Selective image segmentation is the task of extracting one object of interest from an image, based on minimal user input. Recent level set based variational models have shown to be effective and reliable, although they can be sensitive to initialization due to the minimization problems being nonconvex. This sometimes means that successful segmentation relies too heavily on user input or a solution found is only a local minimizer, i.e. not the correct solution. The same principle applies to variational models that extract all objects in an image (global segmentation); however, in recent years, some have been successfully reformulated as convex optimization problems, allowing global minimizers to be found. There are, however, problems associated with extending the convex formulation to the current selective models, which provides the motivation for the proposal of a new selective model. In this paper we propose a new selective segmentation model, combining ideas from global segmentation, that can be reformulated in a convex way such that a global minimizer can be found independently of initialization. Numerical results are given that demonstrate its reliability in terms of removing the sensitivity to initialization present in previous models, and its robustness to user input.

Selective segmentation involves incorporating user input to partition an image into foreground and background, by discriminating between objects of a similar type. Typically, such methods involve introducing additional constraints to generic segmentation approaches. However, we show that this is often inconsistent with respect to common assumptions about the image. The proposed method introduces a new fitting term that is more useful in practice than the Chan–Vese framework. In particular, the idea is to define a term that allows for the background to consist of multiple regions of inhomogeneity. We provide comparative experimental results to alternative approaches to demonstrate the advantages of the proposed method, broadening the possible application of these methods.

Selective segmentation methods involve incorporating user input to partition an image into a foreground and background. Often these methods are sensitive to some aspect of the user input in a counter intuitive manner, making their use in practice difficult. The most robust methods often involve laborious refinement on the part of the user, and sometimes editing/supervision. The proposed method reduces the burden on the user by simplifying the requirements on the input. Specifically, the fitting term does not depend on a distance function and so no selection parameter is introduced. Instead, we consider how the user input relates to some general intensity fitting term to ensure the approach is less sensitive to the decisions or intuition of the user. We give comparisons to existing approaches to show the advantages of the new selective segmentation model.

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.

The geodesic distance-based dual-front curve evolution model is a powerful and efficient solution to the active contours and image segmentation issues. In its basic formulation, the dual-front model regards the meeting interfaces of two adjacent Voronoi regions as the evolving curves in the course of curve evolution. One of the most crucial ingredients for the construction of Voronoi regions or Voronoi diagram is the geodesic metrics and the corresponding geodesic distance. In this paper, we introduce a new type of geodesic metrics that encodes the edge-based anisotropy features, the regionbased homogeneity penalization and asymmetric enhancement. In contrast to the original isotropic dual-front model, the use of the asymmetric enhancement can reduce the risk of shortcuts or leakage problems especially when the initial curves are far away from the target boundaries. Moreover, the proposed dual-front model can be applied for image segmentation in conjunction with various region-based homogeneity terms, whereas the original model only makes use of the piecewise constant case. The numerical experiments on both synthetic and real images show that the proposed model indeed achieves encouraging results.