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+Title: Hierarchical Unsupervised 3D Instance Segmentation
+
+URL Source: https://arxiv.org/html/2407.10084
+
+Published Time: Tue, 16 Jul 2024 00:41:13 GMT
+
+Markdown Content:
+1 1 institutetext: Princeton University, Princeton NJ 08544, USA 2 2 institutetext: Springer Heidelberg, Tiergartenstr.17, 69121 Heidelberg, Germany 2 2 email: lncs@springer.com
+
+[http://www.springer.com/gp/computer-science/lncs](http://www.springer.com/gp/computer-science/lncs)3 3 institutetext: ABC Institute, Rupert-Karls-University Heidelberg, Heidelberg, Germany 
+
+3 3 email: {abc,lncs}@uni-heidelberg.de
+Supplementary Material for Part2Object: 
+
+Hierarchical Unsupervised 3D Instance Segmentation
+--------------------------------------------------------------------------------------------
+
+Second Author\orcidlink 1111-2222-3333-4444 2233 Third Author\orcidlink 2222–3333-4444-5555 33
+
+In the Appendix, we provide additional information regarding,
+
+*   •Implementation Details (Appendix[0.A](https://arxiv.org/html/2407.10084v1#Pt0.A1 "Appendix 0.A Implementation Details ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation")) 
+*   •Pseudo-code for Hierarchical Clustering (Appendix[0.B](https://arxiv.org/html/2407.10084v1#Pt0.A2 "Appendix 0.B Pseudo-code for Hierarchical Clustering ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation")) 
+*   •Detailed Results on Cross-dataset Generalization (Appendix[0.C](https://arxiv.org/html/2407.10084v1#Pt0.A3 "Appendix 0.C Detailed Results on Cross-dataset Generalization ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation")) 
+*   •Qualitative Results (Appendix[0.D](https://arxiv.org/html/2407.10084v1#Pt0.A4 "Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation")) 
+*   •Analysis on Part Results (Appendix[0.E](https://arxiv.org/html/2407.10084v1#Pt0.A5 "Appendix 0.E Analysis on Part Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation")) 
+
+Appendix 0.A Implementation Details
+-----------------------------------
+
+Table 1: The hyper-parameter configuration for training Hi-Mask3D, where * denote data-efficient setting.
+
+Configuration ScanNet ScanNet*S3DIS*
+Optimizer AdamW AdamW AdamW
+Learning rate (LR)1×10−4 1 superscript 10 4 1\times 10^{-4}1 × 10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT 1×10−4 1 superscript 10 4 1\times 10^{-4}1 × 10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT 1×10−4 1 superscript 10 4 1\times 10^{-4}1 × 10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT
+Scheduler OneCycleLR OneCycleLR OneCycleLR
+Batch size 4 4 4
+Epochs 600 600 600
+Part Queries Number 300 300 300 300 300 300 300 300 300 300 300 300
+Object Queries Number 150 150 150 150 150 150 150 150 150 150 150 150
+Voxel Size 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02
+Filter Out Classes None Wall, Floor None
+
+In this section, we provide implementation details of the training configuration. As shown in Table[1](https://arxiv.org/html/2407.10084v1#Pt0.A1.T1 "Table 1 ‣ Appendix 0.A Implementation Details ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation"), when training Hi-Mask3D under different settings, we maintain the same hyper-parameters for all configurations except for “Filter Out Classes”. In the unsupervised class-agnostic setting, where semantic categories are not distinguished, we do not filter out any classes based on semantic labels when training Hi-Mask3D on ScanNet pseudo-labels extracted from our Part2Object. In the case of data-efficient settings, following Mask3D[Schult23mask3d], we filter out background classes (wall and floor) in ScanNetv2[dai2017scannet] and nothing in S3DIS[s3dis].
+
+Following Unscene3D[rozenberszki2023unscene3d], to conduct class-agnostic experiments, we treat all objects equally without distinguishing between different object categories and only differentiate between foreground and background. All methods do not use DBSCAN[dbscan] as post-processing during the inference stage.
