Abstract
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 [11], Averintsev [1], and Besag [3], were first applied to the images by Cross and Jain [9], Hassner and Sklansky [23], Lebedev et al. [25], Derin et al. [10], Geman and Geman [15]. 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.
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References
Averintsev, M.B.: Description of Markov random fields by Gibbs conditional probabilities. Probability Theory and Its Applications, 17, 21–35 (1972). In Russian.
Barndorif-Nielsen, O.: Information and Exponential Families in Statistical Theory. Chichester: Wiley 1978.
Besag, J.E.: Spatial interaction and the statistical analysis of lattice systems. J. Royal Stat. Soc. London, B36, 192–236 (1974).
Besag, J.E.: On the statistical analysis of dirty pictures. J. Royal Stat. Soc. London, B48, 259–302 (1986).
Brodatz, P.: Textures. New York: Dover Publications 1966.
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.
Chellappa, R., Kashyap, R.L., Manjunath, B.S.: Model-based texture segmentation and classification, In: Chen C.H., Pau L.F., Weng P.S.P. (eds.): Handbook of pattern recognition and computer vision. Singapore: World Publishing 1993, pp. 277–310.
Cohen, F.S., Patel, M.A.S.: Modeling and synthesis of images of 3D textured surfaces. CVGIP: Graphical Models and Image Processing, 53, 501–510 (1991).
Cross, G.R., Jain, A.K.: Markov random field texture models. IEEE Trans. Pattern Anal. Machine Intell., 5, 25–39 (1983).
Derin, H., Elliot, H., Cristi, R., Geman, D.: Bayes smoothing algorithm for segmentation of images modelled by Markov random fields. IEEE Trans. Pattern Anal. Machine Intell., 6, 707–720 (1984).
Dobrushin, R.L.: Gibbs random fields for lattice systems with pairwise interaction. Functional Analysis and Its Applications, 2, 31–43 (1968). [In Russian].
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.
Dubes, R.C., Jain, A.K.: Random field models in image analysis. J. of Applied Statistics, 16, 131–164 (1989).
Elfadel, I.M., Pikard, R.W.: Gibbs random fields, cooccurrences, and texture modelling. IEEE Trans. Pattern Anal. Machine Intell., 16, 24–37 (1994).
Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intell., 6, 721–741 (1984).
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.
Gimel’farb, G.L.: Texture modelling by multiple pairwise pixel interactions. IEEE Trans. Pattern Anal. Machine Intell., 18, 1110–1114 (1996).
Gimel’farb, G.L.: Non-Markov Gibbs texture model with multiple pairwise pixel interactions. In: Proc. 13th Int. IAPR Conf. on Pattern Recognition, August 25–29, 1996, Vienna, Austria. Vieanna: TU Wien, 1996, pp. 760–764.
Gimel’farb, G.L.: Gibbs models for Bayesian simulation and segmentation of piecewise-unifirm textures. Ibid.,pp. 591–595.
Gimel’farb, G.L., Jain, A.K.: On retrieving textured images from an image database. Pattern Recognition, 29, 1461–1483 (1996).
Gimel’farb, G.L., Zalesny, A,V.: Low-level Bayesian segmentation of piecewisehomogeneous noisy and textured images. Int. J. of Imaging Systems and Technology, 3, 227–243 (1991).
Haralick, R.M.: Statistical and structural approaches to textures. Proc. IEEE, 67, 786–804 (1979).
Hassner, M., Sklansky, J.: The use of Markov random fields as models of textures. Computer Graphics and Image Processing, 12, 357–370 (1980).
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.
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].
Metropolis N., Rosenbluth A.W., Rosenbluth M. N., Teller A. H., Teller E.: Equations of state calculations by fast computing machines. J. of Chemical Physics 21, 1087–1091 (1953).
Pickard R., Graszyk C., Mann S., Wachman J., Pickard L., Campbell L.: VisTex Database. Cambridge: MIT Media Lab. 1995.
Tuceryan M., Jain A.K.: Texture analysis. In: Chen C.H., Pau L.F., Weng P.S.P. (eds.): Handbook of pattern recognition and computer vision. Singapore: World Publishing 1993, pp. 235–276.
Wazan, M.: Stochastic Approximation. Cambridge: University Press, 1969.
Younes, L.: Estimation and annealing for Gibbsian fields. Annales de l’Institut Henri Poincare, 24, 269–294 (1988).
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Gimel’farb, G.L. (1997). Non-Markov Gibbs image model with almost local pairwise pixel interactions. In: Solina, F., Kropatsch, W.G., Klette, R., Bajcsy, R. (eds) Advances in Computer Vision. Advances in Computing Science. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6867-7_10
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DOI: https://doi.org/10.1007/978-3-7091-6867-7_10
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