Genus zero surface conformal mapping and its application to brain surface mapping.

Xianfeng Gu; Yalin Wang; Tony F Chan; Paul M Thompson; Shing-Tung Yau

doi:10.1007/978-3-540-45087-0_15

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Genus zero surface conformal mapping and its application to brain surface mapping.

Xianfeng Gu·Yalin Wang·Tony F Chan·Paul M Thompson·Shing-Tung Yau

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Abstract

It is well known that any genus zero surface can be mapped conformally onto the sphere and any local portion thereof onto a disk. However, it is not trivial to find a general method which finds a conformal mapping between two general genus zero surfaces. We propose a new variational method which can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. We demonstrate the feasibility of our algorithm by applying it to the cortical surface matching problem. We use a mesh structure to represent the brain surface. Further constraints are added to ensure that the conformal map is unique. Empirical tests on MRI data show that the mappings preserve angular relationships, are stable in MRIs acquired at different times, and are robust to differences in data triangulation, and resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.

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Algorithms Brain Brain Mapping Computer Simulation Humans Image Enhancement Image Interpretation, Computer-Assisted Imaging, Three-Dimensional Magnetic Resonance Imaging Models, Biological Pattern Recognition, Automated Subtraction Technique Comparative Study Evaluation Study Journal Article

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Xianfeng Gu, Yalin Wang, Tony F Chan, Paul M Thompson, Shing-Tung Yau. 2003. Genus zero surface conformal mapping and its application to brain surface mapping.. https://doi.org/10.1007/978-3-540-45087-0_15

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