2004/08/01 by Xianfeng Gu, Yalin Wang, Tony F. Chan +2 · 3 citations
Engineering · Computer Science · Mathematics · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computer Graphics and Visualization Techniques #Conformal map #Triangulation #Surface (topology) #Mathematics #Zero (linguistics) #Genus #Harmonic map #Topology (electrical circuits) #Algorithm #Computer science #Pure mathematics #Mathematical analysis #Geometry #Combinatorics
paper · doi:10.1109/tmi.2004.831226
openalex publication_date 2004/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.