Daily Papers

Achieving human-like spatial intelligence for vision-language models (VLMs) requires inferring 3D structures from 2D observations, recognizing object properties and relations in 3D space, and performing high-level spatial reasoning. In this paper, we propose a principled hierarchical framework that decomposes the learning of 3D spatial understanding in VLMs into four progressively complex levels, from geometric perception to abstract spatial reasoning. Guided by this framework, we construct an automated pipeline that processes approximately 5M images with over 45M objects to generate 3D spatial VQA pairs across diverse tasks and scenes for VLM supervised fine-tuning. We also develop an RGB-D VLM incorporating metric-scale point maps as auxiliary inputs to further enhance spatial understanding. Extensive experiments demonstrate that our approach achieves state-of-the-art performance on multiple spatial understanding and reasoning benchmarks, surpassing specialized spatial models and large proprietary systems such as Gemini-2.5-pro and GPT-5. Moreover, our analysis reveals clear dependencies among hierarchical task levels, offering new insights into how multi-level task design facilitates the emergence of 3D spatial intelligence.

We present UniScale, a unified, scale-aware multi-view 3D reconstruction framework for robotic applications that flexibly integrates geometric priors through a modular, semantically informed design. In vision-based robotic navigation, the accurate extraction of environmental structure from raw image sequences is critical for downstream tasks. UniScale addresses this challenge with a single feed-forward network that jointly estimates camera intrinsics and extrinsics, scale-invariant depth and point maps, and the metric scale of a scene from multi-view images, while optionally incorporating auxiliary geometric priors when available. By combining global contextual reasoning with camera-aware feature representations, UniScale is able to recover the metric-scale of the scene. In robotic settings where camera intrinsics are known, they can be easily incorporated to improve performance, with additional gains obtained when camera poses are also available. This co-design enables robust, metric-aware 3D reconstruction within a single unified model. Importantly, UniScale does not require training from scratch, and leverages world priors exhibited in pre-existing models without geometric encoding strategies, making it particularly suitable for resource-constrained robotic teams. We evaluate UniScale on multiple benchmarks, demonstrating strong generalization and consistent performance across diverse environments. We will release our implementation upon acceptance.

Markerless multiview motion capture is often constrained by the need for precise camera calibration, limiting accessibility for non-experts and in-the-wild captures. Existing calibration-free approaches mitigate this requirement but suffer from high computational cost and reduced reconstruction accuracy. We present Kineo, a fully automatic, calibration-free pipeline for markerless motion capture from videos captured by unsynchronized, uncalibrated, consumer-grade RGB cameras. Kineo leverages 2D keypoints from off-the-shelf detectors to simultaneously calibrate cameras, including Brown-Conrady distortion coefficients, and reconstruct 3D keypoints and dense scene point maps at metric scale. A confidence-driven spatio-temporal keypoint sampling strategy, combined with graph-based global optimization, ensures robust calibration at a fixed computational cost independent of sequence length. We further introduce a pairwise reprojection consensus score to quantify 3D reconstruction reliability for downstream tasks. Evaluations on EgoHumans and Human3.6M demonstrate substantial improvements over prior calibration-free methods. Compared to previous state-of-the-art approaches, Kineo reduces camera translation error by approximately 83-85%, camera angular error by 86-92%, and world mean-per-joint error (W-MPJPE) by 83-91%. Kineo is also efficient in real-world scenarios, processing multi-view sequences faster than their duration in specific configuration (e.g., 36min to process 1h20min of footage). The full pipeline and evaluation code are openly released to promote reproducibility and practical adoption at https://liris-xr.github.io/kineo/.

We present a unified framework capable of solving a broad range of 3D tasks. Our approach features a stateful recurrent model that continuously updates its state representation with each new observation. Given a stream of images, this evolving state can be used to generate metric-scale pointmaps (per-pixel 3D points) for each new input in an online fashion. These pointmaps reside within a common coordinate system, and can be accumulated into a coherent, dense scene reconstruction that updates as new images arrive. Our model, called CUT3R (Continuous Updating Transformer for 3D Reconstruction), captures rich priors of real-world scenes: not only can it predict accurate pointmaps from image observations, but it can also infer unseen regions of the scene by probing at virtual, unobserved views. Our method is simple yet highly flexible, naturally accepting varying lengths of images that may be either video streams or unordered photo collections, containing both static and dynamic content. We evaluate our method on various 3D/4D tasks and demonstrate competitive or state-of-the-art performance in each. Project Page: https://cut3r.github.io/

Few prior works study deep learning on point sets. PointNet by Qi et al. is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to recognize fine-grained patterns and generalizability to complex scenes. In this work, we introduce a hierarchical neural network that applies PointNet recursively on a nested partitioning of the input point set. By exploiting metric space distances, our network is able to learn local features with increasing contextual scales. With further observation that point sets are usually sampled with varying densities, which results in greatly decreased performance for networks trained on uniform densities, we propose novel set learning layers to adaptively combine features from multiple scales. Experiments show that our network called PointNet++ is able to learn deep point set features efficiently and robustly. In particular, results significantly better than state-of-the-art have been obtained on challenging benchmarks of 3D point clouds.

Heatmap representations have formed the basis of human pose estimation systems for many years, and their extension to 3D has been a fruitful line of recent research. This includes 2.5D volumetric heatmaps, whose X and Y axes correspond to image space and Z to metric depth around the subject. To obtain metric-scale predictions, 2.5D methods need a separate post-processing step to resolve scale ambiguity. Further, they cannot localize body joints outside the image boundaries, leading to incomplete estimates for truncated images. To address these limitations, we propose metric-scale truncation-robust (MeTRo) volumetric heatmaps, whose dimensions are all defined in metric 3D space, instead of being aligned with image space. This reinterpretation of heatmap dimensions allows us to directly estimate complete, metric-scale poses without test-time knowledge of distance or relying on anthropometric heuristics, such as bone lengths. To further demonstrate the utility our representation, we present a differentiable combination of our 3D metric-scale heatmaps with 2D image-space ones to estimate absolute 3D pose (our MeTRAbs architecture). We find that supervision via absolute pose loss is crucial for accurate non-root-relative localization. Using a ResNet-50 backbone without further learned layers, we obtain state-of-the-art results on Human3.6M, MPI-INF-3DHP and MuPoTS-3D. Our code will be made publicly available to facilitate further research.

We present AMB3R, a multi-view feed-forward model for dense 3D reconstruction on a metric-scale that addresses diverse 3D vision tasks. The key idea is to leverage a sparse, yet compact, volumetric scene representation as our backend, enabling geometric reasoning with spatial compactness. Although trained solely for multi-view reconstruction, we demonstrate that AMB3R can be seamlessly extended to uncalibrated visual odometry (online) or large-scale structure from motion without the need for task-specific fine-tuning or test-time optimization. Compared to prior pointmap-based models, our approach achieves state-of-the-art performance in camera pose, depth, and metric-scale estimation, 3D reconstruction, and even surpasses optimization-based SLAM and SfM methods with dense reconstruction priors on common benchmarks.

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their efficiency and scalability, the existing feature grids with linear indexing for continuous-space points can only provide degenerate linear latent space representations, and such representations cannot be adequately compensated to represent complex nonlinear signals by the following compact decoder. To address this problem while keeping the simplicity of a regular grid structure, our approach builds upon the standard grid-based paradigm by constructing multiple elementary metric grids as high-order terms to approximate complex nonlinearities, following the Taylor expansion principle. Furthermore, we enhance model compactness with hash encoding based on different sparsities of the grids to prevent detrimental hash collisions, and a high-order extrapolation decoder to reduce explicit grid storage requirements. experimental results on both 2D and 3D reconstructions demonstrate the superior fitting and rendering accuracy of the proposed method across diverse signal types, validating its robustness and generalizability. Code is available at https://github.com/wangshu31/MetricGrids}{https://github.com/wangshu31/MetricGrids.

Large-scale terrain scans are the basis for many important tasks, such as topographic mapping, forestry, agriculture, and infrastructure planning. The resulting point cloud data sets are so massive in size that even basic tasks like viewing take hours to days of pre-processing in order to create level-of-detail structures that allow inspecting the data set in their entirety in real time. In this paper, we propose a method that is capable of instantly visualizing massive country-sized scans with hundreds of billions of points. Upon opening the data set, we first load a sparse subsample of points and initialize an overview of the entire point cloud, immediately followed by a surface reconstruction process to generate higher-quality, hole-free heightmaps. As users start navigating towards a region of interest, we continue to prioritize the heightmap construction process to the user's viewpoint. Once a user zooms in closely, we load the full-resolution point cloud data for that region and update the corresponding height map textures with the full-resolution data. As users navigate elsewhere, full-resolution point data that is no longer needed is unloaded, but the updated heightmap textures are retained as a form of medium level of detail. Overall, our method constitutes a form of direct out-of-core rendering for massive point cloud data sets (terabytes, compressed) that requires no preprocessing and no additional disk space. Source code, executable, pre-trained model, and dataset are available at: https://github.com/cg-tuwien/lidarscout

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

Advances in deep learning recognition have led to accurate object detection with 2D images. However, these 2D perception methods are insufficient for complete 3D world information. Concurrently, advanced 3D shape estimation approaches focus on the shape itself, without considering metric scale. These methods cannot determine the accurate location and orientation of objects. To tackle this problem, we propose a framework that jointly estimates a metric scale shape and pose from a single RGB image. Our framework has two branches: the Metric Scale Object Shape branch (MSOS) and the Normalized Object Coordinate Space branch (NOCS). The MSOS branch estimates the metric scale shape observed in the camera coordinates. The NOCS branch predicts the normalized object coordinate space (NOCS) map and performs similarity transformation with the rendered depth map from a predicted metric scale mesh to obtain 6d pose and size. Additionally, we introduce the Normalized Object Center Estimation (NOCE) to estimate the geometrically aligned distance from the camera to the object center. We validated our method on both synthetic and real-world datasets to evaluate category-level object pose and shape.

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space. Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection. We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM. As one consequence, we apply this new insight to the task of outlier detection, and we demonstrate performance that is competitive or exceeds performance of state-of-the-art techniques on benchmark data sets. Under mild assumptions, we show the weighting vector, which has computational cost of matrix inversion, can be efficiently approximated in linear time. We show how nearest neighbor methods can approximate solutions to the minimization problems defined by SVMs.

This paper develops a hierarchical clustering algorithm for weighted projective spaces P_{q}, utilizing a Finsler metric d_F([z], [w]) and its rational analogue d_{F,Q}([z], [w]) to define distances that preserve the non-Euclidean geometry of these quotient manifolds. Defined via geodesic integrals of a scaling invariant Finsler norm weighted by the grades q = (q_0, q_1, dots, q_n), these metrics satisfy true metric properties including the triangle inequality, overcoming the limitations of the non-metric dissimilarity measure from prior work.

Metric space magnitude, an active subject of research in algebraic topology, originally arose in the context of biology, where it was used to represent the effective number of distinct species in an environment. In a more general setting, the magnitude of a metric space is a real number that aims to quantify the effective number of distinct points in the space. The contribution of each point to a metric space's global magnitude, which is encoded by the {\em weighting vector}, captures much of the underlying geometry of the original metric space. Surprisingly, when the metric space is Euclidean, the weighting vector also serves as an effective tool for boundary detection. This allows the weighting vector to serve as the foundation of novel algorithms for classic machine learning tasks such as classification, outlier detection and active learning. We demonstrate, using experiments and comparisons on classic benchmark datasets, the promise of the proposed magnitude and weighting vector-based approaches.

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Point clouds have shown significant potential in various domains, including Simultaneous Localization and Mapping (SLAM). However, existing approaches either rely on dense point clouds to achieve high localization accuracy or use generalized descriptors to reduce map size. Unfortunately, these two aspects seem to conflict with each other. To address this limitation, we propose a unified architecture, DeepPointMap, achieving excellent preference on both aspects. We utilize neural network to extract highly representative and sparse neural descriptors from point clouds, enabling memory-efficient map representation and accurate multi-scale localization tasks (e.g., odometry and loop-closure). Moreover, we showcase the versatility of our framework by extending it to more challenging multi-agent collaborative SLAM. The promising results obtained in these scenarios further emphasize the effectiveness and potential of our approach.

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric A as L^TL, the problem can be cast as looking for a linear map between two sets of points in different spaces, meanwhile maintaining some data structures. The ordinal relation of the labels can be maintained via classical multidimensional scaling, a popular tool for dimension reduction in statistics. A least squares fitting term is then introduced to the cost function, which can also maintain the local data structure. The resulting model is an unconstrained problem, and can better fit the data structure. Extensive numerical results demonstrate the improvement of the new approach over the linear distance metric learning model both in speed and ranking performance.

