a\\hat{y}_b}$ , and calculate the norm of the projected vector",
+        "bbox": [
+            496,
+            239,
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+            348
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {z} (p, \\hat {l}) = \\frac {\\left(p - \\hat {y} _ {a}\\right) \\cdot \\left(\\hat {y} _ {b} - \\hat {y} _ {a}\\right)}{\\| \\hat {y} _ {b} - \\hat {y} _ {a} \\| _ {2}} \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            596,
+            354,
+            890,
+            388
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "and the distance between the point and  $\\overrightarrow{\\hat{y}_a\\hat{y}_b}$",
+        "bbox": [
+            500,
+            396,
+            795,
+            414
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {r} (p, \\hat {l}) = \\| p - \\hat {y} _ {a} - \\mathbf {z} (\\hat {y} _ {b} - \\hat {y} _ {a}, \\hat {l}) \\| _ {2} \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            581,
+            420,
+            890,
+            438
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "For simplicity, we use  $\\mathbf{z}_{\\hat{l}}(p)$  to represent  $\\mathbf{z}(p,\\hat{l})$ , and  $\\mathbf{r}_{\\hat{l}}(p)$  to represent  $\\mathbf{r}(p,\\hat{l})$  in the following.",
+        "bbox": [
+            496,
+            446,
+            888,
+            478
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Next, we describe the formulation of each loss function in detail.",
+        "bbox": [
+            496,
+            478,
+            888,
+            506
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Flow Loss. Flow loss considers the predictions from two consecutive frames and encourages consistency of the radial and altitude components of all points with respect to scene flow - limbs should move between frames in a way to keep radial and axial coordinates for all points constant. Formally, we define the forward and backward flow losses  $(\\mathcal{L}_{ff}$  and  $\\mathcal{L}_{bf}$  respectively) for limbs  $\\hat{l}^t = (\\hat{y}_a^t,\\hat{y}_b^t)$  and  $\\hat{l}^{t + 1} = (\\hat{y}_a^{t + 1},\\hat{y}_b^{t + 1})$  for predicted keypoints for timestamp  $t$  and  $t + 1$ .",
+        "bbox": [
+            496,
+            507,
+            890,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {f f} = \\frac {1}{N} \\sum_ {i} \\hat {\\mathbf {W}} _ {i a} ^ {t} \\cdot \\left(\\left| \\mathbf {r} _ {\\hat {l} ^ {t + 1}} \\left(p _ {i} ^ {t} + f _ {i} ^ {t}\\right) - \\mathbf {r} _ {\\hat {l} ^ {t}} \\left(p _ {i} ^ {t}\\right) \\right| + \\right. \\\\ \\left| \\mathbf {z} _ {\\hat {l} ^ {t + 1}} \\left(p _ {i} ^ {t} + f _ {i} ^ {t}\\right) - \\mathbf {z} _ {\\hat {l} ^ {t}} \\left(p _ {i} ^ {t}\\right) \\right|) \\tag {8} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            514,
+            651,
+            890,
+            705
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {b f} = \\frac {1}{N} \\sum_ {i} \\hat {\\mathbf {W}} _ {i a} ^ {t + 1} \\cdot \\left(\\left| \\mathbf {r} _ {\\hat {l} t} \\left(p _ {i} ^ {t + 1} + b _ {i} ^ {t + 1}\\right) - \\mathbf {r} _ {\\hat {l} t + 1} \\left(p _ {i} ^ {t + 1}\\right) \\right| + \\right. \\\\ \\left| \\mathbf {z} _ {\\hat {l} ^ {t}} \\left(p _ {i} ^ {t + 1} + b _ {i} ^ {t + 1}\\right) - \\mathbf {z} _ {\\hat {l} ^ {t + 1}} \\left(p _ {i} ^ {t + 1}\\right) \\right|) \\tag {9} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            514,
+            734,
+            890,
+            787
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "$f^t$  is the forward flow for each point  $p^t \\in \\mathbf{P}^t$  and  $b^{t+1}$  is the backward flow for each point  $p^{t+1} \\in \\mathbf{P}^{t+1}$ . We use Neural Scene Flow Prior [14] to estimate flow for two consecutive frames of points. The overall flow loss for frame  $t$  is",
+        "bbox": [
+            496,
+            792,
+            890,
+            854
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {f l o w}} = \\frac {1}{| L |} \\sum_ {\\hat {l} t} \\frac {\\mathcal {L} _ {f f} + \\mathcal {L} _ {b f}}{2} \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            604,
+            859,
+            890,
+            896
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "1160",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/e2241ea31bfe3b1b334d4aec242957af7570a85f23e0d4f8a61bd8a2d7a27339.jpg",
+        "image_caption": [
+            "Stage I: Initialization on Synthetic Data",
+            "Unsupervised Losses"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            109,
+            112,
+            455,
+            224
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/e6c46fcd903a52cbf3d9ea1d82cf231f133ad9db0823c9be84fb08d9e6962afb.jpg",
+        "image_caption": [
+            "Stage II: Unsupervised Learning on In-the-Wild Data"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            500,
+            116,
+            883,
+            220
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/c19e32e7f6e091575f8c198f70f1411cfba5908a5377ce6ddceddb13810fe484.jpg",
+        "image_caption": [
+            "Flow loss"
+        ],
+        "image_footnote": [
+            "(a) After moving, points stay in the same place (despite rotation around axis) within each limb's local cylindrical coordinate system."
