Design of morphological filters using genetic algorithms

The design of optimum morphological and other non linear filters based in set, rank and logic is a non trivial task. The search space of possible solutions grows very rapidly with the number of filter parameters such as window size and signal bit depth. One of the simplest methods to estimate optimum parameters is to use the iterative search technique known as genetic algorithms. This paper will describe a new tighter bound for the convergence of genetic algorithms. It will also present an approach to the design of morphological filters using genetic algorithms. It uses iterative search techniques to probe the solution space in a way which models evolution in nature. Both practical and theoretical results achieved in this area will be included: 1. A new improved upper bound, which has recently been derived by the authors, gives the number of GA generations required to guarantee (with a pre-specified certainty) that the optimal solution has been located. Unlike the previously accepted bound it reduces with increasing population size. 2. Results using soft morphological filters designed by genetic algorithms in film restoration will be shown. The GA method is simple in its approach and bypasses the need for highly complex models of the process. As well as providing an interesting perspective to the non linear design debate, solutions found in this way may prove to be complementary to more analytical approaches by both confirming and even prompting new solutions by these routes.