A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity
This work addresses image segmentation for applications requiring noise robustness, but it is incremental as it builds on existing variational and fuzzy methods.
The authors tackled image segmentation by proposing a variational multiphase model using fuzzy membership functions and L1-norm fidelity, which proved more robust to outliers like impulse noise and maintained better contrast compared to L2-norm methods.
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.