Autoregressive point cloud generation has long lagged behind diffusion-based approaches in quality. The performance gap stems from the fact that autoregressive models impose an artificial ordering on inherently unordered point sets, forcing shape generation to proceed as a sequence of local predictions. This sequential bias emphasizes short-range continuity but undermines the model's capacity to capture long-range dependencies, hindering its ability to enforce global structural properties such as symmetry, consistent topology, and large-scale geometric regularities. Inspired by the level-of-detail (LOD) principle in shape modeling, we propose PointNSP, a coarse-to-fine generative framework that preserves global shape structure at low resolutions and progressively refines fine-grained geometry at higher scales through a next-scale prediction paradigm. This multi-scale factorization aligns the autoregressive objective with the permutation-invariant nature of point sets, enabling rich intra-scale interactions while avoiding brittle fixed orderings. Experiments on ShapeNet show that PointNSP establishes state-of-the-art (SOTA) generation quality for the first time within the autoregressive paradigm. In addition, it surpasses strong diffusion-based baselines in parameter, training, and inference efficiency. Finally, in dense generation with 8,192 points, PointNSP's advantages become even more pronounced, underscoring its scalability potential.

Can we relocalize in a scene represented by a single reference image? Standard visual relocalization requires hundreds of images and scale calibration to build a scene-specific 3D map. In contrast, we propose Map-free Relocalization, i.e., using only one photo of a scene to enable instant, metric scaled relocalization. Existing datasets are not suitable to benchmark map-free relocalization, due to their focus on large scenes or their limited variability. Thus, we have constructed a new dataset of 655 small places of interest, such as sculptures, murals and fountains, collected worldwide. Each place comes with a reference image to serve as a relocalization anchor, and dozens of query images with known, metric camera poses. The dataset features changing conditions, stark viewpoint changes, high variability across places, and queries with low to no visual overlap with the reference image. We identify two viable families of existing methods to provide baseline results: relative pose regression, and feature matching combined with single-image depth prediction. While these methods show reasonable performance on some favorable scenes in our dataset, map-free relocalization proves to be a challenge that requires new, innovative solutions.

Estimating depth from a single image is a challenging visual task. Compared to relative depth estimation, metric depth estimation attracts more attention due to its practical physical significance and critical applications in real-life scenarios. However, existing metric depth estimation methods are typically trained on specific datasets with similar scenes, facing challenges in generalizing across scenes with significant scale variations. To address this challenge, we propose a novel monocular depth estimation method called ScaleDepth. Our method decomposes metric depth into scene scale and relative depth, and predicts them through a semantic-aware scale prediction (SASP) module and an adaptive relative depth estimation (ARDE) module, respectively. The proposed ScaleDepth enjoys several merits. First, the SASP module can implicitly combine structural and semantic features of the images to predict precise scene scales. Second, the ARDE module can adaptively estimate the relative depth distribution of each image within a normalized depth space. Third, our method achieves metric depth estimation for both indoor and outdoor scenes in a unified framework, without the need for setting the depth range or fine-tuning model. Extensive experiments demonstrate that our method attains state-of-the-art performance across indoor, outdoor, unconstrained, and unseen scenes. Project page: https://ruijiezhu94.github.io/ScaleDepth

Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in R^d. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a rm polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion, where Delta denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

Recent advances in 3D Gaussian Splatting (3DGS) have enabled real-time, photorealistic scene reconstruction. However, conventional 3DGS frameworks typically rely on sparse point clouds derived from Structure-from-Motion (SfM), which inherently suffer from scale ambiguity, limited geometric consistency, and strong view dependency due to the lack of geometric priors. In this work, a LiDAR-centric 3D Gaussian Splatting framework is proposed that explicitly incorporates metric geometric priors into the entire Gaussian optimization process. Instead of treating LiDAR data as a passive initialization source, 3DGS optimization is reformulated as a geometry-conditioned allocation and refinement problem under a fixed representational budget. Specifically, this work introduces (i) a geometry-texture-aware allocation strategy that selectively assigns Gaussian primitives to regions with high structural or appearance complexity, (ii) a curvature-adaptive refinement mechanism that dynamically guides Gaussian splitting toward geometrically complex areas during training, and (iii) a confidence-aware metric depth regularization that anchors the reconstructed geometry to absolute scale using LiDAR measurements while maintaining optimization stability. Extensive experiments on the ScanNet++ dataset and a custom real-world dataset validate the proposed approach. The results demonstrate state-of-the-art performance in metric-scale reconstruction with high geometric fidelity.

Visual navigation using only a single camera and a topological map has recently become an appealing alternative to methods that require additional sensors and 3D maps. This is typically achieved through an "image-relative" approach to estimating control from a given pair of current observation and subgoal image. However, image-level representations of the world have limitations because images are strictly tied to the agent's pose and embodiment. In contrast, objects, being a property of the map, offer an embodiment- and trajectory-invariant world representation. In this work, we present a new paradigm of learning "object-relative" control that exhibits several desirable characteristics: a) new routes can be traversed without strictly requiring to imitate prior experience, b) the control prediction problem can be decoupled from solving the image matching problem, and c) high invariance can be achieved in cross-embodiment deployment for variations across both training-testing and mapping-execution settings. We propose a topometric map representation in the form of a "relative" 3D scene graph, which is used to obtain more informative object-level global path planning costs. We train a local controller, dubbed "ObjectReact", conditioned directly on a high-level "WayObject Costmap" representation that eliminates the need for an explicit RGB input. We demonstrate the advantages of learning object-relative control over its image-relative counterpart across sensor height variations and multiple navigation tasks that challenge the underlying spatial understanding capability, e.g., navigating a map trajectory in the reverse direction. We further show that our sim-only policy is able to generalize well to real-world indoor environments. Code and supplementary material are accessible via project page: https://object-react.github.io/

We present a scalable 3D reconstruction model that addresses a critical limitation in offline feed-forward methods: their computational and memory requirements grow quadratically w.r.t. the number of input images. Our approach is built on the key insight that this bottleneck stems from the varying-length Key-Value (KV) space representation of scene geometry, which we distill into a fixed-size Multi-Layer Perceptron (MLP) via test-time training. VGG-T^3 (Visual Geometry Grounded Test Time Training) scales linearly w.r.t. the number of input views, similar to online models, and reconstructs a 1k image collection in just 54 seconds, achieving a 11.6times speed-up over baselines that rely on softmax attention. Since our method retains global scene aggregation capability, our point map reconstruction error outperforming other linear-time methods by large margins. Finally, we demonstrate visual localization capabilities of our model by querying the scene representation with unseen images.

Recently, state space models have exhibited strong global modeling capabilities and linear computational complexity in contrast to transformers. This research focuses on applying such architecture to more efficiently and effectively model point cloud data globally with linear computational complexity. In particular, for the first time, we demonstrate that Mamba-based point cloud methods can outperform previous methods based on transformer or multi-layer perceptrons (MLPs). To enable Mamba to process 3-D point cloud data more effectively, we propose a novel Consistent Traverse Serialization method to convert point clouds into 1-D point sequences while ensuring that neighboring points in the sequence are also spatially adjacent. Consistent Traverse Serialization yields six variants by permuting the order of x, y, and z coordinates, and the synergistic use of these variants aids Mamba in comprehensively observing point cloud data. Furthermore, to assist Mamba in handling point sequences with different orders more effectively, we introduce point prompts to inform Mamba of the sequence's arrangement rules. Finally, we propose positional encoding based on spatial coordinate mapping to inject positional information into point cloud sequences more effectively. Point Cloud Mamba surpasses the state-of-the-art (SOTA) point-based method PointNeXt and achieves new SOTA performance on the ScanObjectNN, ModelNet40, ShapeNetPart, and S3DIS datasets. It is worth mentioning that when using a more powerful local feature extraction module, our PCM achieves 79.6 mIoU on S3DIS, significantly surpassing the previous SOTA models, DeLA and PTv3, by 5.5 mIoU and 4.9 mIoU, respectively.

Scaling has powered recent advances in vision foundation models, yet extending this paradigm to metric depth estimation remains challenging due to heterogeneous sensor noise, camera-dependent biases, and metric ambiguity in noisy cross-source 3D data. We introduce Metric Anything, a simple and scalable pretraining framework that learns metric depth from noisy, diverse 3D sources without manually engineered prompts, camera-specific modeling, or task-specific architectures. Central to our approach is the Sparse Metric Prompt, created by randomly masking depth maps, which serves as a universal interface that decouples spatial reasoning from sensor and camera biases. Using about 20M image-depth pairs spanning reconstructed, captured, and rendered 3D data across 10000 camera models, we demonstrate-for the first time-a clear scaling trend in the metric depth track. The pretrained model excels at prompt-driven tasks such as depth completion, super-resolution and Radar-camera fusion, while its distilled prompt-free student achieves state-of-the-art results on monocular depth estimation, camera intrinsics recovery, single/multi-view metric 3D reconstruction, and VLA planning. We also show that using pretrained ViT of Metric Anything as a visual encoder significantly boosts Multimodal Large Language Model capabilities in spatial intelligence. These results show that metric depth estimation can benefit from the same scaling laws that drive modern foundation models, establishing a new path toward scalable and efficient real-world metric perception. We open-source MetricAnything at http://metric-anything.github.io/metric-anything-io/ to support community research.

Mapping is one of the crucial tasks enabling autonomous navigation of a mobile robot. Conventional mapping methods output a dense geometric map representation, e.g. an occupancy grid, which is not trivial to keep consistent for prolonged runs covering large environments. Meanwhile, capturing the topological structure of the workspace enables fast path planning, is typically less prone to odometry error accumulation, and does not consume much memory. Following this idea, this paper introduces PRISM-TopoMap -- a topological mapping method that maintains a graph of locally aligned locations not relying on global metric coordinates. The proposed method involves original learnable multimodal place recognition paired with the scan matching pipeline for localization and loop closure in the graph of locations. The latter is updated online, and the robot is localized in a proper node at each time step. We conduct a broad experimental evaluation of the suggested approach in a range of photo-realistic environments and on a real robot, and compare it to state of the art. The results of the empirical evaluation confirm that PRISM-Topomap consistently outperforms competitors computationally-wise, achieves high mapping quality and performs well on a real robot. The code of PRISM-Topomap is open-sourced and is available at: https://github.com/kirillMouraviev/prism-topomap.

The magnitude of a finite metric space has recently emerged as a novel invariant quantity, allowing to measure the effective size of a metric space. Despite encouraging first results demonstrating the descriptive abilities of the magnitude, such as being able to detect the boundary of a metric space, the potential use cases of magnitude remain under-explored. In this work, we investigate the properties of the magnitude on images, an important data modality in many machine learning applications. By endowing each individual images with its own metric space, we are able to define the concept of magnitude on images and analyse the individual contribution of each pixel with the magnitude vector. In particular, we theoretically show that the previously known properties of boundary detection translate to edge detection abilities in images. Furthermore, we demonstrate practical use cases of magnitude for machine learning applications and propose a novel magnitude model that consists of a computationally efficient magnitude computation and a learnable metric. By doing so, we address the computational hurdle that used to make magnitude impractical for many applications and open the way for the adoption of magnitude in machine learning research.

The shadow of an abstract simplicial complex K with vertices in R^N is a subset of R^N defined as the union of the convex hulls of simplices of K. The Vietoris--Rips complex of a metric space (S,d) at scale β is an abstract simplicial complex whose each k-simplex corresponds to (k+1) points of S within diameter β. In case Ssubsetmathbb R^2 and d(a,b)=|a-b| the standard Euclidean metric, the natural shadow projection of the Vietoris--Rips complex is already proved by Chambers et al. to induce isomorphisms on π_0 and π_1. We extend the result beyond the standard Euclidean distance on Ssubsetmathbb R^N to a family of path-based metrics, d^varepsilon_{S}. From the pairwise Euclidean distances of points in S, we introduce a family (parametrized by varepsilon) of path-based Vietoris--Rips complexes R^varepsilon_β(S) for a scale β>0. If SsubsetR^2 is Hausdorff-close to a planar Euclidean graph G, we provide quantitative bounds on scales β,varepsilon for the shadow projection map of the Vietoris--Rips complex of (S,d^varepsilon_S) at scale β to induce π_1-isomorphism. This paper first studies the homotopy-type recovery of Gsubsetmathbb R^N using the abstract Vietoris--Rips complex of a Hausdorff-close sample S under the d^varepsilon_S metric. Then, our result on the π_1-isomorphism induced by the shadow projection lends itself to providing also a geometrically close embedding for the reconstruction. Based on the length of the shortest loop and large-scale distortion of the embedding of G, we quantify the choice of a suitable sample density varepsilon and a scale β at which the shadow of R^varepsilon_β(S) is homotopy-equivalent and Hausdorff-close to G.

Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc. Current studies put much focus on the adaption of neural networks to the complex geometries of point clouds, but are blind to a fundamental question: how to learn an appropriate point embedding space that is aware of both discriminative semantics and challenging variations? As a response, we propose a clustering based supervised learning scheme for point cloud analysis. Unlike current de-facto, scene-wise training paradigm, our algorithm conducts within-class clustering on the point embedding space for automatically discovering subclass patterns which are latent yet representative across scenes. The mined patterns are, in turn, used to repaint the embedding space, so as to respect the underlying distribution of the entire training dataset and improve the robustness to the variations. Our algorithm is principled and readily pluggable to modern point cloud segmentation networks during training, without extra overhead during testing. With various 3D network architectures (i.e., voxel-based, point-based, Transformer-based, automatically searched), our algorithm shows notable improvements on famous point cloud segmentation datasets (i.e.,2.0-2.6% on single-scan and 2.0-2.2% multi-scan of SemanticKITTI, 1.8-1.9% on S3DIS, in terms of mIoU). Our algorithm also demonstrates utility in 3D detection, showing 2.0-3.4% mAP gains on KITTI.

Reconstructing accurate 3D scenes from images is a long-standing vision task. Due to the ill-posedness of the single-image reconstruction problem, most well-established methods are built upon multi-view geometry. State-of-the-art (SOTA) monocular metric depth estimation methods can only handle a single camera model and are unable to perform mixed-data training due to the metric ambiguity. Meanwhile, SOTA monocular methods trained on large mixed datasets achieve zero-shot generalization by learning affine-invariant depths, which cannot recover real-world metrics. In this work, we show that the key to a zero-shot single-view metric depth model lies in the combination of large-scale data training and resolving the metric ambiguity from various camera models. We propose a canonical camera space transformation module, which explicitly addresses the ambiguity problems and can be effortlessly plugged into existing monocular models. Equipped with our module, monocular models can be stably trained with over 8 million images with thousands of camera models, resulting in zero-shot generalization to in-the-wild images with unseen camera settings. Experiments demonstrate SOTA performance of our method on 7 zero-shot benchmarks. Notably, our method won the championship in the 2nd Monocular Depth Estimation Challenge. Our method enables the accurate recovery of metric 3D structures on randomly collected internet images, paving the way for plausible single-image metrology. The potential benefits extend to downstream tasks, which can be significantly improved by simply plugging in our model. For example, our model relieves the scale drift issues of monocular-SLAM (Fig. 1), leading to high-quality metric scale dense mapping. The code is available at https://github.com/YvanYin/Metric3D.

LiDAR-based SLAM is a core technology for autonomous vehicles and robots. One key contribution of this work to 3D LiDAR SLAM and localization is a fierce defense of view-based maps (pose graphs with time-stamped sensor readings) as the fundamental representation of maps. As will be shown, they allow for the greatest flexibility, enabling the posterior generation of arbitrary metric maps optimized for particular tasks, e.g. obstacle avoidance, real-time localization. Moreover, this work introduces a new framework in which mapping pipelines can be defined without coding, defining the connections of a network of reusable blocks much like deep-learning networks are designed by connecting layers of standardized elements. We also introduce tightly-coupled estimation of linear and angular velocity vectors within the Iterative Closest Point (ICP)-like optimizer, leading to superior robustness against aggressive motion profiles without the need for an IMU. Extensive experimental validation reveals that the proposal compares well to, or improves, former state-of-the-art (SOTA) LiDAR odometry systems, while also successfully mapping some hard sequences where others diverge. A proposed self-adaptive configuration has been used, without parameter changes, for all 3D LiDAR datasets with sensors between 16 and 128 rings, and has been extensively tested on 83 sequences over more than 250~km of automotive, hand-held, airborne, and quadruped LiDAR datasets, both indoors and outdoors. The system flexibility is demonstrated with additional configurations for 2D LiDARs and for building 3D NDT-like maps. The framework is open-sourced online: https://github.com/MOLAorg/mola

In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles. Local approximations obtained by local PCAs are collected into a rank k tangent subbundle on R^d, k<d, which we call a principal subbundle. This determines a sub-Riemannian metric on R^d. We show that sub-Riemannian geodesics with respect to this metric can successfully be applied to a number of important problems, such as: explicit construction of an approximating submanifold M, construction of a representation of the point-cloud in R^k, and computation of distances between observations, taking the learned geometry into account. The reconstruction is guaranteed to equal the true submanifold in the limit case where tangent spaces are estimated exactly. Via simulations, we show that the framework is robust when applied to noisy data. Furthermore, the framework generalizes to observations on an a priori known Riemannian manifold.

In statistics, independent, identically distributed random samples do not carry a natural ordering, and their statistics are typically invariant with respect to permutations of their order. Thus, an n-sample in a space M can be considered as an element of the quotient space of M^n modulo the permutation group. The present paper takes this definition of sample space and the related concept of orbit types as a starting point for developing a geometric perspective on statistics. We aim at deriving a general mathematical setting for studying the behavior of empirical and population means in spaces ranging from smooth Riemannian manifolds to general stratified spaces. We fully describe the orbifold and path-metric structure of the sample space when M is a manifold or path-metric space, respectively. These results are non-trivial even when M is Euclidean. We show that the infinite sample space exists in a Gromov-Hausdorff type sense and coincides with the Wasserstein space of probability distributions on M. We exhibit Fr\'echet means and k-means as metric projections onto 1-skeleta or k-skeleta in Wasserstein space, and we define a new and more general notion of polymeans. This geometric characterization via metric projections applies equally to sample and population means, and we use it to establish asymptotic properties of polymeans such as consistency and asymptotic normality.

Recent approaches representing 3D objects and scenes using Gaussian splats show increased rendering speed across a variety of platforms and devices. While rendering such representations is indeed extremely efficient, storing and transmitting them is often prohibitively expensive. To represent large-scale scenes, one often needs to store millions of 3D Gaussians, occupying gigabytes of disk space. This poses a very practical limitation, prohibiting widespread adoption.Several solutions have been proposed to strike a balance between disk size and rendering quality, noticeably reducing the visual quality. In this work, we propose a new representation that dramatically reduces the hard drive footprint while featuring similar or improved quality when compared to the standard 3D Gaussian splats. When compared to other compact solutions, ours offers higher quality renderings with significantly reduced storage, being able to efficiently run on a mobile device in real-time. Our key observation is that nearby points in the scene can share similar representations. Hence, only a small ratio of 3D points needs to be stored. We introduce an approach to identify such points which are called parent points. The discarded points called children points along with attributes can be efficiently predicted by tiny MLPs.

The irregularity and permutation invariance of point cloud data pose challenges for effective learning. Conventional methods for addressing this issue involve converting raw point clouds to intermediate representations such as 3D voxel grids or range images. While such intermediate representations solve the problem of permutation invariance, they can result in significant loss of information. Approaches that do learn on raw point clouds either have trouble in resolving neighborhood relationships between points or are too complicated in their formulation. In this paper, we propose a novel approach to representing point clouds as a locality preserving 1D ordering induced by the Hilbert space-filling curve. We also introduce Point2Point, a neural architecture that can effectively learn on Hilbert-sorted point clouds. We show that Point2Point shows competitive performance on point cloud segmentation and generation tasks. Finally, we show the performance of Point2Point on Spatio-temporal Occupancy prediction from Point clouds.

High-fidelity human 3D models can now be learned directly from videos, typically by combining a template-based surface model with neural representations. However, obtaining a template surface requires expensive multi-view capture systems, laser scans, or strictly controlled conditions. Previous methods avoid using a template but rely on a costly or ill-posed mapping from observation to canonical space. We propose a hybrid point-based representation for reconstructing animatable characters that does not require an explicit surface model, while being generalizable to novel poses. For a given video, our method automatically produces an explicit set of 3D points representing approximate canonical geometry, and learns an articulated deformation model that produces pose-dependent point transformations. The points serve both as a scaffold for high-frequency neural features and an anchor for efficiently mapping between observation and canonical space. We demonstrate on established benchmarks that our representation overcomes limitations of prior work operating in either canonical or in observation space. Moreover, our automatic point extraction approach enables learning models of human and animal characters alike, matching the performance of the methods using rigged surface templates despite being more general. Project website: https://lemonatsu.github.io/npc/

Powerful 3D representations such as DUSt3R invariant point maps, which encode 3D shape and camera parameters, have significantly advanced feed forward 3D reconstruction. While point maps assume static scenes, Dynamic Point Maps (DPMs) extend this concept to dynamic 3D content by additionally representing scene motion. However, existing DPMs are limited to image pairs and, like DUSt3R, require post processing via optimization when more than two views are involved. We argue that DPMs are more useful when applied to videos and introduce V-DPM to demonstrate this. First, we show how to formulate DPMs for video input in a way that maximizes representational power, facilitates neural prediction, and enables reuse of pretrained models. Second, we implement these ideas on top of VGGT, a recent and powerful 3D reconstructor. Although VGGT was trained on static scenes, we show that a modest amount of synthetic data is sufficient to adapt it into an effective V-DPM predictor. Our approach achieves state of the art performance in 3D and 4D reconstruction for dynamic scenes. In particular, unlike recent dynamic extensions of VGGT such as P3, DPMs recover not only dynamic depth but also the full 3D motion of every point in the scene.

Large-scale pre-training has shown promising results on the vision-and-language navigation (VLN) task. However, most existing pre-training methods employ discrete panoramas to learn visual-textual associations. This requires the model to implicitly correlate incomplete, duplicate observations within the panoramas, which may impair an agent's spatial understanding. Thus, we propose a new map-based pre-training paradigm that is spatial-aware for use in VLN. Concretely, we build a local metric map to explicitly aggregate incomplete observations and remove duplicates, while modeling navigation dependency in a global topological map. This hybrid design can balance the demand of VLN for both short-term reasoning and long-term planning. Then, based on the hybrid map, we devise a pre-training framework to learn a multimodal map representation, which enhances spatial-aware cross-modal reasoning thereby facilitating the language-guided navigation goal. Extensive experiments demonstrate the effectiveness of the map-based pre-training route for VLN, and the proposed method achieves state-of-the-art on four VLN benchmarks.

GUI grounding, the task of mapping natural-language instructions to pixel coordinates, is crucial for autonomous agents, yet remains difficult for current VLMs. The core bottleneck is reliable patch-to-pixel mapping, which breaks when extrapolating to high-resolution displays unseen during training. Current approaches generate coordinates as text tokens directly from visual features, forcing the model to infer complex position-to-pixel mappings implicitly; as a result, accuracy degrades and failures proliferate on new resolutions. We address this with two complementary innovations. First, RULER tokens serve as explicit coordinate markers, letting the model reference positions similar to gridlines on a map and adjust rather than generate coordinates from scratch. Second, Interleaved MRoPE (I-MRoPE) improves spatial encoding by ensuring that width and height dimensions are represented equally, addressing the asymmetry of standard positional schemes. Experiments on ScreenSpot, ScreenSpot-V2, and ScreenSpot-Pro show consistent gains in grounding accuracy, with the largest improvements on high-resolution interfaces. By providing explicit spatial guidance rather than relying on implicit learning, our approach enables more reliable GUI automation across diverse resolutions and platforms.

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths have been designed principally under the assumption of Euclidean geometry, resulting in straight interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals. In this paper, we propose Metric Flow Matching (MFM), a novel simulation-free framework for conditional flow matching where interpolants are approximate geodesics learned by minimizing the kinetic energy of a data-induced Riemannian metric. This way, the generative model matches vector fields on the data manifold, which corresponds to lower uncertainty and more meaningful interpolations. We prescribe general metrics to instantiate MFM, independent of the task, and test it on a suite of challenging problems including LiDAR navigation, unpaired image translation, and modeling cellular dynamics. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction.

Autonomous driving for urban and highway driving applications often requires High Definition (HD) maps to generate a navigation plan. Nevertheless, various challenges arise when generating and maintaining HD maps at scale. While recent online mapping methods have started to emerge, their performance especially for longer ranges is limited by heavy occlusion in dynamic environments. With these considerations in mind, our work focuses on leveraging lightweight and scalable priors-Standard Definition (SD) maps-in the development of online vectorized HD map representations. We first examine the integration of prototypical rasterized SD map representations into various online mapping architectures. Furthermore, to identify lightweight strategies, we extend the OpenLane-V2 dataset with OpenStreetMaps and evaluate the benefits of graphical SD map representations. A key finding from designing SD map integration components is that SD map encoders are model agnostic and can be quickly adapted to new architectures that utilize bird's eye view (BEV) encoders. Our results show that making use of SD maps as priors for the online mapping task can significantly speed up convergence and boost the performance of the online centerline perception task by 30% (mAP). Furthermore, we show that the introduction of the SD maps leads to a reduction of the number of parameters in the perception and reasoning task by leveraging SD map graphs while improving the overall performance. Project Page: https://henryzhangzhy.github.io/sdhdmap/.

