Research On Digital Image Segmentation Algorithms Based On Markov Random Field And Fuzzy Clustering

Currently, Markov Random Field and Fuzzy Image Segmentation algorithms have become important fields in image processing research. In image processing system, segmentation process is one of the most important steps. More precisely, image segmentation is defined as the process of assigning a label to every pixel in an image such that pixels with the same label share certain visual characteristics. Several general-purpose algorithms and techniques have been developed for image segmentation. In order to effectively solve image segmentation problem for a specific problem domain, these techniques often have to be combined with knowledge domains, as there is no general solution to image segmentation problems.Our research focused on how pixels display differently with different regions. We investigated a new approach to image segmentation, developed and implemented algorithms based on similarities or dissimilarities of the pixels in a given image.The central theme of this dissertation is the development of a fully Markov unsupervised algorithm to achieve image segmentation. Existing literature falls short of such a goal, only providing many algorithms capable of solving subsets of this highly challenging problem. Unsupervised segmentation is the process of identifying and locating the constituent regions of an observed image, while having no prior knowledge of the number of regions. In this regard, in our work we consider the use of Bayesian framework to model the image, so that the unsupervised segmentation process can be considered as a problem of single optimization. However, we have discovered that throughout the literature, the commonly adopted optimization model is a hierarchical image model whose underlying components are various forms of Markov Random Fields. Gaussian Markov Random Field models are used to model the textural content of the image regions, while a Potts model provides a regularization function for the image segmentation as could be seen in our work. The optimization process of such highly complicated models is an area that has been challenging researchers for several decades. So the main contribution of this thesis is to develop new techniques for Markov unsupervised segmentation to be carried out using a single optimization process. It is hoped that these algorithms will facilitate and enhance the future study of hierarchical image models and in particular enable the discovery of further models capable of more precise fitting of real world data.Markov Random Field segmentation models and their optimizations deal with the selection of features to identify the textural contents of an observed image. In the light of the above, new algorithms have been proposed for the attainment of a balance between the two concepts: unsupervised segmentation and optimization process. Furthermore, Statistical Mechanics forms an important part of this work. The prevalent use of Markov Chain Monte Carlo algorithms is encountered and in particular, the use of the Reversible Jump Sampling algorithm being of great significance is encountered too. The combination of several of these algorithms enabled us to achieve the single optimization framework, which makes us obtained the most successful novel algorithms used in this dissertation.However, for the color images segmentation, we have proposed a method which considers that the regions are defined as connected sets of pixels belonging to the same class. Our approach considers simultaneously both the connectivity and colorimetric properties of the pixels in order to build classes which can be non-equiprobable.We defined the color connectivity degree of a set of pixels as a connectivity measurement of a set of pixels whose colors belong to a color interval. We suppose that pixels of each region in the image can be associated to a class of pixels, and that a class is a set of pixels whose color connectivity degree presents a high value. The problem here is identifying these sets.In this context, we have defined an original data structure of Markovianity, the color connectivity degree, which counts in an organized and hierarchical way the color connectivity degrees of all possible sets of pixels that an image can contain.For each one of these images, we decompose the image at three composite (RGB) and propose an analysis method for each. In order to gather pixels belonging to the same region from the results obtained by the Tree Marginal Classification processes, we model the image by a Region Adjacency Graph and propose a fuzzy analysis for it.Finally, through our various experiments with the partitioning of image by similarity graphs, the efficiency of this method has been effectively proven.