In the context of image restoration, optimal binary openings estimate an ideal random set from an observed random set. If we consider optimization relative to a homothetic scalar that governs structuring element sizes, then opening optimization can be placed into the context of optimal granulometric bandpass filters and solution for the optimization problem for the signal-union-noise model can be given in terms of the granulometric spectral densities (GSDs) of the signal and noise. The robustness question arises if the signal and noise GSDs are parameterized, so that the model can assume a family of states: specifically, what is the cost of applying an optimal opening designed for one pair of GSDs to a model corresponding to a different pari of GSDs. This paper addresses the robustness problem in the context of a prior distribution for the parameters governing the signal and noise GSDs. It does so by considering the mean robustness, which is defined for each state of nature to be the expected increase in error resulting from using the optimal opening for that states across all states. Moreover, it considers a global filter that is defined for all states via the expected optimal homothetic scalar. Finally, it compares Bayesian robust openings to minimix robust openings.

Date Published: 25 June 1999
PDF: 9 pages
Proc. SPIE 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems, (25 June 1999); doi: 10.1117/12.351330

Published in SPIE Proceedings Vol. 3816:
Mathematical Modeling, Bayesian Estimation, and Inverse Problems
Françoise J. Prêteux; Ali Mohammad-Djafari; Edward R. Dougherty, Editor(s)