The design of optimal morphological filters, in the binary or gray scale domain, involves a computationally intense search procedure that, in practice, can be intractable. The present work provides a practical method for optimal morphological filter design that is based on the statistical estimation theory and lattice theory. A link is made between optimal morphological filter and the conditional probability distribution. For a given conditional probability distribution a morphological filter may or may not exist. If a morphological filter exists, then the method designs the one that is optimal among morphological and all other filters. If an optimal morphological filter does not exist for the given conditional distribution then, an algorithm called the switching algorithm is used. The switching algorithm is employed to transform the probability distribution in a way such that a optimal morphological filter can be designed for the transformed probability distribution and the final increase in the mean squared error is minimum. The method has been applied on binary and gray-scale image restoration and has proven to be very efficient, in restoring the various different types of degradations considered. The results obtained using the optimal morphological filters are compared against ones obtained by using median filters. Overall the performance of the optimal morphological filters is superior to that of median filters. Computationally the performance of the method is extremely fast and efficient, even in cases where switching was required.
Library of Congress Subject Headings
Image processing--Mathematics; Morphisms (Mathematics); Digital filters (Mathematics)
Department, Program, or Center
Electrical Engineering (KGCOE)
Swarnakar, Vivek, "Optimal morphological filters" (1993). Thesis. Rochester Institute of Technology. Accessed from
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