Abstract
In this chapter, we discuss the potential of Gibbs distributions (GDs) as models in image processing applications. We briefly review the definitions and basic concepts of Markov random fields (MRFs) and GDs and present some realizations from these distributions. The use of statistical models and methods in image processing has increased considerably over the recent years. Most of these studies involve the use of MRF models and processing techniques based on these models. The pioneering work on MRFs due to Dobrushin [1], Wong [2], and Woods [3] involves extending the Markovian property in one dimension to higher dimensions. However, due to lack of causality in two dimensions the extension is not straightforward. Some properties in one dimension, for example, the equivalence of one-sided and two-sided Markovianity, do not carry over to two dimensions. The early work by Abend et al. [4] presents a causal characterization for a class of MRFs called Markov mesh random fields. This work also includes a formulation pointing out the Gibbsian property of a Markov chain without fully realizing the connection. Other attempts in extending the Markovian property to two dimensions include the autoregressive models: the “simultaneous autoregressive” (SAR) models and the “conditional Markov” models introduced by Chellappa and Kashyap [5].
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Derin, H. (1986). The Use of Gibbs Distributions In Image Processing. In: Blake, I.F., Poor, H.V. (eds) Communications and Networks. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4904-7_12
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DOI: https://doi.org/10.1007/978-1-4612-4904-7_12
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