Behavior of adaptive digital erosions

Design of statistically optimal erosion-based filters is problematic due to the complexity of the search process. Specialized search techniques and constraints on optimality are used to mitigate the full search. Adaptation of structuring elements has also ben employed. The present paper looks at the behavior of an adaptive filter relative to the actual optimal filter for a single erosion in two models, signal-union-noise and dilation. It does so in the context of state transitions, where filter states are stacks that determine the structuring element upon thresholding.