+        ],
+        "bbox": [
+            91,
+            276,
+            197,
+            347
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/ee82e58063d9c4b155af987824ad367617c17e974f3bc1a2ff60e862b13eb8fb.jpg",
+        "image_caption": [
+            "Figure 2. Overview of our method. In Stage I, we warm-up the keypoint predictor and body part segmentation predictor on a small synthetic dataset. Then, in Stage II we refine the 3D keypoint predictions on a large in-the-wild dataset with unsupervised losses. The main losses are depicted on the bottom."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            218,
+            277,
+            346,
+            349
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/4705f627c4c7da48ea1250dc5f5c6d455383ec604cac68cabb703e4aecea0e16.jpg",
+        "image_caption": [
+            "Points-to-limb loss"
+        ],
+        "image_footnote": [
+            "(b) Minimize points-to-limb distance to encourage the limb to stay within the body."
+        ],
+        "bbox": [
+            410,
+            292,
+            563,
+            342
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/9136ace268ca2b5d4dd47262bdc7e07315e5ff57d75fa2c86dd65ab0c40c1236.jpg",
+        "image_caption": [
+            "Symmetry loss"
+        ],
+        "image_footnote": [
+            "(c) Points are symmetrical around limb. (i.e. points with similar height z have similar radius r)"
+        ],
+        "bbox": [
+            689,
+            297,
+            831,
+            340
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "By design, the flow loss value is the same if the radial and axial values for all points in a local coordinate system are the same in consecutive frames. This would happen if a limb in both frames are shifted in their respective orthogonal direction by the same amount. Theoretically, it is unlikely to happen for all limbs, but empirically we observe that with flow loss alone the skeleton would move out of the point cloud. Therefore, we need additional losses to make the keypoints stay within the body.",
+        "bbox": [
+            75,
+            419,
+            468,
+            554
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Points-to-Limb Loss. For a predicted limb  $\\hat{l} = (\\hat{y}_a, \\hat{y}_b)$ , we want the points on this limb to be close to it. Hence, we introduce a points-to-limb (p2l) loss",
+        "bbox": [
+            75,
+            554,
+            468,
+            599
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {p 2 l} ^ {\\hat {l}} = \\frac {1}{N} \\sum_ {i} \\hat {\\mathbf {W}} _ {i a} \\mathbf {d} \\left(p _ {i}, \\hat {l}\\right) \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            184,
+            604,
+            468,
+            637
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{d}$  is the Euclidean distance function between a point and a line segment. We sum over all points to get the overall points-to-limb loss,",
+        "bbox": [
+            75,
+            648,
+            468,
+            694
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {p} 2 \\mathrm {l}} = \\frac {1}{| L |} \\sum_ {\\hat {l}} \\mathcal {L} _ {\\mathrm {p} 2 \\mathrm {l}} ^ {\\hat {l}} \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            212,
+            693,
+            468,
+            728
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Symmetry Loss. Symmetry loss encourages the predicted limb  $\\hat{l}$  to be in a position such that all points around this limb are roughly symmetrical around it. That is to say, points with similar axial coordinates  $\\mathbf{z}_{\\hat{l}}$  should have similar radial values  $\\mathbf{r}_{\\hat{l}}$ . To that end, we introduce symmetry loss,",
+        "bbox": [
+            75,
+            739,
+            468,
+            815
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {s y m} ^ {\\hat {l}} = \\frac {1}{N} \\sum_ {i} \\hat {\\mathbf {W}} _ {i a} \\left(\\mathbf {r} _ {\\hat {l}} \\left(p _ {i}\\right) - \\bar {\\mathbf {r}} _ {\\hat {l}} \\left(p _ {i}\\right)\\right) ^ {2} \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            145,
+            839,
+            468,
+            871
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\bar{\\mathbf{r}}_i(p_i)$  is the weighted mean of radial values of points",
+        "bbox": [
+            76,
+            885,
+            468,
+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "with similar axial coordinates as  $p_i$ ,",
+        "bbox": [
+            500,
+            420,
+            736,
+            435
