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Fractal coding, which is coding with the self-similarity of the image as redundancy, has recently been studied extensively. In this paper, a method of fractal video coding is proposed in which the redundancy along the time axis is eliminated from a sequence of videos by the orthogonal transformation and then the results are rearranged according to the frequency components before fractal video coding. In comparison with the conventional fractal video coding, the average PSNR is improved with almost identical information content. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(3): 36–47, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20248 [ABSTRACT FROM AUTHOR]

Fractal image coding is an image compression method that utilizes the self-similarity which is inherent in a natural image. The picture quality of the restored image depends on the detection of adequate self-similarity in the original image. However, for the conventional technique that uses square blocks, it is troublesome to detect good self-similarity in edge parts that have steep changes in gradation values. Therefore, in this paper, the authors perform regional division for each block and use separate contractive transformations in each divided region to implement superior self-similarity detection. This technique can reproduce more apparent edges than the conventional technique that uses square blocks and the SN ratio is improved by 1 to 2 dB at the same bit rate. Also, although the coding performance of the conventional fractal image coding technique is worse than that of JPEG, the proposed technique shows nearly equivalent PSNR to JPEG in the vicinity of 2 to 3 bpp. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(8): 1–8, 2005; Published online in Wiley InterScience (www.interscience.wiley. com). DOI 10.1002/ecjc.20153 [ABSTRACT FROM AUTHOR]

In order to evaluate fractal dimensions based on the self-affine characteristics of time series signals, a method of estimation of fractal dimensions by using fractional integro-differential equations is proposed. The time series of fractional Brownian functions can be converted to uncorrelated random noise by fractional integro-differentiation of an appropriate order. By comparing the correlation characteristics of the converted data and the reference data by the maximum likelihood estimation method, the fractal dimension can be evaluated from the minimum of the likelihood function. The estimation accuracy of the proposed method is improved by a factor of about 1.5 in comparison with the maximum likelihood estimation method in which the dimension of the reference data is varied. The standard deviation of the estimation results per reference datum is reduced by a factor of about 0.8. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(4): 30–39, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10136 [ABSTRACT FROM AUTHOR]

In order to improve the approximation capability of fractal coding, a fractal coding method using multiple domains is proposed in which an approximation is carried out by superposition of contracted images from multiple domain blocks. By combining the multidomain method with the multiscaling procedure of dividing blocks into regions and individually providing the scaling coefficients of brightness, a contraction transform with even better degrees of approximation is obtained and edge reconstruction is improved. As a result, excellent reconstructed images are obtained even for complicated images for which high reproducibility cannot be realized with the conventional fractal coding. Also, it is possible to reproduce contour regions containing edges. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(2): 79–87, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10081 [ABSTRACT FROM AUTHOR]

A novel bipolar logistic chaos neuron model (bLCN) is proposed as an example of nonmonotonic neuron models for hardware implementation. The activation function is approximated in quadratic form, which is reminiscent of logistic mapping, instead of the sinusoidal form previously investigated. In this report, we shall analyze the bifurcation characteristics and the corresponding invariant measures of the monotonic chaos neuron model (MCN), the periodic chaos neuron model (PCN) proposed earlier, and the bLCN. We shall confirm that the PCN and bLCN have symmetric response, in contrast to the MCN. Furthermore, we shall present an electronic circuit model of the presently proposed bLCN, and compare it with the numerical model. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(11): 46–56, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10063 [ABSTRACT FROM AUTHOR]

This paper proposes a back propagation method using a periodic activation function for a hierarchical neural network and examines its learning capability. As a specific learning problem, the paper addresses the n-bit parity problem and conducts a learning process by using a three-layer neural network. The computer simulation results indicate an increased learning coefficient range achieving a 100% learning success rate with an improved speed of learning compared with a neural network model using a monotonic activation function. In addition, the new method lessens the influence of the initial value that is set at the beginning of a learning process, and reduces the degree of dependency on parameters. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(3): 11–19, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1136 [ABSTRACT FROM AUTHOR]

