Abstract
Morphological granulometries are frequently used as descriptors of granularity, or texture, within a binary image. In this paper, we study the problem of estimating the (discrete) size distribution and size density of a random binary image by means of empirical, as well as, Monte Carlo estimators. Theoretical and experimental results demonstrate superiority of the Monte Carlo estimation approach, and suitability of mathematical morphology in studying important properties of a particular binary random image model, widely known as a Markov random field model.
This work has been supported by the office of Naval Research, Mathematical, Computer, and Information Sciences Division, under ONR Grant N00014-90–1345.
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References
G. Matheron, Random Sets and Integral Geometry. New York: Wiley, 1975.
J. Serra, Image Analysis and Mathematical Morphology. London: Academic Press, 1982.
P. Maragos, “Pattern spectrum and multiscale shape representation,” IEEE Transactions on Pattern Analysis and Machine Intelligence,vol. 11, pp. 701–716, 1989.
D. Schonfeld, and J. Goutsias, “Optimal morphological pattern restoration from noisy binary images,” IEEE Transactions on Pattern Analysis and Machine Intelligence,vol. 13, pp. 14–29, 1991.
R. M. Haralick, “Model-based morphology: Simple and complex shapes,” In Visual Form: Analysis and Recognition, C. Arcelli, L. P. Cordella, and G. Sanniti di Baja, Eds., pp. 275–285. New York: Plenum Press, 1992.
E. R. Dougherty, R. M. Haralick, Y. Chen, C. Agerskov, U. Jacobi, and P. H. Sloth, “Estimation of optimal morphological T-opening parameters based on independent observation of signal and noise pattern spectra,” Signal Processing, vol. 29, pp. 265–281, 1992.
E. R. Dougherty, and J. B. Pelz, “Morphological granulometric analysis of electrophotographic images—Size distribution statistics for process control,”Optical Engineering, vol. 30, pp. 438–445, 1991.
E. R. Dougherty, J. B. Pelz, F. Sand, and A. Lent, “Morphological image segmentation by local granulometric size distributions,”Journal of Electronic Imaging, vol. 1, pp. 46–60, 1992.
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, pp. 1181–1198, 1992.
S. Archambault, and M. Moore, “Statistiques morphologiques pour l’ajustement d’images,” International Statistical Review, vol. 61, pp. 283–297, 1993.
J. Goutsias, “Morphological analysis of discrete random shapes,” Journal of Mathematical Imaging and Vision, vol. 2, pp. 193–215, 1992.
F. Sand, and E. R. Dougherty, “Asymptotic normality of the morphological pattern-spectrum moments and orthogonal granulometric generators,” Journal of Visual Communication and Image Representation,vol. 3, pp. 203–214, 1992.
B. Bettoli, and E. R. Dougherty, “Linear granulometric moments of noisy binary images,” Journal of Mathematical Imaging and Vision, vol. 3, pp. 299–319, 1993.
M. Moore, and S. Archambault, “On the asymptotic behavior of some statistics based on morphological operations.” In Spatial Statistics and Imaging, A. Possolo, Ed., vol. 20, pp. 258–274. Hayward, California: Institute of Mathematical Statistics, Lecture Notes—Monograph Series, 1991.
J. Besag, and P. J. Green, “Spatial statistics and Bayesian computation,” Journal of the Royal Statistical Society, Series B, vol. 55, pp. 25–37, 1993.
K. G. Wilson, “Problems in physics with many scales of length,” Scientific American, vol. 24, pp. 158–177, 1979.
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Sivakumar, K., Goutsias, J. (1994). Monte Carlo Estimation of Morphological Granulometric Discrete Size Distributions. In: Serra, J., Soille, P. (eds) Mathematical Morphology and Its Applications to Image Processing. Computational Imaging and Vision, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1040-2_30
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DOI: https://doi.org/10.1007/978-94-011-1040-2_30
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