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\bar {\\mathbf {r}} _ {\\hat {l}} \\left(p _ {i}\\right) = \\frac {\\sum_ {j} K _ {h} \\left(\\mathbf {z} _ {\\hat {l}} \\left(p _ {i}\\right) , \\mathbf {z} _ {\\hat {l}} \\left(p _ {j}\\right)\\right) \\left(\\hat {\\mathbf {W}} _ {i *} \\cdot \\hat {\\mathbf {W}} _ {j *}\\right) \\mathbf {r} _ {\\hat {l}} \\left(p _ {j}\\right)}{\\sum_ {j} K _ {h} \\left(\\mathbf {z} _ {\\hat {l}} \\left(p _ {i}\\right) , \\mathbf {z} _ {\\hat {l}} \\left(p _ {j}\\right)\\right) \\left(\\hat {\\mathbf {W}} _ {i *} \\cdot \\hat {\\mathbf {W}} _ {j *}\\right)} \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            504,
+            444,
+            890,
+            484
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "$K_{h}$  is Gaussian kernel with bandwidth  $h$ , i.e.  $K_{h}(x,y) = e^{-(\\frac{x - y}{h})^{2}}$ .  $\\hat{\\mathbf{W}}_{i*} \\in \\mathbb{R}^{J}$  is the  $i_{th}$  row of  $\\hat{\\mathbf{W}}$ , and the dot product  $\\hat{\\mathbf{W}}_{i*} \\cdot \\hat{\\mathbf{W}}_{j*}$  measures the similarity of part assignment of point  $i$  and  $j$ , as we want the value of  $\\bar{r}_i^k$  to be calculated using the points from the same part as point  $i$ .",
+        "bbox": [
+            498,
+            491,
+            890,
+            568
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The overall symmetry loss is over all points,",
+        "bbox": [
+            500,
+            569,
+            792,
+            584
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {s y m} = \\frac {1}{| L |} \\sum_ {l \\in L} \\mathcal {L} _ {s y m} ^ {l} \\tag {15}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            624,
+            592,
+            890,
+            625
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Joint-to-Part Loss. In addition, we encourage each joint to be close to the center of the points on that part using a joint-to-part loss.",
+        "bbox": [
+            496,
+            632,
+            890,
+            676
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {j 2 p} ^ {j} = \\left\\| \\hat {y} _ {j} - \\frac {\\sum_ {i} \\hat {\\mathbf {W}} _ {i j} p _ {i}}{\\sum_ {i} \\hat {\\mathbf {W}} _ {i j}} \\right\\| _ {2} \\tag {16}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            606,
+            686,
+            890,
+            724
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We sum over all joints to get the overall joint-to-part loss.",
+        "bbox": [
+            500,
+            732,
+            888,
+            748
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {j 2 p} = \\frac {1}{J} \\sum_ {j} \\mathcal {L} _ {j 2 p} ^ {j} \\tag {17}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            635,
+            768,
+            890,
+            801
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Note that although the ground truth location of joints are not in the center of points on the corresponding part, keeping this loss is essential in making the unsupervised training more robust.",
+        "bbox": [
+            496,
+            811,
+            890,
+            869
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "In practice, jointly optimizing  $\\hat{\\mathbf{W}}$  and  $\\hat{\\mathbf{Y}}$  in Stage II leads to unstable training curves. Hence, we use the pre-trained",
+        "bbox": [
+            498,
+            869,
+            890,
+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "1161",
+        "bbox": [
+            483,
+            944,
+            513,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/94c477a0fef43640d8aee39e48a863e21dfb0607695fb10236540fe888404a00.jpg",
+        "image_caption": [
+            "Figure 3. Effect of unsupervised losses on perturbed skeleton."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            118,
+            460,
+            258
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "segmentation branch from Stage I to run segmentation inference to get the segmentation labels on all of the training samples in the beginning of Stage II, and  $\\hat{\\mathbf{W}}$  is the one-hot encoding of the predicted segmentation labels.",
+        "bbox": [
+            75,
+            306,
+            468,
+            366
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Segmentation Loss. Lastly, we notice that keeping the segmentation loss at this stage further regularizes the backbone and leads to better quantitative performance. We use the inferred segmentation  $\\hat{\\mathbf{W}}$  as the surrogate ground truth and minimize cross entropy as in Eq. (4).",
+        "bbox": [
+            75,
+            366,
+            468,
+            441
