Finding correspondences between shapes is a fundamental problem in computer
vision and graphics, which is relevant for many applications, including 3D
reconstruction, object tracking, and style transfer. The vast majority of
correspondence methods aim to find a solution between pairs of shapes, even if
multiple instances of the same class are available. While isometries are often
studied in shape correspondence problems, they have not been considered
explicitly in the multi-matching setting. This paper closes this gap by
proposing a novel optimisation formulation for isometric multi-shape matching.
We present a suitable optimisation algorithm for solving our formulation and
provide a convergence and complexity analysis. Our algorithm obtains
multi-matchings that are by construction provably cycle-consistent. We
demonstrate the superior performance of our method on various datasets and set
the new state-of-the-art in isometric multi-shape matching.

本文提出了新型的等距多形状匹配问题的优化公式，并介绍了适合解决这种公式的优化算法，提供了收敛性和复杂性分析，对不同数据集进行了实验，取得了最新的等距多形状匹配的最好表现。