3D Shape Correspondence by Isometry-Driven Greedy Optimization

Abstract

We present an automatic method that establishes 3D cor-respondence between isometric shapes. Our goal is to find an optimal correspondence between two given (nearly) iso-metric shapes, that minimizes the amount of deviation from isometry. We cast the problem as a complete surface cor-respondence problem. Our method first divides the given shapes to be matched into surface patches of equal area and then seeks for a mapping between the patch centers which we refer to as base vertices. Hence the correspondence is established in a fast and robust manner at a relatively coarse level as imposed by the patch radius. We optimize the isometry cost in two steps. In the first step, the base vertices are transformed into spectral domain based on geodesic affinity, where the isometry errors are minimized in poly-nomial time by complete bipartite graph matching. The re-sulting correspondence serves as a good initialization for the second step of optimization in which we explicitly min-imize the isometry cost via an iterative greedy algorithm in the original 3D Euclidean space. We demonstrate the per-formance of our method on various isometric (or nearly iso-metric) pairs of shapes for some of which the ground-truth correspondence is available. 1.