Daily Papers

We introduce a new framework for molecular graph generation with 3D molecular generative models. Our Synthetic Coordinate Embedding (SyCo) framework maps molecular graphs to Euclidean point clouds via synthetic conformer coordinates and learns the inverse map using an E(n)-Equivariant Graph Neural Network (EGNN). The induced point cloud-structured latent space is well-suited to apply existing 3D molecular generative models. This approach simplifies the graph generation problem - without relying on molecular fragments nor autoregressive decoding - into a point cloud generation problem followed by node and edge classification tasks. Further, we propose a novel similarity-constrained optimization scheme for 3D diffusion models based on inpainting and guidance. As a concrete implementation of our framework, we develop EDM-SyCo based on the E(3) Equivariant Diffusion Model (EDM). EDM-SyCo achieves state-of-the-art performance in distribution learning of molecular graphs, outperforming the best non-autoregressive methods by more than 30% on ZINC250K and 16% on the large-scale GuacaMol dataset while improving conditional generation by up to 3.9 times.

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.

Single-cell technologies generate high-dimensional point clouds of cells, enabling detailed characterization of complex patient states and treatment responses. Yet each patient is represented by an irregular point cloud rather than a simple vector, making it difficult to directly quantify and compare biological differences between individuals. Nonlinear methods such as kernels and neural networks achieve predictive accuracy but act as black boxes, offering little biological interpretability. To address these limitations, we adapt the Linear Optimal Transport (LOT) framework to this setting, embedding irregular point clouds into a fixed-dimensional Euclidean space while preserving distributional structure. This embedding provides a principled linear representation that preserves optimal transport geometry while enabling downstream analysis. It also forms a registration between any two patients, enabling direct comparison of their cellular distributions. Within this space, LOT enables: (i) accurate and interpretable classification of COVID-19 patient states, where classifier weights map back to specific markers and spatial regions driving predictions; and (ii) synthetic data generation for patient-derived organoids, exploiting the linearity of the LOT embedding. LOT barycenters yield averaged cellular profiles representing combined conditions or samples, supporting drug interaction testing. Together, these results establish LOT as a unified framework that bridges predictive performance, interpretability, and generative modeling. By transforming heterogeneous point clouds into structured embeddings directly traceable to the original data, LOT opens new opportunities for understanding immune variation and treatment effects in high-dimensional biological systems.

We present Assembler, a scalable and generalizable framework for 3D part assembly that reconstructs complete objects from input part meshes and a reference image. Unlike prior approaches that mostly rely on deterministic part pose prediction and category-specific training, Assembler is designed to handle diverse, in-the-wild objects with varying part counts, geometries, and structures. It addresses the core challenges of scaling to general 3D part assembly through innovations in task formulation, representation, and data. First, Assembler casts part assembly as a generative problem and employs diffusion models to sample plausible configurations, effectively capturing ambiguities arising from symmetry, repeated parts, and multiple valid assemblies. Second, we introduce a novel shape-centric representation based on sparse anchor point clouds, enabling scalable generation in Euclidean space rather than SE(3) pose prediction. Third, we construct a large-scale dataset of over 320K diverse part-object assemblies using a synthesis and filtering pipeline built on existing 3D shape repositories. Assembler achieves state-of-the-art performance on PartNet and is the first to demonstrate high-quality assembly for complex, real-world objects. Based on Assembler, we further introduce an interesting part-aware 3D modeling system that generates high-resolution, editable objects from images, demonstrating potential for interactive and compositional design. Project page: https://assembler3d.github.io

We consider the problem of computing persistent homology (PH) for large-scale Euclidean point cloud data, aimed at downstream machine learning tasks, where the exponential growth of the most widely-used Vietoris-Rips complex imposes serious computational limitations. Although more scalable alternatives such as the Alpha complex or sparse Rips approximations exist, they often still result in a prohibitively large number of simplices. This poses challenges in the complex construction and in the subsequent PH computation, prohibiting their use on large-scale point clouds. To mitigate these issues, we introduce the Flood complex, inspired by the advantages of the Alpha and Witness complex constructions. Informally, at a given filtration value rgeq 0, the Flood complex contains all simplices from a Delaunay triangulation of a small subset of the point cloud X that are fully covered by balls of radius r emanating from X, a process we call flooding. Our construction allows for efficient PH computation, possesses several desirable theoretical properties, and is amenable to GPU parallelization. Scaling experiments on 3D point cloud data show that we can compute PH of up to dimension 2 on several millions of points. Importantly, when evaluating object classification performance on real-world and synthetic data, we provide evidence that this scaling capability is needed, especially if objects are geometrically or topologically complex, yielding performance superior to other PH-based methods and neural networks for point cloud data. Source code and datasets are available on https://github.com/plus-rkwitt/flooder.

Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these symmetries while being expressive and computationally efficient. For example, Euclidean motion invariant/equivariant graph or point cloud neural networks. We introduce Frame Averaging (FA), a general purpose and systematic framework for adapting known (backbone) architectures to become invariant or equivariant to new symmetry types. Our framework builds on the well known group averaging operator that guarantees invariance or equivariance but is intractable. In contrast, we observe that for many important classes of symmetries, this operator can be replaced with an averaging operator over a small subset of the group elements, called a frame. We show that averaging over a frame guarantees exact invariance or equivariance while often being much simpler to compute than averaging over the entire group. Furthermore, we prove that FA-based models have maximal expressive power in a broad setting and in general preserve the expressive power of their backbone architectures. Using frame averaging, we propose a new class of universal Graph Neural Networks (GNNs), universal Euclidean motion invariant point cloud networks, and Euclidean motion invariant Message Passing (MP) GNNs. We demonstrate the practical effectiveness of FA on several applications including point cloud normal estimation, beyond 2-WL graph separation, and n-body dynamics prediction, achieving state-of-the-art results in all of these benchmarks.

In this paper, we introduce an SE(3) diffusion model-based point cloud registration framework for 6D object pose estimation in real-world scenarios. Our approach formulates the 3D registration task as a denoising diffusion process, which progressively refines the pose of the source point cloud to obtain a precise alignment with the model point cloud. Training our framework involves two operations: An SE(3) diffusion process and an SE(3) reverse process. The SE(3) diffusion process gradually perturbs the optimal rigid transformation of a pair of point clouds by continuously injecting noise (perturbation transformation). By contrast, the SE(3) reverse process focuses on learning a denoising network that refines the noisy transformation step-by-step, bringing it closer to the optimal transformation for accurate pose estimation. Unlike standard diffusion models used in linear Euclidean spaces, our diffusion model operates on the SE(3) manifold. This requires exploiting the linear Lie algebra se(3) associated with SE(3) to constrain the transformation transitions during the diffusion and reverse processes. Additionally, to effectively train our denoising network, we derive a registration-specific variational lower bound as the optimization objective for model learning. Furthermore, we show that our denoising network can be constructed with a surrogate registration model, making our approach applicable to different deep registration networks. Extensive experiments demonstrate that our diffusion registration framework presents outstanding pose estimation performance on the real-world TUD-L, LINEMOD, and Occluded-LINEMOD datasets.

Deep point cloud registration methods face challenges to partial overlaps and rely on labeled data. To address these issues, we propose UDPReg, an unsupervised deep probabilistic registration framework for point clouds with partial overlaps. Specifically, we first adopt a network to learn posterior probability distributions of Gaussian mixture models (GMMs) from point clouds. To handle partial point cloud registration, we apply the Sinkhorn algorithm to predict the distribution-level correspondences under the constraint of the mixing weights of GMMs. To enable unsupervised learning, we design three distribution consistency-based losses: self-consistency, cross-consistency, and local contrastive. The self-consistency loss is formulated by encouraging GMMs in Euclidean and feature spaces to share identical posterior distributions. The cross-consistency loss derives from the fact that the points of two partially overlapping point clouds belonging to the same clusters share the cluster centroids. The cross-consistency loss allows the network to flexibly learn a transformation-invariant posterior distribution of two aligned point clouds. The local contrastive loss facilitates the network to extract discriminative local features. Our UDPReg achieves competitive performance on the 3DMatch/3DLoMatch and ModelNet/ModelLoNet benchmarks.

Integrating a notion of symmetry into point cloud neural networks is a provably effective way to improve their generalization capability. Of particular interest are E(3) equivariant point cloud networks where Euclidean transformations applied to the inputs are preserved in the outputs. Recent efforts aim to extend networks that are E(3) equivariant, to accommodate inputs made of multiple parts, each of which exhibits local E(3) symmetry. In practical settings, however, the partitioning into individually transforming regions is unknown a priori. Errors in the partition prediction would unavoidably map to errors in respecting the true input symmetry. Past works have proposed different ways to predict the partition, which may exhibit uncontrolled errors in their ability to maintain equivariance to the actual partition. To this end, we introduce APEN: a general framework for constructing approximate piecewise-E(3) equivariant point networks. Our primary insight is that functions that are equivariant with respect to a finer partition will also maintain equivariance in relation to the true partition. Leveraging this observation, we propose a design where the equivariance approximation error at each layers can be bounded solely in terms of (i) uncertainty quantification of the partition prediction, and (ii) bounds on the probability of failing to suggest a proper subpartition of the ground truth one. We demonstrate the effectiveness of APEN using two data types exemplifying part-based symmetry: (i) real-world scans of room scenes containing multiple furniture-type objects; and, (ii) human motions, characterized by articulated parts exhibiting rigid movement. Our empirical results demonstrate the advantage of integrating piecewise E(3) symmetry into network design, showing a distinct improvement in generalization compared to prior works for both classification and segmentation tasks.

We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii) to approximate Partial Differential Equations (PDEs) on manifolds, (iii) learn solution maps for Laplace-Beltrami (LB) operators, and (iv) to solve Bayesian inverse problems for identifying manifold shapes. The methods allow for handling geometries of general shape including point-cloud representations. The developed GNPs provide approaches for incorporating the roles of geometry in data-driven learning of operators.

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being sampled onto a uniform physical grid suffer significant aliasing error and information loss. Moreover, signals can exist in different topological structures as, for example, points, lines, surfaces and volumes. It has been challenging to analyze signals with mixed topologies (for example, point cloud with surface mesh). To this end, we develop mathematical formulations for Non-Uniform Fourier Transforms (NUFT) to directly, and optimally, sample nonuniform data signals of different topologies defined on a simplex mesh into the spectral domain with no spatial sampling error. The spectral transform is performed in the Euclidean space, which removes the translation ambiguity from works on the graph spectrum. Our representation has four distinct advantages: (1) the process causes no spatial sampling error during the initial sampling, (2) the generality of this approach provides a unified framework for using CNNs to analyze signals of mixed topologies, (3) it allows us to leverage state-of-the-art backbone CNN architectures for effective learning without having to design a particular architecture for a particular data structure in an ad-hoc fashion, and (4) the representation allows weighted meshes where each element has a different weight (i.e., texture) indicating local properties. We achieve results on par with the state-of-the-art for the 3D shape retrieval task, and a new state-of-the-art for the point cloud to surface reconstruction task.

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.

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 .