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Training objective. The overall training objective during Stage II is to minimize",
+        "bbox": [
+            76,
+            441,
+            468,
+            469
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathcal {L} = \\lambda_ {f l o w} \\mathcal {L} _ {f l o w} + \\lambda_ {\\mathrm {p 2 l}} \\mathcal {L} _ {\\mathrm {p 2 l}} + \\lambda_ {s y m} \\mathcal {L} _ {s y m} \\\\ + \\lambda_ {\\mathrm {j} 2 \\mathrm {p}} \\mathcal {L} _ {\\mathrm {j} 2 \\mathrm {p}} + \\lambda_ {\\mathrm {s e g}} \\mathcal {L} _ {\\mathrm {s e g}} \\tag {18} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            91,
+            484,
+            468,
+            520
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To illustrate the effect of the three unsupervised losses  $(\\mathcal{L}_{flow}, \\mathcal{L}_{p2l}$  and  $\\mathcal{L}_{sym})$ , we show the result of applying these losses on a perturbed ground truth skeleton (Fig. 3). As shown, the proposed unsupervised losses effectively moves the perturbed skeleton to locations that are closer to ground truth.",
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Implementation Details",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The predictor model  $f$  consists of a transformer backbone with fully connected layers for predicting joints and segmentation respectively. We use the same transformer backbone as in HUM3DIL [29]. A fully connected layer is applied to the output of transformer head to regress the predicted  $\\hat{W}$  and  $\\hat{Y}$  respectively. There are 352,787 trainable parameters in total. We set the maximum number of input LiDAR points to 1024, and zero-pad or downsample the point clouds with fewer or more number of points. The flow is obtained using a self-supervised test-time optimization method [14]. The network is trained on 4 TPUs. We train Stage I for 200 epochs and Stage II for 75 epochs, both with batch size 32, base learning rate of  $1e - 4$ , and exponential decay 0.9. Stage I and II each finishes in about 6 hours. The loss weights in Eq. (5) are  $\\lambda_{kp} = 0.5$  and  $\\lambda_{seg} = 1$ .",
+        "bbox": [
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+            674,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The loss weights in Eq. (18) are  $\\lambda_{flow} = 0.02$ ,  $\\lambda_{p2l} = 0.01$ ,  $\\lambda_{sym} = 0.5$ ,  $\\lambda_{j2p} = 2$ , and  $\\lambda_{seg} = 0.5$ . The kernel bandwidth Eq. (14) is 0.1.",
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Dataset and Metrics",
+        "text_level": 1,
+        "bbox": [
+            498,
+            152,
+            691,
+            167
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We construct a synthetic dataset with 1,000 sequences of 16-frame raycasted point clouds for Stage I training. Each sequence starts with the same standing pose and ends in a random pose. We find that data augmentation is essential in Stage I training. To simulate real-world noisy background and occlusion, we apply various data augmentations to the synthetic data, including randomly downsample, random mask, add ground clusters, add background clusters, add a second person, add noise to each point, scale the person. We include examples of augmented synthetic data in Fig. 4.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/46b0b01e293159ea5e03a7b82bbd0621d66fb8aa7fa3b31e0c0263f694d1b38a.jpg",
+        "image_caption": [
+            "Figure 4. Data augmentations applied to the synthetic point clouds (colored by ground truth segmentation labels). Ground truth skeletons are shown in purple. Background points are in blue."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In Stage II, we train on the entire Waymo Open dataset (WOD) training set (with around 200,000 unlabeled samples). As the official WOD testing subset is hidden from the public, we randomly choose  $50\\%$  of the validation set as the validation split, and the rest as the test split for benchmarking. We report average Mean Per Joint Position Error (MPJPE) on test set at the end of each stage. Formally, for a single sample, let  $\\hat{Y} \\in \\mathcal{R}^{J \\times 3}$  be the predicted keypoints,  $Y \\in \\mathcal{R}^{J \\times 3}$  the ground truth keypoints, and  $v \\in \\{0,1\\}^J$  the visibility indicator annotated per keypoint.",
