Abstract
The Vese-Chan model for multiphase image segmentation uses m binary label functions to construct 2m characteristic functions for different phases/regions systematically; the terms in this model have moderate degrees comparing with other schemes of multiphase segmentation. However, if the number of desired regions is less than 2m, there exist some empty phases which need costly parameter estimation for segmentation purpose. In this paper, we propose an automatic construction method for characteristic functions via transformation between a natural number and its binary expression, and thus, the characteristic functions of empty phases can be written and recognized naturally. In order to avoid the redundant parameter estimations of these regions, we add area constraints in the original model to replace the corresponding region terms to preserve its systematic form and achieve high efficiency. Additionally, we design the alternating direction method of multipliers (ADMM) for the proposed modified model to decompose it into some simple sub-problems of optimization, which can be solved using Gauss-Seidel iterative method or generalized soft thresholding formulas. Some numerical examples for gray images and color images are presented finally to demonstrate that the proposed model has the same or better segmentation effects as the original one, and it reduces the estimation of redundant parameters and improves the segmentation efficiency.
Highlights
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
Motivated by the relationship between the Heaviside function of a level set function and a binary label function, the piecewise constant level set function method was adopted to two-phase image segmentation [11] combined with convex relaxation and thresholding techniques with high efficiency
The models for multiphase image segmentation using variational level set method as mentioned in the previous paragraph have been extended to the counterparts using piecewise constant level set function method successively, such as, [12] used n binary label functions to partition n regions, [13] used m binary label functions for n = 2m regions, and [14] used one piecewise constant level set function for all regions
Summary
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. It is a natural extension of the twophase image segmentation based on the variational image analysis paradigm. The models for multiphase image segmentation using variational level set method as mentioned in the previous paragraph have been extended to the counterparts using piecewise constant level set function method successively, such as, [12] used n binary label functions to partition n regions, [13] used m binary label functions for n = 2m regions, and [14] used one piecewise constant level set function for all regions. To achieve higher computation efficiency for the optimization problems, Goldstein and Osher [15] proposed the split Bregman method, and Duan et al [16] proposed some fast projection methods without re-initialization
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