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

Current learning-based methods predict NeRF or 3D Gaussians from point clouds to achieve photo-realistic rendering but still depend on categorical priors, dense point clouds, or additional refinements. Hence, we introduce a novel point cloud rendering method by predicting 2D Gaussians from point clouds. Our method incorporates two identical modules with an entire-patch architecture enabling the network to be generalized to multiple datasets. The module normalizes and initializes the Gaussians utilizing the point cloud information including normals, colors and distances. Then, splitting decoders are employed to refine the initial Gaussians by duplicating them and predicting more accurate results, making our methodology effectively accommodate sparse point clouds as well. Once trained, our approach exhibits direct generalization to point clouds across different categories. The predicted Gaussians are employed directly for rendering without additional refinement on the rendered images, retaining the benefits of 2D Gaussians. We conduct extensive experiments on various datasets, and the results demonstrate the superiority and generalization of our method, which achieves SOTA performance. The code is available at https://github.com/murcherful/GauPCRender}{https://github.com/murcherful/GauPCRender.

We present a learning-based method, namely GeoUDF,to tackle the long-standing and challenging problem of reconstructing a discrete surface from a sparse point cloud.To be specific, we propose a geometry-guided learning method for UDF and its gradient estimation that explicitly formulates the unsigned distance of a query point as the learnable affine averaging of its distances to the tangent planes of neighboring points on the surface. Besides,we model the local geometric structure of the input point clouds by explicitly learning a quadratic polynomial for each point. This not only facilitates upsampling the input sparse point cloud but also naturally induces unoriented normal, which further augments UDF estimation. Finally, to extract triangle meshes from the predicted UDF we propose a customized edge-based marching cube module. We conduct extensive experiments and ablation studies to demonstrate the significant advantages of our method over state-of-the-art methods in terms of reconstruction accuracy, efficiency, and generality. The source code is publicly available at https://github.com/rsy6318/GeoUDF.

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.

This paper tries to address a fundamental question in point cloud self-supervised learning: what is a good signal we should leverage to learn features from point clouds without annotations? To answer that, we introduce a point cloud representation learning framework, based on geometric feature reconstruction. In contrast to recent papers that directly adopt masked autoencoder (MAE) and only predict original coordinates or occupancy from masked point clouds, our method revisits differences between images and point clouds and identifies three self-supervised learning objectives peculiar to point clouds, namely centroid prediction, normal estimation, and curvature prediction. Combined with occupancy prediction, these four objectives yield an nontrivial self-supervised learning task and mutually facilitate models to better reason fine-grained geometry of point clouds. Our pipeline is conceptually simple and it consists of two major steps: first, it randomly masks out groups of points, followed by a Transformer-based point cloud encoder; second, a lightweight Transformer decoder predicts centroid, normal, and curvature for points in each voxel. We transfer the pre-trained Transformer encoder to a downstream peception model. On the nuScene Datset, our model achieves 3.38 mAP improvment for object detection, 2.1 mIoU gain for segmentation, and 1.7 AMOTA gain for multi-object tracking. We also conduct experiments on the Waymo Open Dataset and achieve significant performance improvements over baselines as well.

The increasing demand for virtual reality applications has highlighted the significance of crafting immersive 3D assets. We present a text-to-3D 360^{circ} scene generation pipeline that facilitates the creation of comprehensive 360^{circ} scenes for in-the-wild environments in a matter of minutes. Our approach utilizes the generative power of a 2D diffusion model and prompt self-refinement to create a high-quality and globally coherent panoramic image. This image acts as a preliminary "flat" (2D) scene representation. Subsequently, it is lifted into 3D Gaussians, employing splatting techniques to enable real-time exploration. To produce consistent 3D geometry, our pipeline constructs a spatially coherent structure by aligning the 2D monocular depth into a globally optimized point cloud. This point cloud serves as the initial state for the centroids of 3D Gaussians. In order to address invisible issues inherent in single-view inputs, we impose semantic and geometric constraints on both synthesized and input camera views as regularizations. These guide the optimization of Gaussians, aiding in the reconstruction of unseen regions. In summary, our method offers a globally consistent 3D scene within a 360^{circ} perspective, providing an enhanced immersive experience over existing techniques. Project website at: http://dreamscene360.github.io/

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.

Spatial intelligence spans a rich suite of abilities, including visualising and transforming shapes, mentally rotating objects, judging relational positions and containment, and estimating numerosity. However, it still remains a critical unresolved challenge for Multimodal Large Language Models (MLLMs).To fill this gap, we propose to treat Euclidean geometry problem-solving as a surrogate task. Specifically, we meticulously constructed a curated multimodal dataset, called Euclid30K, comprising approximately 30K plane and solid geometry problems. To enable the model to acquire and apply Euclidean principles from these geometry problems, we employed Group Relative Policy Optimization (GRPO) to finetune the Qwen2.5VL family and RoboBrain2.0 family, inspiring the models to identify shapes, count, and relate entities, and perform multi-step deductive reasoning using Euclidean principles. Our experiments demonstrate that the resulting models achieve substantial zero-shot gains across four spatial reasoning benchmarks (Super-CLEVR, Omni3DBench, VSI-Bench, and MindCube) without any task-specific adaptations. Notably, after training on the Euclid30K, the mean VSI-Bench accuracy of all evaluated models rose from 34.5% to 40.5%, improving by 5.5 percentage points. Among them, RoboBrain2.0-Euclid-7B achieves 49.6\% accuracy, surpassing the previous state-of-the-art model, Spatial-MLLM.To our knowledge, this is the first systematic study showing that geometry-centric fine-tuning can confer vision-language models with broadly transferable spatial skills. Code and Euclid30K dataset can be found in https://zgca-ai4edu.github.io/Euclids_Gift.

LiDAR-based 3D sensors provide point clouds, a canonical 3D representation used in various scene understanding tasks. Modern LiDARs face key challenges in several real-world scenarios, such as long-distance or low-albedo objects, producing sparse or erroneous point clouds. These errors, which are rooted in the noisy raw LiDAR measurements, get propagated to downstream perception models, resulting in potentially severe loss of accuracy. This is because conventional 3D processing pipelines do not retain any uncertainty information from the raw measurements when constructing point clouds. We propose Probabilistic Point Clouds (PPC), a novel 3D scene representation where each point is augmented with a probability attribute that encapsulates the measurement uncertainty (or confidence) in the raw data. We further introduce inference approaches that leverage PPC for robust 3D object detection; these methods are versatile and can be used as computationally lightweight drop-in modules in 3D inference pipelines. We demonstrate, via both simulations and real captures, that PPC-based 3D inference methods outperform several baselines using LiDAR as well as camera-LiDAR fusion models, across challenging indoor and outdoor scenarios involving small, distant, and low-albedo objects, as well as strong ambient light. Our project webpage is at https://bhavyagoyal.github.io/ppc .

We present PI3DETR, an end-to-end framework that directly predicts 3D parametric curve instances from raw point clouds, avoiding the intermediate representations and multi-stage processing common in prior work. Extending 3DETR, our model introduces a geometry-aware matching strategy and specialized loss functions that enable unified detection of differently parameterized curve types, including cubic B\'ezier curves, line segments, circles, and arcs, in a single forward pass. Optional post-processing steps further refine predictions without adding complexity. This streamlined design improves robustness to noise and varying sampling densities, addressing critical challenges in real world LiDAR and 3D sensing scenarios. PI3DETR sets a new state-of-the-art on the ABC dataset and generalizes effectively to real sensor data, offering a simple yet powerful solution for 3D edge and curve estimation.

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.

Point clouds provide a flexible geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. While hand-designed features on point clouds have long been proposed in graphics and vision, however, the recent overwhelming success of convolutional neural networks (CNNs) for image analysis suggests the value of adapting insight from CNN to the point cloud world. Point clouds inherently lack topological information so designing a model to recover topology can enrich the representation power of point clouds. To this end, we propose a new neural network module dubbed EdgeConv suitable for CNN-based high-level tasks on point clouds including classification and segmentation. EdgeConv acts on graphs dynamically computed in each layer of the network. It is differentiable and can be plugged into existing architectures. Compared to existing modules operating in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked applied to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. We show the performance of our model on standard benchmarks including ModelNet40, ShapeNetPart, and S3DIS.

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often effective to incorporate global topological features, which are typically extracted by persistent homology. In the calculation of persistent homology for a point cloud, we choose a filtration for the point cloud, an increasing sequence of spaces. Since the performance of machine learning methods combined with persistent homology is highly affected by the choice of a filtration, we need to tune it depending on data and tasks. In this paper, we propose a framework that learns a filtration adaptively with the use of neural networks. In order to make the resulting persistent homology isometry-invariant, we develop a neural network architecture with such invariance. Additionally, we show a theoretical result on a finite-dimensional approximation of filtration functions, which justifies the proposed network architecture. Experimental results demonstrated the efficacy of our framework in several classification tasks.

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.

There is a growing number of tasks that work directly on point clouds. As the size of the point cloud grows, so do the computational demands of these tasks. A possible solution is to sample the point cloud first. Classic sampling approaches, such as farthest point sampling (FPS), do not consider the downstream task. A recent work showed that learning a task-specific sampling can improve results significantly. However, the proposed technique did not deal with the non-differentiability of the sampling operation and offered a workaround instead. We introduce a novel differentiable relaxation for point cloud sampling that approximates sampled points as a mixture of points in the primary input cloud. Our approximation scheme leads to consistently good results on classification and geometry reconstruction applications. We also show that the proposed sampling method can be used as a front to a point cloud registration network. This is a challenging task since sampling must be consistent across two different point clouds for a shared downstream task. In all cases, our approach outperforms existing non-learned and learned sampling alternatives. Our code is publicly available at https://github.com/itailang/SampleNet.

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.

Registration of distant outdoor LiDAR point clouds is crucial to extending the 3D vision of collaborative autonomous vehicles, and yet is challenging due to small overlapping area and a huge disparity between observed point densities. In this paper, we propose Group-wise Contrastive Learning (GCL) scheme to extract density-invariant geometric features to register distant outdoor LiDAR point clouds. We mark through theoretical analysis and experiments that, contrastive positives should be independent and identically distributed (i.i.d.), in order to train densityinvariant feature extractors. We propose upon the conclusion a simple yet effective training scheme to force the feature of multiple point clouds in the same spatial location (referred to as positive groups) to be similar, which naturally avoids the sampling bias introduced by a pair of point clouds to conform with the i.i.d. principle. The resulting fully-convolutional feature extractor is more powerful and density-invariant than state-of-the-art methods, improving the registration recall of distant scenarios on KITTI and nuScenes benchmarks by 40.9% and 26.9%, respectively. Code is available at https://github.com/liuQuan98/GCL.

k-nearest neighbor (k-NN) search is a fundamental primitive in geometry processing and computer graphics. While spatial partitioning structures such as kd-trees are standard, they are often manifold-blind, failing to exploit the intrinsic low-dimensional structure of points sampled from 2-manifolds. Recent advances in dynamic programming-based nearest neighbor search (DP-NNS) leverage incrementally constructed Voronoi diagrams to accelerate queries, where each site p maintains a list of successors that progressively refine its Voronoi cell. However, DP-NNS is restricted to single nearest neighbor (k=1) searches, precluding their adoption in applications that require local neighborhood statistics. In this paper, we generalize the DP-NNS framework to support arbitrary k-NN queries for manifold-aligned data. Our approach is founded on the geometric observation that if p_i is the nearest neighbor of a query q in P, then the second nearest neighbor of q must reside either within the prefix set P_{1:i-1} = {p_1, \dots, p_{i-1}} or within p_i's successor list. By recursively extending this principle, we introduce Manifold k-NN, a recursive algorithmic scheme that significantly outperforms conventional kd-trees for manifold-aligned data. Our method achieves a 1\times--10\times speedup in volume-to-surface query scenarios and inherently supports dynamic prefix queries -- enabling k-NN searches within any subset P_{1:m} (m \leq n) with zero overhead. Furthermore, we extend the framework to support point deletion via local Delaunay updates, providing a complete suite of dynamic operations for point set modification. Comprehensive experiments on diverse geometric datasets demonstrate the efficiency and broad applicability of our approach for modern graphics pipelines. Source code is available at https://github.com/sssomeone/manifold-knn.

