Targeted image segmentation using graph methods

Traditional image segmentation is the process of subdividing an image into smaller regions based on some notion of homogeneity or cohesiveness among groups of pixels. Several prominent traditional seg-mentation algorithms have been based on graph theoretic methods [1, 2, 3, 4, 5, 6]. However, these methods have been notoriously difficult to quantitatively evaluate since there is no formal definition of the segmenta-tion problem (see [7, 8] for some approaches to evaluating traditional segmentation algorithms). In contrast to the traditional image segmentation scenario, many real-world applications of image seg-mentation instead focus on identifying those pixels belonging to a specific object or objects (which we will call targeted segmentation) for which there are some known characteristics. In this chapter, we focus only on the extraction of a single object (i.e., labeling each pixel as object or background). The segmentation of a specific object from the background is not just a special case of the traditional image segmentation problem which is restricted to two labels. Instead, a targeted image segmentation algorithm must input the additional information that determines which object is being segmented. This additional information, which we will call target specification, can take many forms: user interaction, appearance models, pairwise pixel affinity models, contrast polarity, shape models, topology specification, relational information and/or feature 2 Image Processing and Analysing Graphs: Theory and Practice inclusion. The ideal targeted image segmentation algorithm could input any or all of the target specification information that is available about the target object and use it to produce a high-quality segmentation. Graph-theoretic methods have provided a strong basis for approaching the targeted image segmentation problem. One aspect of graph-theoretic methods that has made them so appropriate for this problem is that it is fairly straightforward to incorporate different kinds of target specification (or, at least, to prove that they are NP-Hard). In this chapter, we begin by showing how the image graph may be constructed to accommodate general target specification and review several of the most prominent models for targeted image segmentation, with an emphasis on their commonalities. Having established the general models, we show specifically how the various types of target specification may be used to identify the target object. A targeted image segmentation algorithm consists of two parts — A target specification which identifies the desired object and a regularization which completes the segmentation from the target specification. The goal of the regularization algorithm is to incorporate …