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: