Morphological representation of order-statistics filters

We propose a comprehensive theory for the morphological bounds on order-statistics filters (and their repeated iterations). Conditions are derived for morphological openings and closings to serve as bounds (lower and upper, respectively) on order-statistics filters (and their repeated iterations). Under various assumptions, morphological open-closings and close-openings are also shown to serve as (tighter) bounds (lower and upper, respectively) on iterations of order-statistics filters. Simulations of the application of the results presented to image restoration are finally provided.

[1]  J. Goutsias,et al.  Optimal Morphological Pattern Restoration from Noisy Binary Images , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[2]  Dan Schonfeld.  Optimal Structuring Elements for the Morphological Pattern Restoration of Binary Images , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Petros Maragos,et al.  Morphological filters-Part II: Their relations to median, order-statistic, and stack filters , 1987, IEEE Trans. Acoust. Speech Signal Process..

[4]  Dan Schonfeld,et al.  Morphological bounds on nonlinear filters , 1992, Other Conferences.

[5]  R.J.P. de Figueiredo,et al.  Order filters , 1985, Proceedings of the IEEE.