We developed a general method for global surface conformal parameterization. For
genus zero surface, our algorithm can find a conformal mapping between any two genus
zero manifolds by minimizing the harmonic energy. We apply this algorithm 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 rosolution. Compared with other brain surface conformal mapping
algorithms, our algorithm is more stable and has good extensibility. In our new research,
we further extended the algorithm to find a 3D volumetric harmonic map from a 3D brain
volumetric model to a solid sphere. Experimental results and furture work will be
discussed.
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