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When we look at an object on a screen, even if we see a black and white binary image for each individual pixel, we experience that we can recognize the pixels as a pseudo halftone image when all pixels are viewed at once. In a previous paper, we showed aspects of vision that are performed hierarchically via the external world, retina, and brain according to a one-dimensional visual model and equivalence approximation method. The purpose of this paper is to clarify a strict, concrete analysis of evaluation methods for various types of modulated images according to a two-dimensional visual model and construct an objective evaluation method to be used for matching with subjective evaluations. This formal method is the basis of the previously published two-dimensional equivalence approximation method. We selected the pulse density four division image as the comparison standard and used a simple binary image, random dither image, least mean error image, and ordered dither image as modulated images to show specific values for the best numbers of approximation terms M0,N0 and obtain the measure of approximation with the reconstructed images to perform comparison inspections with subjective quality evaluations of these images. We evaluated the subjective quality by using the subjective mean ranking MOS of 15 assessors. From these results, we reconfirmed that the subjective quality of various modulated images can be objectively evaluated according to the measure of approximation. As a result, we clarified the strict, concrete analysis of evaluation methods for various types of modulated images according to the two-dimensional visual model of the formal method and constructed an objective evaluation method to be used for matching with subjective evaluations. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 87(10): 54–70, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.20120 [ABSTRACT FROM AUTHOR]

This paper considers waveform observation by the normal-type natural observation transform, and discusses the instantaneous relation between the waveform to be observed and the normal-type basic observed value sequence. The relation is similar to the uncertainty relation in the Fourier transform. Although the global uncertainty relation in the normal-type natural observation transform is clearly formulated already, the result is still insufficient for the theory of natural observation, where the instantaneous handling of the waveform has to be formulated. From such a viewpoint, the relation shown in this paper is significant, as a basic property in the instantaneous handling of the waveform by the theory of natural observation. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(8): 61–70, 2000 [ABSTRACT FROM AUTHOR]

The natural observation transform is a new formulation of the time waveform as a transform, when a waveform is observed in the short-term (instantaneous) region specified by the time-constant parameter at an arbitrary time. The basic observed value sequence not only includes the considered time, but also the information extracted from the waveform in the region specified by the time-constant parameter. Based on the above property of the natural observation transform, the object of the transform is not the input waveform itself, but the waveform appearing in the region specified by the time and the time-constant parameter. This paper notes this situation, and discusses the uncertainty that exists between the behavior of the waveform, which is the object of the normal natural observation transform in the whole time region, and the aspect in which the basic observation values are distributed in the sequence for the whole time region. Based on the result of investigation, the optimality criterion for the time-constant parameter is proposed using the equivalent time-constant, and a method of determining the optimal value is shown. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(8): 30–38, 2000 [ABSTRACT FROM AUTHOR]

An integral equation must be solved in order to analyze principal components for a set of general visual patterns. But in the practical case, we usually depend on numerical analysis by processing the data with a computer system. For the purpose of analyzing sets of similar patterns we propose a typical set called a “set of root visual patterns” because it enables us to derive an exact solution for the above equation. In this paper, we succeed in formulating the distribution of eigenvalues for general similar pattern sets from the exact solution. Further, we make sure that the formula is well applied to some practical cases, and it appears that these results will bring useful insights for improving the performance of pattern discrimination methods. © 2000 Scripta Technica, Syst Comp Jpn, 31(8): 49–58, 2000 [ABSTRACT FROM AUTHOR]

It is fundamentally important in waveform recognition to provide a method for systematic description of the changing nature of the given waveform at an arbitrary time. This paper presents a solution to this problem based on the natural observation method proposed by the author. After the definition of the instance is introduced, regulating the infinitesimal time interval at the time of interest, the instantaneous derived waveform series is derived from the input waveform by successive observations. A set of practical analysis methods has been studied theoretically for determining the mathematical structure of the instantaneous waveform for the observations. [ABSTRACT FROM AUTHOR]

