procrustes analysis

This paper addresses the problem of visual relative pose estimation. We propose a novel modeling framework based on dual rotation parameterization: jointly optimizing the rotation matrices of two cameras directly on the SO(3) manifold, bypassing conventional essential matrix decomposition or end-to-end pose regression paradigms. Our method introduces a geometrically grounded coordinate transformation and three differentiable, geometrically consistent energy functions, minimized jointly within a Riemannian optimization framework. The approach achieves strong robustness, high accuracy, and excellent generalization across diverse relative pose tasks—including two-view pose estimation and Structure-from-Motion (SfM) initialization—outperforming state-of-the-art methods by significant margins. To foster reproducibility and community advancement, we release our source code, demonstration videos, and benchmark datasets.

Existing geometric assembly methods rely on surface matching, which struggles with interlocking parts requiring simultaneous satisfaction of surface shape compatibility and volumetric complementarity (i.e., “convex–concave” fitting). This work is the first to explicitly model both attributes of interlocking structures. We propose a compositional matching framework: (1) volumetric occupancy inversion to encode complementary spatial occupation, and (2) an equivariant neural network that jointly learns shape orientation and cross-region correspondences, enabling rotation-robust global alignment. By jointly reasoning about geometry and topology, our approach mitigates local matching ambiguities inherent in surface-only methods. Extensive evaluation on multiple geometric assembly benchmarks demonstrates significant improvements over state-of-the-art methods, validating superior accuracy, generalization across unseen part configurations, and robustness to pose variations and partial observations.

Embedding models trained independently on similar data capture stable semantic meanings but yield inconsistent representation spaces, hindering interoperability across models. This work addresses compatibility challenges in multimodal search and model upgrades via orthogonal transformation-based embedding alignment. Theoretically, we derive the first tight Procrustes alignment error bound, proving the existence of a near-isometric orthogonal transformation that approximately preserves pairwise inner products—establishing rigorous theoretical foundations for alignment. Methodologically, we employ efficient Procrustes analysis as a post-hoc alignment procedure, preserving the intrinsic geometric structure of each embedding space while enabling cross-model alignment. Experiments demonstrate substantial improvements in model retraining compatibility, text retrieval fusion accuracy, and cross-modal search performance; our method achieves state-of-the-art results in hybrid multimodal search.

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 work addresses the problem of establishing dense intrinsic correspondences between non-rigid manifolds. We propose a matrix completion framework that jointly incorporates geometric priors—specifically, manifold Laplacian-guided constraints—and sparse functional landmark localization. Methodologically, we are the first to integrate Laplacian-based geometric regularization with ℓ₁-norm sparsity promotion into a unified matrix completion model, effectively mitigating overfitting under limited supervision and enabling precise identification of functionally consistent regions. Optimization is performed via an efficient numerical algorithm. Extensive evaluation on standard non-rigid matching benchmarks (e.g., FAUST, TOSCA) demonstrates state-of-the-art performance: our method achieves the highest overall accuracy and, under highly sparse supervision (fewer than 10 seed points), reduces average correspondence error by 18.7% compared to the best prior approach—substantially improving robustness and generalization capability.

This work addresses the limited robustness and discriminability of local features under arbitrary 3D rotations in point cloud registration by proposing the first strictly rotation-equivariant registration framework that operates without a local reference frame. Built upon SO(3) representation theory, the method employs spherical harmonics to construct a rotation-equivariant neural network that jointly learns rotation-invariant descriptors and equivariant geometric features. This design enables each putative correspondence to directly model the underlying rigid transformation, substantially reducing reliance on extensive RANSAC sampling. Experiments on the 3DMatch, 3DLoMatch, and KITTI benchmarks demonstrate that the proposed approach achieves significantly higher registration accuracy than existing methods under large rotational perturbations.

Establishing dense correspondences for 3D shapes in real-world scenarios is challenged by the absence of annotations, high resolution, topological distortions, and heterogeneous shape representations. This work proposes the ATM framework, which adopts a “model-then-match” paradigm by integrating pretrained vision foundation models with parametric shape priors to learn a unified shape representation in a shared parameter space from multi-view renderings. Dense correspondences are achieved in a zero-shot manner through geometric consistency constraints and spectral refinement, eliminating the need for correspondence-labeled training data. The method is inherently robust to topological noise and seamlessly handles diverse representations—including meshes, point clouds, and 3D Gaussians. It significantly outperforms existing approaches on non-isometric benchmarks, reducing correspondence errors by 73% on TOPKIDS and 37% on SMAL, while maintaining high efficiency and accuracy on wild scans with up to 200,000 vertices.

This work addresses the problem of estimating the pose of a known 3D shape from an unoccluded orthographic silhouette without relying on feature point correspondences. The method leverages the continuity of silhouette area along rotational trajectories to construct a precomputed silhouette signature response surface and introduces the aspect ratio of a fitted ellipse as a global shape signature. This enables an efficient, resolution-guided branch-and-bound search over the rotation space. To the best of our knowledge, this is the first approach capable of achieving globally optimal pose estimation using only silhouettes for arbitrary shapes, including non-convex and high-genus geometries. Experiments on both synthetic and real-world data demonstrate that the proposed method significantly outperforms existing techniques in both accuracy and computational efficiency.

This work addresses the limitations of existing panoramic stitching methods, which rely on pairwise feature matching and often fail to maintain multi-view geometric consistency in complex scenes characterized by weak textures, large disparities, or repetitive patterns, leading to misalignments and distortions. To overcome these challenges, the authors propose a photogrammetry-driven global alignment framework that leverages estimated camera poses to align images in 3D space. They introduce a novel 3D-aware Transformer architecture that explicitly models multi-view geometric consistency through joint feature optimization and cross-view information aggregation. Key contributions include the first formulation of multi-view consistency in 3D space, a Transformer-based 3D-aware stitching network, and the creation of the first large-scale real-world panoramic stitching dataset. Experiments demonstrate that the proposed method significantly outperforms state-of-the-art approaches in both alignment accuracy and visual quality, particularly exhibiting superior robustness and consistency in challenging scenarios.

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.