Parametric and Non-Parametric Clustering for Segmentation

Abstract

In this chapter, we contrast the medical image segmentation problem with general image segmentation and introduce several state-of-the-art segmentation techniques based on clustering. Specifically, we will consider two types of clustering, one parametric, and the other non-parametric, to group pixels into contiguous regions. In the first approach which is a statistical clustering scheme based on parametric Gaussian Mixture Models (GMMs), we develop the basic formalism and add variations and extensions to include a priori knowledge or context of the task at hand. In this formalism, each cluster is modeled as a Gaussian in the feature space. Each model component (Gaussian) can be assigned a semantic meaning; its automated extraction can be translated to the detection of an important image region, its segmentation as well as its tracking in time. We will demonstrate the GMM approach for segmentation of MR brain images. This will illustrate how the use of statistical modeling tools, in particular unsupervised clustering using Expectation-Maximization (EM) and modeling the image content via GM M, provides for robust tissue segmentation as well as brain lesion detection, segmentation and tracking in time. In the second approach, we take a non-parameterized graph-theoretic clustering approach to segmentation, and demonstrate how spatio-temporal features could be used to improve graphical clustering. In this approach, the image information is represented as a graph and the image segmentation task is positioned as a graph partitioning problem. A global criterion for graph partitioning based on normalized cuts is used. However, the weights of the edges now reflect spatio-temporal similarity between pixels. We derive a robust way of estimating temporal (motion) information in such imagery using a variant of Demon's algorithm. This approach will be illustrated in the domain of cardiac echo videos as an example of moving medical imagery.