3D Surface Matching and Recognition Using Conformal Geometry
Sen Wang, Yang Wang, Miao Jin, Xianfeng Gu, Dimitris Samaras
CVPR 2006.
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 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 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 accurate and efficient 3D
surface matching algorithms can be achieved by using conformal
geometric maps. Finally, the performance of conformal
geometric maps is evaluated and analyzed comprehensively
in 3D surface matching with occlusion, noise and resolution
variation. We also provide a series of experiments
on real 3D face data that achieve high recognition rates.