Stabilised bias field: segmentation with intensity inhomogeneity

Abstract

Automatic segmentation in the variational framework is a challenging task within the field of imaging sciences. Achieving robustness is a major problem, particularly for images with high levels of intensity inhomogeneity. The two-phase piecewise-constant case of the Mumford-Shah formulation is most suitable for images with simple and homogeneous features where the intensity variation is limited. However, it has been applied to many different types of synthetic and real images after some adjustments to the formulation. Recent work has incorporated bias field estimation to allow for intensity inhomogeneity, with great success in terms of segmentation quality. However, the framework and assumptions involved lead to inconsistencies in the method that can adversely affect results. In this paper we address the task of generalising the piecewise-constant formulation, to approximate minimisers of the original Mumford-Shah formulation. We first review existing methods for treating inhomogeneity, and demonstrate the inconsistencies with the bias field estimation framework. We propose a modified variational model to account for these problems by introducing an additional constraint, and detail how the exact minimiser can be approximated in the context of this new formulation. We extend this concept to selective segmentation with the introduction of a distance selection term. These models are minimised with convex relaxation methods, where the global minimiser can be found for a fixed fitting term. Finally, we present numerical results that demonstrate an improvement to existing methods in terms of reliability and parameter dependence, and results for selective segmentation in the case of intensity inhomogeneity.

Parameter-Free Selective Segmentation With Convex Variational Methods

“…In this section we introduce the method in the context of piecewise-constant segmentation, in a similar way to CDS, as many of the examples of interest contain target objects with approximately homogeneous intensities. However, it is consistent with related methods that do not include this assumption, such as [27], [28], [29], [34], and many others. First, we will introduce the details behind the fitting term we define to incorporate some foreground markers, w f (x) ∈ {0, 1}.…”

“…as in Chan and Vese [4] and the corresponding convex formulation [17], where c 1 , c 2 ∈ R are the average intenities in the foreground and background, respectively. This was extended to cases of intensity inhomogeneity in [27] and is consistent with other types of data fitting term, such as [28] and [29]. This selective fitting term is defined as follows, weighted by a selection parameter:…”

Chan–Vese Reformulation for Selective Image Segmentation

“…Alternative choices of data fitting terms can be used when different assumptions are made on the image, z . Examples include [1, 2, 16, 25, 40, 43]. We note that multiphase approaches [9, 42] are also closely related to this formulation although in this paper we focus on the two-phase problem due to associated applications of interest.…”

Dual-Channel Active Contour Model for Megakaryocytic Cell Segmentation in Bone Marrow Trephine Histology Images

“…Brown et al propose a multi-phase active contour model for global multiple region segmentation [36]. Although all these methods improve segmentation accuracy of the CV model on images with weak edges and intensity inhomogeneities, they are all sensitive to the position of the initial contour and the value of parameters [32], [35], [37], [38].…”