Harmonic Maps and Their Applications in Surface Matching

* The surface-matching problem is investigated in this paper using a mathematical tool called harmonic maps. The theory of harmonic maps studies the mapping between different metric manifolds from the energyminimization point of view. With the application of harmonic maps, a surface representation called harmonic shape images is generated to represent and match 3D freeform surfaces. The basic idea of harmonic shape images is to map a 3D surface patch with disc topology to a 2D domain and encode the shape information of the surface patch into the 2D image. This simplifies the surface-matching problem to a 2D image-matching problem. Due to the application of harmonic maps in generating harmonic shape images, harmonic shape images have the following advantages: they have sound mathematical background; they preserve both the shape and continuity of the underlying surfaces; and they are robust to occlusion and independent of any specific surface sampling scheme. The performance of surface m...

• Type: Conference
• Year: 1999
• Where: CVPR
• Authors: Dongmei Zhang, Martial Hebert
• Keywords: 3D Surface Patch, Computer Vision, CVPR 1999, Harmonic Maps, Harmonic Shape Images, Shape Information, Surface Sampling Scheme