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Title: Tree-structured graphical models and image analysis
Author: Felderhof, Stephen N.
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2003
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The thesis examines tree-structured graphical models within the domain of image and image sequence analysis. It looks at three issues: firstly, a comparison of generative and discriminative approaches to the use of tree-structured belief networks for static image segmentation; secondly, an approach to image sequence coding and segmentation in which information is incorporated in a temporal manner using an extension to the dynamic tree model of Williams and Adams (1999) and Storkey and Williams (2002); and finally, an investigation of the products of experts architecture in which each individual expert is a tree-structured Gaussian process. With regard to the first problem, in Bayesian image analysis the problem of image segmentation involves each pixel in an image being assigned one of a predefined finite number of labels. This requires the fusion of local predictions for the class labels with a prior model for the label images. A number of authors have taken a genera­tive approach using Gaussian mixture models to model the probability of the image given the labels thereby connecting the label field to the image data. This is com­pared to the discriminative approach in which a multi-layer perceptron (MLP) is used to approximate the probability of the pixel classification given the image data, and the scaled-likelihood method is then used to fuse this with the prior label model. An evaluation of the classification results obtained is presented. Both the maximum a posteriori segmentation, and also the uncertainty, as evidenced e.g. by the pixelwise posterior marginal entropies, are examined. The results show that the discriminative approach performs better. The second issue addresses the proposition that given a temporal sequence of images, having information about (or having performed inference for) previous frames should provide useful knowledge about the current frame. Position encoding dynamic trees (PEDT) have been demonstrated to be useful models for individual images. Here they are extended so as to allow them to model image sequences. In the theory and experiments presented, it is shown that the PEDT model can be used for the analysis of ordered sequences of images. A theoretical framework is provided within which the current prior model is updated sequentially using the variational approximation to the posterior probability distribution from the previous time frame. Experimental results are presented demonstrating improved coding and segmentation performance. It is also shown that substantial improvements in image coding cost can be achieved by coding the changes in the highest variational posterior probability tree structures between frames using a method presented. Thirdly, the thesis looks at the products of experts (PoE) model which was intro­duced by Hinton (1999). It is examined using a PoE model in which each expert is a Gaussian. This gives rise to a product model that is also Gaussian. However, if each expert is constrained to be a tree structured Gaussian process (TSGP) the product of these then has a more complex structure than the individual trees. By way of comparison, a framework within which the resultant process is constructed from the sum of tree-structured Gaussian processes is also considered; the result of this method is also a Gaussian process. There is an investigation of the approximation of various target stationary processes with these Product of Experts and Sum of Experts models. The results show that the preferred choice between the two models depends on the type of target process. We also show that for AR(1) and MA(2) target processes, an exact representation of these processes using only two component TSGPs can be found.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available