+
+Appendix 0.B Pseudo-code for Hierarchical Clustering
+----------------------------------------------------
+
+In this section, we provide the pseudo-code of our Part2Object hierarchical clustering. The model weights and code will be made publicly available upon publication.
+
+Data:clusters
+
+{c i t}i=1 N t superscript subscript subscript superscript 𝑐 𝑡 𝑖 𝑖 1 subscript 𝑁 𝑡\{c^{t}_{i}\}_{i=1}^{N_{t}}{ italic_c start_POSTSUPERSCRIPT italic_t end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT } start_POSTSUBSCRIPT italic_i = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_N start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT end_POSTSUPERSCRIPT
+, cluster features
+
+{𝒇 i t}i=1 N t superscript subscript superscript subscript 𝒇 𝑖 𝑡 𝑖 1 subscript 𝑁 𝑡\{\boldsymbol{f}_{i}^{t}\}_{i=1}^{N_{t}}{ bold_italic_f start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_t end_POSTSUPERSCRIPT } start_POSTSUBSCRIPT italic_i = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_N start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT end_POSTSUPERSCRIPT
+,
+
+3D objectness priors
+
+B 3⁢D superscript 𝐵 3 𝐷 B^{3D}italic_B start_POSTSUPERSCRIPT 3 italic_D end_POSTSUPERSCRIPT
+
+Result:clusters
+
+{c k t+1}k=1 N t+1 superscript subscript subscript superscript 𝑐 𝑡 1 𝑘 𝑘 1 subscript 𝑁 𝑡 1\{c^{t+1}_{k}\}_{k=1}^{N_{t+1}}{ italic_c start_POSTSUPERSCRIPT italic_t + 1 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT } start_POSTSUBSCRIPT italic_k = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_N start_POSTSUBSCRIPT italic_t + 1 end_POSTSUBSCRIPT end_POSTSUPERSCRIPT
+, cluster features
+
+{𝒇 k t+1}k=1 N t+1 superscript subscript superscript subscript 𝒇 𝑘 𝑡 1 𝑘 1 subscript 𝑁 𝑡 1\{\boldsymbol{f}_{k}^{t+1}\}_{k=1}^{N_{t+1}}{ bold_italic_f start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_t + 1 end_POSTSUPERSCRIPT } start_POSTSUBSCRIPT italic_k = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_N start_POSTSUBSCRIPT italic_t + 1 end_POSTSUBSCRIPT end_POSTSUPERSCRIPT
+
+1
+
+2 iou_threshold
+
+←←\leftarrow←0.6 0.6 0.6 0.6
+
+3
+
+4 for _every pairs (i,j)𝑖 𝑗(i,j)( italic\_i , italic\_j )_ do
+
+5 if _rank⁢(sim⁢(𝐟 i t,𝐟 j t))≤K rank sim superscript subscript 𝐟 𝑖 𝑡 superscript subscript 𝐟 𝑗 𝑡 𝐾\text{rank}(\text{sim}(\boldsymbol{f}\_{i}^{t},\boldsymbol{f}\_{j}^{t}))\leq K rank ( sim ( bold\_italic\_f start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_t end\_POSTSUPERSCRIPT , bold\_italic\_f start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT start\_POSTSUPERSCRIPT italic\_t end\_POSTSUPERSCRIPT ) ) ≤ italic\_K and d⁢i⁢s⁢t⁢(c i t,c j t)≤T 𝑑 𝑖 𝑠 𝑡 subscript superscript 𝑐 𝑡 𝑖 subscript superscript 𝑐 𝑡 𝑗 𝑇 dist({c}^{t}\_{i},{c}^{t}\_{j})\leq T italic\_d italic\_i italic\_s italic\_t ( italic\_c start\_POSTSUPERSCRIPT italic\_t end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT , italic\_c start\_POSTSUPERSCRIPT italic\_t end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT ) ≤ italic\_T_ then
