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
It is well known that any genus zero surface can be mapped
conformally onto the sphere
and any local portion thereof onto a disk. However, it is not trivial to find
a general method which finds a conformal mapping between two general genus zero
surfaces. We propose a new variational method which can find a unique mapping between any two genus zero
manifolds by minimizing the harmonic energy of the map.
We demonstrate the feasibility of
our algorithm by applying it 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 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.
Figures (click on each for a larger version):
X. Gu, Y. Wang, T.F. Chan, P.M. Thompson and S.-T. Yau, "
Genus Zero Surface Conformal Mapping and Its Application to Brain Surface Mapping", IEEE Transaction on Medical Imaging, 23(8), Aug. 2004, pp. 949-958
Y. Wang, X. Gu, T. F. Chan, P. M. Thompson and S.-T. Yau,
Intrinsic Brain Surface Conformal Mapping using a Variational Method",
Medical Imaging 2004: Image Processing, J. M. Fitzpatrick and M. Sonka (Eds.) Proceedings of SPIE, Vol. 5370, 2004, pp. 241-252
X. Gu, Y. Wang, T. F. Chan, P. M. Thompson and S.-T. Yau,
Genus Zero Surface Conformal Mapping and Its Application to Brain Surface Mapping",
C. Taylor and J. Alison Noble (Eds.), Information Processing in Medical Imaging,18th International Conference, IPMI 2003, Ambleside, UK, July 2003. Proceedings, pp. 172-184