Deep neural networks are prone to adversarial examples that maliciously alter the network's outcome. Due to the increasing popularity of 3D sensors in safety-critical systems and the vast deployment of deep learning models for 3D point sets, there is a growing interest in adversarial attacks and defenses for such models. So far, the research has focused on the semantic level, namely, deep point cloud classifiers. However, point clouds are also widely used in a geometric-related form that includes encoding and reconstructing the geometry. In this work, we are the first to consider the problem of adversarial examples at a geometric level. In this setting, the question is how to craft a small change to a clean source point cloud that leads, after passing through an autoencoder model, to the reconstruction of a different target shape. Our attack is in sharp contrast to existing semantic attacks on 3D point clouds. While such works aim to modify the predicted label by a classifier, we alter the entire reconstructed geometry. Additionally, we demonstrate the robustness of our attack in the case of defense, where we show that remnant characteristics of the target shape are still present at the output after applying the defense to the adversarial input. Our code is publicly available at https://github.com/itailang/geometric_adv.

We present EuLearn, the first surface datasets equitably representing a diversity of topological types. We designed our embedded surfaces of uniformly varying genera relying on random knots, thus allowing our surfaces to knot with themselves. EuLearn contributes new topological datasets of meshes, point clouds, and scalar fields in 3D. We aim to facilitate the training of machine learning systems that can discern topological features. We experimented with specific emblematic 3D neural network architectures, finding that their vanilla implementations perform poorly on genus classification. To enhance performance, we developed a novel, non-Euclidean, statistical sampling method adapted to graph and manifold data. We also introduce adjacency-informed adaptations of PointNet and Transformer architectures that rely on our non-Euclidean sampling strategy. Our results demonstrate that incorporating topological information into deep learning workflows significantly improves performance on these otherwise challenging EuLearn datasets.

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.

Classic 3D scene graph generation approaches fail to work in real-time due to the heavy computational cost of environment mapping and the need to generate intermediate point-cloud representations. To alleviate this issue, a recent work eschews point clouds in favor of a lightweight Gaussian distribution for each object. This approximation drastically speeds up inference and enables real-time 3D scene graph generation. However, the representation has two key weaknesses. 1) Each object is approximated by a single 3D Gaussian, which causes a severe loss of 3D geometric detail. 2) The discrepancy between this approximation and the true object geometry exacerbates the inaccurate merging of object candidates during online inference. To address these issues, we propose NoPA, which represents each object as a separate non-parametric distribution. This formulation retains 3D geometric information while preserving real-time inference of the parametric Gaussian formulation. To build upon our novel object representation, we propose a tailored merging strategy to recover coherent object instances. Specifically, we leverage maximum mean discrepancy on kernel density estimates to enable robust merging of object candidates during online exploration while minimizing added computational complexity. The key is to maintain a fixed particle set per object. Furthermore, to rectify the relation loss caused by misclassified objects, NoPA propagates relationships between objects with high affinity. Experiments show that NoPA substantially outperforms current methods without sacrificing real-time inference speed.

Diffusion models excel at 2D outpainting, but extending them to 360^circ panoramic completion from unposed perspective images is challenging due to the geometric and topological mismatch between perspective projections and spherical panoramas. We present Gimbal360, a principled framework that explicitly bridges perspective observations and spherical panoramas. We introduce a Canonical Viewing Space that regularizes projective geometry and provides a consistent intermediate representation between the two domains. To anchor in-the-wild inputs to this space, we propose a Differentiable Auto-Leveling module that stabilizes feature orientation without requiring camera parameters at inference. Panoramic generation also introduces a topological challenge. Standard generative architectures assume a bounded Euclidean image plane, while Equirectangular Projection (ERP) panoramas exhibit intrinsic S^1 periodicity. Euclidean operations therefore break boundary continuity. We address this mismatch by enforcing topological equivariance in the latent space to preserve seamless periodic structure. To support this formulation, we introduce Horizon360, a curated large-scale dataset of gravity-aligned panoramic environments. Extensive experiments show that explicitly standardizing geometric and topological priors enables Gimbal360 to achieve state-of-the-art performance in structurally consistent 360^circ scene completion.

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

LiDAR point clouds are fundamental to various applications, yet the extreme sparsity of high-precision geometric details hinders efficient context modeling, thereby limiting the compression speed and performance of existing methods. To address this challenge, we propose a compact representation for efficient predictive lossless coding. Our framework comprises two lightweight modules. First, the Geometry Re-Densification Module iteratively densifies encoded sparse geometry, extracts features at a dense scale, and then sparsifies the features for predictive coding. This module avoids costly computation on highly sparse details while maintaining a lightweight prediction head. Second, the Cross-scale Feature Propagation Module leverages occupancy cues from multiple resolution levels to guide hierarchical feature propagation, enabling information sharing across scales and reducing redundant feature extraction. Additionally, we introduce an integer-only inference pipeline to enable bit-exact cross-platform consistency, which avoids the entropy-coding collapse observed in existing neural compression methods and further accelerates coding. Experiments demonstrate competitive compression performance at real-time speed. Code will be released upon acceptance. Code is available at https://github.com/pengpeng-yu/FastPCC.

3D perception, especially point cloud classification, has achieved substantial progress. However, in real-world deployment, point cloud corruptions are inevitable due to the scene complexity, sensor inaccuracy, and processing imprecision. In this work, we aim to rigorously benchmark and analyze point cloud classification under corruptions. To conduct a systematic investigation, we first provide a taxonomy of common 3D corruptions and identify the atomic corruptions. Then, we perform a comprehensive evaluation on a wide range of representative point cloud models to understand their robustness and generalizability. Our benchmark results show that although point cloud classification performance improves over time, the state-of-the-art methods are on the verge of being less robust. Based on the obtained observations, we propose several effective techniques to enhance point cloud classifier robustness. We hope our comprehensive benchmark, in-depth analysis, and proposed techniques could spark future research in robust 3D perception.

Point cloud is an important type of geometric data structure. Due to its irregular format, most researchers transform such data to regular 3D voxel grids or collections of images. This, however, renders data unnecessarily voluminous and causes issues. In this paper, we design a novel type of neural network that directly consumes point clouds and well respects the permutation invariance of points in the input. Our network, named PointNet, provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing. Though simple, PointNet is highly efficient and effective. Empirically, it shows strong performance on par or even better than state of the art. Theoretically, we provide analysis towards understanding of what the network has learnt and why the network is robust with respect to input perturbation and corruption.

Point cloud registration is the task of estimating the rigid transformation that aligns a pair of point cloud fragments. We present an efficient and robust framework for pairwise registration of real-world 3D scans, leveraging Hough voting in the 6D transformation parameter space. First, deep geometric features are extracted from a point cloud pair to compute putative correspondences. We then construct a set of triplets of correspondences to cast votes on the 6D Hough space, representing the transformation parameters in sparse tensors. Next, a fully convolutional refinement module is applied to refine the noisy votes. Finally, we identify the consensus among the correspondences from the Hough space, which we use to predict our final transformation parameters. Our method outperforms state-of-the-art methods on 3DMatch and 3DLoMatch benchmarks while achieving comparable performance on KITTI odometry dataset. We further demonstrate the generalizability of our approach by setting a new state-of-the-art on ICL-NUIM dataset, where we integrate our module into a multi-way registration pipeline.

In this paper we address the task of finding representative subsets of points in a 3D point cloud by means of a point-wise ordering. Only a few works have tried to address this challenging vision problem, all with the help of hard to obtain point and cloud labels. Different from these works, we introduce the task of point-wise ordering in 3D point clouds through self-supervision, which we call self-ordering. We further contribute the first end-to-end trainable network that learns a point-wise ordering in a self-supervised fashion. It utilizes a novel differentiable point scoring-sorting strategy and it constructs an hierarchical contrastive scheme to obtain self-supervision signals. We extensively ablate the method and show its scalability and superior performance even compared to supervised ordering methods on multiple datasets and tasks including zero-shot ordering of point clouds from unseen categories.

Perceiving the environment via cameras is crucial for Reinforcement Learning (RL) in robotics. While images are a convenient form of representation, they often complicate extracting important geometric details, especially with varying geometries or deformable objects. In contrast, point clouds naturally represent this geometry and easily integrate color and positional data from multiple camera views. However, while deep learning on point clouds has seen many recent successes, RL on point clouds is under-researched, with only the simplest encoder architecture considered in the literature. We introduce PointPatchRL (PPRL), a method for RL on point clouds that builds on the common paradigm of dividing point clouds into overlapping patches, tokenizing them, and processing the tokens with transformers. PPRL provides significant improvements compared with other point-cloud processing architectures previously used for RL. We then complement PPRL with masked reconstruction for representation learning and show that our method outperforms strong model-free and model-based baselines on image observations in complex manipulation tasks containing deformable objects and variations in target object geometry. Videos and code are available at https://alrhub.github.io/pprl-website

We introduce a new trajectory optimization method for robotic grasping based on a point-cloud representation of robots and task spaces. In our method, robots are represented by 3D points on their link surfaces. The task space of a robot is represented by a point cloud that can be obtained from depth sensors. Using the point-cloud representation, goal reaching in grasping can be formulated as point matching, while collision avoidance can be efficiently achieved by querying the signed distance values of the robot points in the signed distance field of the scene points. Consequently, a constrained nonlinear optimization problem is formulated to solve the joint motion and grasp planning problem. The advantage of our method is that the point-cloud representation is general to be used with any robot in any environment. We demonstrate the effectiveness of our method by performing experiments on a tabletop scene and a shelf scene for grasping with a Fetch mobile manipulator and a Franka Panda arm. The project page is available at https://irvlutd.github.io/GraspTrajOpt

Open-vocabulary 3D scene understanding is indispensable for embodied agents. Recent works leverage pretrained vision-language models (VLMs) for object segmentation and project them to point clouds to build 3D maps. Despite progress, a point cloud is a set of unordered coordinates that requires substantial storage space and does not directly convey occupancy information or spatial relation, making existing methods inefficient for downstream tasks, e.g., path planning and text-based object retrieval. To address these issues, we propose Octree-Graph, a novel scene representation for open-vocabulary 3D scene understanding. Specifically, a Chronological Group-wise Segment Merging (CGSM) strategy and an Instance Feature Aggregation (IFA) algorithm are first designed to get 3D instances and corresponding semantic features. Subsequently, an adaptive-octree structure is developed that stores semantics and depicts the occupancy of an object adjustably according to its shape. Finally, the Octree-Graph is constructed where each adaptive-octree acts as a graph node, and edges describe the spatial relations among nodes. Extensive experiments on various tasks are conducted on several widely-used datasets, demonstrating the versatility and effectiveness of our method. Code is available https://github.com/yifeisu/OV-Octree-Graph{here}.

