Globally Optimal Surface Mapping for Surfaces with Arbitrary Topology
IEEE Transactions on Visualization and Computer Graphics
Xin Li, Yunfan Bao, Xiaohu Guo, Miao Jin, Xianfeng Gu, and Hong Qin
Computing smooth and optimal one-to-one maps
between surfaces of same topology is a fundamental problem in
computer graphics and such a method provides us a ubiquitous
tool for geometric 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 angular
distortions among different shapes. This paper proposes and
develops a novel quasi-conformal surface mapping framework
to globally minimize the stretching energy inevitably introduced
between two different shapes. The existing state-of-the-art intersurface
mapping techniques only afford local optimization either
on surface patches via boundary cutting or on the simpli.ed base
domain, lacking rigorous mathematical foundation and analysis.
We design and articulate an automatic variational algorithm that
can reach the global distortion minimum for surface mapping
between shapes of arbitrary topology, and our algorithm is sorely
founded upon the intrinsic geometry structure of surfaces. To
our best knowledge, this is the .rst attempt towards numerically
computing globally optimal maps. Consequently, our mapping
framework offers a powerful computational tool for graphics
and visualization tasks such as data and texture transfer, shape
morphing, and shape matching.