Conformal Geometry and Its Applications on 3D Shape Matching, Recognition, and Stitching

—Three-dimensional shape matching is a fundamental issue in computer vision with many applications such as shape registration, 3D object recognition, and classification. However, shape matching with noise, occlusion, and clutter is a challenging problem. In this paper, we analyze a family of quasi-conformal maps including harmonic maps, conformal maps, and least-squares conformal maps with regards to 3D shape matching. As a result, we propose a novel and computationally efficient shape matching framework by using least-squares conformal maps. According to conformal geometry theory, each 3D surface with disk topology can be mapped to a 2D domain through a global optimization and the resulting map is a diffeomorphism, i.e., one-to-one and onto. This allows us to simplify the 3D shape-matching problem to a 2D image-matching problem, by comparing the resulting 2D parametric maps, which are stable, insensitive to resolution changes and robust to occlusion, and noise. Therefore, highly acc...

• Type: Journal
• Year: 2007
• Where: PAMI
• Authors: Sen Wang, Yang Wang, Miao Jin, Xianfeng David Gu, Dimitris Samaras
• Keywords: Conformal Maps, PAMI 2007, Shape Matching, —Three-dimensional Shape