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Least square conformal mapping with spring energy

Mapping the cortical surface into a canonical coordinate space is an important means to study the structure and functional of the brain. Levy et al. (2002) proposed a least square conformal maps method by representing conformal energy as the square sense of the Cauchy-Riemann equation. It obtains good results in both angular distortion and computation time, although it introduces certain metric and area distortion, especially when applied to the complex cortical surface. Recently, Ju et al. (2004) extended the least square method to spherical conformal map. To reduce the metric and area distortion while maintaining the conformal map and computation efficiency, we designed and added the spring energy to the least square conformal maps. Our results show that the least square conformal mapping with spring energy controls metric and area distortion effectively with computational efficiency. The least square conformal mapping with spring energy is also extended to spherical mapping