Computationally efficient stochastic image modeling using bilateral Markov mesh random fields

Markov random fields and their application to image modeling has been the topic of research for many years. An ideal image model takes an image to a model space from which the image can be recovered completely. Establishing such a model is quite challenging. Deriving a computationally efficient and applicable joint probability density function of an image has being pursued for decades. Deterministic image models treat an image having a certain density function. Real images are then approximated using mathematical models of the density function. A well-established image modeling approach is random field modeling. These models are mostly derived using Markov Random Fields (MRFs). The wide applicability of MRFs is offset by several shortcomings. First, and most importantly, computation of these models is not practically feasible. Second, they require imposing conditions on boundary, isotropy and translation invariance. Third, the parameters defining a MRF are not unique and their calculation is normally quite difficult due to normalization. These shortcomings limit the utilization of conventional MRFs to different image processing and pattern recognition applications. Therefore, the main thrust of this dissertation is to introduce a new Markov mesh random field, named bilateral Markov mesh random field (BMMRF), in order to overcome some of the limitations of conventional MRFs. Based on the introduced random field, computationally efficient image models are proposed. This model is applicable to various image processing applications including image restoration and texture generation.