Optimal Mask Filtering of Discrete Random Sets under a Union/Intersection Noise Model

We consider the problem of estimating realizations of highly nonstationary Discrete Random Sets, distorted by a degradation process which can be described by a union/intersection model. We start by presenting some important structural results concerning the probabilistic description of Discrete Random Sets defined on a finite lattice. Then we propose a family of filters which can be viewed as lattice operators, and, for each degradation model, derive the optimal filter by means of minimizing a suitable fidelity criterion.