Three-dimensional (3D) point cloud analysis has become central to applications ranging from autonomous driving and robotics to forestry and ecological monitoring. Although numerous deep learning methods have been proposed for point cloud understanding, including supervised backbones, self-supervised pre-training (SSL), and parameter-efficient fine-tuning (PEFT), their implementations are scattered across incompatible codebases with differing data pipelines, evaluation protocols, and configuration formats, making fair comparisons difficult. We introduce , a unified, extensible PyTorch library that integrates over 55 model configurations covering 29 supervised architectures, seven SSL pre-training methods, and five PEFT strategies, all within a single registry-based framework supporting classification, semantic segmentation, part segmentation, and few-shot learning. provides standardised training runners, cross-validation with stratified K-fold splitting, automated LaTeX/CSV table generation, built-in Friedman/Nemenyi statistical testing with critical-difference diagrams for rigorous multi-model comparison, and a comprehensive test suite with 2\,200+ automated tests validating every configuration end-to-end. The code is available at https://github.com/said-ohamouddou/LIDARLearn under the MIT licence.

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.

3D surface reconstruction from point clouds is a key step in areas such as content creation, archaeology, digital cultural heritage, and engineering. Current approaches either try to optimize a non-data-driven surface representation to fit the points, or learn a data-driven prior over the distribution of commonly occurring surfaces and how they correlate with potentially noisy point clouds. Data-driven methods enable robust handling of noise and typically either focus on a global or a local prior, which trade-off between robustness to noise on the global end and surface detail preservation on the local end. We propose PPSurf as a method that combines a global prior based on point convolutions and a local prior based on processing local point cloud patches. We show that this approach is robust to noise while recovering surface details more accurately than the current state-of-the-art. Our source code, pre-trained model and dataset are available at: https://github.com/cg-tuwien/ppsurf

Nowadays, pre-training big models on large-scale datasets has become a crucial topic in deep learning. The pre-trained models with high representation ability and transferability achieve a great success and dominate many downstream tasks in natural language processing and 2D vision. However, it is non-trivial to promote such a pretraining-tuning paradigm to the 3D vision, given the limited training data that are relatively inconvenient to collect. In this paper, we provide a new perspective of leveraging pre-trained 2D knowledge in 3D domain to tackle this problem, tuning pre-trained image models with the novel Point-to-Pixel prompting for point cloud analysis at a minor parameter cost. Following the principle of prompting engineering, we transform point clouds into colorful images with geometry-preserved projection and geometry-aware coloring to adapt to pre-trained image models, whose weights are kept frozen during the end-to-end optimization of point cloud analysis tasks. We conduct extensive experiments to demonstrate that cooperating with our proposed Point-to-Pixel Prompting, better pre-trained image model will lead to consistently better performance in 3D vision. Enjoying prosperous development from image pre-training field, our method attains 89.3% accuracy on the hardest setting of ScanObjectNN, surpassing conventional point cloud models with much fewer trainable parameters. Our framework also exhibits very competitive performance on ModelNet classification and ShapeNet Part Segmentation. Code is available at https://github.com/wangzy22/P2P.

We introduce ECLAIR (Extended Classification of Lidar for AI Recognition), a new outdoor large-scale aerial LiDAR dataset designed specifically for advancing research in point cloud semantic segmentation. As the most extensive and diverse collection of its kind to date, the dataset covers a total area of 10km^2 with close to 600 million points and features eleven distinct object categories. To guarantee the dataset's quality and utility, we have thoroughly curated the point labels through an internal team of experts, ensuring accuracy and consistency in semantic labeling. The dataset is engineered to move forward the fields of 3D urban modeling, scene understanding, and utility infrastructure management by presenting new challenges and potential applications. As a benchmark, we report qualitative and quantitative analysis of a voxel-based point cloud segmentation approach based on the Minkowski Engine.

Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based approach that consists of neurons with spherical decision surfaces and operates on point clouds. Such spherical neurons are obtained by conformal embedding of Euclidean space and have recently been revisited in the context of learning representations of point sets. Focusing on 3D geometry, we exploit the isometry property of spherical neurons and derive a 3D steerability constraint. After training spherical neurons to classify point clouds in a canonical orientation, we use a tetrahedron basis to quadruplicate the neurons and construct rotation-equivariant spherical filter banks. We then apply the derived constraint to interpolate the filter bank outputs and, thus, obtain a rotation-invariant network. Finally, we use a synthetic point set and real-world 3D skeleton data to verify our theoretical findings. The code is available at https://github.com/pavlo-melnyk/steerable-3d-neurons.

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.

Reliable odometry is essential for mobile robots as they increasingly enter more challenging environments, which often contain little information to constrain point cloud registration, resulting in degraded LiDAR-Inertial Odometry (LIO) accuracy or even divergence. To address this, we present BIEVR-LIO, a novel approach designed specifically to exploit subtle variations in the available geometry for improved robustness. We propose a high-resolution map representation that stores surfaces as compact voxel-wise oriented height images. This representation can directly be used for registration without the calculation of intermediate geometric primitives while still supporting efficient updates. Since informative geometry is often sparsely distributed in the environment, we further propose a map-informed point sampling strategy to focus registration on geometrically informative regions, improving robustness in uninformative environments while reducing computational cost compared to global high-resolution sampling. Experiments across multiple sensors, platforms, and environments demonstrates state-of-the-art performance in well-constrained scenes and substantial improvements in challenging scenarios where baseline methods diverge. Additionally, we demonstrate that the fine-grained geometry captured by BIEVR-LIO can be used for downstream tasks such as elevation mapping for robot locomotion.

Accurate detection of objects in 3D point clouds is a central problem in many applications, such as autonomous navigation, housekeeping robots, and augmented/virtual reality. To interface a highly sparse LiDAR point cloud with a region proposal network (RPN), most existing efforts have focused on hand-crafted feature representations, for example, a bird's eye view projection. In this work, we remove the need of manual feature engineering for 3D point clouds and propose VoxelNet, a generic 3D detection network that unifies feature extraction and bounding box prediction into a single stage, end-to-end trainable deep network. Specifically, VoxelNet divides a point cloud into equally spaced 3D voxels and transforms a group of points within each voxel into a unified feature representation through the newly introduced voxel feature encoding (VFE) layer. In this way, the point cloud is encoded as a descriptive volumetric representation, which is then connected to a RPN to generate detections. Experiments on the KITTI car detection benchmark show that VoxelNet outperforms the state-of-the-art LiDAR based 3D detection methods by a large margin. Furthermore, our network learns an effective discriminative representation of objects with various geometries, leading to encouraging results in 3D detection of pedestrians and cyclists, based on only LiDAR.

We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks and numerical methods. We show how our GNPs can be trained to learn robust latent representations for the differential geometry of point-clouds to provide estimates of metric, curvature, and other shape-related features. We demonstrate how our pre-trained GNPs can be used (i) to estimate the geometric properties of surfaces of arbitrary shape and topologies with robustness in the presence of noise, (ii) to approximate solutions of geometric partial differential equations (PDEs) on manifolds, and (iii) to solve equations for shape deformations such as curvature driven flows. We release codes and weights for using GNPs in the package geo_neural_op. This allows for incorporating our pre-trained GNPs as components for reuse within existing and new data processing pipelines. The GNPs also can be used as part of numerical solvers involving geometry or as part of methods for performing inference and other geometric tasks.

Point-cloud data collected in real-world applications are often incomplete. Data is typically missing due to objects being observed from partial viewpoints, which only capture a specific perspective or angle. Additionally, data can be incomplete due to occlusion and low-resolution sampling. Existing completion approaches rely on datasets of predefined objects to guide the completion of noisy and incomplete, point clouds. However, these approaches perform poorly when tested on Out-Of-Distribution (OOD) objects, that are poorly represented in the training dataset. Here we leverage recent advances in text-guided image generation, which lead to major breakthroughs in text-guided shape generation. We describe an approach called SDS-Complete that uses a pre-trained text-to-image diffusion model and leverages the text semantics of a given incomplete point cloud of an object, to obtain a complete surface representation. SDS-Complete can complete a variety of objects using test-time optimization without expensive collection of 3D information. We evaluate SDS Complete on incomplete scanned objects, captured by real-world depth sensors and LiDAR scanners. We find that it effectively reconstructs objects that are absent from common datasets, reducing Chamfer loss by 50% on average compared with current methods. Project page: https://sds-complete.github.io/

Learning signed distance functions (SDFs) from 3D point clouds is an important task in 3D computer vision. However, without ground truth signed distances, point normals or clean point clouds, current methods still struggle from learning SDFs from noisy point clouds. To overcome this challenge, we propose to learn SDFs via a noise to noise mapping, which does not require any clean point cloud or ground truth supervision for training. Our novelty lies in the noise to noise mapping which can infer a highly accurate SDF of a single object or scene from its multiple or even single noisy point cloud observations. Our novel learning manner is supported by modern Lidar systems which capture multiple noisy observations per second. We achieve this by a novel loss which enables statistical reasoning on point clouds and maintains geometric consistency although point clouds are irregular, unordered and have no point correspondence among noisy observations. Our evaluation under the widely used benchmarks demonstrates our superiority over the state-of-the-art methods in surface reconstruction, point cloud denoising and upsampling. Our code, data, and pre-trained models are available at https://github.com/mabaorui/Noise2NoiseMapping/

This paper proposes a new method to infer keypoints from arbitrary object categories in practical scenarios where point cloud data (PCD) are noisy, down-sampled and arbitrarily rotated. Our proposed model adheres to the following principles: i) keypoints inference is fully unsupervised (no annotation given), ii) keypoints position error should be low and resilient to PCD perturbations (robustness), iii) keypoints should not change their indexes for the intra-class objects (semantic coherence), iv) keypoints should be close to or proximal to PCD surface (compactness). We achieve these desiderata by proposing a new self-supervised training strategy for keypoints estimation that does not assume any a priori knowledge of the object class, and a model architecture with coupled auxiliary losses that promotes the desired keypoints properties. We compare the keypoints estimated by the proposed approach with those of the state-of-the-art unsupervised approaches. The experiments show that our approach outperforms by estimating keypoints with improved coverage (+9.41%) while being semantically consistent (+4.66%) that best characterizes the object's 3D shape for downstream tasks. Code and data are available at: https://github.com/IITPAVIS/SC3K

Generation of 3D data by deep neural network has been attracting increasing attention in the research community. The majority of extant works resort to regular representations such as volumetric grids or collection of images; however, these representations obscure the natural invariance of 3D shapes under geometric transformations and also suffer from a number of other issues. In this paper we address the problem of 3D reconstruction from a single image, generating a straight-forward form of output -- point cloud coordinates. Along with this problem arises a unique and interesting issue, that the groundtruth shape for an input image may be ambiguous. Driven by this unorthodox output form and the inherent ambiguity in groundtruth, we design architecture, loss function and learning paradigm that are novel and effective. Our final solution is a conditional shape sampler, capable of predicting multiple plausible 3D point clouds from an input image. In experiments not only can our system outperform state-of-the-art methods on single image based 3d reconstruction benchmarks; but it also shows a strong performance for 3d shape completion and promising ability in making multiple plausible predictions.

We present TreeON, a novel neural-based framework for reconstructing detailed 3D tree point clouds from sparse top-down geodata, using only a single orthophoto and its corresponding Digital Surface Model (DSM). Our method introduces a new training supervision strategy that combines both geometric supervision and differentiable shadow and silhouette losses to learn point cloud representations of trees without requiring species labels, procedural rules, terrestrial reconstruction data, or ground laser scans. To address the lack of ground truth data, we generate a synthetic dataset of point clouds from procedurally modeled trees and train our network on it. Quantitative and qualitative experiments demonstrate better reconstruction quality and coverage compared to existing methods, as well as strong generalization to real-world data, producing visually appealing and structurally plausible tree point cloud representations suitable for integration into interactive digital 3D maps. The codebase, synthetic dataset, and pretrained model are publicly available at https://angelikigram.github.io/treeON/.

