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Issue No.01 - January (2011 vol.33)
pp: 16-29
Frederic Lehmann , Institut TELECOM, TELECOM SudParis, Evry
We consider the problem of semi-supervised segmentation of textured images. Existing model-based approaches model the intensity field of textured images as a Gauss-Markov random field to take into account the local spatial dependencies between the pixels. Classical Bayesian segmentation consists of also modeling the label field as a Markov random field to ensure that neighboring pixels correspond to the same texture class with high probability. Well-known relaxation techniques are available which find the optimal label field with respect to the maximum a posteriori or the maximum posterior mode criterion. But, these techniques are usually computationally intensive because they require a large number of iterations to converge. In this paper, we propose a new Bayesian framework by modeling two-dimensional textured images as the concatenation of two one-dimensional hidden Markov autoregressive models for the lines and the columns, respectively. A segmentation algorithm, which is similar to turbo decoding in the context of error-correcting codes, is obtained based on a factor graph approach. The proposed method estimates the unknown parameters using the Expectation-Maximization algorithm.
Texture segmentation, Markov random field, hidden Markov autoregressive model, factor graph, forward-backward algorithm, turbo processing.
Frederic Lehmann, "Turbo Segmentation of Textured Images", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.33, no. 1, pp. 16-29, January 2011, doi:10.1109/TPAMI.2010.58
[1] M. Tuceryan and A.K. Jain, "Texture Analysis," The Handbook of Pattern Recognition and Computer Vision, second ed., World Scientific Publishing Co., 1998.
[2] J.W. Woods, "Two-Dimensional Discrete Markovian Fields," IEEE Trans. Information Theory, vol. 18, no. 2, pp. 232-240, Mar. 1972.
[3] R. Chellappa, "Two-Dimensional Discrete Gaussian Markov Field Models for Image Processing," Progress in Pattern Recognition, Elsevier Science Publishing Co., 1984.
[4] B.S. Manjunath and R. Chellappa, "Unsupervised Texture Segmentation Using Markov Random Field Models," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 5, pp. 478-482, May 1991.
[5] A.K. Jain and R.C. Dubes, Algorithms for Clustering Data. Prentice Hall, 1988.
[6] S. Geman and D. Geman, "Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 721-741, Nov. 1984.
[7] J.J.K. Ó Ruanaidh and W.J. Fitzgerald, Numerical Bayesian Methods Applied to Signal Processing. Springer-Verlag, 1996.
[8] J. Marroquin, S. Mitter, and T. Poggio, "Probabilistic Solution to Ill-Posed Problems in Computational Vision," J. Am. Statistical Assoc., vol. 82, no. 397, pp. 76-89, Mar. 1987.
[9] B.S. Manjunath, T. Simchony, and R. Chellappa, "Stochastic and Deterministic Networks for Texture Segmentation," IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 38, no. 6, pp. 1039-1049, June 1990.
[10] J.E. Besag, "On the Statistical Analysis of Dirty Pictures," J. Royal Statistical Soc., Series B, vol. 48, no. 3, pp. 259-302, 1986.
[11] R. Zabih and V. Kolmogorov, "Spatially Coherent Clustering Using Graph Cuts," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 437-444, June/July 2004.
[12] Y. Boykov and V. Kolmogorov, "An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 9, pp. 1124-1137, Sept. 2004.
[13] N. Giordana and W. Pieczynski, "Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 5, pp. 465-475, May 1997.
[14] L.E. Baum, T. Petrie, G. Soules, and N. Weiss, "A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains," Annals of Math. Statistics, vol. 41, no. 1, pp. 164-171, 1970.
[15] J.D. Hamilton, "Analysis of Time Series Subject to Changes in Regime," J. Econometrics, vol. 45, pp. 39-70, 1990.
[16] J. Chiang, Z.J. Wang, and M.J. McKeown, "A Hidden Markov, Multivariate Autoregressive (HMM-mAR) Network Framework for Analysis of Surface EMG (sEMG) Data," IEEE Trans. Signal Processing, vol. 56, no. 8, pp. 4069-4080, Aug. 2008.