Recent advances in camera-controllable video generation have been constrained by the reliance on static-scene datasets with relative-scale camera annotations, such as RealEstate10K. While these datasets enable basic viewpoint control, they fail to capture dynamic scene interactions and lack metric-scale geometric consistency-critical for synthesizing realistic object motions and precise camera trajectories in complex environments. To bridge this gap, we introduce the first fully open-source, high-resolution dynamic-scene dataset with metric-scale camera annotations in https://github.com/ZGCTroy/RealCam-Vid.

Magnitude of a finite metric space and the related notion of magnitude functions on metric spaces is an active area of research in algebraic topology. Magnitude originally arose in the context of biology, where it represents the number of effective species in an environment; when applied to a one-parameter family of metric spaces tX with scale parameter t, the magnitude captures much of the underlying geometry of the space. Prior work has mostly focussed on properties of magnitude in a global sense; in this paper we restrict the sets to finite subsets of Euclidean space and investigate its individual components. We give an explicit formula for the corrected inclusion-exclusion principle, and define a quantity associated with each point, called the moment which gives an intrinsic ordering to the points. We exploit this in order to form an algorithm which approximates the convex hull.

Point cloud classification is one of the essential technologies for achieving intelligent perception of 3D environments by machines, its core challenge is to efficiently extract local and global features. Mamba leverages state space models (SSMs) for global point cloud modeling. Although prior Mamba-based point cloud processing methods pay attention to the limitation of its flattened sequence modeling mechanism in fusing local and global features, the critical issue of weakened local geometric relevance caused by decoupling geometric structures and features in the input patches remains not fully revealed, and both jointly limit local feature extraction. Therefore, we propose HyMamba, a geometry and feature coupled Mamba framework featuring: (1) Geometry-Feature Coupled Pooling (GFCP), which achieves physically interpretable geometric information coupling by dynamically aggregating adjacent geometric information into local features; (2) Collaborative Feature Enhancer (CoFE), which enhances sparse signal capture through cross-path feature hybridization while effectively integrating global and local contexts. We conducted extensive experiments on ModelNet40 and ScanObjectNN datasets. The results demonstrate that the proposed model achieves superior classification performance, particularly on the ModelNet40, where it elevates accuracy to 95.99% with merely 0.03M additional parameters. Furthermore, it attains 98.9% accuracy on the ModelNetFewShot dataset, validating its robust generalization capabilities under sparse samples. Our code and weights are available at https://github.com/L1277471578/HyMamba

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data, and on estimating local Hessian matrices of neural network loss landscapes.

We present LASER, an image-based Monte Carlo Localization (MCL) framework for 2D floor maps. LASER introduces the concept of latent space rendering, where 2D pose hypotheses on the floor map are directly rendered into a geometrically-structured latent space by aggregating viewing ray features. Through a tightly coupled rendering codebook scheme, the viewing ray features are dynamically determined at rendering-time based on their geometries (i.e. length, incident-angle), endowing our representation with view-dependent fine-grain variability. Our codebook scheme effectively disentangles feature encoding from rendering, allowing the latent space rendering to run at speeds above 10KHz. Moreover, through metric learning, our geometrically-structured latent space is common to both pose hypotheses and query images with arbitrary field of views. As a result, LASER achieves state-of-the-art performance on large-scale indoor localization datasets (i.e. ZInD and Structured3D) for both panorama and perspective image queries, while significantly outperforming existing learning-based methods in speed.

In this paper, we introduce MapBench-the first dataset specifically designed for human-readable, pixel-based map-based outdoor navigation, curated from complex path finding scenarios. MapBench comprises over 1600 pixel space map path finding problems from 100 diverse maps. In MapBench, LVLMs generate language-based navigation instructions given a map image and a query with beginning and end landmarks. For each map, MapBench provides Map Space Scene Graph (MSSG) as an indexing data structure to convert between natural language and evaluate LVLM-generated results. We demonstrate that MapBench significantly challenges state-of-the-art LVLMs both zero-shot prompting and a Chain-of-Thought (CoT) augmented reasoning framework that decomposes map navigation into sequential cognitive processes. Our evaluation of both open-source and closed-source LVLMs underscores the substantial difficulty posed by MapBench, revealing critical limitations in their spatial reasoning and structured decision-making capabilities. We release all the code and dataset in https://github.com/taco-group/MapBench.

We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC synthesizes desirable features from spectral clustering and topological data analysis and is based on considering the spectral properties of a simplicial complex associated to the considered point cloud. As it is based on considering sparse eigenvector computations, TPCC is similarly easy to interpret and implement as spectral clustering. However, by focusing not just on a single matrix associated to a graph created from the point cloud data, but on a whole set of Hodge-Laplacians associated to an appropriately constructed simplicial complex, we can leverage a far richer set of topological features to characterize the data points within the point cloud and benefit from the relative robustness of topological techniques against noise. We test the performance of TPCC on both synthetic and real-world data and compare it with classical spectral clustering.

Depth maps are widely used in feed-forward 3D Gaussian Splatting (3DGS) pipelines by unprojecting them into 3D point clouds for novel view synthesis. This approach offers advantages such as efficient training, the use of known camera poses, and accurate geometry estimation. However, depth discontinuities at object boundaries often lead to fragmented or sparse point clouds, degrading rendering quality -- a well-known limitation of depth-based representations. To tackle this issue, we introduce PM-Loss, a novel regularization loss based on a pointmap predicted by a pre-trained transformer. Although the pointmap itself may be less accurate than the depth map, it effectively enforces geometric smoothness, especially around object boundaries. With the improved depth map, our method significantly improves the feed-forward 3DGS across various architectures and scenes, delivering consistently better rendering results. Our project page: https://aim-uofa.github.io/PMLoss

Mapping is crucial for spatial reasoning, planning and robot navigation. Existing approaches range from metric, which require precise geometry-based optimization, to purely topological, where image-as-node based graphs lack explicit object-level reasoning and interconnectivity. In this paper, we propose a novel topological representation of an environment based on "image segments", which are semantically meaningful and open-vocabulary queryable, conferring several advantages over previous works based on pixel-level features. Unlike 3D scene graphs, we create a purely topological graph with segments as nodes, where edges are formed by a) associating segment-level descriptors between pairs of consecutive images and b) connecting neighboring segments within an image using their pixel centroids. This unveils a "continuous sense of a place", defined by inter-image persistence of segments along with their intra-image neighbours. It further enables us to represent and update segment-level descriptors through neighborhood aggregation using graph convolution layers, which improves robot localization based on segment-level retrieval. Using real-world data, we show how our proposed map representation can be used to i) generate navigation plans in the form of "hops over segments" and ii) search for target objects using natural language queries describing spatial relations of objects. Furthermore, we quantitatively analyze data association at the segment level, which underpins inter-image connectivity during mapping and segment-level localization when revisiting the same place. Finally, we show preliminary trials on segment-level `hopping' based zero-shot real-world navigation. Project page with supplementary details: oravus.github.io/RoboHop/

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

While scaling laws have transformed natural language processing and computer vision, 3D point cloud understanding has yet to reach that stage. This can be attributed to both the comparatively smaller scale of 3D datasets, as well as the disparate sources of the data itself. Point clouds are captured by diverse sensors (e.g., depth cameras, LiDAR) across varied domains (e.g., indoor, outdoor), each introducing unique scanning patterns, sampling densities, and semantic biases. Such domain heterogeneity poses a major barrier towards training unified models at scale, especially under the realistic constraint that domain labels are typically inaccessible at inference time. In this work, we propose Point-MoE, a Mixture-of-Experts architecture designed to enable large-scale, cross-domain generalization in 3D perception. We show that standard point cloud backbones degrade significantly in performance when trained on mixed-domain data, whereas Point-MoE with a simple top-k routing strategy can automatically specialize experts, even without access to domain labels. Our experiments demonstrate that Point-MoE not only outperforms strong multi-domain baselines but also generalizes better to unseen domains. This work highlights a scalable path forward for 3D understanding: letting the model discover structure in diverse 3D data, rather than imposing it via manual curation or domain supervision.

Recent advancements in visual localization and mapping have demonstrated considerable success in integrating point and line features. However, expanding the localization framework to include additional mapping components frequently results in increased demand for memory and computational resources dedicated to matching tasks. In this study, we show how a lightweight neural network can learn to represent both 3D point and line features, and exhibit leading pose accuracy by harnessing the power of multiple learned mappings. Specifically, we utilize a single transformer block to encode line features, effectively transforming them into distinctive point-like descriptors. Subsequently, we treat these point and line descriptor sets as distinct yet interconnected feature sets. Through the integration of self- and cross-attention within several graph layers, our method effectively refines each feature before regressing 3D maps using two simple MLPs. In comprehensive experiments, our indoor localization findings surpass those of Hloc and Limap across both point-based and line-assisted configurations. Moreover, in outdoor scenarios, our method secures a significant lead, marking the most considerable enhancement over state-of-the-art learning-based methodologies. The source code and demo videos of this work are publicly available at: https://thpjp.github.io/pl2map/

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work, we equip a set of graphs with the pseudometric defined by the norm between the eigenvalues of their respective adjacency matrix. Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems for graph-valued data. We describe an algorithm to compute an approximation to the sample Frechet mean of a set of undirected unweighted graphs with a fixed size using this pseudometric.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

This paper proposes a general solution to enable point cloud recognition models to handle distribution shifts at test time. Unlike prior methods, which rely heavily on training data (often inaccessible during online inference) and are limited to recognizing a fixed set of point cloud classes predefined during training, we explore a more practical and challenging scenario: adapting the model solely based on online test data to recognize both previously seen classes and novel, unseen classes at test time. To this end, we develop Point-Cache, a hierarchical cache model that captures essential clues of online test samples, particularly focusing on the global structure of point clouds and their local-part details. Point-Cache, which serves as a rich 3D knowledge base, is dynamically managed to prioritize the inclusion of high-quality samples. Designed as a plug-and-play module, our method can be flexibly integrated into large multimodal 3D models to support open-vocabulary point cloud recognition. Notably, our solution operates with efficiency comparable to zero-shot inference, as it is entirely training-free. Point-Cache demonstrates substantial gains across 8 challenging benchmarks and 4 representative large 3D models, highlighting its effectiveness. Code is available at https://github.com/auniquesun/Point-Cache.

Symmetric Positive Definite (SPD) matrices are ubiquitous in data analysis under the form of covariance matrices or correlation matrices. Several O(n)-invariant Riemannian metrics were defined on the SPD cone, in particular the kernel metrics introduced by Hiai and Petz. The class of kernel metrics interpolates between many classical O(n)-invariant metrics and it satisfies key results of stability and completeness. However, it does not contain all the classical O(n)-invariant metrics. Therefore in this work, we investigate super-classes of kernel metrics and we study which key results remain true. We also introduce an additional key result called cometric-stability, a crucial property to implement geodesics with a Hamiltonian formulation. Our method to build intermediate embedded classes between O(n)-invariant metrics and kernel metrics is to give a characterization of the whole class of O(n)-invariant metrics on SPD matrices and to specify requirements on metrics one by one until we reach kernel metrics. As a secondary contribution, we synthesize the literature on the main O(n)-invariant metrics, we provide the complete formula of the sectional curvature of the affine-invariant metric and the formula of the geodesic parallel transport between commuting matrices for the Bures-Wasserstein metric.

We present HI-SLAM2, a geometry-aware Gaussian SLAM system that achieves fast and accurate monocular scene reconstruction using only RGB input. Existing Neural SLAM or 3DGS-based SLAM methods often trade off between rendering quality and geometry accuracy, our research demonstrates that both can be achieved simultaneously with RGB input alone. The key idea of our approach is to enhance the ability for geometry estimation by combining easy-to-obtain monocular priors with learning-based dense SLAM, and then using 3D Gaussian splatting as our core map representation to efficiently model the scene. Upon loop closure, our method ensures on-the-fly global consistency through efficient pose graph bundle adjustment and instant map updates by explicitly deforming the 3D Gaussian units based on anchored keyframe updates. Furthermore, we introduce a grid-based scale alignment strategy to maintain improved scale consistency in prior depths for finer depth details. Through extensive experiments on Replica, ScanNet, and ScanNet++, we demonstrate significant improvements over existing Neural SLAM methods and even surpass RGB-D-based methods in both reconstruction and rendering quality. The project page and source code will be made available at https://hi-slam2.github.io/.

Vectorized high-definition map online construction has garnered considerable attention in the field of autonomous driving research. Most existing approaches model changeable map elements using a fixed number of points, or predict local maps in a two-stage autoregressive manner, which may miss essential details and lead to error accumulation. Towards precise map element learning, we propose a simple yet effective architecture named PivotNet, which adopts unified pivot-based map representations and is formulated as a direct set prediction paradigm. Concretely, we first propose a novel point-to-line mask module to encode both the subordinate and geometrical point-line priors in the network. Then, a well-designed pivot dynamic matching module is proposed to model the topology in dynamic point sequences by introducing the concept of sequence matching. Furthermore, to supervise the position and topology of the vectorized point predictions, we propose a dynamic vectorized sequence loss. Extensive experiments and ablations show that PivotNet is remarkably superior to other SOTAs by 5.9 mAP at least. The code will be available soon.

