Mean-absolute-error theorem for computational morphology
Robert P. Loce, Edward R. Dougherty · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
Computational mathematical morphology was developed to provide a unified framework for the design of optimal filters: gray-scale- to-gray-scale, gray-scale-to-binary, and binary-to-binary. The present paper provides as representation for the mean-absolute error of increasing filters in terms of the errors resulting from single-erosion filters. It also provides a recursive form of the representation that can be employed in a computer search algorithm to find optimal filters, in particular, optimal restoration filters.