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+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\operatorname {M P J P E} (Y, \\hat {Y}) = \\frac {1}{\\sum_ {j} v _ {j}} \\sum_ {j \\in [ J ]} v _ {j} \\| y _ {j} - \\hat {y} \\| _ {2} \\tag {19}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Note that in this Stage, we do Hungarian matching between the predicted and annotated keypoints per frame, and then report MPJPE on matched keypoints. We report matched MPJPE because the method is intended for scenarios where correspondence between keypoints in the unlabeled training data and downstream data is unknown.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "1162",
+        "bbox": [
+            482,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/235df5a86dacfa377f2b945d9cac5e30d20a2b314a17b86314d035b487064d79.jpg",
+        "image_caption": [
+            "Figure 5. Visualizations of predictions on WOD at the end of Stage I and Stage II. Points are colored by predicted segmentation labels. Ground truth keypoints are in green and predicted keypoints and skeletons are in red."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            122,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Results",
+        "text_level": 1,
+        "bbox": [
+            76,
+            512,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this section we perform quantitative evaluation of GC-KPL at the end of Stage I and II in Tab. 2. Qualitative results are in Fig. 5. As shown, after first stage where we train on a synthetic dataset constructed from posed body models with carefully chosen data augmentations, we are able to predict reasonable human keypoints on in-the-wild point clouds. The second stage our novel unsupervised losses further refine the predicted keypoints.",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.4. Downstream Task: Few-shot 3D Keypoint Learning",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In this experiment, we show that the backbone of our model benefits from unsupervised training on large amount of unlabeled data, and can be useful for downstream finetuning tasks. We start from our pre-trained backbone after Stage II, and fine-tune with annotated training samples from WOD by minimizing mean per joint error. We include few-shot experiments where we fine-tune with a extremely small amount of data (10% and 1% of the training set), to represent challenging scenarios where there is a limited amount of annotated data.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We include the LiDAR-only version of HUM3DIL (a state-of-the-art model on WOD) [29] as a strong baseline. The quantitative results (Tab. 1) suggest that our back",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "bone learns useful information from the unlabeled in-the-wild data and enables a significant performance boost on the downstream tasks. Compared to a randomly initialized backbone as used in HUM3DIL, our backbone leads to over  $2\\mathrm{cm}$  of decrease in MPJPE in downstream fine-tuning experiments, which is a significant improvement for the 3D human keypoint estimation task.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We visualize the predicted keypoints under different data regime in Fig. 6. As shown, models fine-tuned from our backbone is able to capture fine details on the arms and overall produces more accurate results than HUM3DIL.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To the best of our knowledge, there does not exist previous works on completely unsupervised human keypoint estimation from point clouds. We additionally experiment with using a readout layer on top of the features learned by a state-of-the-art point cloud SSL method 3D-OAE [30], but the MPJPE is  $15\\mathrm{cm}$  (compared to  $10.10\\mathrm{cm}$  from GC-KPL). Hence we consider the baselines we adopt here strong and complete. In Sec. 4.6, we further challenge our method by comparing to the domain adaptation setup and demonstrate that the performance of GC-KPL is still superior.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.5. Domain adaptation",
+        "text_level": 1,
+        "bbox": [
+            500,
+            412,
+            684,
+            429
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In the configuration where we use ground truth labels in Stage I and unsupervised training in Stage II could be seen as a domain adaption (DA) technique. Thus it is useful to compare proposed method with a commonly-used domain adaptation method. We train the same backbone model using a mix of real and synthetic data and a gradient reversal layer (aka DA loss) [5] to help the network to learn domain invariant keypoint features. Results in Tab. 3 demonstrate that GC-KPL yields superior accuracy compared with the DA method (MPJPE 10.1 vs  $11.35\\mathrm{cm}$ ).",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.6. Ablations",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Effect of using GT bounding boxes in pre-processing. We cropped human point clouds from the entire scene by including only points within GT bounding boxes. We also conducted experiments where we train with detected bounding boxes from raw LiDAR scans using a SoTA 3D detector. Results suggest that GC-KPL is robust to noise in 3D detection, as there were no noticeable changes in metrics.