In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity. Then we apply the alternating direction method of multipliers to solve an equivalent problem. All the subproblems can be solved efficiently. Specifically, we propose a fast method to calculate the fuzzy median. Experimental results and comparisons show that the L1-norm based method is more robust to outliers such as impulse noise and keeps better contrast than its L2-norm counterpart. Theoretically, we prove the existence of the minimizer and analyze the convergence of the algorithm.
@article{arxiv.1504.02206,
title = {A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity},
author = {Fang Li and Stanley Osher and Jing Qin and Ming Yan},
journal= {arXiv preprint arXiv:1504.02206},
year = {2016}
}