In this paper, we propose a variational multiphase image segmentation modelbased on fuzzy membership functions and L1-norm fidelity. Then we apply thealternating direction method of multipliers to solve an equivalent problem. Allthe subproblems can be solved efficiently. Specifically, we propose a fastmethod to calculate the fuzzy median. Experimental results and comparisons showthat the L1-norm based method is more robust to outliers such as impulse noiseand keeps better contrast than its L2-norm counterpart. Theoretically, we provethe existence of the minimizer and analyze the convergence of the algorithm.
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