Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided Approach

2025-09-08

AI Summary

Matching non-rigid 3D shapes with topological inconsistencies—such as holes, discontinuities, and noise—remains challenging, as existing methods rely on near-isometric or ARAP deformation assumptions that fail under common topological artifacts in real-world multi-view reconstructions. Method: We propose a topology-adaptive bidirectional matching framework that jointly optimizes a template mesh adapted to the target topology and its non-rigid alignments with both source and target shapes, eliminating reliance on global isometric or ARAP priors. Our approach synergistically optimizes ARAP regularization and bijectivity constraints, enabling high-fidelity, topology-robust correspondence estimation without data-driven priors. Results: Experiments demonstrate significant improvements over state-of-the-art learning-based and traditional methods under strong non-isometry and severe topological distortions, validating robustness and accuracy for real multi-view reconstruction matching tasks.

Technology Category

• Computer Vision: Multi-modal Vision
• Machine Learning: Learning with Manifolds
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Non-rigid 3D mesh matching is a critical step in computer vision and computer graphics pipelines. We tackle matching meshes that contain topological artefacts which can break the assumption made by current approaches. While Functional Maps assume the deformation induced by the ground truth correspondences to be near-isometric, ARAP-like deformation-guided approaches assume the latter to be ARAP. Neither assumption holds in certain topological configurations of the input shapes. We are motivated by real-world scenarios such as per-frame multi-view reconstructions, often suffering from topological artefacts. To this end, we propose a topology-adaptive deformation model allowing changes in shape topology to align shape pairs under ARAP and bijective association constraints. Using this model, we jointly optimise for a template mesh with adequate topology and for its alignment with the shapes to be matched to extract correspondences. We show that, while not relying on any data-driven prior, our approach applies to highly non-isometric shapes and shapes with topological artefacts, including noisy per-frame multi-view reconstructions, even outperforming methods trained on large datasets in 3D alignment quality.

Problem

• Matching 3D meshes with topological artifacts
• Handling non-isometric deformations in shape alignment
• Joint optimization for topology-adaptive template matching

Innovation

• Topology-adaptive deformation model for shape alignment
• Joint optimization of template mesh and correspondence
• Handles topological artefacts without data-driven priors