When the linear prediction coefficients (LPC) are used as a feature parameter of speech, a problem in speech recognition is the variation of LPC due to the difference of the speaker and the effect of the preceding or succeeding utterances. Because of this variation, LPC is distributed in a certain region in the LPC space. This paper proposes a method which approximated the region of distribution by a linear manifold model described in [1], and recognizes the category permitting the variation of LPC. The method is applied to the vowel recognition of CV syllable, and its usefulness is verified experimentally. It is shown first by spectrum analysis experiment that the linear manifold model is useful in the approximation of the variation of the vowel spectrum due to the preceding consonant. Second, a recognition experiment is carried out based on the model, and it is shown that the recognition rate can be improved by a simple model of linear manifold which is suited to computation. [ABSTRACT FROM AUTHOR]

A lattice filter has several advantageous properties for adaptive applications. The gradual increase of the degree of estimation by the regular repetition of the adaptation module is particularly advantageous for hardware realization. In this paper, this adaptation module is called a lattice element and a method is proposed for the design of adaptive filters using such lattice elements. The efficiency of this method is demonstrated by the derivation of orthogonalizing and biorthogonalizing filters. The operation of these filters is tested by computer simulation and some problems arising at higher-order filters are pointed out. [ABSTRACT FROM AUTHOR]

Observation of the waveform is a fundamental problem common to the problem treating various waveforms such as the voice. This paper attempts to provide a rational answer to this problem. Originally, the theory has been developed with the assumption of a simple condition called the natural observation condition. As a result, a simple and complete observation system has been developed which consists of only one original function and two observation types. Traditionally, the concept of a running spectrum has been known for the observation problem of waveforms. In such a concept, the temporal transition of the short-term spectrum is studied. From this viewpoint, the present method is an extension of the concept and places a new theoretical foundation in a rational manner so that unclear points and self-contradictions of the previous theory are corrected. [ABSTRACT FROM AUTHOR]

This paper describes a method of non-stationary analysis based on the geometrical orthogonal projection with least-squares estimation for a linear model. In the past, local stationary analysis and adaptive methods which successively estimate the parameters have been used for this purpose. How- ever, in application to the nonstationarity case as in biomedical signals these methods have the disadvantage that it is difficult to see the physical significance of the parameters. In consideration of this, the present paper defines the backward prediction error space (Ens) consisting of the backward prediction error vector in each dimension and proposes to handle the nonstationarity by expanding the property into the orthogonal states in each dimension. The backward prediction error vectors constitute an orthogonal system in the least-squares estimation and the reflection coefficient is the parameter directly related to this system. The orthogonality can be interpreted in direct relation to the independence of physical functions. As a measure of the non-stationarily, the angle between the vectors is adopted in the BPES. When the parameters which were optimum in the stationary interval are applied to an arbitrary interval, the angle is an exact expression of the discrepancy due to the nonstationarity. By an example of analysis of biomedical signals it is verified that the angle is useful in evaluation of the nonstationarity, especially of that arising from the change of orders. Thus, it is anticipated that the deterministic non- stationary analysis by BPES will provide new information about biological systems. [ABSTRACT FROM AUTHOR]

In natural observation theory, input waveforms are observed using natural observation transforms. Especially in the case of the neighboring type, the effect of the uncertainty principle as it applies to a natural observation transform was clarified by using the equivalent time constant. This paper aims to characterize natural observation transforms of normal type in waveform observation from the point of view of the uncertainty principle. Besides the equivalent time constant, the average degree index is introduced to represent the uncertainty principle. It describes a relation between the equivalent time constant and the variance in the observation degree. This paper gives a new insight into the set of fundamental observed values of normal type from the point of view of observation resolution. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(7): 45–54, 1998 [ABSTRACT FROM AUTHOR]

The similarity method is an effective matching method for pattern recognition, especially for character recognition. However, for waveform recognition in the time domain, it cannot make enough allowance for possible deformations of waveforms and therefore does not show good performance. In this paper, we improve the allowance of the simple similarity by using the pluralizing method. To apply the pluralizing method, waveforms are expressed in the expansion formula with the natural observation theory of normal type. The effectiveness of pluralized simple similarity is verified by a simulation of speaker-independent vowel recognition. Another improvement considering speaker individuality is also mentioned. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(12): 1–9, 1997 [ABSTRACT FROM AUTHOR]

