On the orders of transformation matrices (mod n) and two types of generalized Arnold transformation matrices

With the rapid development of information technology, more and more private and public information is distributed through the Internet. The problem of how to distribute information securely through the Internet has arisen. Recently, a lot of technologies have been developed to ensure the security of information. Information hiding[1] is one of these, ranging from digital watermarking, digital fingerprint to steganography. The scrambling transformation is one of the technologies of image infor…     

Decomposition of transformation matrices for robot vision

The relationship between the three-dimensional coordinates of a point and the corresponding two-dimensional coordinates of its image, as seen by a camera, can be expressed in terms of a 3 by 4 matrix using the homogeneous coordinate system. This matrix is known more generally as the transformation matrix and it is well known that such a matrix can be determined experimentally by measuring the image coordinates of six or more points in space, whose three-dimensional coordinates are known.Such a transformation matrix can be derived analytically from knowledge of the camera position, orientation, focal length and scaling and translation parameters in the image plane. However, the inverse problem of computing the camera location and orientation from the transformation matrix involves solution of simultaneous nonlinear equations in several variables and is considered difficult.In this paper we present a new and simple analytical technique that accomplishes this inversion rather easily. This technique is quite powerful and has applications to a wide variety of problems in Computer Vision for both static and dynamic scenes. The technique has been implemented as a C program running under Unix and works well on real data.     

On the orders of transformation matrices (mod n) and two types of generalized arnold transformation matrices

In this paper, we analyze the structure of the orders of matrices (mod n), and present the relation between the orders of matrices over finite fields and their Jordan normal forms. Then we generalize 2-dimensional Arnold transformation matrix to two types of n-dimensional Arnold transformation matrices: A-type Arnold transformation matrix and B-type transformation matrix, and analyze their orders and other properties based on our earlier results about the orders of matrices.     

A singular loop transformation framework based on non-singular matrices

In this paper, we discuss a loop transformation framework that is based on integer non-singular matrices. The transformations included in this framework are called Λ-transformations and include permutation, skewing and reversal, as well as a transformation calledloop scaling. This framework is more general than existing ones; however, it is also more difficult to generate code in our framework. This paper shows how integer lattice theory can be used to generate efficient code. An added advantage of our framework over existing ones is that there is a simple completion algorithm which, given a partial transformation matrix, produces a full transformation matrix that satisfies all dependences. This completion procedure has applications in parallelization and in the generation of code for NUMA machines. This work was supported by the Cornell Theory Center, NSF Presidential Young Investigator award #CCR-8958543. by NSF Grant #CCR-9008526, and by a grant from the Hewlett-Packard Company.     

Minimal realization of transfer function matrices via oneorthogonal transformation

The minimal realization of a given arbitrary transfer function matrix G(s) is obtained by applying one orthogonal similarity transformation to the controllable realization of G( s). The similarity transformation is derived by computing the QR or the singular value decomposition of a matrix constructed from the coefficients of G(s). It is emphasized that the procedure has not been proved to be numerically stable. Moreover, the matrix to be decomposed is larger than the matrices factorized during the step-by-step procedures given     

Loop closure detection using CNN words

Intelligent Service Robotics - Loop closure detection (LCD) is crucial for the simultaneous localization and mapping system of an autonomous robot. Image features from a convolution neural network...     

Geometric operations using sparse interpolation matrices

Based on the computation of a superset of the implicit support, implicitization of a parametrically given hypersurface is reduced to computing the nullspace of a numeric matrix. Our approach predicts the Newton polytope of the implicit equation by exploiting the sparseness of the given parametric equations and of the implicit polynomial, without being affected by the presence of any base points. In this work, we study how this interpolation matrix expresses the implicit equation as a matrix determinant, which is useful for certain operations such as ray shooting, and how it can be used to reduce some key geometric predicates on the hypersurface, namely membership and sidedness for given query points, to simple numerical operations on the matrix, without need to develop the implicit equation. We illustrate our results with examples based on our Maple implementation.     

Some LP algorithms using orthogonal matrices

The aim of this paper is the exploitation of the properties of orthogonal matrices in the development of a new theoretical approach and in the implementation of iterative routines for solving linear programming problems.     

