Multi-Shape Matching with Cycle Consistency Basis via Functional Maps

Abstract

Multi-shape matching is a central problem in various applications of computer vision and graphics, where cycle consistency constraints play a pivotal role. For this issue, we propose a novel and efficient approach that models multi-shapes as directed graphs for two-stage optimization, i.e., optimizing pairwise correspondence accuracy using landmarks, and refining matching consistency through cycle consistency basis. Specifically, we utilize local mapping distortion to identify landmarks and extract the dimension of the functional space, which is then used to upsample in the spectral domain, thereby producing smoother results. Next, to optimize the consistency of correspondences, we introduce the cycle consistency basis, which succinctly describes all consistent cycles in the collection. We then propose cycle consistency refinement, which resolves inconsistencies in cycles efficiently via the alternating direction method of multipliers. Our approach simultaneously balances the accuracy and consistency of multi-shape matching, achieving lower correspondence errors. Extensive experiments on several public datasets demonstrate the superiority of our approach over current state-of-the-art methods.