Brain Surface Parameterization Using Riemann Surface Structure

Abstract. We develop a general approach that uses holomorphic 1forms to parameterize anatomical surfaces with complex (possibly branching) topology. Rather than evolve the surface geometry to a plane or sphere, we instead use the fact that all orientable surfaces are Riemann surfaces and admit conformal structures, which induce special curvilinear coordinate systems on the surfaces. Based on Riemann surface structure, we can then canonically partition the surface into patches. Each of these patches can be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable. To illustrate the technique, we computed conformal structures for several types of anatomical surfaces in MRI scans of the brain, including the cortex, hippocampus, and lateral ventricles. We found that the resulting parameterizations were consistent across subjects, even for branching structures such as the ventricles, which are otherwise diff...

• Type: Conference
• Year: 2005
• Where: MICCAI
• Authors: Yalin Wang, Xianfeng Gu, Kiralee M. Hayashi, Tony F. Chan, Paul M. Thompson, Shing-Tung Yau
• Keywords: Anatomical Surfaces, Medical Imaging, MICCAI 2005, Orientable Surfaces, Riemann Surfaces