Optimal morphological hit-or-miss filtering of gray-level images

Edward R. Dougherty

doi:10.1117/12.144771

21 May 1993 Optimal morphological hit-or-miss filtering of gray-level images

Edward R. Dougherty

Proceedings Volume 1902, Nonlinear Image Processing IV; (1993) https://doi.org/10.1117/12.144771
Event: IS&T/SPIE's Symposium on Electronic Imaging: Science and Technology, 1993, San Jose, CA, United States

Abstract

The binary hit-or-miss transform is applied to filter digital gray-scale signals. This is accomplished by applying a union of hit-or-miss transforms to an observed signal's umbra and then taking the surface of the filtered umbra as the estimate of the ideal signal. The hit-or-miss union is constructed to provide the optimal mean-absolute-error filter for both the ideal signal and its umbra. The method is developed in detail for thinning hit-or-miss filters and applies at once to the dual thickening filters. It requires the output of the umbra filter to be an umbra, which in general is not true. A key aspect of the paper is the complete characterization of umbra-preserving union-of-hit-or-miss thinning and thickening filters. Taken together, the mean-absolute-error theory and the umbra-preservation characterization provide a full characterization of binary hit-or-miss filtering as applied to digital gray-scale signals. The theory is at once applicable to hit-or-miss filtering of digital gray-scale signals via the three- dimensional binary hit-or-miss transform.

Citation Download Citation

Edward R. Dougherty "Optimal morphological hit-or-miss filtering of gray-level images", Proc. SPIE 1902, Nonlinear Image Processing IV, (21 May 1993); https://doi.org/10.1117/12.144771

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