Brain Surface Conformal Parameterization with the Slit Mapping
IEEE Vis 2008
Yalin Wang1, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, Shing-Tung Yau
Brain surface conformal mapping has been studied intensively.
In this paper, we propose a method that computes a
conformal mapping from a multiply connected mesh to the
so-called slit domain, which consists 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.
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 results, the feature curves are either mapped
to straight lines or a 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.