[17] J. Li, A. Najmi, and R.M. Gray, "Image Classification of Two-Dimensional Hidden Markov Model," IEEE Trans. Signal Processing, vol. 48, no. 2, pp. 517-533, Feb. 2000.
[18] H. Othman and T. Aboulnasr, "A Separable Low Complexity 2D HMM with Application to Face Recognition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 10, pp. 1229-1238, Oct. 2003.
[19] F.R. Kschischang, B.J. Frey, and H.-A. Loeliger, "Factor Graph and the Sum-Product Algorithm," IEEE Trans. Information Theory, vol. 47, no. 2, pp. 498-519, Feb. 2001.
[20] C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon Limit Error-Correcting Coding and Decoding: Turbo Codes," Proc. IEEE Int'l Conf. Comm., pp. 1064-1070, May 1993.
[21] A.P. Dempster, N.M. Laird, and D.B. Rubin, "Maximum Likelihood from Incomplete Data via the EM Algorithm," J. Royal Statistical Soc., Series B, vol. 39, no. 1, pp. 1-38, 1977.
[22] F. Perronnin, J.-L. Dugelay, and K. Rose, "Iterative Decoding of Two-Dimensional Hidden Markov Models," Proc. Int'l Conf. Acoustics, Speech, and Signal Processing, pp. 329-332, Apr. 2003.
[23] M.E. Sargin, A. Altinok, K. Rose, and B.S. Manjunath, "Conditional Iterative Decoding of Two Dimensional Hidden Markov Models," Proc. Int'l Conf. Image Processing, pp. 2552-2555, Oct. 2008.
[24] S. Krishnamachari and R. Chellappa, "Multiresolution Gauss-Markov Random Field Models for Texture Segmentation," IEEE Trans. Image Processing, vol. 6, no. 2, pp. 251-267, Feb. 1997.
[25] T. Randen and J.H. Husoy, "Filtering for Texture Classification: A Comparative Study," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 4, pp. 291-310, Apr. 1999.
[26] S. Lakshmanan and H. Derin, "Simultaneous Parameter Estimation and Segmentation of Gibbs Random Fields Using Simulated Annealing," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 8, pp. 799-813, Aug. 1989.
[27] J. Pearl, Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, 1988.
[28] P.A. Devijver, "Baum's Forward-Backward Algorithm Revisited," Pattern Recognition Letters, vol. 3, pp. 369-373, Dec. 1985.
[29] P. Robertson, E. Villebrun, and P. Hoeher, "Comparison of Optimal and Suboptimal MAP Decoding Algorithms Operating in the Log Domain," Proc. IEEE Int'l Conf. Comm., pp. 1009-1013, June 1995.
[30] L.A. Rabiner, "A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition," Proc. IEEE, vol. 77, no. 2, pp. 257-286, Feb. 1989.
[31] P. Elias, "Error-Free Coding," IRE Trans. Information Theory, vol. 4, pp. 29-37, Sept. 1954.
[32] R.M. Pyndiah, "Near Optimum Decoding of Product Codes: Block Turbo Codes," IEEE Trans. Comm., vol. 46, no. 8, pp. 1003-1010, Aug. 1998.
[33] B. Sklar, "A Primer on Turbo Code Concepts," IEEE Comm. Magazine, vol. 35, pp. 94-102, Dec. 1997.
[34] P. Brodatz, Textures: A Photographic Album for Artists and Designers. Dover Publications, 1966.
[35] D. Martin, C. Fowlkes, D. Tal, and J. Malik, "A Database of Human Segmented Natural Images and Its Application to Evaluating Segmentation Algorithms and Measuring Ecological Statistics," Proc. IEEE Int'l Conf. Computer Vision, pp. 416-423, 2001.
[36] European Space Agency Web Site: , 2009.
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