Unsupervised Multiphase Segmentation: A Phase Balancing Model

Abstract

Variational models have been studied for image segmentation application since the Mumford-Shah functional was introduced in the late 1980s. In this paper, we focus on multiphase segmentation with a new regularization term that yields an unsupervised segmentation model. We propose a functional that automatically chooses a favorable number of phases as it segments the image. The primary driving force of the segmentation is the intensity fitting term while a phase scale measure complements the regularization term. We propose a fast, yet simple, brute-force numerical algorithm and present experimental results showing the robustness and stability of the proposed model.

A Two-Stage Image Segmentation Method Using a Convex Variant of the Mumford--Shah Model and Thresholding

“…In this section, we compare our segmentation model (3.1) with three two-phase segmentation methods proposed in [16,19,53] and five multiphase segmentation methods proposed in [33,47,54,3,45]. Methods [16] and [19] use TV and framelet regularization terms, respectively; therefore, we can compare the performance of these two different regularization approaches with ours.…”

“…For the blur and noisy image, all the multiphase methods we tested [33,47,54,3,45] fail, while our method can provide a very good result; see Figures 1(c)-(d) or 10. We will see that our method is fast compared to popular two-phase segmentation methods [16,19,53] and multiphase segmentation methods [33,47,54,3,45].…”

“…In order to overcome the problem, convex relaxation approaches [7,14,45] and the graph cut method [27] were proposed. There are also many other models related to the Chan-Vese model [16,49], for example, the twophase segmentation algorithms in [19,52,53] and multiphase segmentation algorithms in [3,8,21,32,33,34,35,47,48,54]. Specifically, in [33], the piecewise constant Mumford-Shah model was convexified by using fuzzy membership functions.…”

“…Specifically, in [33], the piecewise constant Mumford-Shah model was convexified by using fuzzy membership functions. In [47], a new regularization term was introduced which allows choosing the number of phases automatically. In [52,53,54], efficient methods based on the fast continuous max-flow method were proposed.…”

“…In section 3, we give the detailed implementation of our method and show that the resulting algorithm converges. In section 4, we compare our method on various synthetic and real images with three two-phase segmentation algorithms [19,16,53] and five multiphase segmentation methods [33,47,54,3,45]. The relationship between our model and models in image restoration is discussed in section 5.…”