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Effect of synthetic dataset size. In our method Stage I serves as a model initialization step where we show that training on a small synthetic dataset (16,000 samples) with properly chosen data augmentations is suffice for the model to learn useful semantics. We further investigate the effect of synthetic dataset size during Stage I. We experiment with larger dataset sizes (160,000 and 1,600,000 samples) and observe that the effect of increasing synthetic dataset size is insignificant on  $\\mathrm{MPJPE}_{\\mathrm{matched}}$  at the end of Stage I - it decreased from  $17.7\\mathrm{cm}$  to  $17.6\\mathrm{cm}$ . Lack of a notable improvements for larger dataset sizes is likely due to limited variability of generated poses in synthetic data (see Supple",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "1163",
+        "bbox": [
+            482,
+            944,
+            514,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/8dc2fe390528e659e81192b9044aa880ff139f08e5825c8a30a66b34d0b122a9.jpg",
+        "image_caption": [
+            "(a) Fine-tune on  $100\\%$  training set"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            122,
+            89,
+            419,
+            407
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/bf2689fb1e1f498337db157c972e6efcc82d78b530c8b7c4f39d2e975113622b.jpg",
+        "image_caption": [
+            "(b) Fine-tune on  $10\\%$  training set"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            421,
+            90,
+            627,
+            407
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/561b3aee6120df91a4d59a2d47092628e9b66ea246cf2d73ff471e17621a1132.jpg",
+        "image_caption": [
+            "(c) Fine-tune on  $1\\%$  training set",
+            "Figure 6. Predicted keypoints from fine-tuning with different amount of annotated data. The points are colored by predicted segmentation labels by our model. Predicted keypoints are shown in red."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            630,
+            90,
+            843,
+            407
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/857d7c4785e6e810c95ce2fa60973eac22a2da6a5d7a2678ff5d5a7fe212d259.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>Backbone</td><td>Stage I supervised</td><td>1% training set MPJPE cm. (gain)</td><td>10% training set MPJPE cm. (gain)</td><td>100% training set MPJPE cm. (gain)</td></tr><tr><td rowspan=\"2\">HUM3DIL [29]</td><td>Randomly initialized</td><td></td><td>19.57</td><td>16.36</td><td>12.21</td></tr><tr><td>Pre-trained on synthetic only</td><td>✓</td><td>18.52 (-1.05)</td><td>15.10 (-1.26)</td><td>11.27 (-0.94)</td></tr><tr><td rowspan=\"3\">GC-KPL</td><td>Pre-trained on 5,000 WOD-train</td><td>✓</td><td>17.87 (-1.70)</td><td>14.51 (-1.85)</td><td>10.73 (-1.48)</td></tr><tr><td>Pre-trained on 200,000 WOD-train</td><td></td><td>17.80 (-1.77)</td><td>14.30 (-2.06)</td><td>10.60 (-1.61)</td></tr><tr><td>Pre-trained on 200,000 WOD-train</td><td>✓</td><td>17.20 (-2.37)</td><td>13.40 (-2.96)</td><td>10.10 (-2.11)</td></tr></table>",
+        "bbox": [
+            78,
+            477,
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+            599
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/2b724ef6ef1e37a1fcd2d5bca2ace917a76c092949837e058db89b07f4a1a1fb.jpg",
+        "table_caption": [
+            "Table 1. Downstream fine-tuning results. Check marks in \"Stage I supervised\" mean that we use ground truth part labels in Stage I, otherwise we use KMeans labels."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Training data</td><td>MPJPEmatchd (↓)</td></tr><tr><td>Synthetic only</td><td>17.70</td></tr><tr><td>5,000 WOD-train</td><td>14.64</td></tr><tr><td>200,000 WOD-train</td><td>13.92</td></tr></table>",
+        "bbox": [
+            130,
+            642,
+            416,
+            720
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/1d0c9bc76f2ad60d39dfc5760a39ca04b7b42e24daf47ba7120fe11b67aabad4.jpg",
+        "table_caption": [
+            "Table 2. Unsupervised learning (Stage II) results."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Domain distribution</td><td>DA loss</td><td>MPJPE (↓)</td></tr><tr><td>100% real</td><td></td><td>12.21</td></tr><tr><td>50/50% real/synthetic</td><td></td><td>12.08</td></tr><tr><td>50/50% real/synthetic</td><td>✓</td><td>11.35</td></tr></table>",
