Optimal nonlinear filter for signal-union-noise and runlength analysis in the directional one-dimensional discrete Boolean random set model

Signal Processing

Volumn 51, Issue 3, 1996, Pages 147-166

  Handley, John C ^a   Dougherty, Edward R ^a  

^a ROCHESTER INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN FUNCTIONS; COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; MATHEMATICAL MODELS; OPTIMIZATION; PROBABILITY; RANDOM PROCESSES; SIGNAL FILTERING AND PREDICTION; SPURIOUS SIGNAL NOISE;

BERNOULLI PROCESS; DISCRETE LINE; GEOMETRIC PROBABILITY LAW; ONE DIMENSIONAL DISCRETE BOOLEAN MODEL; OPTICAL NONLINEAR FILTER; RANDOM LENGTH LINE SEGMENTS; SIGNAL UNION NOISE;

SIGNAL THEORY;

EID: 0030171146     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/0165-1684(96)00040-0     Document Type: Article

References (31)

1. G. Ayala, J. Ferrandiz and F. Montes, "Boolean models: maximum likelihood estimation from circular clumps", Biomet. J., Vol. 32, 1990, pp. 73-78.
2. B. Bettoli and E.R. Dougherty, "Linear granulometric moments of noisy binary images", J. Math. Imaging Vision, Vol. 3, No. 3, August, 1993, pp. 299-319.
3. S. Browne and J.M. Steele, "Transient behavior of coverage processes with applications to the infinite-server queue", J. Appl. Probab., Vol. 30, 1993, pp. 589-602.
4. G. Choquet, Theory of Capacities, Ann. Inst. Fourier, V, 1953-1954.
5. N. Cressie and G.M. Laslett, "Random set theory and problems of modeling", SIAM Rev., Vol. 29, 1987, pp. 557-574.
6. E. R. Dougherty, "Optimal binary morphological bandpass filters induced by granulometric spectral representation", J. Math. Imaging Vision, To appear.
7. E.R. Dougherty and C. Cuciurean-Zapan, "Optimal reconstructive τ-openings for disjoint and statistically modeled nondisjoint grains", Submitted.
8. E.R. Dougherty and J.C. Handley, "Recursive maximum-likelihood estimation in the one-dimensional discrete Boolean random set model", Signal Processing, Vol. 43, No. 1, April 1995, pp. 1-15.
9. E.R. Dougherty, R.M. Haralick, Y. Chen, C. Agerskov, U. Jacobi and P.M. Sloth, "Estimation of optimal morphological τ-opening parameters based on independent observation of signal and noise pattern spectra", Signal Processing, Vol. 29, No. 3, December 1992, pp. 265-281.
10. E.R. Dougherty and R.P. Loce, "Optimal mean-square-absolute-error hit-or-miss filters: Morphological representation and estimation of the binary conditional expectation", Opt. Engrg., Vol. 32, No. 4, April 1993, pp. 815-827.
11. E.R. Dougherty and R.P. Loce, "Precision of morphological-representation estimators for translation-invariant binary filters: Increasing and nonincreasing", Signal Processing, Vol. 40, Nos. 2-3, November 1994, pp. 129-154.
12. E.R. Dougherty, J.T. Newell and J.B. Pelz, "Morphological texture-based maximum-likelihood pixel classification based on local granulometric moments", Pattern Recognition, Vol. 25, No. 10, 1992, pp. 1181-1198.
13. E.R. Dougherty and F. Sand, "Representation of linear granulometric moments for deterministic and random binary images", J. Visual Comm. Image Representation, Vol. 6, No. 1, March 1995, pp. 69-79.
14. V. Dupač, "Parameter estimation in the Poisson field of disks", Biometrika, Vol. 67, 1980, pp. 187-190.
15. J. Goutsias, Modeling random shapes: An introduction to random closed set theory, Technical Report JHU/ECE 90-12, The Johns Hopkins University, Baltimore, 1990.
16. J. Goutsias, "Morphological analysis of discrete random shapes", J. Math. Imaging Vision, Vol. 2, Nos. 2/3, November 1992, pp. 193-215.
17. P. Hall, Introduction to the Theory of Coverage Processes, Wiley, New York, 1988.
18. J.C. Handley and E.R. Dougherty, "Maximum-likelihood estimation for the discrete Boolean model using linear samples", J. Microscopy, Vol. 182, No. 1, April 1996, pp. 67-78.
19. R.M. Haralick, P.L. Katz and E.R. Dougherty, "Model-based morphology: The opening spectrum", Graphical Models and Image Processing, Vol. 57, No. 1, January 1995, pp. 1-12.
20. C. Lantuejoul and M. Schmitt, "Use of two new formulae to estimate the intensity of a Boolean model", GRETSI, Vol. 2, September 1991, pp. 1045-1048.
21. R.P. Loce and E.R. Dougherty, Enhancement and Restoration of Digital Documents: Statistical Design of Nonlinear Algorithms, SPIE Press, Bellingham, WA, 1996.
22. G. Matheron, Random Sets and Integral Geometry, Wiley, New York, 1975.
23. F. Preteux and M. Schmitt, "Boolean texture analysis and synthesis", in: J. Serra, ed., Image Analysis and Mathematical Morphology, Vol. 2, Academic Press, New York, 1988.
24. F. Sand and E.R. Dougherty, "Asymptotic normality of the morphological pattern-spectrum moments and orthogonal granulometric generators", J. Visual Comm. Image Representation, Vol. 3, No. 2, June 1992, pp. 203-214.
25. M. Schmitt, "Estimation of the density in a stationary Boolean model", J. Appl. Probab., Vol. 28, September 1991, pp. 702-708.
26. J. Serra, "The Boolean model and random sets", Computer Graphics and Image Processing, Vol. 12, 1980, pp. 99-126.
27. N.D. Sidiropoulos, J.S. Baras and C.A. Berestein, "Algebraic analysis of the generating functional for discrete random sets and statistical inference for intensity in the discrete Boolean random-set model", J. Math. Imaging Vision, Vol. 4, 1994, pp. 273-290.
28. W. Stadje, "The busy period of the queueing system M/G/∞", J. Appl. Probab., Vol. 22, 1985, pp. 697-704.
29. D. Stoyan, W.S. Kendall and J. Mecke, Stochastic Geometry and Its Applications, Wiley, New York, 1987.
30. L. Takacs, Introduction to the Theory of Queues, Oxford University Press, New York, 1962.
31. W. Weil, "The estimation of mean shape and mean particle number in overlapping particle systems", Adv. Appl. Probab., Vol. 27, No. 1, 1995.