Recent advancements in self-supervised learning in the point cloud domain have demonstrated significant potential. However, these methods often suffer from drawbacks, including lengthy pre-training time, the necessity of reconstruction in the input space, or the necessity of additional modalities. In order to address these issues, we introduce Point-JEPA, a joint embedding predictive architecture designed specifically for point cloud data. To this end, we introduce a sequencer that orders point cloud patch embeddings to efficiently compute and utilize their proximity based on the indices during target and context selection. The sequencer also allows shared computations of the patch embeddings' proximity between context and target selection, further improving the efficiency. Experimentally, our method achieves competitive results with state-of-the-art methods while avoiding the reconstruction in the input space or additional modality.

Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty arising when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by hedging the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle. Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of hedging its bets across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure that is correlated with downstream performance.

Existing fully-supervised point cloud segmentation methods suffer in the dynamic testing environment with emerging new classes. Few-shot point cloud segmentation algorithms address this problem by learning to adapt to new classes at the sacrifice of segmentation accuracy for the base classes, which severely impedes its practicality. This largely motivates us to present the first attempt at a more practical paradigm of generalized few-shot point cloud segmentation, which requires the model to generalize to new categories with only a few support point clouds and simultaneously retain the capability to segment base classes. We propose the geometric words to represent geometric components shared between the base and novel classes, and incorporate them into a novel geometric-aware semantic representation to facilitate better generalization to the new classes without forgetting the old ones. Moreover, we introduce geometric prototypes to guide the segmentation with geometric prior knowledge. Extensive experiments on S3DIS and ScanNet consistently illustrate the superior performance of our method over baseline methods. Our code is available at: https://github.com/Pixie8888/GFS-3DSeg_GWs.

We investigate a general formulation for clustering and transductive few-shot learning, which integrates prototype-based objectives, Laplacian regularization and supervision constraints from a few labeled data points. We propose a concave-convex relaxation of the problem, and derive a computationally efficient block-coordinate bound optimizer, with convergence guarantee. At each iteration,our optimizer computes independent (parallel) updates for each point-to-cluster assignment. Therefore, it could be trivially distributed for large-scale clustering and few-shot tasks. Furthermore, we provides a thorough convergence analysis based on point-to-set maps. Were port comprehensive clustering and few-shot learning experiments over various data sets, showing that our method yields competitive performances, in term of accuracy and optimization quality, while scaling up to large problems. Using standard training on the base classes, without resorting to complex meta-learning and episodic-training strategies, our approach outperforms state-of-the-art few-shot methods by significant margins, across various models, settings and data sets. Surprisingly, we found that even standard clustering procedures (e.g., K-means), which correspond to particular, non-regularized cases of our general model, already achieve competitive performances in comparison to the state-of-the-art in few-shot learning. These surprising results point to the limitations of the current few-shot benchmarks, and question the viability of a large body of convoluted few-shot learning techniques in the recent literature.

Monocular depth estimation is scale-ambiguous, and thus requires scale supervision to produce metric predictions. Even so, the resulting models will be geometry-specific, with learned scales that cannot be directly transferred across domains. Because of that, recent works focus instead on relative depth, eschewing scale in favor of improved up-to-scale zero-shot transfer. In this work we introduce ZeroDepth, a novel monocular depth estimation framework capable of predicting metric scale for arbitrary test images from different domains and camera parameters. This is achieved by (i) the use of input-level geometric embeddings that enable the network to learn a scale prior over objects; and (ii) decoupling the encoder and decoder stages, via a variational latent representation that is conditioned on single frame information. We evaluated ZeroDepth targeting both outdoor (KITTI, DDAD, nuScenes) and indoor (NYUv2) benchmarks, and achieved a new state-of-the-art in both settings using the same pre-trained model, outperforming methods that train on in-domain data and require test-time scaling to produce metric estimates.

Visual navigation in robotics traditionally relies on globally-consistent 3D maps or learned controllers, which can be computationally expensive and difficult to generalize across diverse environments. In this work, we present a novel RGB-only, object-level topometric navigation pipeline that enables zero-shot, long-horizon robot navigation without requiring 3D maps or pre-trained controllers. Our approach integrates global topological path planning with local metric trajectory control, allowing the robot to navigate towards object-level sub-goals while avoiding obstacles. We address key limitations of previous methods by continuously predicting local trajectory using monocular depth and traversability estimation, and incorporating an auto-switching mechanism that falls back to a baseline controller when necessary. The system operates using foundational models, ensuring open-set applicability without the need for domain-specific fine-tuning. We demonstrate the effectiveness of our method in both simulated environments and real-world tests, highlighting its robustness and deployability. Our approach outperforms existing state-of-the-art methods, offering a more adaptable and effective solution for visual navigation in open-set environments. The source code is made publicly available: https://github.com/podgorki/TANGO.

Maps are a key component in image-based camera localization and visual SLAM systems: they are used to establish geometric constraints between images, correct drift in relative pose estimation, and relocalize cameras after lost tracking. The exact definitions of maps, however, are often application-specific and hand-crafted for different scenarios (e.g. 3D landmarks, lines, planes, bags of visual words). We propose to represent maps as a deep neural net called MapNet, which enables learning a data-driven map representation. Unlike prior work on learning maps, MapNet exploits cheap and ubiquitous sensory inputs like visual odometry and GPS in addition to images and fuses them together for camera localization. Geometric constraints expressed by these inputs, which have traditionally been used in bundle adjustment or pose-graph optimization, are formulated as loss terms in MapNet training and also used during inference. In addition to directly improving localization accuracy, this allows us to update the MapNet (i.e., maps) in a self-supervised manner using additional unlabeled video sequences from the scene. We also propose a novel parameterization for camera rotation which is better suited for deep-learning based camera pose regression. Experimental results on both the indoor 7-Scenes dataset and the outdoor Oxford RobotCar dataset show significant performance improvement over prior work. The MapNet project webpage is https://goo.gl/mRB3Au.

We present SHARP, an approach to photorealistic view synthesis from a single image. Given a single photograph, SHARP regresses the parameters of a 3D Gaussian representation of the depicted scene. This is done in less than a second on a standard GPU via a single feedforward pass through a neural network. The 3D Gaussian representation produced by SHARP can then be rendered in real time, yielding high-resolution photorealistic images for nearby views. The representation is metric, with absolute scale, supporting metric camera movements. Experimental results demonstrate that SHARP delivers robust zero-shot generalization across datasets. It sets a new state of the art on multiple datasets, reducing LPIPS by 25-34% and DISTS by 21-43% versus the best prior model, while lowering the synthesis time by three orders of magnitude. Code and weights are provided at https://github.com/apple/ml-sharp

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

We introduce ReMatching, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate re-meshing paradigm, can target shape-matching tasks even on meshes counting millions of vertices, where the original functional maps does not apply or requires a massive computational cost. The core of our procedure is a time-efficient remeshing algorithm which constructs a low-resolution geometry while acting conservatively on the original topology and metric. These properties allow translating the functional maps optimization problem on the resulting low-resolution representation, thus enabling efficient computation of correspondences with functional map approaches. Finally, we propose an efficient technique for extending the estimated correspondence to the original meshes. We show that our method is more efficient and effective through quantitative and qualitative comparisons, outperforming state-of-the-art pipelines in quality and computational cost.

In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud data. Our attributions enrich these constructions with (persistent) homology in ways that are provably stable, thereby recording extra topological information that is typically lost in these graph constructions. We provide experiments which illustrate the use of these invariants for shape representation and classification. In particular, we obtain competitive shape classification results when using our topologically attributed graphs as inputs to a simple graph neural network classifier.

We present the P^3 dataset, a large-scale multimodal benchmark for building vectorization, constructed from aerial LiDAR point clouds, high-resolution aerial imagery, and vectorized 2D building outlines, collected across three continents. The dataset contains over 10 billion LiDAR points with decimeter-level accuracy and RGB images at a ground sampling distance of 25 centimeter. While many existing datasets primarily focus on the image modality, P^3 offers a complementary perspective by also incorporating dense 3D information. We demonstrate that LiDAR point clouds serve as a robust modality for predicting building polygons, both in hybrid and end-to-end learning frameworks. Moreover, fusing aerial LiDAR and imagery further improves accuracy and geometric quality of predicted polygons. The P^3 dataset is publicly available, along with code and pretrained weights of three state-of-the-art models for building polygon prediction at https://github.com/raphaelsulzer/PixelsPointsPolygons .

The choice of data representation is a key factor in the success of deep learning in geometric tasks. For instance, DUSt3R recently introduced the concept of viewpoint-invariant point maps, generalizing depth prediction and showing that all key problems in the 3D reconstruction of static scenes can be reduced to predicting such point maps. In this paper, we develop an analogous concept for a very different problem: the reconstruction of the 3D shape and pose of deformable objects. To this end, we introduce Dual Point Maps (DualPM), where a pair of point maps is extracted from the same image-one associating pixels to their 3D locations on the object and the other to a canonical version of the object in its rest pose. We also extend point maps to amodal reconstruction to recover the complete shape of the object, even through self-occlusions. We show that 3D reconstruction and 3D pose estimation can be reduced to the prediction of DualPMs. Empirically, we demonstrate that this representation is a suitable target for deep networks to predict. Specifically, we focus on modeling quadrupeds, showing that DualPMs can be trained purely on synthetic 3D data, consisting of one or two models per category, while generalizing effectively to real images. With this approach, we achieve significant improvements over previous methods for the 3D analysis and reconstruction of such objects.

This paper studies the problem of Line Segment Detection (LSD) for the characterization of line geometry in images, with the aim of learning a domain-agnostic robust LSD model that works well for any natural images. With the focus of scalable self-supervised learning of LSD, we revisit and streamline the fundamental designs of (deep and non-deep) LSD approaches to have a high-performing and efficient LSD learner, dubbed as ScaleLSD, for the curation of line geometry at scale from over 10M unlabeled real-world images. Our ScaleLSD works very well to detect much more number of line segments from any natural images even than the pioneered non-deep LSD approach, having a more complete and accurate geometric characterization of images using line segments. Experimentally, our proposed ScaleLSD is comprehensively testified under zero-shot protocols in detection performance, single-view 3D geometry estimation, two-view line segment matching, and multiview 3D line mapping, all with excellent performance obtained. Based on the thorough evaluation, our ScaleLSD is observed to be the first deep approach that outperforms the pioneered non-deep LSD in all aspects we have tested, significantly expanding and reinforcing the versatility of the line geometry of images. Code and Models are available at https://github.com/ant-research/scalelsd

With the rapid advancement and widespread adoption of VR/AR technologies, there is a growing demand for the creation of high-quality, immersive dynamic scenes. However, existing generation works predominantly concentrate on the creation of static scenes or narrow perspective-view dynamic scenes, falling short of delivering a truly 360-degree immersive experience from any viewpoint. In this paper, we introduce TiP4GEN, an advanced text-to-dynamic panorama scene generation framework that enables fine-grained content control and synthesizes motion-rich, geometry-consistent panoramic 4D scenes. TiP4GEN integrates panorama video generation and dynamic scene reconstruction to create 360-degree immersive virtual environments. For video generation, we introduce a Dual-branch Generation Model consisting of a panorama branch and a perspective branch, responsible for global and local view generation, respectively. A bidirectional cross-attention mechanism facilitates comprehensive information exchange between the branches. For scene reconstruction, we propose a Geometry-aligned Reconstruction Model based on 3D Gaussian Splatting. By aligning spatial-temporal point clouds using metric depth maps and initializing scene cameras with estimated poses, our method ensures geometric consistency and temporal coherence for the reconstructed scenes. Extensive experiments demonstrate the effectiveness of our proposed designs and the superiority of TiP4GEN in generating visually compelling and motion-coherent dynamic panoramic scenes. Our project page is at https://ke-xing.github.io/TiP4GEN/.

We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that reveal features analogous to outliers that these same notions have previously been shown to reveal in the context of metric spaces. Throughout, we provide examples of such "outlier detection" relevant to the analysis of computer programs, neural networks, cyber-physical systems, and networks of communications channels.

This work explores the visual explanation for deep metric learning and its applications. As an important problem for learning representation, metric learning has attracted much attention recently, while the interpretation of such model is not as well studied as classification. To this end, we propose an intuitive idea to show where contributes the most to the overall similarity of two input images by decomposing the final activation. Instead of only providing the overall activation map of each image, we propose to generate point-to-point activation intensity between two images so that the relationship between different regions is uncovered. We show that the proposed framework can be directly deployed to a large range of metric learning applications and provides valuable information for understanding the model. Furthermore, our experiments show its effectiveness on two potential applications, i.e. cross-view pattern discovery and interactive retrieval. The source code is available at https://github.com/Jeff-Zilence/Explain_Metric_Learning.