+        "bbox": [
+            109,
+            756,
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+            834
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Unsupervised domain adaptation results evaluated on WOD validation set.",
+        "bbox": [
+            75,
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+            868
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "mental for details).",
+        "bbox": [
+            500,
+            646,
+            627,
+            659
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Effect of using ground truths on synthetic data. While our described pipeline does not use any kind of manual labels, we do use ground truth segmentation and keypoints on synthetic dataset in Stage I because they are readily available. Here we further experiment with a variation where we do not use any kind of ground truths in Stage I (first row in Tab. 4). Instead, we use KMeans clusters and cluster centers as surrogate ground truths for model initialization, similar to [1]. Note that we are able to establish correspondence between KMeans clusters from different samples due to the fact that in our data generation process, each synthetic sequence starts with the same starting standing pose. Hence, we can run KMeans clustering on the starting pose that is shared among all sequences, and for subsequent samples within each sequence, we do Hungarian matching using",
+        "bbox": [
+            496,
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+            888
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "1164",
+        "bbox": [
+            483,
+            944,
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+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/5baa9cd0ea4f591b5697b46de878005b3516974af871b926c862c73b534bf5b7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td colspan=\"2\"></td><td colspan=\"3\">Stage I</td><td colspan=\"6\">Stage II</td></tr><tr><td>No.</td><td>Exp.</td><td>\\( \\mathcal{L}_{kp} \\)</td><td>\\( \\mathcal{L}_{seg} \\)</td><td>\\( MPJPE_{matched} \\)</td><td>\\( \\mathcal{L}_{j2p} \\)</td><td>\\( \\mathcal{L}_{seg} \\)</td><td>\\( \\mathcal{L}_{sym} \\)</td><td>\\( \\mathcal{L}_{p2l} \\)</td><td>\\( \\mathcal{L}_{flow} \\)</td><td>\\( MPJPE_{matched} \\)</td></tr><tr><td>1</td><td>Effect of using KMeans labels in Stage I</td><td>✓</td><td>✓</td><td>19.2</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>14.5</td></tr><tr><td>2</td><td>Effect of \\( \\mathcal{L}_{kp} \\) in Stage I</td><td></td><td>✓</td><td>N/A</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>14.2</td></tr><tr><td>3</td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>15.0</td></tr><tr><td>4</td><td>Effect of warmup losses in Stage II</td><td></td><td></td><td></td><td>✓</td><td></td><td>✓</td><td>✓</td><td>✓</td><td>14.2</td></tr><tr><td>5</td><td></td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td>15.2</td></tr><tr><td>6</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td>✓</td><td>30.1</td></tr><tr><td>7</td><td></td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td></td><td>✓</td><td>15.6</td></tr><tr><td>8</td><td></td><td></td><td></td><td></td><td></td><td></td><td>✓</td><td>✓</td><td></td><td>25.7</td></tr><tr><td>9</td><td rowspan=\"2\">Effect of unsupervised losses in Stage II</td><td></td><td></td><td></td><td>✓</td><td>✓</td><td></td><td>✓</td><td>✓</td><td>14.3</td></tr><tr><td>10</td><td></td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td></td><td>✓</td><td>14.9</td></tr><tr><td>11</td><td></td><td></td><td></td><td></td><td>✓</td><td>✓</td><td>✓</td><td>���</td><td></td><td>14.4</td></tr><tr><td>12</td><td></td><td></td><td></td><td></td><td>✓</td><td>✓</td><td></td><td></td><td></td><td>14.9</td></tr><tr><td colspan=\"2\">Full model (GC-KPL)</td><td>✓</td><td>✓</td><td>17.7</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>✓</td><td>13.9</td></tr></table>",
+        "bbox": [
+            76,
+            88,
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+            308
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 4. Ablations studies on the effect of individual loss term in our method. Experiments 3 through 12 are using both losses in Stage I. Full model is using GT labels for Stage I.",
+        "bbox": [
+            75,