LiDAR-based 3D point cloud recognition has benefited various applications. Without specially considering the LiDAR point distribution, most current methods suffer from information disconnection and limited receptive field, especially for the sparse distant points. In this work, we study the varying-sparsity distribution of LiDAR points and present SphereFormer to directly aggregate information from dense close points to the sparse distant ones. We design radial window self-attention that partitions the space into multiple non-overlapping narrow and long windows. It overcomes the disconnection issue and enlarges the receptive field smoothly and dramatically, which significantly boosts the performance of sparse distant points. Moreover, to fit the narrow and long windows, we propose exponential splitting to yield fine-grained position encoding and dynamic feature selection to increase model representation ability. Notably, our method ranks 1st on both nuScenes and SemanticKITTI semantic segmentation benchmarks with 81.9% and 74.8% mIoU, respectively. Also, we achieve the 3rd place on nuScenes object detection benchmark with 72.8% NDS and 68.5% mAP. Code is available at https://github.com/dvlab-research/SphereFormer.git.

Recent progress in 3D generation has been driven largely by models conditioned on images or text, while readily available 3D priors are still underused. In many real-world scenarios, the visible-region point cloud are easy to obtain from active sensors such as LiDAR or from feed-forward predictors like VGGT, offering explicit geometric constraints that current methods fail to exploit. In this work, we introduce Points-to-3D, a diffusion-based framework that leverages point cloud priors for geometry-controllable 3D asset and scene generation. Built on a latent 3D diffusion model TRELLIS, Points-to-3D first replaces pure-noise sparse structure latent initialization with a point cloud priors tailored input formulation.A structure inpainting network, trained within the TRELLIS framework on task-specific data designed to learn global structural inpainting, is then used for inference with a staged sampling strategy (structural inpainting followed by boundary refinement), completing the global geometry while preserving the visible regions of the input priors. In practice, Points-to-3D can take either accurate point-cloud priors or VGGT-estimated point clouds from single images as input. Experiments on both objects and scene scenarios consistently demonstrate superior performance over state-of-the-art baselines in terms of rendering quality and geometric fidelity, highlighting the effectiveness of explicitly embedding point-cloud priors for achieving more accurate and structurally controllable 3D generation. Project page: https://jiatongxia.github.io/points2-3D/

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.

Recent advances in pretraining 3D point cloud encoders (e.g., Point-BERT, Point-MAE) have produced powerful models, whose abilities are typically evaluated on geometric or semantic tasks. At the same time, topological descriptors have been shown to provide informative summaries of a shape's multiscale structure. In this paper we pose the question whether topological information can be derived from features produced by 3D encoders. To address this question, we first introduce DONUT, a synthetic benchmark with controlled topological complexity, and propose FILTR (Filtration Transformer), a learnable framework to predict persistence diagrams directly from frozen encoders. FILTR adapts a transformer decoder to treat diagram generation as a set prediction task. Our analysis on DONUT reveals that existing encoders retain only limited global topological signals, yet FILTR successfully leverages information produced by these encoders to approximate persistence diagrams. Our approach enables, for the first time, data-driven extraction of persistence diagrams from raw point clouds through an efficient learnable feed-forward mechanism.

3D Point Cloud Semantic Segmentation (PCSS) is attracting increasing interest, due to its applicability in remote sensing, computer vision and robotics, and due to the new possibilities offered by deep learning techniques. In order to provide a needed up-to-date review of recent developments in PCSS, this article summarizes existing studies on this topic. Firstly, we outline the acquisition and evolution of the 3D point cloud from the perspective of remote sensing and computer vision, as well as the published benchmarks for PCSS studies. Then, traditional and advanced techniques used for Point Cloud Segmentation (PCS) and PCSS are reviewed and compared. Finally, important issues and open questions in PCSS studies are discussed.

Recently, image-to-3D approaches have significantly advanced the generation quality and speed of 3D assets based on large reconstruction models, particularly 3D Gaussian reconstruction models. Existing large 3D Gaussian models directly map 2D image to 3D Gaussian parameters, while regressing 2D image to 3D Gaussian representations is challenging without 3D priors. In this paper, we propose a large Point-to-Gaussian model, that inputs the initial point cloud produced from large 3D diffusion model conditional on 2D image to generate the Gaussian parameters, for image-to-3D generation. The point cloud provides initial 3D geometry prior for Gaussian generation, thus significantly facilitating image-to-3D Generation. Moreover, we present the Attention mechanism, Projection mechanism, and Point feature extractor, dubbed as APP block, for fusing the image features with point cloud features. The qualitative and quantitative experiments extensively demonstrate the effectiveness of the proposed approach on GSO and Objaverse datasets, and show the proposed method achieves state-of-the-art performance.

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

This study introduces a novel framework, G3Reg, for fast and robust global registration of LiDAR point clouds. In contrast to conventional complex keypoints and descriptors, we extract fundamental geometric primitives, including planes, clusters, and lines (PCL) from the raw point cloud to obtain low-level semantic segments. Each segment is represented as a unified Gaussian Ellipsoid Model (GEM), using a probability ellipsoid to ensure the ground truth centers are encompassed with a certain degree of probability. Utilizing these GEMs, we present a distrust-and-verify scheme based on a Pyramid Compatibility Graph for Global Registration (PAGOR). Specifically, we establish an upper bound, which can be traversed based on the confidence level for compatibility testing to construct the pyramid graph. Then, we solve multiple maximum cliques (MAC) for each level of the pyramid graph, thus generating the corresponding transformation candidates. In the verification phase, we adopt a precise and efficient metric for point cloud alignment quality, founded on geometric primitives, to identify the optimal candidate. The algorithm's performance is validated on three publicly available datasets and a self-collected multi-session dataset. Parameter settings remained unchanged during the experiment evaluations. The results exhibit superior robustness and real-time performance of the G3Reg framework compared to state-of-the-art methods. Furthermore, we demonstrate the potential for integrating individual GEM and PAGOR components into other registration frameworks to enhance their efficacy. Code: https://github.com/HKUST-Aerial-Robotics/G3Reg

We present a probabilistic model for point cloud generation, which is fundamental for various 3D vision tasks such as shape completion, upsampling, synthesis and data augmentation. Inspired by the diffusion process in non-equilibrium thermodynamics, we view points in point clouds as particles in a thermodynamic system in contact with a heat bath, which diffuse from the original distribution to a noise distribution. Point cloud generation thus amounts to learning the reverse diffusion process that transforms the noise distribution to the distribution of a desired shape. Specifically, we propose to model the reverse diffusion process for point clouds as a Markov chain conditioned on certain shape latent. We derive the variational bound in closed form for training and provide implementations of the model. Experimental results demonstrate that our model achieves competitive performance in point cloud generation and auto-encoding. The code is available at https://github.com/luost26/diffusion-point-cloud.

With the recent availability and affordability of commercial depth sensors and 3D scanners, an increasing number of 3D (i.e., RGBD, point cloud) datasets have been publicized to facilitate research in 3D computer vision. However, existing datasets either cover relatively small areas or have limited semantic annotations. Fine-grained understanding of urban-scale 3D scenes is still in its infancy. In this paper, we introduce SensatUrban, an urban-scale UAV photogrammetry point cloud dataset consisting of nearly three billion points collected from three UK cities, covering 7.6 km^2. Each point in the dataset has been labelled with fine-grained semantic annotations, resulting in a dataset that is three times the size of the previous existing largest photogrammetric point cloud dataset. In addition to the more commonly encountered categories such as road and vegetation, urban-level categories including rail, bridge, and river are also included in our dataset. Based on this dataset, we further build a benchmark to evaluate the performance of state-of-the-art segmentation algorithms. In particular, we provide a comprehensive analysis and identify several key challenges limiting urban-scale point cloud understanding. The dataset is available at http://point-cloud-analysis.cs.ox.ac.uk.

Geometry and color information provided by the point clouds are both crucial for 3D scene understanding. Two pieces of information characterize the different aspects of point clouds, but existing methods lack an elaborate design for the discrimination and relevance. Hence we explore a 3D self-supervised paradigm that can better utilize the relations of point cloud information. Specifically, we propose a universal 3D scene pre-training framework via Geometry-Color Contrast (Point-GCC), which aligns geometry and color information using a Siamese network. To take care of actual application tasks, we design (i) hierarchical supervision with point-level contrast and reconstruct and object-level contrast based on the novel deep clustering module to close the gap between pre-training and downstream tasks; (ii) architecture-agnostic backbone to adapt for various downstream models. Benefiting from the object-level representation associated with downstream tasks, Point-GCC can directly evaluate model performance and the result demonstrates the effectiveness of our methods. Transfer learning results on a wide range of tasks also show consistent improvements across all datasets. e.g., new state-of-the-art object detection results on SUN RGB-D and S3DIS datasets. Codes will be released at https://github.com/Asterisci/Point-GCC.

We present a Non-parametric Network for 3D point cloud analysis, Point-NN, which consists of purely non-learnable components: farthest point sampling (FPS), k-nearest neighbors (k-NN), and pooling operations, with trigonometric functions. Surprisingly, it performs well on various 3D tasks, requiring no parameters or training, and even surpasses existing fully trained models. Starting from this basic non-parametric model, we propose two extensions. First, Point-NN can serve as a base architectural framework to construct Parametric Networks by simply inserting linear layers on top. Given the superior non-parametric foundation, the derived Point-PN exhibits a high performance-efficiency trade-off with only a few learnable parameters. Second, Point-NN can be regarded as a plug-and-play module for the already trained 3D models during inference. Point-NN captures the complementary geometric knowledge and enhances existing methods for different 3D benchmarks without re-training. We hope our work may cast a light on the community for understanding 3D point clouds with non-parametric methods. Code is available at https://github.com/ZrrSkywalker/Point-NN.

3D vision has rapidly evolved, driven by increasingly diverse data representations, learning paradigms, and modeling strategies. Yet the field remains fragmented across representations and benchmarks, making it difficult to develop unified perspectives on efficiency, fidelity, and scalability. This work provides a data-centric taxonomy of 3D vision that connects geometric representations, datasets, learning frameworks, and applications within a single conceptual map. We begin by analysing the principal structural representations of 3D data--point clouds, meshes, voxels, and 3D Gaussians--along with their acquisition pipelines. We then examine how dataset design, benchmark construction, and supervision regimes shape recent advances, spanning 2D-supervised 3D learning, implicit neural representations, and 4D world modeling. Through this integrative lens, we clarify the relationships among representations, learning paradigms, and downstream tasks in reconstruction, generation, and video modeling, offering a consolidated view of emerging trends toward balancing efficiency and fidelity and toward multimodal geometric grounding.

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.

One of the main challenges in LiDAR-based 3D object detection is that the sensors often fail to capture the complete spatial information about the objects due to long distance and occlusion. Two-stage detectors with point cloud completion approaches tackle this problem by adding more points to the regions of interest (RoIs) with a pre-trained network. However, these methods generate dense point clouds of objects for all region proposals, assuming that objects always exist in the RoIs. This leads to the indiscriminate point generation for incorrect proposals as well. Motivated by this, we propose Point Generation R-CNN (PG-RCNN), a novel end-to-end detector that generates semantic surface points of foreground objects for accurate detection. Our method uses a jointly trained RoI point generation module to process the contextual information of RoIs and estimate the complete shape and displacement of foreground objects. For every generated point, PG-RCNN assigns a semantic feature that indicates the estimated foreground probability. Extensive experiments show that the point clouds generated by our method provide geometrically and semantically rich information for refining false positive and misaligned proposals. PG-RCNN achieves competitive performance on the KITTI benchmark, with significantly fewer parameters than state-of-the-art models. The code is available at https://github.com/quotation2520/PG-RCNN.

