Computing extremal Teichmüller map of multiply-connected domains via Beltrami holomorphic flow. (English) Zbl 1316.65036
Authors’ abstract: A numerical method for computing the extremal Teichmüller map between multiply-connected domains is presented. Given two multiply-connected domains, there exists a unique Teichmüller 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 flow (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.
Reviewer: Allal Ghanmi (Rabat)
MSC:
| 65E05 | General theory of numerical methods in complex analysis (potential theory, etc.) |
| 30C62 | Quasiconformal mappings in the complex plane |
| 30C75 | Extremal problems for conformal and quasiconformal mappings, other methods |
| 30F60 | Teichmüller theory for Riemann surfaces |
Keywords:
Teichmüller map; extremal map; multiply-connected domains; Beltrami holomorphic flow; quasiconformal map; iterative algorithmReferences:
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