+            316,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "inter-cluster Chamfer distance to establish correspondence between clusters from consecutive frames. We observe that although initializing with surrogate ground truths leads to slightly inferior performance in Stage I, after training with the losses in Stage II the drop in performance is less visible. Overall, downstream fine-tuning performance is comparable to our best model (10.6/14.3/17.8 vs. 10.1/13.4/17.2 cm when fine-tuned on  $100\\% / 10\\% / 1\\%$  of the data, see Tab. 1). This experiment suggests that method does not require any kind of ground truths, even during initialization stage.",
+        "bbox": [
+            75,
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+            503
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Effect of Losses. In this section we further investigate the effect of each component in our pipeline (Tab. 4). First, we note that  $\\mathcal{L}_{seg}$  in Stage I is essential because we need an initialized segmentation model to get the body part assignment for each point in order to calculate the losses in Stage II. Therefore, we only experiment with a variation of Stage I training without  $\\mathcal{L}_{kp}$ , and we observe that  $\\mathcal{L}_{kp}$  is useful in warming up the backbone for later stages. Next, we take the backbone from Stage I (trained with both  $\\mathcal{L}_{kp}$  and  $\\mathcal{L}_{seg}$ ), and study the effect of individual losses in Stage II. Experiments No.  $3/4/5$  show that it is helpful to include  $\\mathcal{L}_{j2p}$  and  $\\mathcal{L}_{seg}$  while having all other three unsupervised losses. In experiments  $6/7/8$  we take out  $\\mathcal{L}_{j2p}$  and  $\\mathcal{L}_{seg}$ , and investigate the effect of individual unsupervised losses. As shown the training becomes rather unstable if we further eliminate any of the three losses. We observe qualitatively that the metric worsens drastically because the limbs quickly move out of the human body. Experiments No.  $3/4/5$  suggest that  $\\mathcal{L}_{j2p}$  and  $\\mathcal{L}_{seg}$  are useful regularizers that make sure the limbs stay within the body, and the unsupervised losses further improve the performance by refining the keypoint location.",
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+        "type": "text",
+        "text": "4.7. Limitations and Future Work",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The task of keypoint location could be considered as a dual problem for semantic segmentation. In this work we",
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+    {
+        "type": "text",
+        "text": "use a simple segmentation network based on the same architecture as our keypoint estimation model. Using a superior segmentation model could lead to further improvements.",
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+    {
+        "type": "text",
+        "text": "The proposed flow loss depends on quality of the estimated flow of LiDAR points. In this work we used a simple but reasonable method to estimate flow between two frames of LiDAR points called Neural Scene Flow prior [14]. Quality of the unsupervised keypoint estimation could be improved by using a more advanced flow estimator tailored for point clouds on human body surfaces.",
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+    {
+        "type": "text",
+        "text": "Lastly, we use a part of the HUM3DIL [29] model which takes only LiDAR point cloud as input. The full HUM3DIL model was designed for multi-modal inputs and attains better performance. Thus, another interesting direction is to leverage multi-modal inputs.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "In this work, we approached the problem of 3D human pose estimation using points clouds in-the-wild, introduced a method (GC-KPL) for learning 3D human keypoints from point clouds without using any manual 3D keypoint annotations. We shown that the proposed novel losses are effective for unsupervised keypoint learning on Waymo Open Dataset. Through downstream experiments we demonstrated that GC-KPL can additionally serve as a self-supervised representation method to learn from large quantity of in-the-wild human point clouds. In addition, GC-KPL compares favorably with a commonly used domain adaptation technique. The few-shot experiments empirically verified that using only  $10\\%$  of available 3D keypoint annotation the fine-tuned model reached comparable performance to the state-of-the-art model training on the entire dataset. These results opens up exciting possibility to utilize massive amount of sensor data in autonomous driving to improve pedestrian 3D keypoint estimation.",
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+    {
+        "type": "page_number",
+        "text": "1165",
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+    },
+    {
+        "type": "text",
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