@inproceedings{eae8140d35f84284b0c42f495c29c2d1,

title = "Brain surface conformal parameterization",

abstract = "We develop a general approach that uses holomorphic 1-forms 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. We can then automatically partition the surface using a critical graph that connects zero points in the conformal structure on the surface. The trajectories of iso-parametric curves canonically partition a surface into patches. Each of these patches is either a topological disk or a cylinder and can be conformally mapped to a parallelogram by integrating a holomorphic 1-form defined on the surface. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable. To illustrate the technique, we computed conformai 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 difficult to parameterize. Compared with other variational approaches based on surface inflation, our technique works on surfaces with arbitrary complexity while guaranteeing minimal distortion in the parameterization. It also generates grids on surfaces for PDE-based signal processing.",

keywords = "Brain mapping, Conforaml net, Critical graph, Riemann surface structure",

author = "Y. Wang and Xianfeng Gu and Hayashi, {Kiralee M.} and Chan, {Tony F.} and Thompson, {Paul M.} and Yau, {Shing Tung}",

year = "2005",

month = dec,

day = "1",

language = "English (US)",

isbn = "0889865140",

series = "Proceedings of the Eighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005",

pages = "76--81",

editor = "M.H. Hamza",

booktitle = "Proceedings of the Eighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005",

note = "Eighth IASTED International Conference on Computer Graphics and Imaging, CGIM 2005 ; Conference date: 15-08-2005 Through 17-08-2005",

}