The optimal-morphological-=basis switching algorithm

Designing optimal morpholgical filters, even in the binary case, involves a time-consuming search procedure that, in practice, can be intractable. The present paper provides an algorithm for filter design that is based upon the relationship between the optimal morphological filter and the conditional expectation. A morphological filter may not exist for a given conditional probability distribuition. If one exists, the algorithm determines the filter, optimal among morphological and other filters, almost instantaneously. If not, it changes the probability ensuring minimum increase in mean square error and determines the optimal morphological filter.