Optimal single-stage restoration of subtractive noise corrupted images by a morphological closing

Larry R. Rystrom; Robert M. Haralick; Philip L. Katz

doi:10.1117/12.210717

1 July 1995 Optimal single-stage restoration of subtractive noise corrupted images by a morphological closing

Larry R. Rystrom, Robert M. Haralick, Philip L. Katz

Author Affiliations +

Journal of Electronic Imaging, Vol. 4, Issue 3, (July 1995). https://doi.org/10.1117/12.210717

Abstract

Restoration of subtractive noise on a binary image by a single morphological operation, closing, is analyzed. Restoration by closing alone is appropriate under particular explicitly defined random noise models, based respectively on erosion, independent pixel subtractive noise, and independent pixel subtractive noise followed by dilation. Since in general it is not possible to perfectly restore subtractive noise, we use the Hausdorff metric to measure the residual error in restoration. This metric is an appropriate one because of its geometric interpretation in terms of set coverings. We describe a best first search procedure to find a structuring element for closing that is optimal in the sense of minimizing the mean Hausdorff error. The search procedure's utility function is based on the calculation of certain probabilities related to the noise model, namely the probability of one set being the subset of another set and some related probabilities. We describe how a bound on these probabilities can be efficiently computed to speed up the search process.

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Larry R. Rystrom, Robert M. Haralick, and Philip L. Katz "Optimal single-stage restoration of subtractive noise corrupted images by a morphological closing," Journal of Electronic Imaging 4(3), (1 July 1995). https://doi.org/10.1117/12.210717

Published: 1 July 1995

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