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Multiple Resolution Segmentation of Textured Images
February 1991 (vol. 13 no. 2)
pp. 99-113

A multiple resolution algorithm is presented for segmenting images into regions with differing statistical behavior. In addition, an algorithm is developed for determining the number of statistically distinct regions in an image and estimating the parameters of those regions. Both algorithms use a causal Gaussian autoregressive model to describe the mean, variance, and spatial correlation of the image textures. Together, the algorithms can be used to perform unsupervised texture segmentation. The multiple resolution segmentation algorithm first segments images at coarse resolution and then progresses to finer resolutions until individual pixels are classified. This method results in accurate segmentations and requires significantly less computation than some previously known methods. The field containing the classification of each pixel in the image is modeled as a Markov random field. Segmentation at each resolution is then performed by maximizing the a posteriori probability of this field subject to the resolution constraint. At each resolution, the a posteriori probability is maximized by a deterministic greedy algorithm which iteratively chooses the classification of individual pixels or pixel blocks. The unsupervised parameter estimation algorithm determines both the number of textures and their parameters by minimizing a global criterion based on the AIC information criterion. Clusters corresponding to the individual textures are formed by alternately estimating the cluster parameters and repartitioning the data into those clusters. Concurrently, the number of distinct textures is estimated by combining clusters until a minimum of the criterion is reached.

[1] H. Derin and H. Elliott, "Modeling and segmentation of noisy and textured images using Gibbs random fields,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, pp. 39-55, Jan. 1987.
[2] C.S. Won and H. Derin, "Segmentation of noisy textured images using simulated annealing," inProc. ICASSP 87, Dallas, TX, 1987, pp. 14.4.1-14.4.4.
[3] H. Derin and C. S. Won, "A parallel image segmentation algorithm using relaxation with varying neighborhoods and its mapping to array processors,"Comput. Vision Graphics Image Processing, vol. 40, pp. 54-78, Oct. 1987.
[4] J. Besag, "On the statistical analysis of dirty pictures,"J. Roy. Statist. Soc. B, vol. 48, no. 3, pp. 259-302, 1986.
[5] J. Besag, "Spatial interaction and the statistical analysis of lattice systems,"J. Roy. Statist. Soc. B, vol. 36, no. 2, pp. 192-236, 1974.
[6] S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 721-741, Nov. 1984.
[7] A. Jain, "Advances in mathematical models for image processing,"Proc. IEEE, vol. 69, pp. 502-528, May 1981.
[8] R. Kashyap and R. Chellapa, "Estimation and choice of neighbors in spatial interaction models of images,"IEEE Trans. Inform. Theory, vol. IT-29, pp. 60-72, Jan. 1983.
[9] N. Metropolis,et al., "Equations of state calculations by fast computing machines,"J. Chem. Phys., vol. 21, pp. 1087-1091, 1953.
[10] J. Hutchinson, C. Koch, J. Luo, and C. Mead, "Computing motion using analog and binary resistive networks,"Computer, vol. 21, pp. 53-63, Mar. 1988.
[11] C. Bouman and B. Liu, "Segmentation of textured images using a multiple resolution approach," inProc. IEEE Int. Conf. Acoust., Speech, Signal Processing, New York, Apr. 11-14, 1988, pp. 1124-1127.
[12] C. Bouman and B. Liu, "A multiple resolution approach to regularization," inProc. SPIE Conf. Visual Communication and Image Processing, Cambridge, MA, Nov. 9-11, 1988, pp. 512-520.
[13] D. Terzopoulos, "Image analysis using multigrid relaxation methods,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 129-139, Mar. 1986.
[14] H. Akaike, "A new look at the statistical model identification,"IEEE Trans. Automat. Contr., vol. AC-19, pp. 716-723, Dec. 1974.
[15] J. Zhang and J. W. Modestino, "A model-fitting approach to cluster validation with application to stochastic model-based image segmentation," inProc. ICASSP 88, New York, 1988.
[16] J. Zhang and J. W. Modestino, "Unsupervised image segmentation using a Gaussian model," inProc. 1988 Conf. Information Sciences and Systems, Princeton, NJ, 1988.
[17] R. Duda and P. Hart,Pattern Classification and Scene Analysis. New York: Wiley, 1973.
[18] S.D. Silvey,Statistical Inference. London: Chapman and Hall, 1975.
[19] A. Dempster, N. Laird, and D. Rubin, "Maximum likelihood from incomplete data via the EM algorithm,"J. Roy. Statist. Soc. B, vol. 39, no. 1, pp. 1-38, 1977.
[20] E. Redner and H. Walker, "Mixture densities, maximum likelihood and the EM algorithm,"SIAM Rev., vol. 26, no. 2, Apr. 1984.
[21] L. Baum, T. Petrie, G. Soules, and N. Weiss, "A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains,"Ann. Math. Statist., vol. 41, no. 1, pp. 164-171, 1970.
[22] D. E. Knuth,The Art of Computer Programming, Vol. 3, Reading, MA: Addison-Wesley, 1973.

Index Terms:
pattern recognition; picture processing; parameter estimation; textured images; statistical behavior; causal Gaussian autoregressive model; mean; variance; spatial correlation; unsupervised texture segmentation; multiple resolution segmentation; coarse resolution; Markov random field; posteriori probability; deterministic greedy algorithm; classification; AIC information criterion; parameter estimation; pattern recognition; picture processing; probability; statistics
C. Bouman, B. Liu, "Multiple Resolution Segmentation of Textured Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 99-113, Feb. 1991, doi:10.1109/34.67641
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