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.

翻译：形状之间的对应关系找到是计算机视觉和图形学中的一个基本问题，它涉及到许多应用，包括三维重建、对象跟踪和风格迁移。绝大多数对应方法旨在寻找成对形状之间的解，即使同一类别的多个实例可用也是如此。虽然等距性在形状对应问题中经常被研究，但在多匹配设置中并未明确考虑。本文通过提出一种新颖的等距多形状匹配优化公式来填补这一空白。我们提出了一种合适的优化算法来解决我们的公式，并提供了收敛性和复杂性分析。我们的算法获得的多匹配结果在构造上保证了循环一致性。我们在各种数据集上展示了我们方法的优越性能，并在等距多形状匹配中树立了新的标杆。