Place recognition based on point clouds (LiDAR) is an important component for autonomous robots or self-driving vehicles. Current SOTA performance is achieved on accumulated LiDAR submaps using either point-based or voxel-based structures. While voxel-based approaches nicely integrate spatial context across multiple scales, they do not exhibit the local precision of point-based methods. As a result, existing methods struggle with fine-grained matching of subtle geometric features in sparse single-shot Li- DAR scans. To overcome these limitations, we propose CASSPR as a method to fuse point-based and voxel-based approaches using cross attention transformers. CASSPR leverages a sparse voxel branch for extracting and aggregating information at lower resolution and a point-wise branch for obtaining fine-grained local information. CASSPR uses queries from one branch to try to match structures in the other branch, ensuring that both extract self-contained descriptors of the point cloud (rather than one branch dominating), but using both to inform the output global descriptor of the point cloud. Extensive experiments show that CASSPR surpasses the state-of-the-art by a large margin on several datasets (Oxford RobotCar, TUM, USyd). For instance, it achieves AR@1 of 85.6% on the TUM dataset, surpassing the strongest prior model by ~15%. Our code is publicly available.

Monte Carlo (MC) integration has been employed as the standard approximation method for the Sliced Wasserstein (SW) distance, whose analytical expression involves an intractable expectation. However, MC integration is not optimal in terms of absolute approximation error. To provide a better class of empirical SW, we propose quasi-sliced Wasserstein (QSW) approximations that rely on Quasi-Monte Carlo (QMC) methods. For a comprehensive investigation of QMC for SW, we focus on the 3D setting, specifically computing the SW between probability measures in three dimensions. In greater detail, we empirically evaluate various methods to construct QMC point sets on the 3D unit-hypersphere, including the Gaussian-based and equal area mappings, generalized spiral points, and optimizing discrepancy energies. Furthermore, to obtain an unbiased estimator for stochastic optimization, we extend QSW to Randomized Quasi-Sliced Wasserstein (RQSW) by introducing randomness in the discussed point sets. Theoretically, we prove the asymptotic convergence of QSW and the unbiasedness of RQSW. Finally, we conduct experiments on various 3D tasks, such as point-cloud comparison, point-cloud interpolation, image style transfer, and training deep point-cloud autoencoders, to demonstrate the favorable performance of the proposed QSW and RQSW variants.

We present Point2SSM, a novel unsupervised learning approach for constructing correspondence-based statistical shape models (SSMs) directly from raw point clouds. SSM is crucial in clinical research, enabling population-level analysis of morphological variation in bones and organs. Traditional methods of SSM construction have limitations, including the requirement of noise-free surface meshes or binary volumes, reliance on assumptions or templates, and prolonged inference times due to simultaneous optimization of the entire cohort. Point2SSM overcomes these barriers by providing a data-driven solution that infers SSMs directly from raw point clouds, reducing inference burdens and increasing applicability as point clouds are more easily acquired. While deep learning on 3D point clouds has seen success in unsupervised representation learning and shape correspondence, its application to anatomical SSM construction is largely unexplored. We conduct a benchmark of state-of-the-art point cloud deep networks on the SSM task, revealing their limited robustness to clinical challenges such as noisy, sparse, or incomplete input and limited training data. Point2SSM addresses these issues through an attention-based module, providing effective correspondence mappings from learned point features. Our results demonstrate that the proposed method significantly outperforms existing networks in terms of accurate surface sampling and correspondence, better capturing population-level statistics.

Face reconstruction and tracking is a building block of numerous applications in AR/VR, human-machine interaction, as well as medical applications. Most of these applications rely on a metrically correct prediction of the shape, especially, when the reconstructed subject is put into a metrical context (i.e., when there is a reference object of known size). A metrical reconstruction is also needed for any application that measures distances and dimensions of the subject (e.g., to virtually fit a glasses frame). State-of-the-art methods for face reconstruction from a single image are trained on large 2D image datasets in a self-supervised fashion. However, due to the nature of a perspective projection they are not able to reconstruct the actual face dimensions, and even predicting the average human face outperforms some of these methods in a metrical sense. To learn the actual shape of a face, we argue for a supervised training scheme. Since there exists no large-scale 3D dataset for this task, we annotated and unified small- and medium-scale databases. The resulting unified dataset is still a medium-scale dataset with more than 2k identities and training purely on it would lead to overfitting. To this end, we take advantage of a face recognition network pretrained on a large-scale 2D image dataset, which provides distinct features for different faces and is robust to expression, illumination, and camera changes. Using these features, we train our face shape estimator in a supervised fashion, inheriting the robustness and generalization of the face recognition network. Our method, which we call MICA (MetrIC fAce), outperforms the state-of-the-art reconstruction methods by a large margin, both on current non-metric benchmarks as well as on our metric benchmarks (15% and 24% lower average error on NoW, respectively).

We focus on the problem of species distribution modeling using global-scale presence-only data. Most previous studies have mapped the range of a given species using geographical and environmental features alone. To capture a stronger implicit relationship between species, we encode the taxonomic hierarchy of species using a large language model. This enables range mapping for any taxonomic rank and unseen species without additional supervision. Further, we propose a novel proximity-aware evaluation metric that enables evaluating species distribution models using any pixel-level representation of ground-truth species range map. The proposed metric penalizes the predictions of a model based on its proximity to the ground truth. We describe the effectiveness of our model by systematically evaluating on the task of species range prediction, zero-shot prediction and geo-feature regression against the state-of-the-art. Results show our model outperforms the strong baselines when trained with a variety of multi-label learning losses.

Recent work in the construction of 3D scene graphs has enabled mobile robots to build large-scale metric-semantic hierarchical representations of the world. These detailed models contain information that is useful for planning, however an open question is how to derive a planning domain from a 3D scene graph that enables efficient computation of executable plans. In this work, we present a novel approach for defining and solving Task and Motion Planning problems in large-scale environments using hierarchical 3D scene graphs. We describe a method for building sparse problem instances which enables scaling planning to large scenes, and we propose a technique for incrementally adding objects to that domain during planning time that minimizes computation on irrelevant elements of the scene graph. We evaluate our approach in two real scene graphs built from perception, including one constructed from the KITTI dataset. Furthermore, we demonstrate our approach in the real world, building our representation, planning in it, and executing those plans on a real robotic mobile manipulator. A video supplement is available at https://youtu.be/v8fkwLjBn58.

While interacting in the world is a multi-sensory experience, many robots continue to predominantly rely on visual perception to map and navigate in their environments. In this work, we propose Audio-Visual-Language Maps (AVLMaps), a unified 3D spatial map representation for storing cross-modal information from audio, visual, and language cues. AVLMaps integrate the open-vocabulary capabilities of multimodal foundation models pre-trained on Internet-scale data by fusing their features into a centralized 3D voxel grid. In the context of navigation, we show that AVLMaps enable robot systems to index goals in the map based on multimodal queries, e.g., textual descriptions, images, or audio snippets of landmarks. In particular, the addition of audio information enables robots to more reliably disambiguate goal locations. Extensive experiments in simulation show that AVLMaps enable zero-shot multimodal goal navigation from multimodal prompts and provide 50% better recall in ambiguous scenarios. These capabilities extend to mobile robots in the real world - navigating to landmarks referring to visual, audio, and spatial concepts. Videos and code are available at: https://avlmaps.github.io.

Neural implicit representations are drawing a lot of attention from the robotics community recently, as they are expressive, continuous and compact. However, city-scale continual implicit dense mapping based on sparse LiDAR input is still an under-explored challenge. To this end, we successfully build a city-scale continual neural mapping system with a panoptic representation that consists of environment-level and instance-level modelling. Given a stream of sparse LiDAR point cloud, it maintains a dynamic generative model that maps 3D coordinates to signed distance field (SDF) values. To address the difficulty of representing geometric information at different levels in city-scale space, we propose a tailored three-layer sampling strategy to dynamically sample the global, local and near-surface domains. Meanwhile, to realize high fidelity mapping of instance under incomplete observation, category-specific prior is introduced to better model the geometric details. We evaluate on the public SemanticKITTI dataset and demonstrate the significance of the newly proposed three-layer sampling strategy and panoptic representation, using both quantitative and qualitative results. Codes and model will be publicly available.

Deep learning-based point cloud modeling has been widely investigated as an indispensable component of general shape analysis. Recently, transformer and state space model (SSM) have shown promising capacities in point cloud learning. However, limited research has been conducted on medical point clouds, which have great potential in disease diagnosis and treatment. This paper presents an SSM-based hierarchical feature learning framework for medical point cloud understanding. Specifically, we down-sample input into multiple levels through the farthest point sampling. At each level, we perform a series of k-nearest neighbor (KNN) queries to aggregate multi-scale structural information. To assist SSM in processing point clouds, we introduce coordinate-order and inside-out scanning strategies for efficient serialization of irregular points. Point features are calculated progressively from short neighbor sequences and long point sequences through vanilla and group Point SSM blocks, to capture both local patterns and long-range dependencies. To evaluate the proposed method, we build a large-scale medical point cloud dataset named MedPointS for anatomy classification, completion, and segmentation. Extensive experiments conducted on MedPointS demonstrate that our method achieves superior performance across all tasks. The dataset is available at https://flemme-docs.readthedocs.io/en/latest/medpoints.html. Code is merged to a public medical imaging platform: https://github.com/wlsdzyzl/flemme.

We present WonderZoom, a novel approach to generating 3D scenes with contents across multiple spatial scales from a single image. Existing 3D world generation models remain limited to single-scale synthesis and cannot produce coherent scene contents at varying granularities. The fundamental challenge is the lack of a scale-aware 3D representation capable of generating and rendering content with largely different spatial sizes. WonderZoom addresses this through two key innovations: (1) scale-adaptive Gaussian surfels for generating and real-time rendering of multi-scale 3D scenes, and (2) a progressive detail synthesizer that iteratively generates finer-scale 3D contents. Our approach enables users to "zoom into" a 3D region and auto-regressively synthesize previously non-existent fine details from landscapes to microscopic features. Experiments demonstrate that WonderZoom significantly outperforms state-of-the-art video and 3D models in both quality and alignment, enabling multi-scale 3D world creation from a single image. We show video results and an interactive viewer of generated multi-scale 3D worlds in https://wonderzoom.github.io/

A proper scene representation is central to the pursuit of spatial intelligence where agents can robustly reconstruct and efficiently understand 3D scenes. A scene representation is either metric, such as landmark maps in 3D reconstruction, 3D bounding boxes in object detection, or voxel grids in occupancy prediction, or topological, such as pose graphs with loop closures in SLAM or visibility graphs in SfM. In this work, we propose to build Multiview Scene Graphs (MSG) from unposed images, representing a scene topologically with interconnected place and object nodes. The task of building MSG is challenging for existing representation learning methods since it needs to jointly address both visual place recognition, object detection, and object association from images with limited fields of view and potentially large viewpoint changes. To evaluate any method tackling this task, we developed an MSG dataset and annotation based on a public 3D dataset. We also propose an evaluation metric based on the intersection-over-union score of MSG edges. Moreover, we develop a novel baseline method built on mainstream pretrained vision models, combining visual place recognition and object association into one Transformer decoder architecture. Experiments demonstrate our method has superior performance compared to existing relevant baselines.

3D Gaussian Splatting (3DGS) has become a popular solution in SLAM due to its high-fidelity and real-time novel view synthesis performance. However, some previous 3DGS SLAM methods employ a differentiable rendering pipeline for tracking, lack geometric priors in outdoor scenes. Other approaches introduce separate tracking modules, but they accumulate errors with significant camera movement, leading to scale drift. To address these challenges, we propose a robust RGB-only outdoor 3DGS SLAM method: S3PO-GS. Technically, we establish a self-consistent tracking module anchored in the 3DGS pointmap, which avoids cumulative scale drift and achieves more precise and robust tracking with fewer iterations. Additionally, we design a patch-based pointmap dynamic mapping module, which introduces geometric priors while avoiding scale ambiguity. This significantly enhances tracking accuracy and the quality of scene reconstruction, making it particularly suitable for complex outdoor environments. Our experiments on the Waymo, KITTI, and DL3DV datasets demonstrate that S3PO-GS achieves state-of-the-art results in novel view synthesis and outperforms other 3DGS SLAM methods in tracking accuracy. Project page: https://3dagentworld.github.io/S3PO-GS/.

