We propose a method for the recovery of projective structure and motion by the factorization of the rank 1 matrix containing the images of all points in all views. In our method, the unknowns are the 3D motion and relative depths of the set of points, not their 3D positions. The coordinates of the points along the camera plane are given by their image positions in the first frame. The knowledge of the coordinates along the camera plane enables us to solve the SFM problem by iteratively factorizing the rank 1 matrix. This simplifies the decomposition compared with the SVD (Singular Value Decomposition). Experiments with both simulated and real data show that the method is efficient for the recovery of projective structure and motion.

In this paper, we briefly describe a fast Jacket transform based on simple matrices factorization. The proposed algorithm needs fewer and simpler computations than that of the existing methods, which are RJ's [2], Lee's [7] and Yang's algorithm [8]. Therefore, it can be easily applied to develop the efficient fast algorithm for signal processing and data communications.

Feature point tracking over a video sequence fails when the points go out of the field of view or behind other objects. In this paper, we extend such interrupted tracking by imposing the constraint that under the affine camera model all feature trajectories should be in an affine space. Our method consists of iterations for optimally extending the trajectories and for optimally estimating the affine space, coupled with an outlier removal process. Using real video images, we demonstrate that our method can restore a sufficient number of trajectories for detailed 3-D reconstruction.

Methods usually employed for carrying out division in logic are based on algebraic or Boolean techniques. Algebraic division is fast but results may be less than optimal. Boolean division will yield better results but generally it is much slower because a minimization step is required. In [4], Kim and Dietmeyer proposed a new type of division, called extended algebraic division, and described a heuristic algorithm for it. A feature is that, unlike Boolean division, it does not require a minimization step. The present paper is concerned with an efficient algorithm for exact extended algebraic division. The algorithm was developed within the SIS environment, a program for logic synthesis developed at U.C. Berkeley. Experiments on factoring PLA's demonstrate a significant improvement in quality with a reasonable increase in run time.

Techniques for human-motion recovery are applicable to a variety of areas, such as sports, dancing, virtual reality, and video-game production. The people who work in this area focus their attention on recovering information on the motion of individuals rather than groups of people. It is important to demonstrate the possibility of recovering descriptions of the 3-D motion in team sports, since such information is able to provide us with a variety of information on the relations among players. This paper presents a new experimental result on 3-D motion recovery from a team sport. The result was obtained by a non-rigid shape recovery technique based on images from uncalibrated cameras. The technique was applied to recovering the 3-D motion of the players in a mini-basketball game which was played in a gymnasium. Some attention is focused on the analysis of the players' motion. Satisfactory results were obtained.

The mathematical theory of bicomplex electromagnetic waves in two-dimensional scattering and diffraction problems is developed. The Vekua's integral expression for the two-dimensional fields valid only in the closed source-free region is generalized into the radiating field. The boundary-value problems for scattering and diffraction are formulated in the bicomplex space. The complex function of a single variable, which obeys the Cauchy-Riemann relations and thus expresses low-frequency aspects of the near field at a wedge of the scatterer, is connected with the radiating field by an integral operator having a suitable kernel. The behaviors of this complex function in the whole space are discussed together with those of the far-zone field or the amplitude of angular spectrum. The Hilbert's factorization scheme is used to find out a linear transformation from the far-zone field to the bicomplex-valued function of a single variable. This transformation is shown to be unique. The new integral expression for the field scattered by a thin metallic strip is also obtained.

The reconstruction of motion and structure from multiple images is fundamental and important problem in computer vision. This paper highlights the recovery of the camera motion and the object shape under some camera projection model from feature correspondences especially the epipolar geometry and the factorization method for mainly used projection models.

This paper describes a factorization-based algorithm that reconstructs 3D object structure as well as motion from a set of multiple uncalibrated perspective images. The factorization method introduced by Tomasi-Kanade is believed to be applicable under the assumption of linear approximations of imaging system. In this paper we describe that the method can be extended to the case of truly perspective images if projective depths are recovered. We established this fact by interpreting their purely mathematical theory in terms of the projective geometry of the imaging system and thereby, giving physical meanings to the parameters involved. We also provide a method to recover them using the fundamental matrices and epipoles estimated from pairs of images in the image set. Our method is applicable for general cases where the images are not taken by a single moving camera but by different cameras having individual camera parameters. The experimental results clearly demonstrates the feasibility of the proposed method.

In this paper, an algorithm for Boolean factoring is presented. The algorithm is based on a technique of rectangle covering. A distinctive feature of the algorithm is that no minimization step is required to achieve Boolean factoring. The method for computing Boolean products rests on the concepts of super-product, extended kernel and extended co-kernel-cube matrix. Results of a comparison with the algorithms GOOD_FACTOR and QUICK_FACTOR implemented in SIS are presented. SIS is a program for logic synthesis developed at the University of Berkeley. All performed tests indicate that the proposed algorithm realizes a good tradeoff between factoring quality and computing time.

It is shown from the Hilberts theory that if the real function Π(θ) has no zeros over the interval [0, 2π], it can be factorized into a product of the factor π+(θ) and its complex conjugate π-(θ)(=). This factorization is tested to decompose a real far-zone field pattern having zeros. To this end, the factorized factors are described in terms of bicomplex mathematics. In our bicomplex mathematics, the temporal imaginary unit "j" is newly defined to distinguish from the spatial imaginary unit i, both of which satisfy i2=-1 and j2=-1.

