Morphological filter mean-absolute-error theorem
Robert P. Loce, Edward R. Dougherty · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1992
The general characterization of optimal morphological filters is based on the Matheron representation for morphological filters. As conceived in its most general form, optimal- morphological-filter design involves a search over potential bases of structuring elements that can be used to form the Matheron erosion expansion. The present paper provides expressions for the mean-absolute error of general binary morphological filters formed from erosion bases in terms of mean-absolute errors of single-erosion filters. The theorem has a recursive form and use of this form in the derivation of optimal-filter bases is demonstrated.