OPTIMAL STRUCTURING ELEMENTS FOR THE MORPHOLOGICAL PATTERN RESTORATION OF BINARY IMAGES

In this paper, we derive the optimal structuring elements of morpholog ical filters in image restoration. The expected pattern transformation of random sets is presented. An estimation theory framework for rando m sets is subsequently proposed. This framework is based on the least mean difference (LMD) estimator. The least mean difference (LMD) estim ator is defined to minimize the cardinality of the expected pattern tr ansformation of the set-difference of the parameter and the estimate. Several important results for the determination of the least mean diff erence (LMD) estimator are derived. The least mean difference (LMD) st ructuring elements of morphological filters in image restoration are f inally derived.