In this paper color image compression using a fuzzy Hopfield-model net based on rough-set reasoning is created to generate optimal codebook based on Vector Quantization (VQ) in Discrete Wavelet Transform (DWT). The main purpose is to embed rough-set learning scheme into the fuzzy Hopfield network to construct a compression system named Rough Fuzzy Hopfield Net (RFHN). First a color image is decomposed into 3-D pyramid structure with various frequency bands. Then the RFHN is used to create different codebooks for various bands. The energy function of RFHN is defined as the upper- and lower-bound fuzzy membership grades between training samples and codevectors. Finally, near global-minimum codebooks in frequency domain can be obtained when the energy function converges to a stable state. Therefore, only 32/N pixels are selected as the training samples if a 3N-dimensional color image was used. In the simulation results, the proposed network not only reduces the consuming time but also preserves the compression performance.

This paper describes the application of an unsupervised parallel approach called the Annealed Hopfield Neural Network (AHNN) using a modified cost function with moment and entropy preservation for magnetic resonance image (MRI) classification. In the AHNN, the neural network architecture is same as the original 2-D Hopfield net. And a new cooling schedule is embedded in order to make the modified energy function to converge to an equilibrium state. The idea is to formulate a clustering problem where the criterion for the optimum classification is chosen as the minimization of the Euclidean distance between training vectors and cluster-center vectors. In this article, the intensity of a pixel in an original image, the first moment combined with its neighbors, and their gray-level entropy are used to construct a 3-component training vector to map a neuron into a two-dimensional annealed Hopfield net. Although the simulated annealing method can yield the global minimum, it is very time-consuming with asymptotic iterations. In addition, to resolve the optimal problem using Hopfield or simulated annealing neural networks, the weighting factors to combine the penalty terms must be determined. The quality of final result is very sensitive to these weighting factors, and feasible values for them are difficult to find. Using the AHNN for magnetic resonance image classification, the need of finding weighting factors in the energy function can be eliminated and the rate of convergence is much faster than that of simulated annealing. The experimental results show that better and more valid solutions can be obtained using the AHNN than the previous approach in classification of the computer generated images. Promising solutions of MRI segmentation can be obtained using the proposed method. In addition, the convergence rates with different cooling schedules in the test phantom will be discussed.

In this paper, the application of an unsupervised parallel approach called the Fuzzy Hopfield Neural Network (FHNN) for vector qunatization in image compression is proposed. The main purpose is to embed fuzzy reasoning strategy into neural networks so that on-line learning and parallel implementation for codebook design are feasible. The object is to cast a clustering problem as a minimization process where the criterion for the optimum vector qunatization is chosen as the minimization of the average distortion between training vectors. In order to generate feasible results, a fuzzy reasoning strategy is included in the Hopfield neural network to eliminate the need of finding weighting factors in the energy function that is formulated and based on a basic concept commonly used in pattern classification, called the "within-class scatter matrix" principle. The suggested fuzzy reasoning strategy has been proven to allow the network to learn more effectively than the conventional Hopfield neural network. The FHNN based on the within-class scatter matrix shows the promising results in comparison with the c-means and fuzzy c-means algorithms.