An Adaptive Hybrid Morphological Method for Designing Translation Invariant Morphological Operators

— In this paper an adaptive hybrid morphological method is presented for designing translation invariant morphological operators via Matheron Decomposition and via Banon and Barrera Decomposition. It consists of a hybrid model composed of a Modular Morphological Neural Network (MMNN) and an evolutionary search mechanism: the adaptive Genetic Algorithm (GA) (adaptive rates in genetic operators). The proposed method searches for initial weights, architecture and number of modules in the MMNN; then each element of the adaptive GA population is trained via the Back Propagation (BP) algorithm. Also, it is presented and experimental investigation with the proposed method using a relevant application in image processing, the restoration of noisy images, where it veri es that the method proposed herein allows seamless and ef cient design of translation invariant morphological operators of either increasing or nonincreasing types, and the results are discussed and compared, in terms of Noise to Signal Ratio (NSR), with the previously methods proposed in literature, showing the robustness of the proposed method. Keywords— Translation Invariant Morphological Operators, Morphological Neural Networks, Evolutionary Computation, Hybrid Systems, Image Restoration.