Most real-world 3D measurements from depth sensors are incomplete, and to address this issue the point cloud completion task aims to predict the complete shapes of objects from partial observations. Previous works often adapt an encoder-decoder architecture, where the encoder is trained to extract embeddings that are used as inputs to generate predictions from the decoder. However, the learned embeddings have sparse distribution in the feature space, which leads to worse generalization results during testing. To address these problems, this paper proposes a hyperspherical module, which transforms and normalizes embeddings from the encoder to be on a unit hypersphere. With the proposed module, the magnitude and direction of the output hyperspherical embedding are decoupled and only the directional information is optimized. We theoretically analyze the hyperspherical embedding and show that it enables more stable training with a wider range of learning rates and more compact embedding distributions. Experiment results show consistent improvement of point cloud completion in both single-task and multi-task learning, which demonstrates the effectiveness of the proposed method.

In this paper, we question whether we have a reliable self-supervised point cloud model that can be used for diverse 3D tasks via simple linear probing, even with limited data and minimal computation. We find that existing 3D self-supervised learning approaches fall short when evaluated on representation quality through linear probing. We hypothesize that this is due to what we term the "geometric shortcut", which causes representations to collapse to low-level spatial features. This challenge is unique to 3D and arises from the sparse nature of point cloud data. We address it through two key strategies: obscuring spatial information and enhancing the reliance on input features, ultimately composing a Sonata of 140k point clouds through self-distillation. Sonata is simple and intuitive, yet its learned representations are strong and reliable: zero-shot visualizations demonstrate semantic grouping, alongside strong spatial reasoning through nearest-neighbor relationships. Sonata demonstrates exceptional parameter and data efficiency, tripling linear probing accuracy (from 21.8% to 72.5%) on ScanNet and nearly doubling performance with only 1% of the data compared to previous approaches. Full fine-tuning further advances SOTA across both 3D indoor and outdoor perception tasks.

Place recognition is a key module for long-term SLAM systems. Current LiDAR-based place recognition methods usually use representations of point clouds such as unordered points or range images. These methods achieve high recall rates of retrieval, but their performance may degrade in the case of view variation or scene changes. In this work, we explore the potential of a different representation in place recognition, i.e. bird's eye view (BEV) images. We observe that the structural contents of BEV images are less influenced by rotations and translations of point clouds. We validate that, without any delicate design, a simple VGGNet trained on BEV images achieves comparable performance with the state-of-the-art place recognition methods in scenes of slight viewpoint changes. For more robust place recognition, we design a rotation-invariant network called BEVPlace. We use group convolution to extract rotation-equivariant local features from the images and NetVLAD for global feature aggregation. In addition, we observe that the distance between BEV features is correlated with the geometry distance of point clouds. Based on the observation, we develop a method to estimate the position of the query cloud, extending the usage of place recognition. The experiments conducted on large-scale public datasets show that our method 1) achieves state-of-the-art performance in terms of recall rates, 2) is robust to view changes, 3) shows strong generalization ability, and 4) can estimate the positions of query point clouds. Source codes are publicly available at https://github.com/zjuluolun/BEVPlace.

We propose a spherical kernel for efficient graph convolution of 3D point clouds. Our metric-based kernels systematically quantize the local 3D space to identify distinctive geometric relationships in the data. Similar to the regular grid CNN kernels, the spherical kernel maintains translation-invariance and asymmetry properties, where the former guarantees weight sharing among similar local structures in the data and the latter facilitates fine geometric learning. The proposed kernel is applied to graph neural networks without edge-dependent filter generation, making it computationally attractive for large point clouds. In our graph networks, each vertex is associated with a single point location and edges connect the neighborhood points within a defined range. The graph gets coarsened in the network with farthest point sampling. Analogous to the standard CNNs, we define pooling and unpooling operations for our network. We demonstrate the effectiveness of the proposed spherical kernel with graph neural networks for point cloud classification and semantic segmentation using ModelNet, ShapeNet, RueMonge2014, ScanNet and S3DIS datasets. The source code and the trained models can be downloaded from https://github.com/hlei-ziyan/SPH3D-GCN.

Recent advances in generative models highlight the power of geometry-aware modeling in manifold-constrained settings. Yet, for natural images, the field remains confined to Euclidean assumptions, failing to exploit the potential of intrinsic geometric structures within the data. In this work, we investigate the geometry of natural images and observe that semantic information is predominantly encoded in directional components, while norm components can be approximated by the global average. This property holds across both RGB and latent spaces, suggesting that natural images can be effectively modeled on a hypersphere. Building on this finding, we introduce Spherical Optimal Transport Flow Matching (SOT-CFM), which utilizes angular distance, and Spherical Flow Matching (SFM), which constrains dynamics directly on the manifold. Our experiments demonstrate that these geometry-aware methods achieve superior performance against Euclidean baselines. Ultimately, this work provides a novel perspective that bridges the gap between Riemannian manifold-based modeling and natural image generation.

We present MoGe, a powerful model for recovering 3D geometry from monocular open-domain images. Given a single image, our model directly predicts a 3D point map of the captured scene with an affine-invariant representation, which is agnostic to true global scale and shift. This new representation precludes ambiguous supervision in training and facilitate effective geometry learning. Furthermore, we propose a set of novel global and local geometry supervisions that empower the model to learn high-quality geometry. These include a robust, optimal, and efficient point cloud alignment solver for accurate global shape learning, and a multi-scale local geometry loss promoting precise local geometry supervision. We train our model on a large, mixed dataset and demonstrate its strong generalizability and high accuracy. In our comprehensive evaluation on diverse unseen datasets, our model significantly outperforms state-of-the-art methods across all tasks, including monocular estimation of 3D point map, depth map, and camera field of view. Code and models can be found on our project page.

Point cloud analysis is challenging due to the irregularity of the point cloud data structure. Existing works typically employ the ad-hoc sampling-grouping operation of PointNet++, followed by sophisticated local and/or global feature extractors for leveraging the 3D geometry of the point cloud. Unfortunately, the sampling-grouping operations do not address the point cloud's irregularity, whereas the intricate local and/or global feature extractors led to poor computational efficiency. In this paper, we introduce a novel DualNorm module after the sampling-grouping operation to effectively and efficiently address the irregularity issue. The DualNorm module consists of Point Normalization, which normalizes the grouped points to the sampled points, and Reverse Point Normalization, which normalizes the sampled points to the grouped points. The proposed framework, PointNorm, utilizes local mean and global standard deviation to benefit from both local and global features while maintaining a faithful inference speed. Experiments show that we achieved excellent accuracy and efficiency on ModelNet40 classification, ScanObjectNN classification, ShapeNetPart Part Segmentation, and S3DIS Semantic Segmentation. Code is available at https://github.com/ShenZheng2000/PointNorm-for-Point-Cloud-Analysis.

Although various 3D datasets with different functions and scales have been proposed recently, it remains challenging for individuals to complete the whole pipeline of large-scale data collection, sanitization, and annotation. Moreover, the created datasets usually suffer from extremely imbalanced class distribution or partial low-quality data samples. Motivated by this, we explore the procedurally synthetic 3D data generation paradigm to equip individuals with the full capability of creating large-scale annotated photogrammetry point clouds. Specifically, we introduce a synthetic aerial photogrammetry point clouds generation pipeline that takes full advantage of open geospatial data sources and off-the-shelf commercial packages. Unlike generating synthetic data in virtual games, where the simulated data usually have limited gaming environments created by artists, the proposed pipeline simulates the reconstruction process of the real environment by following the same UAV flight pattern on different synthetic terrain shapes and building densities, which ensure similar quality, noise pattern, and diversity with real data. In addition, the precise semantic and instance annotations can be generated fully automatically, avoiding the expensive and time-consuming manual annotation. Based on the proposed pipeline, we present a richly-annotated synthetic 3D aerial photogrammetry point cloud dataset, termed STPLS3D, with more than 16 km^2 of landscapes and up to 18 fine-grained semantic categories. For verification purposes, we also provide a parallel dataset collected from four areas in the real environment. Extensive experiments conducted on our datasets demonstrate the effectiveness and quality of the proposed synthetic dataset.

With their meaningful geometry and their omnipresence in the 3D world, edges are extremely useful primitives in computer vision. 3D edges comprise of lines and curves, and methods to reconstruct them use either multi-view images or point clouds as input. State-of-the-art image-based methods first learn a 3D edge point cloud then fit 3D edges to it. The edge point cloud is obtained by learning a 3D neural implicit edge field from which the 3D edge points are sampled on a specific level set (0 or 1). However, such methods present two important drawbacks: i) it is not realistic to sample points on exact level sets due to float imprecision and training inaccuracies. Instead, they are sampled within a range of levels so the points do not lie accurately on the 3D edges and require further processing. ii) Such implicit representations are computationally expensive and require long training times. In this paper, we address these two limitations and propose a 3D edge mapping that is simpler, more efficient, and preserves accuracy. Our method learns explicitly the 3D edge points and their edge direction hence bypassing the need for point sampling. It casts a 3D edge point as the center of a 3D Gaussian and the edge direction as the principal axis of the Gaussian. Such a representation has the advantage of being not only geometrically meaningful but also compatible with the efficient training optimization defined in Gaussian Splatting. Results show that the proposed method produces edges as accurate and complete as the state-of-the-art while being an order of magnitude faster. Code is released at https://github.com/kunalchelani/EdgeGaussians.

Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional architecture for learning over concentric spherical feature maps, of which the single sphere representation is a special case. Our hierarchical architecture is based on alternatively learning to incorporate both intra-sphere and inter-sphere information. We show the applicability of our method for two different types of 3D inputs, mesh objects, which can be regularly sampled, and point clouds, which are irregularly distributed. We also propose an efficient mapping of point clouds to concentric spherical images, thereby bridging spherical convolutions on grids with general point clouds. We demonstrate the effectiveness of our approach in improving state-of-the-art performance on 3D classification tasks with rotated data.

Point clouds are naturally sparse, while image pixels are dense. The inconsistency limits feature fusion from both modalities for point-wise scene flow estimation. Previous methods rarely predict scene flow from the entire point clouds of the scene with one-time inference due to the memory inefficiency and heavy overhead from distance calculation and sorting involved in commonly used farthest point sampling, KNN, and ball query algorithms for local feature aggregation. To mitigate these issues in scene flow learning, we regularize raw points to a dense format by storing 3D coordinates in 2D grids. Unlike the sampling operation commonly used in existing works, the dense 2D representation 1) preserves most points in the given scene, 2) brings in a significant boost of efficiency, and 3) eliminates the density gap between points and pixels, allowing us to perform effective feature fusion. We also present a novel warping projection technique to alleviate the information loss problem resulting from the fact that multiple points could be mapped into one grid during projection when computing cost volume. Sufficient experiments demonstrate the efficiency and effectiveness of our method, outperforming the prior-arts on the FlyingThings3D and KITTI dataset.

Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems involve non-Euclidean distributions, such as hyperspherical manifolds, where class-specific patterns are governed by angular geometry within hypercones. When modeled in Euclidean space, these angular subtleties are lost, leading to suboptimal generative performance. To address this limitation, we introduce HyperSphereDiff to align hyperspherical structures with directional noise, preserving class geometry and effectively capturing angular uncertainty. We demonstrate both theoretically and empirically that this approach aligns the generative process with the intrinsic geometry of hyperspherical data, resulting in more accurate and geometry-aware generative models. We evaluate our framework on four object datasets and two face datasets, showing that incorporating angular uncertainty better preserves the underlying hyperspherical manifold. Resources are available at: {https://github.com/IAB-IITJ/Harmonizing-Geometry-and-Uncertainty-Diffusion-with-Hyperspheres/}

We propose an alternative formulation of the well-known Hough transform to detect lines in point clouds. Replacing the discretized voting scheme of the classical Hough transform by a continuous score function, its persistent features in the sense of persistent homology give a set of candidate lines. We also devise and implement an algorithm to efficiently compute these candidate lines.

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.

LiDARs are widely used in autonomous robots due to their ability to provide accurate environment structural information. However, the large size of point clouds poses challenges in terms of data storage and transmission. In this paper, we propose a novel point cloud compression and transmission framework for resource-constrained robotic applications, called RCPCC. We iteratively fit the surface of point clouds with a similar range value and eliminate redundancy through their spatial relationships. Then, we use Shape-adaptive DCT (SA-DCT) to transform the unfit points and reduce the data volume by quantizing the transformed coefficients. We design an adaptive bitrate control strategy based on QoE as the optimization goal to control the quality of the transmitted point cloud. Experiments show that our framework achieves compression rates of 40times to 80times while maintaining high accuracy for downstream applications. our method significantly outperforms other baselines in terms of accuracy when the compression rate exceeds 70times. Furthermore, in situations of reduced communication bandwidth, our adaptive bitrate control strategy demonstrates significant QoE improvements. The code will be available at https://github.com/HITSZ-NRSL/RCPCC.git.

Accurate semantic segmentation of terrestrial laser scanning (TLS) point clouds is limited by costly manual annotation. We propose a semi-automated, uncertainty-aware pipeline that integrates spherical projection, feature enrichment, ensemble learning, and targeted annotation to reduce labeling effort, while sustaining high accuracy. Our approach projects 3D points to a 2D spherical grid, enriches pixels with multi-source features, and trains an ensemble of segmentation networks to produce pseudo-labels and uncertainty maps, the latter guiding annotation of ambiguous regions. The 2D outputs are back-projected to 3D, yielding densely annotated point clouds supported by a three-tier visualization suite (2D feature maps, 3D colorized point clouds, and compact virtual spheres) for rapid triage and reviewer guidance. Using this pipeline, we build Mangrove3D, a semantic segmentation TLS dataset for mangrove forests. We further evaluate data efficiency and feature importance to address two key questions: (1) how much annotated data are needed and (2) which features matter most. Results show that performance saturates after ~12 annotated scans, geometric features contribute the most, and compact nine-channel stacks capture nearly all discriminative power, with the mean Intersection over Union (mIoU) plateauing at around 0.76. Finally, we confirm the generalization of our feature-enrichment strategy through cross-dataset tests on ForestSemantic and Semantic3D. Our contributions include: (i) a robust, uncertainty-aware TLS annotation pipeline with visualization tools; (ii) the Mangrove3D dataset; and (iii) empirical guidance on data efficiency and feature importance, thus enabling scalable, high-quality segmentation of TLS point clouds for ecological monitoring and beyond. The dataset and processing scripts are publicly available at https://fz-rit.github.io/through-the-lidars-eye/.

Labelling point clouds fully is highly time-consuming and costly. As larger point cloud datasets with billions of points become more common, we ask whether the full annotation is even necessary, demonstrating that existing baselines designed under a fully annotated assumption only degrade slightly even when faced with 1% random point annotations. However, beyond this point, e.g., at 0.1% annotations, segmentation accuracy is unacceptably low. We observe that, as point clouds are samples of the 3D world, the distribution of points in a local neighborhood is relatively homogeneous, exhibiting strong semantic similarity. Motivated by this, we propose a new weak supervision method to implicitly augment highly sparse supervision signals. Extensive experiments demonstrate the proposed Semantic Query Network (SQN) achieves promising performance on seven large-scale open datasets under weak supervision schemes, while requiring only 0.1% randomly annotated points for training, greatly reducing annotation cost and effort. The code is available at https://github.com/QingyongHu/SQN.

The increasing availability of large-scale global datasets has generated a demand for scalable spatial prediction methods defined on spherical domains. Classical spatial models that rely on Euclidean distance representations are inappropriate for spherical data because planar projections distort geodesic distances and spatial neighborhood structures, while traditional kriging-based prediction methods are often computationally prohibitive for massive datasets. To address these challenges, we propose a Spherical DeepKriging framework for spatial prediction on S^2. The proposed approach constructs a flexible prediction model by integrating thin-plate spline (TPS) basis functions defined intrinsically on the sphere. Simulation studies and real data analyses are presented to demonstrate the superior predictive performance of the proposed method.

Object detection in point clouds is an important aspect of many robotics applications such as autonomous driving. In this paper we consider the problem of encoding a point cloud into a format appropriate for a downstream detection pipeline. Recent literature suggests two types of encoders; fixed encoders tend to be fast but sacrifice accuracy, while encoders that are learned from data are more accurate, but slower. In this work we propose PointPillars, a novel encoder which utilizes PointNets to learn a representation of point clouds organized in vertical columns (pillars). While the encoded features can be used with any standard 2D convolutional detection architecture, we further propose a lean downstream network. Extensive experimentation shows that PointPillars outperforms previous encoders with respect to both speed and accuracy by a large margin. Despite only using lidar, our full detection pipeline significantly outperforms the state of the art, even among fusion methods, with respect to both the 3D and bird's eye view KITTI benchmarks. This detection performance is achieved while running at 62 Hz: a 2 - 4 fold runtime improvement. A faster version of our method matches the state of the art at 105 Hz. These benchmarks suggest that PointPillars is an appropriate encoding for object detection in point clouds.

This paper is about extremely robust and lightweight localisation using LiDAR point clouds based on instance segmentation and graph matching. We model 3D point clouds as fully-connected graphs of semantically identified components where each vertex corresponds to an object instance and encodes its shape. Optimal vertex association across graphs allows for full 6-Degree-of-Freedom (DoF) pose estimation and place recognition by measuring similarity. This representation is very concise, condensing the size of maps by a factor of 25 against the state-of-the-art, requiring only 3kB to represent a 1.4MB laser scan. We verify the efficacy of our system on the SemanticKITTI dataset, where we achieve a new state-of-the-art in place recognition, with an average of 88.4% recall at 100% precision where the next closest competitor follows with 64.9%. We also show accurate metric pose estimation performance - estimating 6-DoF pose with median errors of 10 cm and 0.33 deg.

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.

In recent years, there has been a significant increase in the utilization of deep learning methods, particularly convolutional neural networks (CNNs), which have emerged as the dominant approach in various domains that involve structured grid data, such as picture analysis and processing. Nevertheless, the exponential growth in the utilization of LiDAR and 3D sensors across many domains has resulted in an increased need for the analysis of 3D point clouds. The utilization of 3D point clouds is crucial in various applications, including object recognition and segmentation, as they offer a spatial depiction of things within a three-dimensional environment. In contrast to photos, point clouds exhibit sparsity and lack a regular grid, hence posing distinct processing and computational issues.

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.

Reconstructing meshes from point clouds is an important task in fields such as robotics, autonomous systems, and medical imaging. This survey examines state-of-the-art learning-based approaches to mesh reconstruction, categorizing them into five paradigms: PointNet family, autoencoder architectures, deformation-based methods, point-move techniques, and primitive-based approaches. Each paradigm is explored in depth, detailing the primary approaches and their underlying methodologies. By comparing these techniques, our study serves as a comprehensive guide, and equips researchers and practitioners with the knowledge to navigate the landscape of learning-based mesh reconstruction techniques. The findings underscore the transformative potential of these methods, which often surpass traditional techniques in allowing detailed and efficient reconstructions.

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.

Point cloud completion aims to recover accurate global geometry and preserve fine-grained local details from partial point clouds. Conventional methods typically predict unseen points directly from 3D point cloud coordinates or use self-projected multi-view depth maps to ease this task. However, these gray-scale depth maps cannot reach multi-view consistency, consequently restricting the performance. In this paper, we introduce a GeoFormer that simultaneously enhances the global geometric structure of the points and improves the local details. Specifically, we design a CCM Feature Enhanced Point Generator to integrate image features from multi-view consistent canonical coordinate maps (CCMs) and align them with pure point features, thereby enhancing the global geometry feature. Additionally, we employ the Multi-scale Geometry-aware Upsampler module to progressively enhance local details. This is achieved through cross attention between the multi-scale features extracted from the partial input and the features derived from previously estimated points. Extensive experiments on the PCN, ShapeNet-55/34, and KITTI benchmarks demonstrate that our GeoFormer outperforms recent methods, achieving the state-of-the-art performance. Our code is available at https://github.com/Jinpeng-Yu/GeoFormer{https://github.com/Jinpeng-Yu/GeoFormer}.

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.

Multimodal large language models (MLLMs) have made rapid progress in recent years, yet continue to struggle with low-level visual perception (LLVP) -- particularly the ability to accurately describe the geometric details of an image. This capability is crucial for applications in areas such as robotics, medical image analysis, and manufacturing. In this paper, we first introduce Geoperception, a benchmark designed to evaluate an MLLM's ability to accurately transcribe 2D geometric information from an image. Using this benchmark, we demonstrate the limitations of leading MLLMs, and then conduct a comprehensive empirical study to explore strategies for improving their performance on geometric tasks. Our findings highlight the benefits of certain model architectures, training techniques, and data strategies, including the use of high-fidelity synthetic data and multi-stage training with a data curriculum. Notably, we find that a data curriculum enables models to learn challenging geometry understanding tasks which they fail to learn from scratch. Leveraging these insights, we develop Euclid, a family of models specifically optimized for strong low-level geometric perception. Although purely trained on synthetic multimodal data, Euclid shows strong generalization ability to novel geometry shapes. For instance, Euclid outperforms the best closed-source model, Gemini-1.5-Pro, by up to 58.56% on certain Geoperception benchmark tasks and 10.65% on average across all tasks.

The scale diversity of point cloud data presents significant challenges in developing unified representation learning techniques for 3D vision. Currently, there are few unified 3D models, and no existing pre-training method is equally effective for both object- and scene-level point clouds. In this paper, we introduce UniPre3D, the first unified pre-training method that can be seamlessly applied to point clouds of any scale and 3D models of any architecture. Our approach predicts Gaussian primitives as the pre-training task and employs differentiable Gaussian splatting to render images, enabling precise pixel-level supervision and end-to-end optimization. To further regulate the complexity of the pre-training task and direct the model's focus toward geometric structures, we integrate 2D features from pre-trained image models to incorporate well-established texture knowledge. We validate the universal effectiveness of our proposed method through extensive experiments across a variety of object- and scene-level tasks, using diverse point cloud models as backbones. Code is available at https://github.com/wangzy22/UniPre3D.

