Optimal mean-absolute-error hit-or-miss filters: morphological representation and estimation of the binary conditional expectation

Edward R. Dougherty; Robert P. Loce

doi:10.1117/12.132376

1 April 1993 Optimal mean-absolute-error hit-or-miss filters: morphological representation and estimation of the binary conditional expectation

Edward R. Dougherty, Robert P. Loce

Author Affiliations +

Optical Engineering, Vol. 32, Issue 4, (April 1993). https://doi.org/10.1117/12.132376

Abstract

The hit-or-miss operator is used as the building block of optimal binary restoration filters. Filter design methodologies are given for general-, maximum-, and minimum-noise environments, the latter two producing optimal thinning and thickening filters, respectively, and for iterative filters. The approach is based on the expression of translation-invariant filters as unions of hit-or-miss transforms. Unions of hit-or-miss transforms are expressed as canonical logical sums of products, and the final hit-or-miss templates are obtained by logic reduction. The net effect is a morphological representation and estimation of the conditional expectation, which is the overall optimal mean-absolute-error filter.

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Edward R. Dougherty and Robert P. Loce "Optimal mean-absolute-error hit-or-miss filters: morphological representation and estimation of the binary conditional expectation," Optical Engineering 32(4), (1 April 1993). https://doi.org/10.1117/12.132376

Published: 1 April 1993

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