Globally Optimal Surface Mapping for Surfaces with Arbitrary Topology
IEEE TVCG 2008
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
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 simplified 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 solely
founded upon the intrinsic geometry structure of surfaces. To
our best knowledge, this is the first attempt towards rigorously
and numerically computing globally optimal maps. Consequently,
we demonstrate our mapping framework offers a powerful
computational tool for graphics and visualization tasks such as
data and texture transfer, shape morphing, and shape matching.