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

Abstract

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.

The Vese-Chan model without redundant parameter estimation for multiphase image segmentation

“…Multiphase image segmentation under variational framework has found a lot of applications including multi-target detection and recognition, 3D segmentation and reconstruction in medical images, remote sensing images, etc. [1,2], due to its property of multiple cue integration. The aim of multiphase image segmentation is to partition images into different regions without any overlaps and without any unlabeled region (called in the sequel vacuum) automatically.…”

“…The Mumford-Shah model [3] is fundamental to variational image segmentation; it is a region-based model *Correspondence: zkpan@126.com 1 College of Computer Science and Technology, Qingdao University, Qingdao 266071, China Full list of author information is available at the end of the article which approximates an image to a piecewise smooth one and edges. To circumvent the difficulty of its implementation, Chan and Vese [4] proposed the classical Vese-Chan model under variational level set framework [5] based on reduced Mumford-Shah model with piecewise constant image assumption.…”

L1 Patch-Based Image Partitioning into Homogeneous Textured Regions

“…As a further consequence of the use of the L 1 norm it is robust to impulse noise and outliers. The L 1 norm was also used for segmentation purposes in [15,12]. As in our proposal, [15] also uses fuzzy membership functions [29] and the TV norm to estimate the length of the segmentation boundaries.…”

“…The L 1 norm was also used for segmentation purposes in [15,12]. As in our proposal, [15] also uses fuzzy membership functions [29] and the TV norm to estimate the length of the segmentation boundaries. On the other hand, the classical structure tensor has been used in the literature for texture segmentation purposes [21,22,11].…”

New second order Mumford–Shah model based on Γ-convergence approximation for image processing

“…The second approach involves the use of the characteristic functions for different phases or classes in an image (a phase/class contains pixels having similar characteristic), transforming the 1D terms into the 2D ones. Example methods of this approach include the following: (i) the variational level set method [6][7][8][9][10][11] that combines the classical level set method with the variational method; (ii) the variational label function method, also known as the piecewise constant level set method [12][13][14] or the fuzzy membership function method [15,16]; (iii) the C-convergence elliptic function approximated method [17][18][19][20].…”