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.