In this work we propose to combine the advantages of learning-based and combinatorial formalisms for 3D shape matching. While learning-based shape matching solutions lead to state-of-the-art matching performance, they do not ensure geometric consistency, so that obtained matchings are locally unsmooth. On the contrary, axiomatic methods allow to take geometric consistency into account by explicitly constraining the space of valid matchings. However, existing axiomatic formalisms are impractical since they do not scale to practically relevant problem sizes, or they require user input for the initialisation of non-convex optimisation problems. In this work we aim to close this gap by proposing a novel combinatorial solver that combines a unique set of favourable properties: our approach is (i) initialisation free, (ii) massively parallelisable powered by a quasi-Newton method, (iii) provides optimality gaps, and (iv) delivers decreased runtime and globally optimal results for many instances.

翻译：本文提出将基于学习的方法与组合形式化方法的优势相结合，以解决三维形状匹配问题。基于学习的形状匹配方案虽能实现最先进的匹配性能，但无法保证几何一致性，导致所得匹配结果在局部区域不够平滑。相反，公理方法通过显式约束有效匹配空间来考虑几何一致性。然而，现有公理形式化方法难以实际应用：它们无法扩展至实际相关的问题规模，或需要用户输入来初始化非凸优化问题。本文旨在弥合这一差距，提出一种新型组合求解器，该求解器兼具以下独特优势：(i)无需初始化，(ii)可通过拟牛顿方法实现大规模并行化，(iii)提供最优性间隙，(iv)在多数实例中实现更短的运行时间与全局最优解。