The natural observation theory was originally developed for continuous-time waveforms, and subsequently for discrete-time waveforms. The theories are classified as neighboring, equilibrium, and normal types. However, the derivation of the theory for discrete waveforms was somewhat mathematical and its physical principles for waveform observation were not discussed in sufficient detail. This paper aims to improve the derivation method thoroughly by making the physical principles clear. As a result, the theory of natural observation methods for discrete-time waveforms is formulated by minimizing problems with simple observation error criteria. The natural observation methods derived from the principle are equivalent to the previous ones, although the principles are different from each other. The principles make the physical meanings clear as a basis for developing the theory. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(8): 31–35, 1997 [ABSTRACT FROM AUTHOR]

Natural observation theory was developed in order to make reasonable observations of waveforms under natural observation conditions. This paper aims to clarify the observation characteristics of the theory of neighboring type from the viewpoint of an uncertainty principle. The new concept of equivalent time constant is introduced as a means for representing the uncertainty principle. The representation of the certainty principle in terms of the equivalent time constant has the advantage of representing the uncertainty principle of the Fourier transform more accurately. The uncertainty principle of the natural observation transform of neighboring type is derived by using the representation formula in which the equivalent time constant plays an essential role. This paper gives a detailed presentation of the uncertainty principle and provides a new insight to the set of fundamental observed values of the neighboring type in relation to the resolution of waveform observations. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(7): 11–19, 1997 [ABSTRACT FROM AUTHOR]

A theory of natural observation methods was originally formulated for two-complementary systems; neighboring type and equilibrium type. This paper introduces a new system, normal-type system, that is different from the forementioned two types. One characteristics feature of the normal-type natural observation method is its ability to reconstruct an original waveform from the sum of a finite number of observation values. The natural observation theory of a normal type evolves naturally under the condition that waveform and its power component can be expressed in the sum form. These meanings are discussed by comparing a frequency response of the normal-type natural observation transform with that of a conventional filter bank. Furthermore, a criterion for determining observation parameters I order to realize the natural observation of normal type under a given tolerance of error is described. It is believed that the proposed theory offers new insights into systematization of the natural observation theory. [ABSTRACT FROM AUTHOR]

This paper discusses the eigenvalue problem for the real symmetric matrix, especially the determination of the largest eigenvalue. The largest eigenvalue is the maximum extremum of the objective function called the Rayleigh quotient and can be determined by the steepest descent method. It is known, however, that the steepest descent method suffers from slow convergence because it converges linearly. Especially, when the largest and the nest largest eigenvalues have very close values, the convergence is particularly slow. This paper analyzes this situation and shows that the convergence can be accelerated by combining the steepest descent method with a technique called shaking. Finally, it is demonstrated by a numerical example that the convergence is accelerated drastically by the proposed technique. [ABSTRACT FROM AUTHOR]

The natural observation method provides a procedure to analyze the time-varying characteristics of the continuous-time waveform with mathematical rigor and can resolve the fundamental problem encountered in Fourier analysis method. In this paper, for discrete-time waveforms a discrete natural observation method is proposed which has characteristics similar to those for the continuous natural observation method. Similar to the continuous natural observation theory of normal type, the discrete natural observation theory is introduced by requiring that the waveform values and the power component can be expressed in terms of sum forms. The discrete natural observation method is complete by itself as a discrete type, and not only is it similar in nature to those of the continuous type but also can be shifted naturally to the continuous type as the sampling interval vanishes. [ABSTRACT FROM AUTHOR]

During the past few years, there been a series of paper published on the theory of the natural observation method. As one of the important application of this theory, the problems of acceptance and generation of a general waveform are discusses here. The case of polynomial waveforms and its corresponding theory was published previously. A great extension of the theory which general waveforms is presented here and its full picture is clarified. [ABSTRACT FROM AUTHOR]

