Finding correspondences between 3D shapes is an important and long-standing problem in computer vision, graphics and beyond. A prominent challenge are partial-to-partial shape matching settings, which occur when the shapes to match are only observed incompletely (e.g. from 3D scanning). Although partial-to-partial matching is a highly relevant setting in practice, it is rarely explored. Our work bridges the gap between existing (rather artificial) 3D full shape matching and partial-to-partial real-world settings by exploiting geometric consistency as a strong constraint. We demonstrate that it is indeed possible to solve this challenging problem in a variety of settings. For the first time, we achieve geometric consistency for partial-to-partial matching, which is realized by a novel integer non-linear program formalism building on triangle product spaces, along with a new pruning algorithm based on linear integer programming. Further, we generate a new inter-class dataset for partial-to-partial shape-matching. We show that our method outperforms current SOTA methods on both an established intra-class dataset and our novel inter-class dataset.

翻译：在三维形状之间建立对应关系是计算机视觉、图形学及更广泛领域中一个长期存在的重要问题。其中一个突出挑战是部分到部分形状匹配场景，即当待匹配的形状仅被不完全观测到时（例如通过三维扫描）。尽管部分到部分匹配在实践中具有高度相关性，但相关研究鲜有涉足。本文通过将几何一致性作为强约束，弥合了现有（较为人工）的三维完整形状匹配与部分到部分真实场景之间的鸿沟。我们证明，在多种场景下解决这一难题确实可行。我们首次实现了部分到部分匹配的几何一致性，这一成果基于构建在三角形乘积空间上的新型整数非线性规划形式，并结合了基于线性整数规划的新剪枝算法。此外，我们还生成了一个新的跨类别部分到部分形状匹配数据集。实验表明，我们的方法在已有的类别内数据集和新的跨类别数据集上均优于当前最先进方法。