Image Segmentation Layer

The image segmentation layer aims to use a number of image segmentation schemes and then adopt a mixture of experts model. In other words, on a per pixel basis, a number of segmentation experts make classification decisions that are fused together. The fusion of decisions is possible either using standard combination rules or adaptable scheme (based on determining appropriate weights of combination that are based on image properties). Our approach is based on the use of parametric models of image segmentation.

Recently, GMM have gained considerable prominence in the image segmentation literature since there is a vast range of training data available from which a priori information can be gathered. One of their key strengths is that such statistical models are underpinned by well-founded statistical probability and information theory. In addition, such approaches can be used in supervised or unsupervised modes. In addition, the output of such models is the a posteriori probability estimate that can be used to optimize the model to perform at a given point on the ROC curve. Also, by expressing the result as a posteriori probability, the outputs of various experts can be combined within a unified framework. Finally, the postprocessing of images is cheaper with statistical methods since only those regions that contain suspicious pixels need further examination, as opposed to a region-based approach where all regions must be considered.

The GMM approach does not consider the spatial arrangement of class labels in an image, which can be quite useful for relaxation labeling [28]. Markov random fields (MRF) have been shown as a powerful class of techniques [29-31] for modeling the spatial arrangement of class labels. MRF can be expressed in terms of a probabilistic framework and they can be combined with a statistical observed model of the mammogram. An MRF can increase the homogeneity of the formed regions that leads to a reduction in the false positives.

In this study we propose a Weighted Gaussian Mixture Model (WGMM) for both supervised (WGMMS) and unsupervised (WGMMV) data analysis. A set of GMMs is constructed, each modeling a particular class distribution and capable of being combined into a single unconditional density. We combine the WGMM model with a MRF hidden model and propose two approaches that work for supervised (WGMM;fRF) and unsupervised (WGMMMrf) modes. The four models orexperts (WGMMS, WGMMV, WGMM*RF,and WGMMMRf) eachproducealabel for the test pixel. We use a number of different features, each forming the basis of a different expert and relying on one of the above four models for segmentation. The expert outputs can be combined using well-known expert combination methods. In this chapter we propose an adaptive weighted model (AWM) for the combination of four experts and show that this new method of combination outperforms other popular methods.

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