Brain Surface Conformal Parameterization with Algebraic Functions
Yalin Wang, Xianfeng Gu, Paul Thompson, Tony F. Chan, Shing-Tung Yau
MICCAI 2006
In medical imaging, parameterized 3D surface models are
of great interest for anatomical modeling and visualization, statistical
comparisons of anatomy, and surface-based registration and signal pro-
cessing. Here we introduce a parameterization method based on algebraic
functions. By solving the Yamabe equation with the Ricci °ow method,
we can conformally map a brain surface to a multi-hole disk. The re-
sulting parameterizations do not have any singularities and are intrinsic
and stable. To illustrate the technique, we computed parameterizations
of several types of anatomical surfaces in MRI scans of the brain, in-
cluding the hippocampi and the cerebral cortices with various landmark
curves labeled. For the cerebral cortical surfaces, we show the parameter-
ization results are consistent with selected landmark curves and can be
matched to each other using constrained harmonic maps. Unlike previous
planar conformal parameterization methods, our algorithm does not in-
troduce any singularity points. It also oŽers a method to explicitly match
landmark curves between anatomical surfaces such as the cortex, and to
compute conformal invariants for statistical comparisons of anatomy.