Robust openings in the context of a prior distribution governing the parameters of the random set model

Edward R. Dougherty, Yidong Chen

Research output: Contribution to journalConference articlepeer-review


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 t that governs structuring element sizes, then opening optimization can be placed into the context of optimal granulometric bandpass filters and solution of 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 (of nature): specifically, what is the cost of applying an optimal opening designed for one pair of GSDs to a model corresponding to a different pair 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 state across all states. Moreover, it considers a global filter that is defined for all states via the expected optimal homothetic scalar (relative to the prior distribution of the parameter). Finally, it compares Baysian robust openings to minimax robust openings.

Original languageEnglish (US)
Pages (from-to)57-65
Number of pages9
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 1999
Externally publishedYes
EventProceedings of the 1999 Mathematical Modeling, Bayesian Estimation, and Inverse Problems - Denver, CO, USA
Duration: Jul 21 1999Jul 23 1999

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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