Improved Metric Space for Shape Correspondence

Abstract

Shape correspondence is a fundamental task of finding a map among the elements of a pair of shapes. Particularly, non-rigid shapes add to the challenge of computing correspondences as they have their respective metric structures. In order to establish a mapping between non-rigid shapes, it is necessary to bring them into a common metric space. The idea is to identify shape forms that are invariant to isometric deformations and are embedded in a Euclidean space. These pose-invariant features are then aligned to identify point-to-point correspondences. Geodesic distances have been utilized to compute these shape-invariant forms. However, these distances are quite sensitive to topological noise present in the shape. This work proposes to overcome these challenges by utilizing shape-aware distances to identify invariant forms that are unaffected by topological variations of the shape and are smoother than geodesic distance. These distances along with the non-rigid alignment of shape forms in the Euclidean domain led to an improved point-to-point correspondence, enabling it to work effectively, even when dealing with different triangulations of the shape.