Asymptotic Behavior of Morphological Filters
The connection between morphological and stack filters is used in the analysis of the statistical properties of morphological filters. Closed-form expressions for the output distributions of morphological filters are given, and their statistical symmetry properties are analyzed. Asytotically tight bounds on the expectations of two-dimensional morphological filters, and asymptotic formulas for the variances of one-dimensional morphological filters are derived. These results form the basis for analyzing general asymptotic properties of morphological filters.
Key wordsmorphological filters stack filters statistical properties asymptotic analysis
Unable to display preview. Download preview PDF.
- 2.D. Schonfeld and J. Goutsias, “Optimal morphological pattern restoration from noisy binary images,” IEEE Trans. Patt. Anal. Mach. Intell., vol. PAMI-13, pp. 14–29, 1990.Google Scholar
- 6.P. Rustanius, L. Koskinen, and J. Astola, “Theoretical and experimental analysis of the effects of noise in morphological image processing,” in Proc. SPIE Symp. on Image Algebra and Morphological Image Processing III, San Diego, CA, July 1992.Google Scholar
- 7.E. Dougherty and C. Ciardiana, Morphological Methods in Image and Signal Processing, Prentice-Hall: Englewood Cliffs, NJ, 1988.Google Scholar
- 8.S. Serra, Image Analysis and Mathematical Morphology, Academic Press: London, 1988.Google Scholar
- 14.L. Koskinen, J. Astola, and Y. Neuvo, “Statistical properties of discrete morphological filters,” in Proc. IEEE Int. Symp. on Circuits and Systems, New Orleans, LA, May 1990, pp. 1219–1222.Google Scholar
- 17.L. Koskinen and J. Astola, “Statistical properties of soft morphological filters,” in Proc. SPIE Symp. on Nonlinear Image Processing III, San Jose, CA, February 1992.Google Scholar
- 18.J. Astola and Y. Neuvo, “An efficient tool for analyzing weighted median and stack filters,” submitted to IEEE Trans. Circuits and Systems. Google Scholar
- 19.B. Justusson, “Median filtering: statistical properties,” in Topics in Applied Physics, Two Dimensional Digital Signal Processing II, T.S. Huang, ed., Springer-Verlag: Berlin, 1981.Google Scholar