Conformal Slit Mapping and Its Applications to Brain Surface Parameterization
MICCAI 2008
Yalin Wang, Xiaotian Yin, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, Shing-Tung Yau
We propose a method that computes a conformal mapping
from a multiply connected mesh to the so-called slit domain, which con-
sists of a canonical rectangle or disk in which 3D curved landmarks on
the original surfaces are mapped to concentric or parallel lines in the slit
domain. In this paper, we studied its application to brain surface param-
eterization. After cutting along some landmark curve features on surface
models of the cerebral cortex, we obtain multiple connected domains. By
computing exact harmonic one-forms, closed harmonic one-forms, and
holomorphic one-forms, we are able to build a circular slit mapping that
conformally maps the surface to an annulus with some concentric arcs
and a rectangle with some slits. The whole algorithm is based on solving
linear systems so it is very stable. In the slit domain parameterization re-
sults, the feature curves are either mapped to straight lines or concentric
arcs. This representation is convenient for anatomical visualization, and
may assist statistical comparisons of anatomy, surface-based registration
and signal processing. Preliminary experimental results parameterizing
various brain anatomical surfaces are presented.