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

The Vese-Chan model for multiphase image segmentation uses m binary label functions to construct 2(m) 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 2(m), 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.