Discrete-Index Markov-Type Random Processes

Proceedings of the IEEE

Volumn 77, Issue 10, 1989, Pages 1485-1510

  Derin, Haluk ^a   Kelly, Patrick A ^a  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

IMAGE PROCESSING;

AUTOREGRESSIVE PROCESSES; GIBBS RANDOM FIELDS; MARKOV PROCESSES; SIMULTANEOUS AUTOREGRESSIVE MODELS; STRICT-SENSE MARKOV MODELS; WIDE-SENSE MARKOV MODELS;

PROBABILITY;

EID: 0024752683     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/5.40665     Document Type: Letter

References (49)

1. K. Abend, T.J. Harley, and L.N. Kanal, “Classification of binary random patterns,” IEEE Trans. Inform. Theory, vol. IT-11, pp. 538–544, Oct. 1965.
2. R.B. Ash, Real Analysis and Probability. New York: Academic Press, 1972.
3. J.E. Besag, “Spatial interaction and the statistical analysis of lattice systems,” J. Roy. Stat. Soc, Series B, vol. 36, pp. 192–236, 1974.
4. D. Brook, “On the distinction between the conditional probability and the joint probability approaches in the specification of nearest-neighbor systems,” Biometrika, vol. 51, pp. 481–483, 1964.
5. R. Chellappa and R.L. Kashyap, “Digital image restoration using spatial interaction models,” IEEE Trans. Acous. Sp. Sig. Proc, vol. ASSP-30, pp. 461–472, June 1982.
6. R. Chellappa, Y.-H. Hu, and S.-Y. Kung, “On two-dimensional Markov spectral estimation,” IEEE Trans. Acous. Sp. Sig. Proc, vol. ASSP-31, pp. 836–841, Aug. 1983.
7. R. Chellappa, “Two-dimensional discrete Gaussian Markov random field models for image processing,” in Progress in Pattern Recognition 2. L.N. Kanal and A. Rosenfeld, Eds. Elsevier Science Publishers B.V., 1985.
8. R. Chellappa and S. Chatterjee, “Classification of textures using Gaussian-Markov random fields,” IEEE Trans. Acous. Sp. Sig. Proc, vol. ASSP-33, pp. 959–963, Aug. 1985.
9. G.R. Cross and A.K. Jain, “Markov random field texture models,” IEEE Trans. Pat. An. Mach. Intel., vol. PAMI-5, pp. 25–39, Jan. 1983.
10. H. Derin, H. Elliott, R. Cristi, and D. Geman, “Bayes smoothing algorithms for segmentation of binary images modelled by Markov random fields,” IEEE Trans. Pat. An. Mach. Intel., vol. PAMI-6, pp. 707–720, Nov. 1984.
11. H. Derin and H. Elliott, “Modeling and segmentation of noisy and textured images using Gibbs random fields,” IEEE Trans. Pat. An. Mach. Intel., vol. PAMI-9, pp. 39–55, Jan. 1987.
12. J.L. Doob, Stochastic Processes. New York: Wiley, 1953.
13. R.C. Dubes and A.K. Jain, “Random field models in image analysis,” to appear in Applied Statistics.
14. D.E. Dudgeon and R.M. Mersereau, Multidimensional Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1984.
15. M.P. Ekstrom and J.W. Woods, “Two-dimensional spectral factorization with applications in recursive digital filtering,” IEEE Trans. Acoust. Sp. Sig. Proc, vol. ASSP-24, pp. 115–127, April 1976.
16. H. Elliott, H. Derin, R. Cristi, and D. Geman, “Application of the Gibbs distribution to image segmentation,” 1983 ONR Workshop on Statistical Image Processing and Graphics, Shenandoah National Park, May 1983, appeared in Statistical Image Processing and Graphics, E.J. Wegman and D.J. DePriest, Eds., Dekker, 1986; also in Proc. ICASSP-84, pp. 32.5.1–32.5.4, San Diego, CA, March 1984.
17. S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images,” IEEE Trans. Pat. An. Mach. Intel., vol. PAMI-6, pp. 721–741, Nov. 1984.
18. J.M. Hammersley and P. Clifford, “Markov fields on finite graphs and lattices,” (unpublished).
19. E. Ising, “Beitrag zur theorie des ferromagnetisms,” Zeitschrift Physik, vol. 31, pp. 253–258, 1925.
20. A.K. Jain, “Advances in mathematical models for image processing,” Proc. IEEE, vol. 69, pp. 502–528, May 1981.
21. F.-C. Jeng and J.W. Woods, “On the relationship of the Markov mesh to the NSHP Markov chain,” Pat. Rec. Letters, vol. 5, pp. 273–279, July 1986.
