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.

翻译：在三维形状间建立对应关系是计算机视觉领域长期存在的挑战。尽管已有大量研究致力于完整-完整与部分-完整三维形状匹配，但针对部分-部分场景的研究工作却十分有限，这很可能源于其特有的双重挑战：我们不仅需要计算精确的对应关系，还必须同时确定未知的重叠区域。然而，部分-部分三维形状匹配恰恰反映了最现实的场景，因为在三维扫描等众多实际应用中，形状往往只能被部分观测。本研究首次提出专门针对部分-部分形状匹配独特挑战的整数线性规划方法。该方法以几何一致性作为强先验约束，既能实现重叠区域的鲁棒估计，又能计算保持邻域结构的对应关系。实验结果表明，我们的方法在匹配误差和平滑度方面均能获得高质量的匹配结果。此外，研究还证明该方法相较于既有形式化体系具有更优的可扩展性。