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PAMI
2007

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

8 years 10 months ago
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...
Sen Wang, Yang Wang, Miao Jin, Xianfeng David Gu,
Added 27 Dec 2010
Updated 27 Dec 2010
Type Journal
Year 2007
Where PAMI
Authors Sen Wang, Yang Wang, Miao Jin, Xianfeng David Gu, Dimitris Samaras
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