Effectiveness of extrapolation-directed multistep search in unsupervised design for morphological filters for noise removal

To recover texture images from impulse noise by the opening operator which is one of morphological operations, a suitable structuring element (SE) has to be estimated. In this paper, we apply a Genetic Algorithm (GA) to an unsupervised design problem of SEs. In previous work, it was shown that deterministic Multi-step Crossover Fusion (dMSXF) which is a promising interpolation-directed crossover method worked very well on the design of SEs. However, dMSXF does not work effectively when parents´ characteristics are extremely similar to each other, and an extrapolation search method which explores outside the distribution of the population is required. Here, we introduce deterministic Multi-step Mutation Fusion (dMSMF) as a complementary search of dMSXF for exploring the extrapolation domain to improve the search performance. Through experiments, it is shown that dMSXF+dMSMF can design effective SEs stably.