+
+6 if _not s⁢t⁢o⁢p⁢C⁢r⁢i⁢t⁢e⁢r⁢i⁢a⁢(c i t,c j t,B 3⁢D)𝑠 𝑡 𝑜 𝑝 𝐶 𝑟 𝑖 𝑡 𝑒 𝑟 𝑖 𝑎 subscript superscript 𝑐 𝑡 𝑖 subscript superscript 𝑐 𝑡 𝑗 superscript 𝐵 3 𝐷 stopCriteria({c}^{t}\_{i},{c}^{t}\_{j},B^{3D})italic\_s italic\_t italic\_o italic\_p italic\_C italic\_r italic\_i italic\_t italic\_e italic\_r italic\_i italic\_a ( italic\_c start\_POSTSUPERSCRIPT italic\_t end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_i end\_POSTSUBSCRIPT , italic\_c start\_POSTSUPERSCRIPT italic\_t end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_j end\_POSTSUBSCRIPT , italic\_B start\_POSTSUPERSCRIPT 3 italic\_D end\_POSTSUPERSCRIPT )_ then
+
+7
+
+c k t+1←c i t∪c j t←subscript superscript 𝑐 𝑡 1 𝑘 subscript superscript 𝑐 𝑡 𝑖 subscript superscript 𝑐 𝑡 𝑗{c}^{t+1}_{k}\leftarrow{c}^{t}_{i}\cup{c}^{t}_{j}italic_c start_POSTSUPERSCRIPT italic_t + 1 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ← italic_c start_POSTSUPERSCRIPT italic_t end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ∪ italic_c start_POSTSUPERSCRIPT italic_t end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT
+
+8 end if
+
+9
+
+10 end if
+
+11
+
+12 end for
+
+13 for _every new cluster c k t+1 subscript superscript 𝑐 𝑡 1 𝑘{c}^{t+1}\_{k}italic\_c start\_POSTSUPERSCRIPT italic\_t + 1 end\_POSTSUPERSCRIPT start\_POSTSUBSCRIPT italic\_k end\_POSTSUBSCRIPT_ do
+
+14
+
+𝒇 k t+1←←superscript subscript 𝒇 𝑘 𝑡 1 absent\boldsymbol{f}_{k}^{t+1}\leftarrow bold_italic_f start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_t + 1 end_POSTSUPERSCRIPT ←
+FU(c k t+1)subscript superscript 𝑐 𝑡 1 𝑘({c}^{t+1}_{k})( italic_c start_POSTSUPERSCRIPT italic_t + 1 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT )
+
+15 end for
+
+return
+
+{c k t+1}i=1 N t+1 superscript subscript subscript superscript 𝑐 𝑡 1 𝑘 𝑖 1 subscript 𝑁 𝑡 1\{{c}^{t+1}_{k}\}_{i=1}^{N_{t+1}}{ italic_c start_POSTSUPERSCRIPT italic_t + 1 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT } start_POSTSUBSCRIPT italic_i = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_N start_POSTSUBSCRIPT italic_t + 1 end_POSTSUBSCRIPT end_POSTSUPERSCRIPT
+,
+
+{𝒇 i t+1}i=1 N t+1 superscript subscript superscript subscript 𝒇 𝑖 𝑡 1 𝑖 1 subscript 𝑁 𝑡 1\{\boldsymbol{f}_{i}^{t+1}\}_{i=1}^{N_{t+1}}{ bold_italic_f start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_t + 1 end_POSTSUPERSCRIPT } start_POSTSUBSCRIPT italic_i = 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_N start_POSTSUBSCRIPT italic_t + 1 end_POSTSUBSCRIPT end_POSTSUPERSCRIPT
+
+Algorithm 1 Hierarchical Clustering in Layer t 𝑡 t italic_t
+
+Here s⁢t⁢o⁢p⁢C⁢r⁢i⁢t⁢e⁢r⁢i⁢a 𝑠 𝑡 𝑜 𝑝 𝐶 𝑟 𝑖 𝑡 𝑒 𝑟 𝑖 𝑎 stopCriteria italic_s italic_t italic_o italic_p italic_C italic_r italic_i italic_t italic_e italic_r italic_i italic_a denotes the algorithm from line 263 in submitted paper.
