D. Schonfeld, OPTIMAL STRUCTURING ELEMENTS FOR THE MORPHOLOGICAL PATTERN RESTORATION OF BINARY IMAGES, IEEE transactions on pattern analysis and machine intelligence, 16(6), 1994, pp. 589-601
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.