We describe our implementation of the Hypercube variation of the Multiple Polynomial Quadratic Sieve (HMPQS) integer factorization algorithm on a Parsytec GC computer with 128 processors. HMPQS is a variation on the Quadratic Sieve (QS) algorithm which inspects many quadratic polynomials looking for quadratic residues with small prime factors. The polynomials are organized as the nodes of an n-dimensional cube. We report on the performance of our implementations on factoring several large numbers for the Cunningham Project.

A factorization method for a string polynomial called the constant method is proposed. This uses essentially three operations; classification of monomials, gcrd (greatest common right divisor), and lcrm (least common rigth multiple). This method can be applied to string polynomials except that their constants cannot be reduced to zeros by the linear transformation of variables. To factorize such excluded string polynomials, the naive method is also presented, which computes simply coefficients of two factors of a given polynomial, but is not efficient.

A new method to obtain the coefficients of Daubechies's scaling functions is given, in which it is not necessary to find the complex zeros of polynomials. Consequently it becomes easier to obtain the coefficients of arbitrary order from 2 to 40 with high accuracy.

Two methods of the second step of the elliptic curve method for factoring are known. One is the standard method that is similar to the second step of the p-1 method, and the other is the Brent method that is based on the "birthday paradox." In this paper, we propose a revised standard method and a revised Brent method. On an average, the revised standard method is the most efficient, the standard method is the second efficient, the revised Brent method is the third and the Brent method is the fourth. If the largest prime factor on the order of an elliptic curve is congruent to 1 modulo 3, then the revised Brent method becomes more efficient than the standard method. By applying these methods to unsolved problems in the Cunningham project, we found 18 new prime factors. The largest prime factor among them was 43-digits.

A new application of the factorization method is reported for 3-D shape reconstruction from endoscope image sequences. The feasibility of the method is verified with some theoretical considerations and results of extensive experiments. This method was developed by Tomasi and Kanade, and improved by Poelman and Kanade, with the aim of achieving accurate shape reconstruction by using a large number of points and images, and robustly applying well-understood matrix computations. However, the latter stage of the method, called normalization, is not as easily understandable as the use of singular value decomposition in the first stage. In fact, as shown in this report, many choices are possible for this normalization and a variety of results have been obtained depending on the choice. This method is easy to understand, easy to implement, and provides sufficient accuracy when the approximation used for the optical system is reasonable. However, the details of the theoretical basis require further study.

This paper discusses the fixed-point smoothing and filtering problems given lumped covariance function of a scalar signal process observed with additive white Gaussian noise. The recursive Wiener smoother and filter are derived by applying an invariant imbedding method to the Volterra-type integral equation of the second kind in linear least-squares estimation problems. The resultant estimators in Theorem 2 require the information of the crossvariance function of the state variable with the observed value, the system matrix, the observation vector, the variance of the observation noise and the observed value. Here, it is assumed that the signal process is generated by the state-space model. The spectral factorization problem is also considered in Sects. 1 and 2.

Many methods, based on the concept of key-lock-pair have been proposed for access control in computer protection systems. However, the proposed methods still either lack of dynamic ability or need quite a lot of computation in performing requests of deleting users/files, inserting users/files, or updating access rights of users to files. In this paper we propose a two-key-lock-pair access control method that is based on the unique factorization theorem and a time stamp mechanism. Our method is dynamic and needs a minimum amount of computation in the sense that it only updates at most one key/lock for each access request, which has not been achieved before.

This paper proposes RSA-type cryptosystems over elliptic curves En(O, b) and En(a, O),where En(a, b): y2 x3+ax+b (mod n),and n is a product of from-free primes p and q. Although RSA cryptosystem is not secure against a low exponent attack, RSA-type cryptosystems over elliptic curves seems secure against a low multiplier attack. There are the KMOV cryptosystem and the Demytko cryptosystem that were previously proposed as RSA-type cryptosystems over elliptic curves. The KMOV cryptosystem uses form-restricted primes as p q 2(mod 3)or p q 3(mod 4), and encrypts/decrypts a 2log n-bit message over varied elliptic curves by operating values of x and y coordinates. The Demytko cryptosystem, which is an extension of the KMOV cryptosystem, uses form-free primes, and encrypts/decrypts a log n-bit message over fixed elliptic curves by operating only a value of x coordinates. Our cryptosystems, which are other extensions fo the KMOV cryptosystem, encrypt/decrypt a 2log n-bit message over varied elliptic curves by operating values of x and y coordinates. The Demytko cryptosystem and our cryptosystems have higher security than the KMOV cryptosystem because from-free primes hide two-bit information about prime factors. The encryption/decryption speed in one of our cryptosystems is about 1.25 times faster than that in the Demytko cryptosystem.

This paper tends to analyze the trends of the research in logic synthesis. The first part is devoted to an expertise of the efficiency of factorization methods developed during the last decade and to the proposal of dedicated methods for complex logic blocks. The second part shows the importance of Binary Decision Diagrams as representation of Boolean functions. Their use in the technology mapping phase of multiplexor-based FPGAs in an industrial tool is taken as illustration.

Low-sensitivity digital filters are required for accurate signal processing. Among many low-sensitivity digital filters, a method using complex allpass circuits is well-known. In this paper, a new synthesis of complex allpass circuits is proposed. The proposed synthesis can be realized more easily either only in the z-domain or in the s-domain than conventional methods. The key concept for the synthesis is based on the factorization of lossless scattering matrices. Complex allpass circuits are interpreted as lossless digital two-port circuits, whose scattering matrices are factored. Furthermore, in the cases of Butterworth, Chebyshev and inverse Chebyshev responses, the explicit formulae for multiplier coefficients are derived, which enable us to synthesize the objective circuits directly from the specifications in the s-domain. Finally design examples verify the effectiveness of the proposed method.