Optimal binary filters estimate an ideal random set by means of an observed random set. By parameterizing the ideal and observation random sets, one can examine the robustness of filter design relative to parameter states. This paper addresses the question as to which states possess the most robust optimal filters. Based on the prior distribution of the states, a measure of robustness is defined for each state and the state possessing maximal robustness is determined. The paper focuses on sparse noise, for which an analytic formulation of robustness is known. It proposes a parametric model from which to approximate robustness by estimating model parameters from image data.
