Xin Li, Yunfan Bao, Xiaohu Guo, Miao Jin , Xianfeng Gu, Hong Qin

Center for Visual Computing

Department of Computer Science

State University of New York at Stony Brook

Building smooth one-to-one maps between surfaces with same topology provides a ubiquitous tool for surface modeling and data visualization. Its vast variety of applications includes shape registration/matching, shape blending, material/data transfer, data fusion, information reuse, etc. The mapping quality is typically measured in terms of angle and area distortion. This paper develops a novel quasi-conformal surface mapping framework to globally minimize the stretching energy inevitably introduced between two different shapes. The current state-of-the-art inter-surface mapping techniques only afford local optimization either on surface patches via cutting or on the simplified base domain, lacking rigorous mathematical foundation and analysis. We develop an automatic variational algorithm that can reach the global distortion minimum for surface mapping, and our algorithm is solidly founded upon the intrinsic geometry structure of surfaces. To our best knowledge, this is the first attempt towards numerically computing globally optimal maps and applying it to the data visualization field. Our mapping framework offers a powerful visualization tool to register two surfaces, and as a result of that, the subsequent tasks such as matching, morphing, and data transfer can be easily computed and visualized.

• Final Video: (76MB, divx)
• Video1: Torus maps to Torus (genus-1)
• Video2: Star maps to Rocker Arm (genus-1)
• Video3: Buddha maps to Poly-cube (genus-6)
• Video4: Poly-cube maps to Buddha (genus-6)

• Xin Li, Yunfan Bao, Xiaohu Guo, Miao Jin, Xianfeng Gu, Hong Qin, "Globally Optimal Surface Mapping for Shapes of Arbitrary Topology", in IEEE Transactions on Visualization and Computer Graphics, Vol. 14, No. 4, pp. 805-819, 2008.