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

• Published in: IEEE transactions on medical imaging Vol. 23; no. 8; pp. 949 - 958
• Main Authors: Xianfeng Gu, Yalin Wang, Chan, T.F., Thompson, P.M., Shing-Tung Yau
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2004; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Biomedical imaging; Boundaries; Brain; Brain - anatomy & histology; Brain - physiology; Brain Mapping - methods; Cerebral cortex; Computer Simulation; Conformal mapping; Contracts; Humans; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image resolution; Imaging, Three-Dimensional - methods; Information Storage and Retrieval - methods; Magnetic resonance imaging; Magnetic Resonance Imaging - methods; Mapping; Mathematics; Numerical Analysis, Computer-Assisted; Parametrization; Pattern Recognition, Automated; Preserves; Reproducibility of Results; Robustness; Sensitivity and Specificity; Signal Processing, Computer-Assisted; Subtraction Technique; Surface matching; Testing
• ISSN: 0278-0062; 1558-254X
• DOI: 10.1109/TMI.2004.831226

We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms for surfaces with or without boundaries (Gu and Yau, 2002), (Gu and Yau, 2003). 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 magnetic resonance imaging (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.