We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms with or without boundaries. For genus zero surfaces, our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. In this paper, we apply the 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 resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.

Date Published: 12 May 2004
PDF: 12 pages
Proc. SPIE 5370, Medical Imaging 2004: Image Processing, (12 May 2004); doi: 10.1117/12.534480

Published in SPIE Proceedings Vol. 5370:
Medical Imaging 2004: Image Processing
J. Michael Fitzpatrick; Milan Sonka, Editor(s)