| Summary: | This thesis is concerned with the investigation of a specific approach to the problem of texture segmentation, namely that based on the global optimization of a cost function. Many tasks in image analysis are expressed as global optimization problems in which the general issue is to find the global minimum of a cost function which describes the interaction between the different variables modelling the image features and the interaction of these variables with the data in a given problem. The minimization of such a global cost function is a difficult problem since the number of hidden variables (labels) is very large and the global cost function may have many local minima. This problem can be overcome to a large extent by using a stochastic relaxation algorithm (for example, Simulated annealing). Initially, various classical techniques on texture segmentation are reviewed. Ideally, any texture segmentation algorithm should segment an image, so that there is one to one correspondence between the segmentated edgels and the ground truth edgels. The effectiveness of an algorithm can be quantified in terms of under and over detection errors for each segmented output image. These measures are used throughout this thesis to quantify the quality of the results. A particular method which uses global optimization for texture segmentation is initially identified as potentially interesting and is implemented and studied. The implementation proved that this method suffered from many shortcomings and it is not really as good as it was reported in the literature. As the general approach to the problem is a well established methodology for image processing problems, the rest of the thesis is devoted into different attempts to make this method work. The novel ideas introduced in order to improve the method are: An improved version of the cost function. The use of alternative statistics that characterize each texture. The use of a combination of statistics to charaterize textures. The use of an implicit dictionary of penalizable label configurations, as opposed to an explicit dictionary, leading to penalties applied to anything not acceptable rather than to a selection of unacceptable configurations. The introduction of a modified transfer function that maps statistical differences to label differences. The use of a database of training patterns instead of assuming that one knows a priori which textures are present in the image to be segmented. The use of alternative time schedules with which the model is imposed to the data gradually, in a linear, non-linear and in an adaptive way. The introduction of an enhanced set of labels that allows the use of local orientation of the boundary. The introduction of a novel way to create new states of the system during the process of simulated annealing in order to achieve faster acceleration, by updating the values of 9 label sites instead of a single label site at a time. The results obtained by all these modifications vastly improve the performance of the algorithm from its original version. However, the whole approach does not really produce the quality of the results expected for real applications and it does not exhibit the robustness of a system that could be used in practice. The reason appears to be the bluntness of the statistical tests used to identify the boundary. So, my conclusion is that although global optimization methods are good for edge detection where the data are the local values of the first derivative, the approach is not very appropriate for texture segmentation where one has to rely on statistical differences.
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