+
+Appendix 0.C Detailed Results on Cross-dataset Generalization
+-------------------------------------------------------------
+
+To evaluate the generalization ability of our Hi-Mask3D, we employ a cross-dataset zero-shot generalization setting. In this setting, we utilize three out-of-domain datasets: ScanNet200[scannet200], S3DIS[s3dis] and Replica[straub2019replica], to test the fully supervised class-agnostic Mask3D and our unsupervised Hi-Mask3D. For the ScanNet200 dataset, we use 312 scenes from the validation set. For S3DIS, we use the entire dataset with 6 folds, totaling 272 scenes. For the Replica dataset, following the setup of OpenMask3D[takmaz2023openmask3d], we use 8 scenes (office0, office1, office2, office3, office4, room0, room1, room2). Following OpenMask3D[takmaz2023openmask3d], we first train Mask3D and Hi-Mask3D without segments on ScanNet and conduct generalization experiments on ScanNet200, S3DIS and Replica.
+
+Table 2: Comparison of zero-shot generalization on ScanNet200.
+
+Table 3: Comparison of zero-shot generalization on S3DIS.
+
+Table[2](https://arxiv.org/html/2407.10084v1#Pt0.A3.T2 "Table 2 ‣ Appendix 0.C Detailed Results on Cross-dataset Generalization ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") and Table[3](https://arxiv.org/html/2407.10084v1#Pt0.A3.T3 "Table 3 ‣ Appendix 0.C Detailed Results on Cross-dataset Generalization ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") provide detailed zero-shot performance on ScanNet200 and S3DIS. For ScanNet200, following the standard benchmark, we separately report the performance of head, common, and tail categories. Hi-Mask3D surpasses class-agnostic Mask3D by at least 10.0% mAP@50 and 0.8% mAP in head and common. Additionally, in the prediction for the Tail, Hi-Mask3D achieves performance comparable to that of class-agnostic Mask3D. Hi-Mask3D’s drop in performance on tail categories is primarily due to the difficulty in obtaining the very precise segmentation results for these classes. PSince Hi-Mask3D has never been exposed to manual annotations for these categories, although the mAP@25 score is high (+21.6%), the overall map decreases slightly (-0.9%). For S3DIS, we report mAP@25 and mAP@50 across 6 areas. At mAP@50, our method surpasses class-agnostic Mask3D by at least 2.9%.
+
+Appendix 0.D Qualitative Results
+--------------------------------
+
+Qualitative Comparisons With Other Methods: In Figure[0.D](https://arxiv.org/html/2407.10084v1#Pt0.A4 "Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") and Figure[0.D](https://arxiv.org/html/2407.10084v1#Pt0.A4 "Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation"), we present qualitative comparisons on ScanNet[dai2017scannet]. From top to bottom, we show the point cloud, segmentation results from Felzenswalb[felzenszwalb2004efficient], CutLER’s projection[wang2023cut], our Part2Object, the prediction results obtained from Hi-Mask3D through self-training and ground truth. The qualitative results indicate that our approach, compared to other methods, avoids over-segmentation and achieves complete, clear object masks. Additionally, through the object-ness prior, our method alleviates under-segmentation, leads to the separation of spatially connected objects, such as a computer on a desk (see Figure[0.D](https://arxiv.org/html/2407.10084v1#Pt0.A4 "Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") column 3) or a chair adjacent to the desk(see Figure[0.D](https://arxiv.org/html/2407.10084v1#Pt0.A4 "Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") column 1).
+
+Figure 1: Qualitative Comparisons with Other Methods. We present qualitative comparisons of different methods on ScanNet, showcasing scenes numbered 0427_00, 0015_00 and 0598_00 from left to right. Compared to Felzenswalb and CutLER projection (line 2 and line 3), our Part2Object (line 4) yields more comprehensive and clearer segmentation results. For instance, in scenes 0427_00 and 0015_00 (columns 1 and 2), objects like tables and chairs are segmented more distinctly. Moreover, our Hi-Mask3D (line 5), after self-training, effectively rectifies under-segmented objects present in pseudo-labels, as observed computers in scene 0598_00 (column 3). 
