register meshes

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.

Traditional point-to-point or point-to-plane distance metrics in non-rigid point cloud registration suffer from slow convergence and geometric detail loss. To address this, we propose a symmetric point-to-plane distance metric that jointly enforces positional and normal-based geometric constraints, significantly improving geometric fidelity. Methodologically, we introduce the first symmetric distance formulation for non-rigid registration and integrate it with a deformation-graph-based coarse alignment followed by an alternating optimization scheme within the Majorization-Minimization (MM) framework—balancing robustness, accuracy, and efficiency. Extensive experiments on multiple benchmark datasets demonstrate that our approach achieves state-of-the-art registration accuracy while maintaining high computational efficiency. The source code is publicly available.

In large-scale Structure-from-Motion (SfM), sparse inter-view overlap and drastic viewpoint changes—especially in aerial-to-ground scenarios—lead to low cross-image feature matching density and weak geometric consistency. To address this, we propose a geometry-guided hybrid matching paradigm: (1) geometric verification is formulated as an optimization problem based on Sampson distance; (2) detector-agnostic dense matching is fused with detector-driven sparse anchor guidance, where sparse anchors constrain and enhance the geometric consistency of dense matches; and (3) multi-view geometric consistency is explicitly modeled. Our method significantly improves both matching density and accuracy, outperforming state-of-the-art approaches in extreme large-scale settings. Consequently, camera pose estimation becomes more accurate, and the reconstructed 3D point cloud achieves higher completeness and fidelity.

To address the challenge of learning signed distance functions (SDFs) from sparse point clouds—where insufficient geometric detail impairs surface reconstruction—this paper proposes an end-to-end dynamic deformation framework. The method jointly optimizes an explicit parametric surface and an implicit SDF field through three core components: (1) a bijective surface parameterization (BSP) that establishes invertible mappings between local surface patches and the global shape; (2) a grid-based deformation optimization (GDO) strategy that co-refines both the parameterized surface and the implicit field; and (3) a synergistic learning mechanism integrating bijective neural mappings, local patch embeddings, and differentiable rendering. Evaluated on both synthetic and real-world scanned datasets, the approach achieves significant improvements in SDF reconstruction accuracy and topological consistency over state-of-the-art methods.

In point cloud registration, existing methods suffer from fixed iterative optimization paths, implicit correspondence refinement, and single-projection updates prone to local optima. This work introduces, for the first time, denoising diffusion models into the space of doubly stochastic matrices to explicitly model and optimize the distribution of matching matrices. Instead of fixed iterations, it employs the diffusion reverse process—enabling initialization from arbitrary inputs (e.g., white noise)—and integrates Sinkhorn regularization with differentiable geometric feature encoding to enable gradient-guided global matching search. Evaluated on 3DMatch/3DLoMatch and 4DMatch/4DLoMatch benchmarks, our approach achieves significant improvements in both rigid and non-rigid registration accuracy, correspondence quality, and robustness over RAFT-style methods and conventional feature-distance-based approaches.

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.

This work proposes DC-Reg, a novel framework addressing the challenge of achieving globally optimal point cloud registration under partial overlap and large initial misalignment. The method introduces a unified difference-of-convex (DC) decomposition of the coupled objective function involving both transformation and correspondence variables, enabling the construction of a globally concave lower bound that significantly tightens the search space in branch-and-bound (BnB) optimization. By jointly exploiting the structural interdependence between transformation and correspondence variables, DC-Reg overcomes the limitations of conventional per-term relaxation strategies. Integrated with rotation-invariant features and an efficient solver for the linear assignment problem, the approach demonstrates faster convergence than existing global methods on both synthetic data and the 3DMatch benchmark, while exhibiting superior robustness under extreme noise and outlier conditions.

Recovering editable, parameterized CAD construction sequences from geometric inputs such as meshes remains a fundamental challenge in design and manufacturing. This work proposes an IoU-driven hybrid optimization framework that, for the first time, formulates the reconstruction problem as structured CAD program optimization. By leveraging geometric feedback, the method iteratively fits and validates a rich set of parametric operations—including fillets and chamfers—within the procedural representation. The approach enables end-to-end image-to-CAD reconstruction across multiple modalities and significantly outperforms existing methods on established benchmarks, achieving superior performance in both volumetric IoU and Chamfer distance metrics. Moreover, it substantially reduces redundancy in the reconstructed programs, enabling efficient and high-fidelity recovery of complex CAD models.

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.

Existing methods for non-rigid mesh sequence registration often suffer from reliance on per-instance optimization, limited category generalization, support for only pairwise inputs, or incomplete output correspondences. This work proposes a feed-forward neural network that leverages a topology-aware point representation and a multimodal encoding scheme to construct a global motion embedding, enabling a lightweight decoder to directly predict vertex deformations. The approach achieves efficient and complete multi-frame registration without iterative optimization and inherently supports motion interpolation at arbitrary time steps as well as high-quality mesh morphing. It demonstrates state-of-the-art performance across diverse object categories and complex non-rigid motions.