Projetos de operadores invariantes à translação via treinamento de redes neurais.

Abstract

The main objective of this thesis is to develop an analytic method for designing translation-invariant operators via neural network training. A new neural network architecture, called Modular Morphological Neural Network (MMNN), is defined using a fundamental result of minimal representations for translation-invariant set mappings via Mathematical Morphology, proposed by Banon and Barrera (1991). The MMNN general architecture is capable of learning both binary and gray-scale translationinvariant operators. For its training, ideas of the Back-Propagation (BP) algorithm and the methodology proposed by Pessoa and Maragos (1997) for overcoming the problem of non-differentiability of rank functions are used. Also is developped an alternative MMNN training method via Genetic Algorithms (GA), and provide a comparative analysis of BP vs. GA training in problems of image restoration and pattern recognition. The MMNN structure can be viewed as a special case of the Morphological/ Rank/Linear Neural Network (MRL-NN) proposed by Pessoa and Maragos (1997), but with specific architecture and training rules. The effectiveness of the proposed BP and GA training algorithms for MMNNs is encouraging, offering alternative design tools for the important class of translation-invariant operators.