+
+Input
+Felzenswalb[felzenszwalb2004efficient]
+CutLER[wang2023cut]
+Pseudo Label
+Ours
+GT
+
+Figure 2: Qualitative Comparisons with Other Methods. We present qualitative comparisons of different methods on ScanNet, showcasing scenes numbered 0355_00, 0609_00, and 0081_01. 
+
+Input
+Felzenswalb[felzenszwalb2004efficient]
+CutLER[wang2023cut]
+Pseudo Label
+Ours
+GT
+
+Qualitative Comparisons With Different Clustering Methods: In Figure[3](https://arxiv.org/html/2407.10084v1#Pt0.A4.F3 "Figure 3 ‣ Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation"), we present qualitative comparisons of different clustering methods. From left to right, the images depict the input scene, single-layer clustering with varying hyper-parameters, hierarchical clustering without object-ness prior, our clustering results, and ground truth. Compared to hierarchical clustering, single-layer clustering struggles to achieve suitable granularity simultaneously for objects of different sizes and geometric structures, often resulting in either over-segmentation or under-segmentation (see the table in Figure[3](https://arxiv.org/html/2407.10084v1#Pt0.A4.F3 "Figure 3 ‣ Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") row 4). In the absence of object-ness prior guidance, objects tend to merge with adjacent objects or background elements (such as walls or floors) during the hierarchical clustering process (see the bag in Figure[3](https://arxiv.org/html/2407.10084v1#Pt0.A4.F3 "Figure 3 ‣ Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") row 7). Our method effectively addresses these issues, yielding object masks closely resembling the ground truth in an unsupervised setting.
+
+Figure 3: The comparison of clustering results between different clustering methods.
+
+![Image 1: Refer to caption](https://arxiv.org/html/2407.10084v1/figs/appendix_fig/cluster2.png)
+
+Figure 4: Different objects and their object parts.
+
+Input
+P^Part superscript^𝑃 Part\hat{P}^{\text{Part}}over^ start_ARG italic_P end_ARG start_POSTSUPERSCRIPT Part end_POSTSUPERSCRIPT
+P Part superscript 𝑃 Part P^{\text{Part}}italic_P start_POSTSUPERSCRIPT Part end_POSTSUPERSCRIPT
+P^Object superscript^𝑃 Object\hat{P}^{\text{Object}}over^ start_ARG italic_P end_ARG start_POSTSUPERSCRIPT Object end_POSTSUPERSCRIPT
+P Object superscript 𝑃 Object P^{\text{Object}}italic_P start_POSTSUPERSCRIPT Object end_POSTSUPERSCRIPT
+GT
+
+Appendix 0.E Analysis on Part Results
+-------------------------------------
+
+The qualitative results in Figure[0.D](https://arxiv.org/html/2407.10084v1#Pt0.A4 "Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") demonstrate that our Hi-Mask3D can learn the hierarchical semantic relation between objects and their parts. Row 3 of Figure[0.D](https://arxiv.org/html/2407.10084v1#Pt0.A4 "Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") displays the Part predictions generated by the Hi-Mask3D. It is evident that compared to row 2, Hi-Mask3D can segment the various parts of objects more distinctly. For example, it can differentiate between the backrest, seat cushion, and armrests of a sofa (Figure[0.D](https://arxiv.org/html/2407.10084v1#Pt0.A4 "Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") column 1), as well as the tabletop and legs of a table (Figure[0.D](https://arxiv.org/html/2407.10084v1#Pt0.A4 "Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") column 3). The predictions of Hi-Mask3D are notably superior to those of the pseudo-labels because the model learns that objects consist of multiple parts. Therefore, it can combine the parts of objects that are segmented separately in the pseudo-labels (Figure[0.D](https://arxiv.org/html/2407.10084v1#Pt0.A4 "Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") column 1,2,3), as well as separate multiple objects that are merged (Figure[0.D](https://arxiv.org/html/2407.10084v1#Pt0.A4 "Appendix 0.D Qualitative Results ‣ Supplementary Material for Part2Object: Hierarchical Unsupervised 3D Instance Segmentation") column 4,5).