Non-Markov Gibbs image model with almost local pairwise pixel interactions
Markov/Gibbs models represent digital images as samples of Markov random fields (MRF) on finite 2D lattices with Gibbs probability distributions (GPD). Most of the known models take account of only pairwise pixel interactions. These models, studied in general form by Dobrushin , Averintsev , and Besag , were first applied to the images by Cross and Jain , Hassner and Sklansky , Lebedev et al. , Derin et al. , Geman and Geman . Later, they were studied in numerous works (see, for instance, surveys [24, 13, 7, 28]). The models have features useful for describing and analysing image textures.
KeywordsGray Level Interaction Structure Markov Random Field Stochastic Approximation Exponential Family
Unable to display preview. Download preview PDF.
- Averintsev, M.B.: Description of Markov random fields by Gibbs conditional probabilities. Probability Theory and Its Applications, 17, 21–35 (1972). In Russian.Google Scholar
- Barndorif-Nielsen, O.: Information and Exponential Families in Statistical Theory. Chichester: Wiley 1978.Google Scholar
- Brodatz, P.: Textures. New York: Dover Publications 1966.Google Scholar
- Chetverikov, D., Haralick, R.M.: Texture anisotropy, symmetry, regularity: Recovering structure and orientation from interaction maps. In: Proc. of the 6th British Machine Vision Conf., Sept. 11–14, 1995, Birmingham. Sheffield: Univ. of Sheffield 1995, 57–66.Google Scholar
- Dobrushin, R.L.: Gibbs random fields for lattice systems with pairwise interaction. Functional Analysis and Its Applications, 2, 31–43 (1968). [In Russian].Google Scholar
- Dobrushin, R.L., Pigorov, S.A.: Theory of random fields. In: Proc. 1975 IEEE-USSR Joint Workshop on Information Theory, December 1995, Moscow, USSR. New York: IEEE 1976, pp. 39–49.Google Scholar
- Gidas, B.: Parameter estimation for Gibbs distributions from fully observed data. In: Chellappa R., Jain A. (eds.): Markov random fields: theory and applications. Boston: Academic Press 1993, pp. 471–483.Google Scholar
- Gimel’farb, G.L.: Gibbs models for Bayesian simulation and segmentation of piecewise-unifirm textures. Ibid.,pp. 591–595.Google Scholar
- Kashyap, R.L.: Image models. In: Young, T. Y., Fu, K.-S. (eds.): Handbook on pattern recognition and image processing. Orlando: Academic Press 1986, pp. 247–279.Google Scholar
- Lebedev D.S., Bezruk A.A., Novikov V.M.: Markov Probabilistic Model of Image and Picture. Moscow: VINITI 1983 (Preprint: Inst. of Information Transmission Problems, Acad. of Sci. of the USSR). [In Russian].Google Scholar
- Pickard R., Graszyk C., Mann S., Wachman J., Pickard L., Campbell L.: VisTex Database. Cambridge: MIT Media Lab. 1995.Google Scholar
- Wazan, M.: Stochastic Approximation. Cambridge: University Press, 1969.Google Scholar