Genus Zero Surface Conformal Mapping and Its Application to Brain Surface Mapping
Xianfeng Gu, Yalin Wang*, Tony F. Chan, Paul M. Thompson, and Shing-Tung Yau
IEEE Transaction on Medical Imaging, 23(8), Aug. 2004, pp. 949-958.
We developed a general method for global conformal
parameterizations based on the structure of the cohomology group
of holomorphic one-forms for surfaces with or without boundaries
(Gu and Yau, 2002), (Gu and Yau, 2003). For genus zero surfaces,
our algorithm can find a unique mapping between any two genus
zero manifolds by minimizing the harmonic energy of the map. In
this paper, we apply the algorithm to the cortical surface matching
problem. We use a mesh structure to represent the brain surface.
Further constraints are added to ensure that the conformal map is
unique. Empirical tests on magnetic resonance imaging (MRI) data
show that the mappings preserve angular relationships, are stable
in MRIs acquired at different times, and are robust to differences in
data triangulation, and resolution. Compared with other brain surface
conformal mapping algorithms, our algorithm is more stable
and has good extensibility.