Oberseminar Numerische Mathematik / Scientific Computing
Xue-Cheng Tai
University of Bergen, Norway and Nanyang Technological Univ, Singapore
Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach and graph cuts algorithms
Abstract:
This talk is devoted to the optimization problem of continuous multi- partitioning, or multi-labeling, which is based on a convex relaxation of the continuous Potts model. In contrast to previous efforts, which are trying to tackle the optimal labeling problem in a direct manner, we first propose a novel dual model and then build up a corresponding duality- based approach. By analyzing the dual formulation, we can show that the relaxation is often exact, i.e. the optimal solution is also globally optimal to the nonconvex Potts model. In order to deal with the nonsmooth dual problem, we suggest a smoothing method based on the log-sum exponential function and also indicate that such smoothing approach gives rise to the novel smoothed primal-dual model and suggests labelings with maximum entropy. Such smoothing method for the dual model produces an expectation maximization algorithm for the multi-labeling problem. Numerical experiments show competitive performance in terms of quality Pott’s mode.
In the end, we will also present several recent algorithms for computing global minimizers based on graph cut approaches. This talk is based on joint works with Egil Bae and Jing Yuan.
| Datum: | 11.04.10 | Zeit: | 17:00 Uhr | Ort: | FU Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin. | Raum: | Raum 031 im Erdgeschoss |