Title: NEXUS: Neighborhood-Enhanced Correspondence Optimization Strategy for Shape Correspondences
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Shape Correspondence

Abstract: Shape correspondence is a cornerstone of computer graphics, enabling applications such as shape registration, deformation transfer, and animation. We introduce NEXUS (Neighborhood-Enhanced Correspondence Optimization Strategy), a novel framework that integrates local and global optimization to address the shape correspondence problem effectively. Our primary contribution is the Local Neighborhood Consistency (LNC) metric, a computationally efficient and robust measure for assessing correspondence quality using mesh connectivity rather than geodesic distances. Unlike prior metrics like Local Map Distortion (LMD), LNC is faster to compute (linear in number of edges in mesh adjacency), and is more resilient to non-isometric deformations. We couple LNC with a seeded graph matching approach to refine correspondences, achieving superior accuracy and speed compared to existing methods. Experimental results demonstrate NEXUS's effectiveness across diverse datasets, including near-isometric, non-isometric, and topologically noisy shapes. We also address implementation errors in prior LMD-based methods and highlight NEXUS's limitations, such as sensitivity to significant mesh connectivity discrepancies. Our work simplifies and accelerates shape correspondence pipelines while maintaining or improving accuracy.