This Article 
 Bibliographic References 
 Add to: 
Classification of Rotated and Scaled Textured Images Using Gaussian Markov Random Field Models
February 1991 (vol. 13 no. 2)
pp. 192-202

Consideration is given to the problem of classifying a test textured image that is obtained from one of C possible parent texture classes, after possibly applying unknown rotation and scale changes to the parent texture. The training texture images (parent classes) are modeled by Gaussian Markov random fields (GMRFs). To classify a rotated and scaled test texture, the rotation and scale changes are incorporated in the texture model through an appropriate transformation of the power spectral density of the GMRF. For the rotated and scaled image, a bona fide likelihood function that shows the explicit dependence of the likelihood function on the GMRF parameters, as well as on the rotation and scale parameters, is derived. Although, in general, the scaled and/or rotated texture does not correspond to a finite-order GMRF, it is possible nonetheless to write down a likelihood function for the image data. The likelihood function of the discrete Fourier transform of the image data corresponds to that of a white nonstationary Gaussian random field, with the variance at each pixel (i,j) being a known function of the rotation, the scale, the GMRF model parameters, and (i,j). The variance is an explicit function of the appropriately sampled power spectral density of the GMRF. The estimation of the rotation and scale parameters is performed in the frequency domain by maximizing the likelihood function associated with the discrete Fourier transform of the image data. Cramer-Rao error bounds on the scale and rotation estimates are easily computed. A modified Bayes decision rule is used to classify a given test image into one of C possible texture classes. The classification power of the method is demonstrated through experimental results on natural textures from the Brodatz album.

[1] A. Rosenfeldet al., "Visual texture analysis," TR 70-116, Univ. Maryland, June 1970.
[2] S. W. Zuckeret al., "Picture segmentation by texture discrimination,"IEEE Trans. Comput., vol. C-24, pp. 1288-1233, Dec. 1975.
[3] S.Y. Lu and S. Fu, "Stochastic tree grammar inference for texture synthesis and discrimination,"Comput. Graphics Image Processing, vol. 9, pp. 234-245, 1979.
[4] F. Tomitaet al., "Description of texture by a structural analysis," inProc. IJCAI-79, 1979.
[5] R. Chin and C. Harlow, "Automated visual inspection: A survey,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-4, no. 6, pp. 557-573, Nov. 1982.
[6] R. Conners, "Towards a set of statistical features which measure visually perceivable qualities of textures," inProc. IEEE Conf. Pattern Recognition Image Processing, 1979.
[7] R. Haralick, "Statistical and structural approaches to texture," inProc. IEEE, vol. 67, no. 5, pp. 610-621, 1979.
[8] B. Julesz, "Visual pattern discrimination,"IRE Trans. Inform. Theory, vol. IT-8, pp. 84-92, 1962.
[9] A. L. Vickers and J. W. Modestino, "A maximum likelihood approach to texture classification,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-4, pp. 61-68, Jan. 1982.
[10] L. S. Davis, S. Johns, and J. K. Aggrawal, "Texture analysis using generalized co-occurrence matrices,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-1, pp. 251-259, July 1979.
[11] M. Galloway, "Texture analysis using gray-level run lengths,"Comput. Graphics Image Processing, vol. 4, pp. 172-179, 1974.
[12] R. W. Conners and C. A. Harlow, "A theoretical comparison of texture algorithms,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-2, pp. 204-222, May 1980.
[13] R. Bajcsy, "Computer description of textured surfaces," inProc. 3rd Int. Joint Conf. Art. Int., Aug. 1973, pp. 572-579.
[14] R. Cross and A. Jain, "Markov random field texture models,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-5, pp. 25-39, 1983.
[15] J. Woods, "Two-dimensional discrete Markov random fields,"IEEE Trans. Inform. Theory,vol. IT-18, pp. 232-240, 1972.
[16] J. Besag, "Spatial interaction and the statistical analysis of lattice systems,"J. Roy. Statistical Soc. B, vol. 36, pp. 192-236, 1974.
[17] R. L. Kashyap, R. Chellappa, and A. Khotanzad, "Texture classification using features derived from random field models,"Pattern Recognition Lett., vol. 1, pp. 43-50, Oct. 1982.
[18] 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.
[19] R. L. Kashyap and A. Khotanzad, "A Model-Based Method for Rotation Invariant Texture Classification,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 472-481, July 1986.
[20] J. Besag and P. Moran, "On the estimation and testing of spatial interaction in Gaussian lattices,"Biometrika, vol. 62, 1975.
[21] P. Davis,Circulant Matrices. New York: Wiley, 1979.
[22] A. Papoulis,Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, 1984.
[23] P. Brodatz,Textures. New York: Dover, 1966.
[24] J. Goutsias and J. Mendel, "Optimal simultaneous detection and estimation of filtered discrete semi-Markov chains,"IEEE Trans. Inform. Theory, vol. 34, pp. 551-568, 1988.
[25] L. Lakshmanan and H. Derin, "Simultaneous parameter estimation and segmentation of Gibbs random fields using simulated annealing,"IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 799-813, Aug. 1989.
[26] S. Zacks,Parametric Statistical Inference. New York: Pergamon, 1981.
[27] A. Jain,Fundamentals of Digital Image Processing. Englewood Cliffs, NJ: Prentice-Hall, 1989.

Index Terms:
pattern recognition; parameter estimation; rotated textured images; scaled textured images; Gaussian Markov random field models; parent texture classes; training texture images; likelihood function; discrete Fourier transform; white nonstationary Gaussian random field; power spectral density; Cramer-Rao error bounds; modified Bayes decision rule; classification power; Brodatz album; Bayes methods; decision theory; parameter estimation; pattern recognition; random processes
F.S. Cohen, Z. Fan, M.A. Patel, "Classification of Rotated and Scaled Textured Images Using Gaussian Markov Random Field Models," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 2, pp. 192-202, Feb. 1991, doi:10.1109/34.67648
Usage of this product signifies your acceptance of the Terms of Use.