The hierarchical IFS coding proposed by the authors is applied to monochrome images. The present method is a fusion of the hierarchical procedure and fractal coding based on the iterated function system (IFS) theory. By using a hierarchical structure based on the Gaussian pyramid, the image is divided into frequency subbands so that the information is compressed. By using the information between the bands, the coding can effectively capture the similarity between the range and the domain. Further, an application of this method to color images is discussed. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(7): 71–78, 2000 [ABSTRACT FROM AUTHOR]

In this paper, a cross-correlation type synergetic neural network is proposed that realizes a perfect association. This model enables perfect association by incorporating synergetic dynamics into a conventional cross-correlation type association memory model. The association sequence is determined by the value of the product of the initial order parameters for an input pattern. Furthermore, we report on the usefulness of introducing chaotic fluctuations from the point of view of applications of this model to the time series configuration of many patterns and the time reduction needed for association. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(9): 37–47, 1998 [ABSTRACT FROM AUTHOR]

In this paper, an autoassociation model is proposed that uses a piecewise linear periodic mapping with parameter control. In practice, the activation function in the present model is controlled through a nonmonotonic periodic mapping between monotonic periodic mappings, so that it realizes high memory capacity without falling into a false memory that is a quasi-stable state of the network. In the present model, by using chaotic dynamics based on the periodic mapping, a memory search model using chaos can be constructed. Further, by providing information on the input, autoassociation can be realized. From the results of a computer simulation, it is found that the present model can realize perfect association with a memory rate of L/N ∼ 0.5 even in the search mode. Further, in asynchronous operation of the network, improvement of the association characteristics and enhancement of the memory capacity (with a memory rate of L/N ∼ 0.56 in the search mode) are confirmed, so that the usefulness of chaos in asynchronous operation is demonstrated. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(1): 52–70, 1998 [ABSTRACT FROM AUTHOR]

A novel IFS coding scheme is proposed for image compression. The present method is based on hierarchical structure or the Gaussian pyramid of contracted images. In comparison with the conventional scheme (IFS or JPEG), the presently introduced hierarchical scheme is found to be useful, especially for relatively low-bit rates. This is considered to be as a result of the subband division of the original image and the existence of the redundancy between the range and domain characteristics in the image. On the basis of the present scheme, it is found that the bit rate may be reduced up to the conventional scheme with the transform coding scheme, for the original monochrome image with 2.56 × 256 size and 8-bit gray-scale levels. [ABSTRACT FROM AUTHOR]

The purpose of this study is to verify that EEC is composed of frequency components with chaotic characteristics. EEC data are decomposed into frequency components, and the chaos and fractal analyses are applied. More precisely, the running spectrum of EEC is derived and the chaos analysis is applied using the Lyspunov spectrum and the correlation dimension. As a result, the existence of the chaotic phenomenon is verified for most of the frequency components used as the objects of the analysis. Ills found also that the fractal properties exist in most of the frequency components. The multifractal analysis is applied to the EEC data, and the generalized dimension of q-th order is determined. It is seen as a result that the reconstruction attractors of EEC an placed by a nonuniform fractal distribution, which is represented by a large number of scaling indices concerning the dimension. [ABSTRACT FROM AUTHOR]

Orthogonal fractal basis functional sets are proposed for the compression of images with long-tail power distributions. These functional sets are generated by the method of midpoint displacements from deterministic theory and are orthogonalized by the method of Schmidt. From computer simulations of transform data compression coding that uses a transform based on these functional sets and a nonuniform quantizer, the functional sets and a nonuniform quantizer, the functional sets proposed in this paper are shown to better preserve the self-similarity of fractal image data when compared to conventional methods that use the discrete cosine functional (DCF). Also, for standard images that possess local and approximate self-similarity fractal characteristics, although the measured SNR performance is lower, the proposed functional sets are preserve the fractal properties of the images. On the other hand, for standard images that do not possess these fractal properties, compression errors are apparent in blocks from both smooth and edge regions of the images. [ABSTRACT FROM AUTHOR]

A chaos neural network with externally controlled parameter is proposed and few applications to an association model and a combinatorial optimization problem are given. It is found that a relatively higher success the association model instead of the conventional model (burdened by chaotic wandering) because unacceptable tripping at a spurious state is a avoided and the traveling salesman problem can be solved using parameter control reminiscent of the annealing in the Boltzman machine. [ABSTRACT FROM AUTHOR]