首次用整数规划解决3D部分重叠形状匹配难题，兼顾精准对应与重叠区域估计。
An Integer Linear Programming Approach to Geometrically Consistent Partial-Partial Shape Matching
- 基于整数线性规划建模，利用几何一致性先验约束匹配
- 在匹配误差和对应平滑性上均优于现有方法
- 可扩展性强，适合真实场景中部分观测的3D形状匹配
3D形状对应关系的建立是计算机视觉中的长期挑战。尽管已有大量研究聚焦全-全和部分-全形状匹配，但针对部分-部分匹配的研究仍十分有限，主要因其独特挑战：需同时确定精确对应关系和未知重叠区域。然而，部分-部分匹配更贴近真实场景，如3D扫描中形状常仅部分可见。本文提出首个专为部分-部分匹配设计的整数线性规划方法。该方法利用几何一致性作为强先验，既能鲁棒地估计重叠区域，又能计算保持邻域结构的对应关系。实验表明，本方法在匹配误差和对应平滑性方面均取得高质量结果，且相比以往形式化方法更具可扩展性。
原文摘要 · Abstract (English)
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.
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