An Integer Linear Programming Approach to Geometrically Consistent Partial-Partial Shape Matching
This addresses a realistic but under-explored challenge in computer vision, such as in 3D scanning, where shapes are often only partially observable, though it appears incremental as it builds on existing shape matching formalisms.
The paper tackles the problem of partial-partial 3D shape matching, which involves finding correspondences between two partially observable shapes, by introducing an integer linear programming approach that uses geometric consistency to estimate overlapping regions and compute smooth correspondences, achieving high-quality results in terms of matching error and smoothness.
The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the partial-partial setting, very likely due to its unique challenges: we must compute accurate correspondences while at the same time find the unknown overlapping region. Nevertheless, partial-partial 3D shape matching reflects the most realistic setting, as in many real-world cases, such as 3D scanning, shapes are only partially observable. In this work, we introduce the first integer linear programming approach specifically designed to address the distinctive challenges of partial-partial shape matching. Our method leverages geometric consistency as a strong prior, enabling both robust estimation of the overlapping region and computation of neighbourhood-preserving correspondences. We empirically demonstrate that our approach achieves high-quality matching results both in terms of matching error and smoothness. Moreover, we show that our method is more scalable than previous formalisms.