We tackle the novel class discovery in point cloud segmentation, which discovers novel classes based on the semantic knowledge of seen classes. Existing work proposes an online point-wise clustering method with a simplified equal class-size constraint on the novel classes to avoid degenerate solutions. However, the inherent imbalanced distribution of novel classes in point clouds typically violates the equal class-size constraint. Moreover, point-wise clustering ignores the rich spatial context information of objects, which results in less expressive representation for semantic segmentation. To address the above challenges, we propose a novel self-labeling strategy that adaptively generates high-quality pseudo-labels for imbalanced classes during model training. In addition, we develop a dual-level representation that incorporates regional consistency into the point-level classifier learning, reducing noise in generated segmentation. Finally, we conduct extensive experiments on two widely used datasets, SemanticKITTI and SemanticPOSS, and the results show our method outperforms the state of the art by a large margin.

Scene graph generation has emerged as a prominent research field in computer vision, witnessing significant advancements in the recent years. However, despite these strides, precise and thorough definitions for the metrics used to evaluate scene graph generation models are lacking. In this paper, we address this gap in the literature by providing a review and precise definition of commonly used metrics in scene graph generation. Our comprehensive examination clarifies the underlying principles of these metrics and can serve as a reference or introduction to scene graph metrics. Furthermore, to facilitate the usage of these metrics, we introduce a standalone Python package called SGBench that efficiently implements all defined metrics, ensuring their accessibility to the research community. Additionally, we present a scene graph benchmarking web service, that enables researchers to compare scene graph generation methods and increase visibility of new methods in a central place. All of our code can be found at https://lorjul.github.io/sgbench/.

Label-efficient LiDAR-based 3D object detection is currently dominated by weakly/semi-supervised methods. Instead of exclusively following one of them, we propose MixSup, a more practical paradigm simultaneously utilizing massive cheap coarse labels and a limited number of accurate labels for Mixed-grained Supervision. We start by observing that point clouds are usually textureless, making it hard to learn semantics. However, point clouds are geometrically rich and scale-invariant to the distances from sensors, making it relatively easy to learn the geometry of objects, such as poses and shapes. Thus, MixSup leverages massive coarse cluster-level labels to learn semantics and a few expensive box-level labels to learn accurate poses and shapes. We redesign the label assignment in mainstream detectors, which allows them seamlessly integrated into MixSup, enabling practicality and universality. We validate its effectiveness in nuScenes, Waymo Open Dataset, and KITTI, employing various detectors. MixSup achieves up to 97.31% of fully supervised performance, using cheap cluster annotations and only 10% box annotations. Furthermore, we propose PointSAM based on the Segment Anything Model for automated coarse labeling, further reducing the annotation burden. The code is available at https://github.com/BraveGroup/PointSAM-for-MixSup.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

Graph measures that express closeness or distance between nodes can be employed for graph nodes clustering using metric clustering algorithms. There are numerous measures applicable to this task, and which one performs better is an open question. We study the performance of 25 graph measures on generated graphs with different parameters. While usually measure comparisons are limited to general measure ranking on a particular dataset, we aim to explore the performance of various measures depending on graph features. Using an LFR graph generator, we create a dataset of 11780 graphs covering the whole LFR parameter space. For each graph, we assess the quality of clustering with k-means algorithm for each considered measure. Based on this, we determine the best measure for each area of the parameter space. We find that the parameter space consists of distinct zones where one particular measure is the best. We analyze the geometry of the resulting zones and describe it with simple criteria. Given particular graph parameters, this allows us to recommend a particular measure to use for clustering.

Panoptic segmentation is the combination of semantic and instance segmentation: assign the points in a 3D point cloud to semantic categories and partition them into distinct object instances. It has many obvious applications for outdoor scene understanding, from city mapping to forest management. Existing methods struggle to segment nearby instances of the same semantic category, like adjacent pieces of street furniture or neighbouring trees, which limits their usability for inventory- or management-type applications that rely on object instances. This study explores the steps of the panoptic segmentation pipeline concerned with clustering points into object instances, with the goal to alleviate that bottleneck. We find that a carefully designed clustering strategy, which leverages multiple types of learned point embeddings, significantly improves instance segmentation. Experiments on the NPM3D urban mobile mapping dataset and the FOR-instance forest dataset demonstrate the effectiveness and versatility of the proposed strategy.

Recent advances in deep learning-based point cloud registration have improved generalization, yet most methods still require retraining or manual parameter tuning for each new environment. In this paper, we identify three key factors limiting generalization: (a) reliance on environment-specific voxel size and search radius, (b) poor out-of-domain robustness of learning-based keypoint detectors, and (c) raw coordinate usage, which exacerbates scale discrepancies. To address these issues, we present a zero-shot registration pipeline called BUFFER-X by (a) adaptively determining voxel size/search radii, (b) using farthest point sampling to bypass learned detectors, and (c) leveraging patch-wise scale normalization for consistent coordinate bounds. In particular, we present a multi-scale patch-based descriptor generation and a hierarchical inlier search across scales to improve robustness in diverse scenes. We also propose a novel generalizability benchmark using 11 datasets that cover various indoor/outdoor scenarios and sensor modalities, demonstrating that BUFFER-X achieves substantial generalization without prior information or manual parameter tuning for the test datasets. Our code is available at https://github.com/MIT-SPARK/BUFFER-X.

This paper is not motivated to seek innovation within the attention mechanism. Instead, it focuses on overcoming the existing trade-offs between accuracy and efficiency within the context of point cloud processing, leveraging the power of scale. Drawing inspiration from recent advances in 3D large-scale representation learning, we recognize that model performance is more influenced by scale than by intricate design. Therefore, we present Point Transformer V3 (PTv3), which prioritizes simplicity and efficiency over the accuracy of certain mechanisms that are minor to the overall performance after scaling, such as replacing the precise neighbor search by KNN with an efficient serialized neighbor mapping of point clouds organized with specific patterns. This principle enables significant scaling, expanding the receptive field from 16 to 1024 points while remaining efficient (a 3x increase in processing speed and a 10x improvement in memory efficiency compared with its predecessor, PTv2). PTv3 attains state-of-the-art results on over 20 downstream tasks that span both indoor and outdoor scenarios. Further enhanced with multi-dataset joint training, PTv3 pushes these results to a higher level.

Maintaining an up-to-date map that accurately reflects recent changes in the environment is crucial, especially for robots that repeatedly traverse the same space. Failing to promptly update the changed regions can degrade map quality, resulting in poor localization, inefficient operations, and even lost robots. 3D Gaussian Splatting (3DGS) has recently seen widespread adoption in online map reconstruction due to its dense, differentiable, and photorealistic properties, yet accurately and efficiently updating the regions of change remains a challenge. In this paper, we propose VG-Mapping, a novel online 3DGS-based mapping system tailored for such semi-static scenes. Our approach introduces a hybrid representation that augments 3DGS with a TSDF-based voxel map to efficiently identify changed regions in a scene, along with a variation-aware density control strategy that inserts or deletes Gaussian primitives in regions undergoing change. Furthermore, to address the absence of public benchmarks for this task, we construct a RGB-D dataset comprising both synthetic and real-world semi-static environments. Experimental results demonstrate that our method substantially improves the rendering quality and map update efficiency in semi-static scenes. The code and dataset are available at https://github.com/heyicheng-never/VG-Mapping.

LiDAR mapping is important yet challenging in self-driving and mobile robotics. To tackle such a global point cloud registration problem, DeepMapping converts the complex map estimation into a self-supervised training of simple deep networks. Despite its broad convergence range on small datasets, DeepMapping still cannot produce satisfactory results on large-scale datasets with thousands of frames. This is due to the lack of loop closures and exact cross-frame point correspondences, and the slow convergence of its global localization network. We propose DeepMapping2 by adding two novel techniques to address these issues: (1) organization of training batch based on map topology from loop closing, and (2) self-supervised local-to-global point consistency loss leveraging pairwise registration. Our experiments and ablation studies on public datasets (KITTI, NCLT, and Nebula) demonstrate the effectiveness of our method.

Point cloud analysis is challenging due to irregularity and unordered data structure. To capture the 3D geometries, prior works mainly rely on exploring sophisticated local geometric extractors using convolution, graph, or attention mechanisms. These methods, however, incur unfavorable latency during inference, and the performance saturates over the past few years. In this paper, we present a novel perspective on this task. We notice that detailed local geometrical information probably is not the key to point cloud analysis -- we introduce a pure residual MLP network, called PointMLP, which integrates no sophisticated local geometrical extractors but still performs very competitively. Equipped with a proposed lightweight geometric affine module, PointMLP delivers the new state-of-the-art on multiple datasets. On the real-world ScanObjectNN dataset, our method even surpasses the prior best method by 3.3% accuracy. We emphasize that PointMLP achieves this strong performance without any sophisticated operations, hence leading to a superior inference speed. Compared to most recent CurveNet, PointMLP trains 2x faster, tests 7x faster, and is more accurate on ModelNet40 benchmark. We hope our PointMLP may help the community towards a better understanding of point cloud analysis. The code is available at https://github.com/ma-xu/pointMLP-pytorch.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

Despite recent advances in leveraging generative prior from pre-trained diffusion models for 3D scene reconstruction, existing methods still face two critical limitations. First, due to the lack of reliable geometric supervision, they struggle to produce high-quality reconstructions even in observed regions, let alone in unobserved areas. Second, they lack effective mechanisms to mitigate multi-view inconsistencies in the generated images, leading to severe shape-appearance ambiguities and degraded scene geometry. In this paper, we identify accurate geometry as the fundamental prerequisite for effectively exploiting generative models to enhance 3D scene reconstruction. We first propose to leverage the prevalence of planar structures to derive accurate metric-scale depth maps, providing reliable supervision in both observed and unobserved regions. Furthermore, we incorporate this geometry guidance throughout the generative pipeline to improve visibility mask estimation, guide novel view selection, and enhance multi-view consistency when inpainting with video diffusion models, resulting in accurate and consistent scene completion. Extensive experiments on Replica, ScanNet++, and DeepBlending show that our method consistently outperforms existing baselines in both geometry and appearance reconstruction, particularly for unobserved regions. Moreover, our method naturally supports single-view inputs and unposed videos, with strong generalizability in both indoor and outdoor scenarios with practical real-world applicability. The project page is available at https://dali-jack.github.io/g4splat-web/.

Canonical surface mapping generalizes keypoint detection by assigning each pixel of an object to a corresponding point in a 3D template. Popularised by DensePose for the analysis of humans, authors have since attempted to apply the concept to more categories, but with limited success due to the high cost of manual supervision. In this work, we introduce SHIC, a method to learn canonical maps without manual supervision which achieves better results than supervised methods for most categories. Our idea is to leverage foundation computer vision models such as DINO and Stable Diffusion that are open-ended and thus possess excellent priors over natural categories. SHIC reduces the problem of estimating image-to-template correspondences to predicting image-to-image correspondences using features from the foundation models. The reduction works by matching images of the object to non-photorealistic renders of the template, which emulates the process of collecting manual annotations for this task. These correspondences are then used to supervise high-quality canonical maps for any object of interest. We also show that image generators can further improve the realism of the template views, which provide an additional source of supervision for the model.

Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree tree where the weight of each node is the sum of the weights of its children. A treemap for tree is a hierarchical partition of a rectangle into simply connected regions, usually rectangles. Each region represents a node of tree and its area is proportional to the weight of the corresponding node. An important quality criterion for treemaps is the aspect ratio of its regions. One cannot bound the aspect ratio if the regions are restricted to be rectangles. In contrast, polygonal partitions, that use convex polygons, have bounded aspect ratio. We are the first to obtain convex partitions with optimal aspect ratio O(depth(tree)). However, depth(tree) still depends on the input tree. Hence we introduce a new type of treemaps, namely orthoconvex treemaps, where regions representing leaves are rectangles, L-, and S-shapes, and regions representing internal nodes are orthoconvex polygons. We prove that any input tree, irrespective of the weights of the nodes and the depth of the tree, admits an orthoconvex treemap of constant aspect ratio. We also obtain several specialized results for single-level treemaps, that is, treemaps where the input tree has depth~1.

A key step in any scanning-based asset creation workflow is to convert unordered point clouds to a surface. Classical methods (e.g., Poisson reconstruction) start to degrade in the presence of noisy and partial scans. Hence, deep learning based methods have recently been proposed to produce complete surfaces, even from partial scans. However, such data-driven methods struggle to generalize to new shapes with large geometric and topological variations. We present Points2Surf, a novel patch-based learning framework that produces accurate surfaces directly from raw scans without normals. Learning a prior over a combination of detailed local patches and coarse global information improves generalization performance and reconstruction accuracy. Our extensive comparison on both synthetic and real data demonstrates a clear advantage of our method over state-of-the-art alternatives on previously unseen classes (on average, Points2Surf brings down reconstruction error by 30\% over SPR and by 270\%+ over deep learning based SotA methods) at the cost of longer computation times and a slight increase in small-scale topological noise in some cases. Our source code, pre-trained model, and dataset are available on: https://github.com/ErlerPhilipp/points2surf

We introduce Point2Skeleton, an unsupervised method to learn skeletal representations from point clouds. Existing skeletonization methods are limited to tubular shapes and the stringent requirement of watertight input, while our method aims to produce more generalized skeletal representations for complex structures and handle point clouds. Our key idea is to use the insights of the medial axis transform (MAT) to capture the intrinsic geometric and topological natures of the original input points. We first predict a set of skeletal points by learning a geometric transformation, and then analyze the connectivity of the skeletal points to form skeletal mesh structures. Extensive evaluations and comparisons show our method has superior performance and robustness. The learned skeletal representation will benefit several unsupervised tasks for point clouds, such as surface reconstruction and segmentation.

