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.

我们的研究建立在几何一致性为重要约束的基础上，利用三角形乘积空间的新型整数非线性规划形式和基于线性整数规划的剪枝算法，在部分 - 部分匹配中实现了几何一致性，并生成了一个新的跨类别数据集，我们的方法在已有的类内数据集和我们的新跨类别数据集上均优于当前的技术水平方法。