chamfer distance computation

To address the lack of objective, reproducible geometric evaluation for point-cloud skeletonization in robotics applications, this work introduces the first systematic, multi-dimensional evaluation framework. It comprises four geometric quality metrics: topological similarity, boundedness, centrality, and smoothness, unified within a single numerical scoring scheme. Methodologically, the framework integrates point-cloud topological analysis, signed distance field modeling, quantitative centrality deviation estimation, and curvature-driven smoothness measurement. We implement an open-source Python evaluation toolkit to support reproducible assessment. Extensive validation on real-world point-cloud data across robotic tasks—including grasping and navigation—demonstrates that our framework significantly improves skeleton quality discrimination accuracy and interpretability. It enables cross-task performance sensitivity analysis and has been adopted by the research community for algorithm development and benchmarking.

Existing point cloud generation evaluation metrics—such as Chamfer Distance—are highly sensitive to geometric imperfections and lack robustness, failing to accurately quantify both local shape consistency and global fidelity. To address these limitations, this work proposes: (1) two novel evaluation metrics—Density-Aware Chamfer Distance (DCD) and Surface Normal Consistency (SNC)—designed to better discriminate sampling non-uniformity and normal vector distortion; and (2) Diffusion Point Transformer, a diffusion-based generative architecture leveraging serialized patch-wise attention, augmented with sample alignment preprocessing to enhance local structural modeling. Evaluated on ShapeNet, our method achieves state-of-the-art generation quality, significantly outperforming leading baselines across multiple metrics. The implementation is publicly available.

Existing 3D shape matching methods predominantly assume complete input shapes, while robust partial-observation matching—more reflective of real-world scenarios—remains underexplored. Current benchmarks suffer from limited scale, unrealistic partiality, and absence of cross-dataset ground-truth correspondences. Method: We introduce the first large-scale, standardized benchmark for partial-observation matching: (1) a programmable geometric perturbation framework that synthesizes photorealistic partial deformations with infinite scalability; (2) integration of seven mainstream datasets with manually annotated cross-dataset full-shape correspondences (2,543 pairs); and (3) a multi-level difficulty evaluation protocol. Results: Comprehensive evaluation reveals substantial performance degradation of state-of-the-art methods under realistic partiality. We publicly release the benchmark—including data, baselines, and an open-source evaluation platform—to establish a new standard and accelerate research in partial 3D shape matching.

This work addresses the lack of physical plausibility in single-image 3D reconstruction. We propose the first physics-compatible reconstruction framework that enforces static equilibrium as a hard constraint. Methodologically, we explicitly decouple and jointly optimize material stiffness, external loading forces, and the static equilibrium geometry; deformation responses are modeled via differentiable physics simulation, enabling gradient-based joint optimization of all variables. Our approach breaks from conventional simplifications—such as rigid-body assumptions or neglect of external forces—by embedding real-world physical constraints directly into the single-image reconstruction pipeline. Evaluated on Objaverse, our method yields reconstructions with significantly improved mechanical stability, suitable for downstream dynamic simulation and 3D printing. Physical validation via real-world force testing further confirms the structural robustness of the generated models.

This paper addresses the challenge of efficiently, differentiably, and robustly measuring geometric discrepancies between 3D point clouds and triangular meshes. To this end, we propose DirDist—a novel implicit metric grounded in Directional Distance Fields (DDFs). DirDist uniquely represents local geometry via DDFs and formulates shape comparison as computing L₂ or Chamfer distances between continuous, co-domain implicit fields, thereby avoiding explicit point correspondences while ensuring differentiability, physical interpretability, and computational efficiency. The method provides a unified framework for diverse tasks including template fitting, rigid/non-rigid registration, scene flow estimation, and human pose optimization. Evaluated across multiple benchmarks, DirDist achieves average error reductions of 27%–41% over state-of-the-art methods, demonstrating substantial improvements in both accuracy and generalization capability.

This work proposes a parameter-free local topographic descriptor for the comparison and rigid alignment of three-dimensional structured point patterns. The method decomposes each point pattern into multiple arms and introduces a normalized finite difference operator along each arm to capture the local variation of height components relative to the underlying planar geometry, thereby integrating fine-grained geometric details with global structural information. By combining Wasserstein distance with Procrustes analysis, the approach enables efficient distributional comparison and precise alignment of point clouds. The proposed descriptor preserves salient local topographic features while significantly enhancing the robustness and accuracy of point pattern matching.

This work addresses the well-known issue of many-to-one collapse in 3D point cloud optimization using Chamfer distance, which arises from its gradient structure and often degrades optimization results. The study is the first to demonstrate that local regularization fails to mitigate this collapse and reveals that non-local coupling is essential for its suppression. To this end, the authors propose a globally coupled framework based on a shared-basis deformation model and a differentiable Material Point Method (MPM) prior. The optimization integrates density-aware reweighting, repulsive forces, and smoothness constraints. Evaluated on 20 3D shape morphing tasks, the method consistently reduces the Chamfer gap, achieving up to a 2.5× improvement on topologically complex models such as the dragon, thereby validating its effectiveness in both 2D and 3D settings.

This work proposes a novel method for constructing high-quality intrinsic triangulations of closed discrete surfaces without altering their original geometry. By performing local operations—such as edge flips, splits, and collapses—directly on the surface and integrating the continuous Dijkstra algorithm with an A* search acceleration strategy, the approach efficiently computes exact geodesic distances, overcoming the traditional reliance on developable triangles. The method introduces an angle quality criterion based on intrinsic distances and employs a feature-length field to control element sizing, enabling adaptive mesh refinement and coarsening, thereby laying the groundwork for high-order mesh generation. Experiments on nearly 5,000 complex models from the Thingi10K dataset demonstrate that the computational cost of geodesic distance calculation is reduced to approximately 3% of that required by conventional methods.

This work addresses the challenge of landmark-based shape modeling by simultaneously preserving invariance under Kendall’s shape space, preventing landmark collisions, and accommodating a variable number of landmarks. To this end, we integrate Kendall’s shape space with the Riemannian structure induced by right-invariant Sobolev metrics on the diffeomorphism group, and introduce a filtered elastic operator whose null space precisely corresponds to rigid motions. This formulation eliminates global rigid transformations and scale while retaining local rigidity, thereby effectively avoiding landmark collisions. Within a Riemannian quotient space framework, we combine numerical geodesic computation with matching algorithms to construct a novel shape space endowed with a regular metric. The resulting framework supports an arbitrary number of landmarks, maintains shape invariance, and enables stable and efficient geodesic and matching computations.

This study addresses the fundamental challenge of estimating correspondences between 3D shape instances under non-rigid deformations by providing a systematic review of existing approaches, which it categorizes into three major paradigms: spectral methods based on functional maps, combinatorial methods incorporating discrete constraints, and deformation-based techniques that directly recover global alignment. For the first time, these three lines of work are unified within a coherent framework, clarifying their historical development, respective strengths, and limitations. A key contribution lies in demonstrating the emerging potential of vision foundation models for zero-shot correspondence tasks. The paper further highlights pressing challenges such as local shape matching, identifies current bottlenecks, and outlines promising future directions, thereby offering both a comprehensive theoretical foundation and practical guidance for advancing research in this domain.