Advances made in electronic computers allows the limit value of the sequence to be determined much more easily now than in the past. However, a problem still arises frequently in which it is difficult to determine the limit value with a high accuracy when a tremendous calculation is required in the determination of each term of the sequence. This paper proposes a theoretical method to estimate the limit value of the sequence with a high accuracy from the viewpoint of the recognition theory. By examining the gradual change of the sequence, the character inherent to the sequence is derived. By utilizing the character, the limit value can be estimated with a high accuracy directly from a small number of terms of the sequence. Lastly, the effectiveness of the proposed estimation method is demonstrated by simple examples. [ABSTRACT FROM AUTHOR]

The theory of natural observation has been proposed as a new method of analysis to replace the Fourier analysis method. It was systematized as a theory with two major types-the neighboring type and the equilibrium type. Especially, although the nucleus of the theory is of standard form, the description with regard to the starting point of the theory in the past has not always been plain and comprehensible. This paper is a radical improvement in this regard and was written to clarify the origin of the theoretical development. Although the previously published theories are not completely revised, this paper is considered significant from the viewpoint of clarification of the base of the theoretical development. [ABSTRACT FROM AUTHOR]

With regard to the theory of natural observation proposed as a new method of waveform analysis and although papers by the author have already been published over the last few years, this paper attempts a generalization based on the theory. As a result, the theory of natural observation can largely be divided into the neighboring type and the equilibrium type. Further, it was clarified that the previous theories belong to the neighboring type. In the treatment of acoustic vibration waveforms such as voice, the hitherto not discussed equilibrium type is desirable. Also, based on the forementioned theories, the general form of natural observation transformation is proposed anew as a substitute for Fourier transformation and, in particular, the standard form thought to be useful hereafter is shown concretely. [ABSTRACT FROM AUTHOR]

Often, in handwriting a character, a natural expansion or contraction occurs even if the writer intends to write the character in a specified size. This paper considers the expansion-contraction phenomenon which appears statistically in drawing a figure in general. A theoretical investigation is presented from the theory of probability, and the shape of the probability distribution governing the phenomenon is analyzed mathematically. The approach also gives an answer from the viewpoint of the theory of probability to the problem where the length is expanded or contracted unintentionally, even if a constant length is intended. This paper shows a typical mathematical approach in which the determination of the shape of the probability density function is reduced to the solution of the special functional equation. It is considered to be interesting also from the viewpoint of the theory. [ABSTRACT FROM AUTHOR]

A few years ago a fundamental theory on natural observation of waveforms was published as the foundation of a new effective method instead of Fourier analysis. In this papers a natural observation filter is proposed based on the theory. The filter has a typical property with regard to perfect reconstruction for a certain characteristics waveform group. The algebraic relation between the structure of the filter and the corresponding waveform group is theoretically clarified. The result of the present paper is expected to be applicable for recognition problems of various waveforms. [ABSTRACT FROM AUTHOR]

A previous paper presented a method of transforming observed images from figure to 2nd-order differential figure. In this paper, the invariance of the figure source equation for observational transformation is discussed, when the theory is formed with the figure source equation as its core. The redefined observational transformation is constructed using three types of mapping: intensive transformation, blur transformation, and isomorphic transformation. The sets of these transformations form groups, and by making use of algebraic properties, it is possible to categorize the images. Furthermore, it is shown that the commutative law for transformational groups can be derived by analyzing their structure. © 1997 Scripta Technica, Inc. Syst Comm Jpn, 28(8): 44–53, 1997 [ABSTRACT FROM AUTHOR]

Theoretical studies on Iijima's “Theory of Pattern Recognition,” which is known as a method of multiple similarity, have shown dearly that there are situations when it is difficult to determine the viewpoint and visual field, important parameters to introduce topological aspects into the pattern space, observing a figure itself. To cope with this problem, this paper proposes transforming the observed image from a figure f(r) to a second-order differential image p(r), called “figure source.” The aim is to reconstruct the theory in such a way as to enable the application of similarity evaluation methods as in the conventional case, without compromising the current theory, and all the necessary proofs are given, In this paper, the figure source equation as well as rules representing its properties are developed, and several related physical quantities arc redefined. [ABSTRACT FROM AUTHOR]

