Project Description:
A numerical method for computing the extremal Teichmuller map between multiply-connected domains is presented. Given two multiply-connected domains, there exists a unique Teichmuller map (T-Map) between them minimizing the conformality distortion. The extremal T-Map can be considered as the `most conformal' map between multiply-connected domains. In this paper, we propose an iterative algorithm to compute the extremal T-Map using the Beltrami holomorphic ow (BHF). The BHF procedure iteratively adjusts the initial map based on a sequence of Beltrami coefficients, which are complex-valued functions defined on the source domain. It produces a sequence of quasi-conformal maps, which converges to the T-Map minimizing the conformality distortion. We test our method on synthetic data together with real human face data. Results show that our algorithm computes the extremal T-Map between two multiply-connected domains of the same topology accurately and efficiently.

Publication:

• T.C. Ng, X.F. Gu, L.M. Lui, Teichmuller extremal map of multiply-connected domains using Beltrami holomorphic flow, 10.1007/s10915-013-9791-z, Journal of Scientific Computing (2013)