Consistent Correspondence Between Arbitrary Manifold Surfaces

Abstract

We propose a novel framework for consistent correspondence between arbitrary manifold meshes. Different from most existing methods, our approach directly maps the connectivity of the source mesh onto the target mesh without needing to segment input meshes, thus effectively avoids dealing with unstable extreme conditions (e.g. complex boundaries or high genus). In this paper, firstly, a novel mean-value Laplacian fitting scheme is proposed, which aims at computing a shape-preserving (conformal) correspondence directly in 3D-to-3D space, efficiently avoiding local optimum caused by the nearest-point search, and achieving good results even with only a few marker points. Secondly, we introduce a vertex relocation and projection approach, which refines the initial fitting result in the way of local conformity. Each vertex of the initial result is gradually projected onto the target model's surface to ensure a complete surface match. Furthermore, we provide a fast and effective approach to automatically detect critic points in the context of consistent correspondence. By fitting these critic points that capture the important features of the target mesh, the output compatible mesh matches the target mesh's profiles quite well. Compared with previous approaches, our scheme is robust, fast, and convenient, thus suitable for common applications.