Fundamental nonlinear filters including M-filters and order statistic filters are formulated generally by the maximum a-posteriori (MAP) estimation and some filters are derived with the aid of the Bayes formula. This MAP-filters reduces to M-filters if a-priori probability distribution is uniform, while the rank filters are derived when a-priori bias exists in the MAP estimation. This MAP-filters are implemented with an analog electronic circuit and the log-likelihood is shown to be a Liapunov function for the dynamics of this circuit.

We propose a non-photorealistic rendering method for generating moire-picture-like color images from color photographs. The proposed method is performed in two steps. First, images with a staircasing effect are generated by a bilateral filter. Second, moire patterns are generated with an improved bilateral filter called an anti-bilateral filter. The characteristic of the anti-bilateral filter is to emphasize gradual boundaries.

In this paper, we propose a method for color error diffusion based on the Neugebauer model for color halftone printing. The Neugebauer model expresses an arbitrary color as a trilinear interpolation of basic colors. The proposed method quantizes the color of each pixel to a basic color which minimizes an accumulated quantization error, and the quantization error is diffused to the ratios of basic colors in subsequent pixels. Experimental results show that the proposed method outperforms conventional color error diffusion methods including separable method in terms of eye model-based mean squared error.

A sufficient condition is given for the waveform relaxation algorithm based on an asynchronous iteration to converge uniformly.

The performance guarantees of the Hopfield networks are given for two simple graph problems. A lower bound of the cutsize is evaluated for the maximum cut problem through the analysis of the eigenvalues at equilibrium states. The condition of constraint satisfaction and an upper bound of the cutsize are also given for the graph bipartitioning problem. In addition an effective numerical scheme is proposed to integrate the differential equations of the Hopfield networks by using backward Euler formula with one-step Gauss-Seidel relaxation. Theoretical estimates of the performance of the algorithm are verified experimentally.

A method of visualization of multimodal images by one monochromatic image is presented on the basis of the projection pursuit approach of the inverse process of the anisotropic diffusion which is a method of image restoration enhancing contrasts at edges. The extension of the projection from a linear one to nonlinear sigmoidal functions enhances the contrast further. The deterministic annealing technique is also incorporated into the optimization process for improving the contrast enhancement ability of the projection. An application of this method to a pair of MRI images of brains reveals its promising performance of superior visualization of tissues.

We present an iterative method for inverse transform of nonlinear image processing. Its convergence is verified for image enhancement by an online software. We also show its application to amplification of the opacity in foggy or underwater images.

We present a simple technique for enhancing multi-modal images. The unsharp masking (UM) is at first nonlinearized to prevent halos around large edges. This edge-preserving UM is then extended to cross-sharpening of multi-modal images where a component image is sharpened with the aid of more clear edges in another component image.

An asynchronous version is proposed for the waveform relaxation-Newton method. A sufficient condition is given for the proposed algorithm to converge.

We propose a method for downsizing line pictures to generate pixel line arts. In our method, topological properties such as connectivity of lines and segments are preserved by allowing slight distortion in the form of objects in input images. When input line pictures are painted with colors, the number of colors is preserved by our method.

A method is presented for selecting items asked for new users to input their preference rates on those items in recommendation systems based on the collaborative filtering. Optimal item selection is formulated by an integer programming problem and we solve it by using a kind of the Hopfield-network-like scheme for interior point methods.

A simple adaptive scheme is proposed for controlling the length of time-steps for numerical simulation of Hopfield's networks.

A semi-supervised classification method is presented. A robust unsupervised spectral mapping method is extended to a semi-supervised situation. Our proposed algorithm is derived by linearization of this nonlinear semi-supervised mapping method. Experiments using the proposed method for some public benchmark data reveal that our method outperforms a supervised algorithm using the linear discriminant analysis for the iris and wine data and is also more accurate than a semi-supervised algorithm of the logistic GRF for the ionosphere dataset.

This letter investigates the convergence property of first-available-task approach which is an asynchronous version of global-timestep Iterated Timing Analysis (ITA). This asynchronous iteration is proven to converge under the same condition as that for the convergence of the global-timestep ITA.

The multirate ITA for a linear circuit is proven to converge under a weaker condition on the capacitance matrix of the circuit or under a stronger condition on the conductance matrix than those for the global-timestep ITA to converge.

Sufficient conditions are given for the transient response of a class of MOS digital circuits composed of inverter-type logic gates, transfer gates and RC ladder networks to vary monotonically with the variations in the characteristics of circuit elements.

The alternative c-means algorithm has recently been presented by Wu and Yang for robust clustering of data. In this letter, we analyze the convergence of this algorithm by transforming it into an equivalent form with the Legendre transform. It is shown that this algorithm converges to a local optimal solution from any starting point.

Feedback of class memberships is incorporated into multimodal pattern classifiers and their unsupervised learning algorithm is presented. Classification decision at low levels is revised by the feedback information which also enables the reconstruction of patterns at low levels. The effects of the feedback are examined for the McGurk effect by using a simple model.

On the basis of a nonnegative and a monotonic property of the solution of a special class of differential equations, the transient responses of a class of MOS digital circuits are proven to have a monotone sensitivity with respect to some transistor parameters.

It is shown by the derivation of solution methods for an elementary optimization problem that the stochastic relaxation in image analysis, the Potts neural networks for combinatorial optimization and interior point methods for nonlinear programming have common formulation of their dynamics. This unification of these algorithms leads us to possibility for real time solution of these problems with common analog electronic circuits.