This paper provides a method of estimating a rotation center to analyze kinematically the movement of a rigid body moving periodically in a two-dimensional (2-D) space. The rotation center, which is derived from an axis point of the human jaw joint, is defined as a point which moves reciprocally in periodic movement. Accordingly, it is called the reciprocating point. Separating a path of the reciprocating point by its turning point, we can divide the path into two parts—the forward path and the backward path. Both paths are identical and hence it appears that any position in one path has its counterpart in the other path. We show that if we have a function corresponding to a pair of positions mentioned in the foregoing, we can estimate the reciprocating point. Then we derive an algorithm which approximates successively the function and the reciprocating point alternatively. This algorithm is proved to be effective for estimating an axis point of the jaw joint. [ABSTRACT FROM AUTHOR]

This paper describes a problem of estimating a kinematically characteristic point of a rigid body moving in a three-dimensional (3-D) space. We call this point the 1-D characteristic point and denote it by P1. The point P1 is characterized by its motion range which forms a curved line. Hence, if the rigid body moves periodically, we can specify P1 as a point which moves reciprocally. This paper proposes a method of estimating P1. By projecting the orbit of a point onto three planes orthogonal with each other, we reduce this estimation problem to that of solving a set of quadratic equations, and we then provide one of its solutions. In addition, we clarify how measurement errors of the motion propagate to an estimation of P1. [ABSTRACT FROM AUTHOR]

In the problem of measuring three-dimensional positions and motion of a rigid body, methods to determine the three-dimensional position from its optical projection data on a two-dimensional plane have been widely used. We have proposed a method using positional relations among the marked points and applied it to three-dimensional movement measurement of the human law. If the positions of three marked points on a rigid body are known, measuring these positions requires only one projection datum at each point to determine the three- dimensional position of the points, since the degree of freedom of a rigid body is six. A previous paper presented formulation of the problem in general form, its solution and theoretical analysis of stability of solution, as well as observation method. This paper analyzes the effect of error associated with measurement on estimating the position of marked points at implementation. Error propagation equations are derived effective for design of measuring instruments. The optimum measuring method is obtained from the viewpoint of error propagation using the result. [ABSTRACT FROM AUTHOR]

In the problem of estimating three-dimensional positions of a rigid body from projection data of marked points fixed set to it onto a two-dimensional plane. We propose a method using positional relations among the marked points. To estimate the positions of the marked points by optical measurement, multiple projection data are generally used at each point. In measuring multiple points attached on a rigid body, it is possible to estimate three-dimensional positions of the points from only a single projection datum at each point, if the position of each point on the rigid body is known. In this paper, the problem formulated ks of three marked points (the least necessary number to estimate the position of a rigid body). The solution is given by an iterative approximation. Furthermore, the relation between the measurement method and the convergence of the iterative approximation is analyzed. Observation is best obtained from tilts point of view. An instrument to measure three-dimensional movement of the human jaw is introduced. [ABSTRACT FROM AUTHOR]

Previously, in the processing of CT projection data, it was assumed that the measured values are independent at each point. Here it is shown that the actual data have a dependent property, which is called the redundancy of the projection data. It is shown that the redundancy is effective for the reduction of the noise sensitivity of the re- construction formula. This paper evaluates the effect qualitatively and experimentally in comparison with the convolution method, which is the mainstream of the present reconstruction procedure. The reconstruction formula (formula II), which was derived in a previous paper to reduce the noise sensitivity utilizing the redundancy, is compared with the convolution method. The analytical comparison with the mean-square error as the evaluation measure, as well as the visual comparison of the actually reconstructed examples, are performed. [ABSTRACT FROM AUTHOR]

This paper discusses the relations between Coulomb's gauge conditions, boundary conditions on the peripheral surface, symmetrical boundary surface and the surface between media of different materials. It is demonstrated that the gauge conditions are indispensable to describe fully the boundary conditions and the necessity and meanings of gauge conditions are discussed theoretically. [ABSTRACT FROM AUTHOR]