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:查找形状之间的对应是计算机视觉和图形中的一个基本问题,这与许多应用程序有关,包括 3D 重建、 对象跟踪和样式传输。 绝大多数的对应方法都旨在寻找形状组合之间的解决方案, 即使存在相同类别的多个实例。 虽然经常以形状对应问题来研究异形, 但是在多配对设置中并没有被明确考虑。 本文通过为异度多形状匹配提出新的优化配方来弥合这一差距。 我们为解析我们的配方提供了合适的优化算法, 并提供趋同和复杂分析。 我们的算法获得了多种匹配, 而这些匹配是建筑可调和循环的。 我们在各种数据集上展示了我们方法的优异形, 并设定了异度多形状匹配的新状态 。