Reconstructing building wireframe from airborne LiDAR point clouds yields a compact, topology-centric representation that enables structural understanding beyond dense meshes. Yet a key limitation persists: conventional methods have failed to achieve accurate wireframe reconstruction in regions afflicted by significant noise, sparsity, or internal corners. This failure stems from the inability to establish an adaptive search space to effectively leverage the rich 3D geometry of large, sparse building point clouds. In this work, we address this challenge with Delaunay Canopy, which utilizes the Delaunay graph as a geometric prior to define a geometrically adaptive search space. Central to our approach is Delaunay Graph Scoring, which not only reconstructs the underlying geometric manifold but also yields region-wise curvature signatures to robustly guide the reconstruction. Built on this foundation, our corner and wire selection modules leverage the Delaunay-induced prior to focus on highly probable elements, thereby shaping the search space and enabling accurate prediction even in previously intractable regions. Extensive experiments on the Building3D Tallinn city and entry-level datasets demonstrate state-of-the-art wireframe reconstruction, delivering accurate predictions across diverse and complex building geometries.

An essential prerequisite for unleashing the potential of supervised deep learning algorithms in the area of 3D scene understanding is the availability of large-scale and richly annotated datasets. However, publicly available datasets are either in relative small spatial scales or have limited semantic annotations due to the expensive cost of data acquisition and data annotation, which severely limits the development of fine-grained semantic understanding in the context of 3D point clouds. In this paper, we present an urban-scale photogrammetric point cloud dataset with nearly three billion richly annotated points, which is three times the number of labeled points than the existing largest photogrammetric point cloud dataset. Our dataset consists of large areas from three UK cities, covering about 7.6 km^2 of the city landscape. In the dataset, each 3D point is labeled as one of 13 semantic classes. We extensively evaluate the performance of state-of-the-art algorithms on our dataset and provide a comprehensive analysis of the results. In particular, we identify several key challenges towards urban-scale point cloud understanding. The dataset is available at https://github.com/QingyongHu/SensatUrban.

Existing polygonal surface reconstruction methods heavily depend on input completeness and struggle with incomplete point clouds. We argue that while current point cloud completion techniques may recover missing points, they are not optimized for polygonal surface reconstruction, where the parametric representation of underlying surfaces remains overlooked. To address this gap, we introduce parametric completion, a novel paradigm for point cloud completion, which recovers parametric primitives instead of individual points to convey high-level geometric structures. Our presented approach, PaCo, enables high-quality polygonal surface reconstruction by leveraging plane proxies that encapsulate both plane parameters and inlier points, proving particularly effective in challenging scenarios with highly incomplete data. Comprehensive evaluations of our approach on the ABC dataset establish its effectiveness with superior performance and set a new standard for polygonal surface reconstruction from incomplete data. Project page: https://parametric-completion.github.io.

Point cloud registration is a task to estimate the rigid transformation between two unaligned scans, which plays an important role in many computer vision applications. Previous learning-based works commonly focus on supervised registration, which have limitations in practice. Recently, with the advance of inexpensive RGB-D sensors, several learning-based works utilize RGB-D data to achieve unsupervised registration. However, most of existing unsupervised methods follow a cascaded design or fuse RGB-D data in a unidirectional manner, which do not fully exploit the complementary information in the RGB-D data. To leverage the complementary information more effectively, we propose a network implementing multi-scale bidirectional fusion between RGB images and point clouds generated from depth images. By bidirectionally fusing visual and geometric features in multi-scales, more distinctive deep features for correspondence estimation can be obtained, making our registration more accurate. Extensive experiments on ScanNet and 3DMatch demonstrate that our method achieves new state-of-the-art performance. Code will be released at https://github.com/phdymz/PointMBF

Achieving human-level dexterity in robots is a key objective in the field of robotic manipulation. Recent advancements in 3D-based imitation learning have shown promising results, providing an effective pathway to achieve this goal. However, obtaining high-quality 3D representations presents two key problems: (1) the quality of point clouds captured by a single-view camera is significantly affected by factors such as camera resolution, positioning, and occlusions caused by the dexterous hand; (2) the global point clouds lack crucial contact information and spatial correspondences, which are necessary for fine-grained dexterous manipulation tasks. To eliminate these limitations, we propose CordViP, a novel framework that constructs and learns correspondences by leveraging the robust 6D pose estimation of objects and robot proprioception. Specifically, we first introduce the interaction-aware point clouds, which establish correspondences between the object and the hand. These point clouds are then used for our pre-training policy, where we also incorporate object-centric contact maps and hand-arm coordination information, effectively capturing both spatial and temporal dynamics. Our method demonstrates exceptional dexterous manipulation capabilities with an average success rate of 90\% in four real-world tasks, surpassing other baselines by a large margin. Experimental results also highlight the superior generalization and robustness of CordViP to different objects, viewpoints, and scenarios. Code and videos are available on https://aureleopku.github.io/CordViP.

This paper concerns the research problem of point cloud registration to find the rigid transformation to optimally align the source point set with the target one. Learning robust point cloud registration models with deep neural networks has emerged as a powerful paradigm, offering promising performance in predicting the global geometric transformation for a pair of point sets. Existing methods firstly leverage an encoder to regress a latent shape embedding, which is then decoded into a shape-conditioned transformation via concatenation-based conditioning. However, different regions of a 3D shape vary in their geometric structures which makes it more sense that we have a region-conditioned transformation instead of the shape-conditioned one. In this paper we present a Region-Aware point cloud Registration, denoted as RAR, to predict transformation for pairwise point sets in the self-supervised learning fashion. More specifically, we develop a novel region-aware decoder (RAD) module that is formed with an implicit neural region representation parameterized by neural networks. The implicit neural region representation is learned with a self-supervised 3D shape reconstruction loss without the need for region labels. Consequently, the region-aware decoder (RAD) module guides the training of the region-aware transformation (RAT) module and region-aware weight (RAW) module, which predict the transforms and weights for different regions respectively. The global geometric transformation from source point set to target one is then formed by the weighted fusion of region-aware transforms. Compared to the state-of-the-art approaches, our experiments show that our RAR achieves superior registration performance over various benchmark datasets (e.g. ModelNet40).

Visual localization is the task of estimating a 6-DoF camera pose of a query image within a provided 3D reference map. Thanks to recent advances in various 3D sensors, 3D point clouds are becoming a more accurate and affordable option for building the reference map, but research to match the points of 3D point clouds with pixels in 2D images for visual localization remains challenging. Existing approaches that jointly learn 2D-3D feature matching suffer from low inliers due to representational differences between the two modalities, and the methods that bypass this problem into classification have an issue of poor refinement. In this work, we propose EP2P-Loc, a novel large-scale visual localization method that mitigates such appearance discrepancy and enables end-to-end training for pose estimation. To increase the number of inliers, we propose a simple algorithm to remove invisible 3D points in the image, and find all 2D-3D correspondences without keypoint detection. To reduce memory usage and search complexity, we take a coarse-to-fine approach where we extract patch-level features from 2D images, then perform 2D patch classification on each 3D point, and obtain the exact corresponding 2D pixel coordinates through positional encoding. Finally, for the first time in this task, we employ a differentiable PnP for end-to-end training. In the experiments on newly curated large-scale indoor and outdoor benchmarks based on 2D-3D-S and KITTI, we show that our method achieves the state-of-the-art performance compared to existing visual localization and image-to-point cloud registration methods.

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.

Diffusion models generating images conditionally on text, such as Dall-E 2 and Stable Diffusion, have recently made a splash far beyond the computer vision community. Here, we tackle the related problem of generating point clouds, both unconditionally, and conditionally with images. For the latter, we introduce a novel geometrically-motivated conditioning scheme based on projecting sparse image features into the point cloud and attaching them to each individual point, at every step in the denoising process. This approach improves geometric consistency and yields greater fidelity than current methods relying on unstructured, global latent codes. Additionally, we show how to apply recent continuous-time diffusion schemes. Our method performs on par or above the state of art on conditional and unconditional experiments on synthetic data, while being faster, lighter, and delivering tractable likelihoods. We show it can also scale to diverse indoors scenes.

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.

Unlike its image based counterpart, point cloud based retrieval for place recognition has remained as an unexplored and unsolved problem. This is largely due to the difficulty in extracting local feature descriptors from a point cloud that can subsequently be encoded into a global descriptor for the retrieval task. In this paper, we propose the PointNetVLAD where we leverage on the recent success of deep networks to solve point cloud based retrieval for place recognition. Specifically, our PointNetVLAD is a combination/modification of the existing PointNet and NetVLAD, which allows end-to-end training and inference to extract the global descriptor from a given 3D point cloud. Furthermore, we propose the "lazy triplet and quadruplet" loss functions that can achieve more discriminative and generalizable global descriptors to tackle the retrieval task. We create benchmark datasets for point cloud based retrieval for place recognition, and the experimental results on these datasets show the feasibility of our PointNetVLAD. Our code and the link for the benchmark dataset downloads are available in our project website. http://github.com/mikacuy/pointnetvlad/

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

This paper advocates the use of implicit surface representation in autoencoder-based self-supervised 3D representation learning. The most popular and accessible 3D representation, i.e., point clouds, involves discrete samples of the underlying continuous 3D surface. This discretization process introduces sampling variations on the 3D shape, making it challenging to develop transferable knowledge of the true 3D geometry. In the standard autoencoding paradigm, the encoder is compelled to encode not only the 3D geometry but also information on the specific discrete sampling of the 3D shape into the latent code. This is because the point cloud reconstructed by the decoder is considered unacceptable unless there is a perfect mapping between the original and the reconstructed point clouds. This paper introduces the Implicit AutoEncoder (IAE), a simple yet effective method that addresses the sampling variation issue by replacing the commonly-used point-cloud decoder with an implicit decoder. The implicit decoder reconstructs a continuous representation of the 3D shape, independent of the imperfections in the discrete samples. Extensive experiments demonstrate that the proposed IAE achieves state-of-the-art performance across various self-supervised learning benchmarks.

We present PIRATR, an end-to-end 3D object detection framework for robotic use cases in point clouds. Extending PI3DETR, our method streamlines parametric 3D object detection by jointly estimating multi-class 6-DoF poses and class-specific parametric attributes directly from occlusion-affected point cloud data. This formulation enables not only geometric localization but also the estimation of task-relevant properties for parametric objects, such as a gripper's opening, where the 3D model is adjusted according to simple, predefined rules. The architecture employs modular, class-specific heads, making it straightforward to extend to novel object types without re-designing the pipeline. We validate PIRATR on an automated forklift platform, focusing on three structurally and functionally diverse categories: crane grippers, loading platforms, and pallets. Trained entirely in a synthetic environment, PIRATR generalizes effectively to real outdoor LiDAR scans, achieving a detection mAP of 0.919 without additional fine-tuning. PIRATR establishes a new paradigm of pose-aware, parameterized perception. This bridges the gap between low-level geometric reasoning and actionable world models, paving the way for scalable, simulation-trained perception systems that can be deployed in dynamic robotic environments. Code available at https://github.com/swingaxe/piratr.

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.

We present the Dayton Annotated LiDAR Earth Scan (DALES) data set, a new large-scale aerial LiDAR data set with over a half-billion hand-labeled points spanning 10 square kilometers of area and eight object categories. Large annotated point cloud data sets have become the standard for evaluating deep learning methods. However, most of the existing data sets focus on data collected from a mobile or terrestrial scanner with few focusing on aerial data. Point cloud data collected from an Aerial Laser Scanner (ALS) presents a new set of challenges and applications in areas such as 3D urban modeling and large-scale surveillance. DALES is the most extensive publicly available ALS data set with over 400 times the number of points and six times the resolution of other currently available annotated aerial point cloud data sets. This data set gives a critical number of expert verified hand-labeled points for the evaluation of new 3D deep learning algorithms, helping to expand the focus of current algorithms to aerial data. We describe the nature of our data, annotation workflow, and provide a benchmark of current state-of-the-art algorithm performance on the DALES data set.