# A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity

arXiv: https://arxiv.org/abs/1504.02206 · HTML: https://mlsanity.com/paper/1504.02206/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2015.

## Built on by (most cited first, 3 of 3)

- [An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation](https://mlsanity.com/paper/2202.10115/) (2022)
- [Difference of Anisotropic and Isotropic TV for Segmentation under Blur and Poisson Noise](https://mlsanity.com/paper/2301.03393/) (2023)
- [An Image Segmentation Model with Transformed Total Variation](https://mlsanity.com/paper/2406.00571/) (2024)

## Abstract (arXiv)

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.