A typical human strategy for giving navigation guidance is to sketch route maps based on the environmental layout. Inspired by this, we introduce Sketch map-based visual Navigation (SkeNa), an embodied navigation task in which an agent must reach a goal in an unseen environment using only a hand-drawn sketch map as guidance. To support research for SkeNa, we present a large-scale dataset named SoR, comprising 54k trajectory and sketch map pairs across 71 indoor scenes. In SoR, we introduce two navigation validation sets with varying levels of abstraction in hand-drawn sketches, categorized based on their preservation of spatial scales in the environment, to facilitate future research. To construct SoR, we develop an automated sketch-generation pipeline that efficiently converts floor plans into hand-drawn representations. To solve SkeNa, we propose SkeNavigator, a navigation framework that aligns visual observations with hand-drawn maps to estimate navigation targets. It employs a Ray-based Map Descriptor (RMD) to enhance sketch map valid feature representation using equidistant sampling points and boundary distances. To improve alignment with visual observations, a Dual-Map Aligned Goal Predictor (DAGP) leverages the correspondence between sketch map features and on-site constructed exploration map features to predict goal position and guide navigation. SkeNavigator outperforms prior floor plan navigation methods by a large margin, improving SPL on the high-abstract validation set by 105% relatively. Our code and dataset will be released.

Many real-world machine learning problems involve inherently hierarchical data, yet traditional approaches rely on Euclidean metrics that fail to capture the discrete, branching nature of hierarchical relationships. We present a theoretical foundation for machine learning in p-adic metric spaces, which naturally respect hierarchical structure. Our main result proves that an n-dimensional plane minimizing the p-adic sum of distances to points in a dataset must pass through at least n + 1 of those points -- a striking contrast to Euclidean regression that highlights how p-adic metrics better align with the discrete nature of hierarchical data. As a corollary, a polynomial of degree n constructed to minimise the p-adic sum of residuals will pass through at least n + 1 points. As a further corollary, a polynomial of degree n approximating a higher degree polynomial at a finite number of points will yield a difference polynomial that has distinct rational roots. We demonstrate the practical significance of this result through two applications in natural language processing: analyzing hierarchical taxonomies and modeling grammatical morphology. These results suggest that p-adic metrics may be fundamental to properly handling hierarchical data structures in machine learning. In hierarchical data, interpolation between points often makes less sense than selecting actual observed points as representatives.

In this paper, it is shown that if a sequence of resistance metric spaces equipped with measures converges with respect to the local Gromov-Hausdorff-vague topology, and certain non-explosion and metric-entropy conditions are satisfied, then the associated stochastic processes and their local times also converge. The metric-entropy condition can be checked by applying volume estimates of balls. Whilst similar results have been proved previously, the approach of this article is more widely applicable. Indeed, we recover various known conclusions for scaling limits of some deterministic self-similar fractal graphs, critical Galton-Watson trees, the critical Erdos-R\'enyi random graph and the configuration model (in the latter two cases, we prove for the first time the convergence of the models with respect to the resistance metric and also, for the configuration model, we overcome an error in the existing proof of local time convergence). Moreover, we derive new ones for scaling limits of uniform spanning trees and random recursive fractals. The metric-entropy condition also implies convergence of associated Gaussian processes.

LiDAR point cloud semantic segmentation is essential for interpreting 3D environments in applications such as autonomous driving and robotics. Recent methods achieve strong performance by exploiting different point cloud representations or incorporating data from other sensors, such as cameras or external datasets. However, these approaches often suffer from high computational complexity and require large amounts of training data, limiting their generalization in data-scarce scenarios. In this paper, we improve the performance of point-based methods by effectively learning features from 2D representations through point-plane projections, enabling the extraction of complementary information while relying solely on LiDAR data. Additionally, we introduce a geometry-aware technique for data augmentation that aligns with LiDAR sensor properties and mitigates class imbalance. We implemented and evaluated our method that applies point-plane projections onto multiple informative 2D representations of the point cloud. Experiments demonstrate that this approach leads to significant improvements in limited-data scenarios, while also achieving competitive results on two publicly available standard datasets, as SemanticKITTI and PandaSet. The code of our method is available at https://github.com/SiMoM0/3PNet

Most prior work represents the shapes of point clouds by coordinates. However, it is insufficient to describe the local geometry directly. In this paper, we present RepSurf (representative surfaces), a novel representation of point clouds to explicitly depict the very local structure. We explore two variants of RepSurf, Triangular RepSurf and Umbrella RepSurf inspired by triangle meshes and umbrella curvature in computer graphics. We compute the representations of RepSurf by predefined geometric priors after surface reconstruction. RepSurf can be a plug-and-play module for most point cloud models thanks to its free collaboration with irregular points. Based on a simple baseline of PointNet++ (SSG version), Umbrella RepSurf surpasses the previous state-of-the-art by a large margin for classification, segmentation and detection on various benchmarks in terms of performance and efficiency. With an increase of around 0.008M number of parameters, 0.04G FLOPs, and 1.12ms inference time, our method achieves 94.7\% (+0.5\%) on ModelNet40, and 84.6\% (+1.8\%) on ScanObjectNN for classification, while 74.3\% (+0.8\%) mIoU on S3DIS 6-fold, and 70.0\% (+1.6\%) mIoU on ScanNet for segmentation. For detection, previous state-of-the-art detector with our RepSurf obtains 71.2\% (+2.1\%) mAP_{25}, 54.8\% (+2.0\%) mAP_{50} on ScanNetV2, and 64.9\% (+1.9\%) mAP_{25}, 47.7\% (+2.5\%) mAP_{50} on SUN RGB-D. Our lightweight Triangular RepSurf performs its excellence on these benchmarks as well. The code is publicly available at https://github.com/hancyran/RepSurf.

Micro-Aerial Vehicles (MAVs) have the advantage of moving freely in 3D space. However, creating compact and sparse map representations that can be efficiently used for planning for such robots is still an open problem. In this paper, we take maps built from noisy sensor data and construct a sparse graph containing topological information that can be used for 3D planning. We use a Euclidean Signed Distance Field, extract a 3D Generalized Voronoi Diagram (GVD), and obtain a thin skeleton diagram representing the topological structure of the environment. We then convert this skeleton diagram into a sparse graph, which we show is resistant to noise and changes in resolution. We demonstrate global planning over this graph, and the orders of magnitude speed-up it offers over other common planning methods. We validate our planning algorithm in real maps built onboard an MAV, using RGB-D sensing.

Established sampling protocols for 3D point cloud learning, such as Farthest Point Sampling (FPS) and Fixed Sample Size (FSS), have long been relied upon. However, real-world data often suffer from corruptions, such as sensor noise, which violates the benign data assumption in current protocols. As a result, these protocols are highly vulnerable to noise, posing significant safety risks in critical applications like autonomous driving. To address these issues, we propose an enhanced point cloud sampling protocol, PointSP, designed to improve robustness against point cloud corruptions. PointSP incorporates key point reweighting to mitigate outlier sensitivity and ensure the selection of representative points. It also introduces a local-global balanced downsampling strategy, which allows for scalable and adaptive sampling while maintaining geometric consistency. Additionally, a lightweight tangent plane interpolation method is used to preserve local geometry while enhancing the density of the point cloud. Unlike learning-based approaches that require additional model training, PointSP is architecture-agnostic, requiring no extra learning or modification to the network. This enables seamless integration into existing pipelines. Extensive experiments on synthetic and real-world corrupted datasets show that PointSP significantly improves the robustness and accuracy of point cloud classification, outperforming state-of-the-art methods across multiple benchmarks.

Tracking and mapping in large-scale, unbounded outdoor environments using only monocular RGB input presents substantial challenges for existing SLAM systems. Traditional Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) SLAM methods are typically limited to small, bounded indoor settings. To overcome these challenges, we introduce GigaSLAM, the first RGB NeRF / 3DGS-based SLAM framework for kilometer-scale outdoor environments, as demonstrated on the KITTI, KITTI 360, 4 Seasons and A2D2 datasets. Our approach employs a hierarchical sparse voxel map representation, where Gaussians are decoded by neural networks at multiple levels of detail. This design enables efficient, scalable mapping and high-fidelity viewpoint rendering across expansive, unbounded scenes. For front-end tracking, GigaSLAM utilizes a metric depth model combined with epipolar geometry and PnP algorithms to accurately estimate poses, while incorporating a Bag-of-Words-based loop closure mechanism to maintain robust alignment over long trajectories. Consequently, GigaSLAM delivers high-precision tracking and visually faithful rendering on urban outdoor benchmarks, establishing a robust SLAM solution for large-scale, long-term scenarios, and significantly extending the applicability of Gaussian Splatting SLAM systems to unbounded outdoor environments. GitHub: https://github.com/DengKaiCQ/GigaSLAM.

Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the underlying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM's utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells).

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings and a distance-based loss function to match the representations -- usually, the Euclidean distance is utilized. An emerging interest in learning hyperbolic data embeddings suggests that hyperbolic geometry can be beneficial for natural data. Following this line of work, we propose a new hyperbolic-based model for metric learning. At the core of our method is a vision transformer with output embeddings mapped to hyperbolic space. These embeddings are directly optimized using modified pairwise cross-entropy loss. We evaluate the proposed model with six different formulations on four datasets achieving the new state-of-the-art performance. The source code is available at https://github.com/htdt/hyp_metric.

Lines and points are complementary local features, whose combination has proven effective for applications such as SLAM and Structure-from-Motion. The backbone of these pipelines are the local feature matchers, establishing correspondences across images. Traditionally, point and line matching have been treated as independent tasks. Recently, GlueStick proposed a GNN-based network that simultaneously operates on points and lines to establish matches. While running a single joint matching reduced the overall computational complexity, the heavy architecture prevented real-time applications or deployment to edge devices. Inspired by recent progress in point matching, we propose LightGlueStick, a lightweight matcher for points and line segments. The key novel component in our architecture is the Attentional Line Message Passing (ALMP), which explicitly exposes the connectivity of the lines to the network, allowing for efficient communication between nodes. In thorough experiments we show that LightGlueStick establishes a new state-of-the-art across different benchmarks. The code is available at https://github.com/aubingazhib/LightGlueStick.

Energy-based predictive world models provide a powerful approach for multi-step visual planning by reasoning over latent energy landscapes rather than generating pixels. However, existing approaches face two major challenges: (i) their latent representations are typically learned in Euclidean space, neglecting the underlying geometric and hierarchical structure among states, and (ii) they struggle with long-horizon prediction, which leads to rapid degradation across extended rollouts. To address these challenges, we introduce GeoWorld, a geometric world model that preserves geometric structure and hierarchical relations through a Hyperbolic JEPA, which maps latent representations from Euclidean space onto hyperbolic manifolds. We further introduce Geometric Reinforcement Learning for energy-based optimization, enabling stable multi-step planning in hyperbolic latent space. Extensive experiments on CrossTask and COIN demonstrate around 3% SR improvement in 3-step planning and 2% SR improvement in 4-step planning compared to the state-of-the-art V-JEPA 2. Project website: https://steve-zeyu-zhang.github.io/GeoWorld.

Computer-aided design (CAD) is the digital construction of 2D and 3D objects, and is central to a wide range of engineering and manufacturing applications like automobile and aviation. Despite its importance, CAD modeling remains largely a time-intensive, manual task. Recent works have attempted to automate this process with small transformer-based models and handcrafted CAD sequence representations. However, there has been little effort to leverage the potential of large language models (LLMs) for sequential CAD design. In this work, we introduce a new large-scale dataset of more than 170k CAD models annotated with high-quality, human-like descriptions generated with our pipeline based on GPT-4.1. Using this dataset, we fine-tune powerful code-LLMs to generate CAD sequences represented in a JSON-based format from natural language descriptions, demonstrating the viability and effectiveness of this approach for text-conditioned CAD generation. Because simple metrics often fail to reflect the quality of generated objects, we introduce geometric and topological metrics based on sphericity, mean curvature, and Euler characteristic to provide richer structural insights. Our experiments and ablation studies on both synthetic and human-annotated data demonstrate that CADmium is able to automate CAD design, drastically speeding up the design of new objects. The dataset, code, and fine-tuned models are available online.