This paper presents an evolutionary morphological approach for designing translation invariant operators for time series forecasting. It consists of an intelligent evolutionary model composed of a modular morphological neural network (MMNN) trained via an improved genetic algorithm (IGA) having optimal genetic operators to accelerate convergence of the genetic algorithm. The proposed design strategy searches for the minimum number of time lags to represent the time series, as well as the weights, architecture and number of modules of the MMNN. An experimental analysis is conducted with the proposed method using six real world financial time series and five well-known performance measurements, demonstrating good performance of MMNN systems for financial time series forecasting.

In the present paper, adaptive genetic algorithm (AGA) is used for training a modular morphological neural network (MMNN) for designing translation invariant operators via Matheron decomposition and via Banon and Barrera decomposition. The operators are applied to restoration of images corrupted by salt and pepper noise. The AGA is used to determine the weights, architecture and number of modules of the MMNN. Results in terms of noise to signal ratio show that the method proposed in the present work lead to a better operators performance when compared to other methods previously proposed in the literature.

This paper presents an improved evolutionary hybrid method for designing morphological operators via the Matheron and the Banon and Barrera decompositions of translation invariant operators. It consists of a hybrid model composed of a modular morphological neural network (MMNN) and an improved genetic algorithm (IGA) having optimal genetic operators to accelerate convergence of the genetic algorithm. The proposed design method looks for initial weights, architecture and number of modules in the MMNN; then each element of the IGA population is trained via the back propagation (BP) algorithm. Optimal morphological operators are applied to image restoration and edge extraction of binary images corrupted by salt and pepper noise. The method proposed herein is capable of performing simultaneous edge extraction and noise removal operations, allowing seamless and efficient design of morphological operators of either increasing or non-increasing types.

The main objective of this work is to develop an analytical 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 translation invariant operators. For its training, ideas of the backpropagation (BP) algorithm and the methodology proposed by Pessoa and Maragos (see Ph.D. thesis, Georgia Institute of Technology, 1997) for overcoming the problem of non-differentiability of the rank functions are used. An alternative MMNN training method via genetic algorithms (GA) is also developed, and a comparative analysis of BP vs. GA training in problems of image restoration and pattern recognition is provided. 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.

A class of morphological/rank/linear (MRL)-filters is presented as a general nonlinear tool for image processing. They consist of a linear combination between a morphological/rank filter and a linear filter. A gradient steepest descent method is proposed to optimally design these filters, using the averaged least mean squares (LMS) algorithm. The filter design is viewed as a learning process, and convergence issues are theoretically and experimentally investigated. A systematic approach is proposed to overcome the problem of nondifferentiability of the nonlinear filter component and to improve the numerical robustness of the training algorithm, which results in simple training equations. Image processing applications in system identification and image restoration are also presented, illustrating the simplicity of training MRL-filters and their effectiveness for image/signal processing.

We formulate a general class of neural network based filters, where each node is a morphological/rank operation. This type of system is computationally efficient since no multiplications are necessary. The introduction of such networks is partially motivated from observations that internal structures of a neuron can generate logic operations. An efficient adaptive optimal design procedure is proposed for these networks, based on the back-propagation algorithm. The procedure is optimal under the LMS criterion. Finally, experimental results are illustrated in problems of noise cancellation, encouraging the use of such class of systems and its training algorithm as important tools for nonlinear signal and image processing.