The three layer neural network (TLNN) is treated, where the nonlinearity of a neuron is of signum. First we propose an expression of the discriminant function of the TLNN, which is called a linear-homogeneous expression. This expression allows the differentiation in spite of the signum property of the neuron. Subsequently a learning algorithm is proposed based on the linear-homogeneous form. The algorithm is an error-correction procedure, which gives a mathematical foundation to heuristic error-correction learnings described in various literatures.

This paper reviews the capability of the three layer neural network (TLNN) with one output neuron. The input set is restricted to a finite subset S of En, and the TLNN implements a function F such as F : S I={1, -1}, i,e., F is a dichotomy of S. How many functions (dichotomies) can it compute by appropriately adjusting parameters in the TLNN? Brief historical review, some theorems on the subject obtained so far, and related topics are presented. Several open problems are also included.

In computer vision and digital image processing it is an important task to estimate an ellipse most fitting a set of points. An ellipse is specified by nonlinearly constrained parameters, which are difficult to be reflected in a criterion function. We show that iterative processes are useful to solve problems in such a case, and propose an iterative procedure to fit an ellipse to a set of points. In the procedure the nonlinear constraints on parameters are represented by a properly defined nonlinear operator. Experimental results on personal computer indicate the effectiveness of the procedure.

An individual identification system is developed. In this system, we unify profile curve identification and full face image identification to obtain more successful recognition rate. In profile cruve identification process, the P-type Fourier descriptor is made use of. In full face image identification process, mosaic density values are made use of. A combination of the two processes shows higher recognition rates than those obtained by each single process.

A learning procedure of a three layer neural network with limited structure, called a multi-valued neural network, is proposed. The three layer net has a single linear neuron in its output layer. All input weights of a number of hidden neurons are identical. The network takes k+1 distinct stable values, where k is the number of hidden neurons. The proposed learning procedure consists of two parts, Phase and Phase . The former is one for the learning of weights between the hidden and output layers, and the latter is one for those between the input and the hidden layers. The network is applied to classification of numerals, which shows the effectiveness of the proposed learning procedure.

This paper discusses psychophysical aspects of human sensory system through a differential-geometrical formulation. The discussions reveal relationships among three fundamental functions--the psychophysical, the DL and the JND functions, which characterize sensory system.