22. J.H. Justice and J.L. Shanks, “Stability criterion for N-dimensional digital filters,” IEEE Trans. Autom. Contr., vol. AC-18, pp. 284–286, June 1973.
23. L.N. Kanal, “Markov mesh models,” in Image Modeling. New York: Academic, pp. 239–243, 1980.
24. R.L. Kashyap, “Analysis and synthesis of image patterns by spatial interaction models,” in Progress In Pattern Recognition, L.N. Kanal and A. Rosenfeld, Eds. New York: Elsevier, North-Holland, 1981, pp. 149–186.
25. R.L. Kashyap, “Finite lattice random field models for finite images,” Proc. Conf. Inform. Sci. Sys., pp. 215–220, 1981.
26. R.L. Kashyap and R. Chellappa, “Estimation and choice of neighbors in spatial-interaction models of images,” IEEE Trans. Inform. Theo., vol. IT-29, No. 1, pp. 60–72, Jan. 1983.
27. R.L. Kashyap, “Characterization and estimation of two-dimensional ARMA models,” IEEE Trans. Inform. Theo., vol. IT-30, pp. 736–745, Sept. 1984.
28. R.L. Kashyap, “Image models,” in Handbook of Pattern Recognition and Image Processing, T.Y. Young and K.S. Fu, Eds. New York: Academic Press, 1986.
29. P.A. Kelly and H. Derin, “A proof of the convergence of finite-lattice simultaneous autoregressive(SAR) fields to infinite-lattice SAR fields,” Tech. Rep #CCS-89–102, Dept. Elect. Comp. Eng., Univ. of Mass., Amherst, MA, May 1989.
30. R. Kindermann and J.L. Snell, Markov Random Fields and Their Applications, vol. 7, Amer. Math. Soc, Providence, Rl, 1980.
31. P. Levy, “A Special problem of Brownian motion, and a general theory of Gaussian random functions,” in Proc. 3rd Berkeley Symp. Math. Stat, and Prob., vol. 2, Berkeley, CA, Univ. of Calif. Press, 1956.
32. P.A.P. Moran, “A Gaussian Markovian process on a square lattice,”;. Appl. Prob., vol. 10, pp. 54–62, 1973.
33. P.A.P. Moran, “Necessary conditions for Markovian processes on a lattice,” J. Appl. Prob., vol. 10, pp. 605–612, 1973.
34. B.T. O'Connor and T.S. Huang, “Stability of general two-dimensional recursive filters,” in Two-Dimensional Digital Signal Processing I, T.S. Huang, Ed. New York: Springer-Ver-lag, 1981, pp. 85–154.
35. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 1st ed. New York: McGraw-Hill, 1965.
36. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, 1984.
37. A. Papoulis, “Predictable processes and Wold's decomposition: A review,” IEEE Trans. Acous. Sp. Sig. Proc, vol. ASSP-33, pp. 933–938, Aug. 1985.
38. D.K. Pickard, “Acurious binary lattice process,” J. Appl. Prob., vol. 14, pp. 717–731, 1977.
39. Y.A. Rosanov, “On Gaussian fields with given conditional distributions,” Theory of Prob. and its Appl., vol. 12, No. 3, pp. 381–391, 1967.
40. Y.A. Rosanov, Markov Random Fields. New York: Springer-Verlag, 1982.
41. G. Sharma and R. Chellappa, “Two-dimensional spectral estimation using noncausal autoregressive models,” IEEE Trans. Inform. Theo., vol. IT-32, pp. 268–275, Mar. 1986.
42. M.G. Strintzis, “Tests of stability of multidi mensional filters,” IEEE Trans. Circ. Syst., vol. CAS-24, pp. 432–437, Aug. 1977.
43. P. Whittle, “On stationary processes in the plane,” Biometrika, vol. 41, pp. 434–449, 1954.
44. E. Wong, Stochastic Processes in Information and Dynamical Systems. Huntington, NY: Krieger, 1979.
45. J.W. Woods, “Two-dimensional discrete Markovian fields,” IEEE Trans. Inform. Theo., vol. IT-18, pp. 232–240, Mar. 1972.
46. J.W. Woods, “Two-dimensional Markov spectral estimation,” IEEE Trans. Inform. Theo., vol. IT-22, pp. 552–559, Sept. 1976.
47. W. Zhang, H. Derin, and P.A. Kelly, “A study of relationships between Markov-type random process models,” presented at the 1986 Int. Symp. on Inform. Theo., Univ. of Mich., Ann Arbor, Ml, October 1986.
48. B.D. Ripley, Statistical Inference for Spatial Processes. Cambridge, U.K.: Cambridge University Press, 1988.
49. D.J. Strauss, “Clustering on coloured lattices,”;. Appl. Prob., vol. 14, pp. 135–143, 1977.