A methodology for shape matching of non-rigid structures based on integrated graphical information

Abstract

Shape matching is a long-studied problem and lies at the core of many applications in statistical shape analysis, virtual reality and human–computer interaction. This paper presents an automatic dense correspondence method to match the mesh vertices of two 3D shapes under near-isometric and non-rigid deformations. The goal is achieved by combining three types of graphic structure information. The method includes three major steps: first, we describe the vertices based on three types of graphical information, Euclidean structure information, Riemannian structure information, and conformal structure information; second, the match between two shapes is formulated as an optimization problem and a novel objective function is proposed; third, we resolve the optimal solution by using the projected descent optimization procedure to solve the objective function. The method is tested on various shape pairs with different poses, surface details, and topological noises. We demonstrate the performance of our approach through an extensive quantitative and qualitative evaluation on several challenging 3D shape matching datasets where we achieve superior performance to existing methods.