3D Surface Matching and Recognition Using Conformal Geometry

3D surface matching is a fundamental issue in computer vision with many applications such as shape registration, 3D object recognition and classification. However, surface matching with noise, occlusion and clutter is a challenging problem. In this paper, we analyze a family of conformal geometric maps including harmonic maps, conformal maps and least squares conformal maps with regards to 3D surface matching. As a result, we propose a novel and computationally efficient surface matching framework that uses 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 surface-matching problem to a 2D image-matching problem, by comparing the resulting 2D conformal geometric maps, which are stable, insensitive to resolution changes and robust to occlusion and noise. Therefore, highly ...

• Type: Conference
• Year: 2006
• Where: CVPR
• Authors: Sen Wang, Yang Wang, Miao Jin, Xianfeng Gu, Dimitris Samaras
• Keywords: Computer Vision, Conformal Geometric Maps, CVPR 2006, Efficient 3d Surface, Squares Conformal Maps, Surface Matching, Surface Matching Framework