Secondary state assignment using connected matrices

This paper deals with the problem of state assignment of a sequential machine so as to achieve reduced dependent assignment of each of the internal variables of the machine. Suitable rearrangement of the flow table in a form referred to as the connected matrix arrangement has been proposed and it has been shown that such an arrangement gives an easy visualization of the existence of reduced dependent assignments. It has been further shown that the connected matrix arrangement enables one to have directly the valid partitions with substitution property (SP) (Stearns and Hartmanis 1966) that can give rise to reduced dependent assignment and thus makes the conventional laborious process of generating all the partitions with SP on the set of states of the machine completely unnecessary.     

Loop summarization using state and transition invariants

This paper presents algorithms for program abstraction based on the principle of loop summarization, which, unlike traditional program approximation approaches (e.g., abstract interpretation), does not employ iterative fixpoint computation, but instead computes symbolic abstract transformers with respect to a set of abstract domains. This allows for an effective exploitation of problem-specific abstract domains for summarization and, as a consequence, the precision of an abstract model may be tailored to specific verification needs. Furthermore, we extend the concept of loop summarization to incorporate relational abstract domains to enable the discovery of transition invariants, which are subsequently used to prove termination of programs. Well-foundedness of the discovered transition invariants is ensured either by a separate decision procedure call or by using abstract domains that are well-founded by construction. We experimentally evaluate several abstract domains related to memory operations to detect buffer overflow problems. Also, our light-weight termination analysis is demonstrated to be effective on a wide range of benchmarks, including OS device drivers.     

Division-free computation of subresultants using Bezout matrices

We present an algorithm to compute the subresultant sequence of two polynomials that completely avoids division in the ground domain, generalizing an algorithm given by Abdeljaoued et al. [J. Abdeljaoued, G. Diaz-Toca, and L. Gonzalez-Vega, Minors of Bezout matrices, subresultants and the parameterization of the degree of the polynomial greatest common divisor, Int. J. Comput. Math. 81 (2004), pp. 1223–1238]. We evaluate determinants of slightly manipulated Bezout matrices using the algorithm of Berkowitz. Although the algorithm gives worse complexity bounds than pseudo-division approaches, our experiments show that our approach is superior for input polynomials with moderate degrees if the ground domain contains indeterminates.     

MATNORM: Calculating NORM using composition matrices

This paper discusses the implementation of an entirely new set of formulas to calculate the CIPW norm. MATNORM does not involve any sophisticated programming skill and has been developed using Microsoft Excel spreadsheet formulas. These formulas are easy to understand and a mere knowledge of the if-then-else construct in MS-Excel is sufficient to implement the whole calculation scheme outlined below. The sequence of calculation used here differs from that of the standard CIPW norm calculation, but the results are very similar. The use of MS-Excel macro programming and other high-level programming languages has been deliberately avoided for simplicity.     

On the transformation of symmetric sparse matrices to the triple diagonal form

The problem of minimizing the number of zero elements that become non-zero during the computation when a sparse symmetric matrix is reduced to a triple diagonal form, either by Givens' or Householder's method, is discussed. Algorithms for minimizing the growth of such non-zero elements are given.     

Column and diagonal‐reduction of polynomial matrices by orthogonal transformation

Many of the applications of polynomial matrices in real world systems require column‐ or diagonally‐reduced polynomial matrices. If a given polynomial matrix is not column‐ or diagonally‐reduced, Callier or Wolowich algorithms, which use unimodular transformations, can be applied for column‐ or diagonal‐reduction, respectively, as a pre‐processing step in the applications. However, Callier and Wolowich algorithms may be unstable, from a numerical viewpoint, because they use elementary column and row operations. The purpose of this paper is to present sufficient conditions for existence of a constant orthogonal transformation of the given polynomial matrix so that it becomes column‐ or diagonally‐reduced. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Resource reservation with mobile hosts using fuzzy matrices

To provide high QoS (Quality of Service) with mobile hosts, service managers must first make resource reservations at subsequent locations to which mobile hosts may visit during the lifetime of the connection. In this paper, we propose a mechanism based on Fuzzy Matrices with movement directions and mobility specifications to predict the locations that a mobile host will visit. Through the fuzzification, defuzzification, and inference procedures, a resource reservation scheduling was performed. Our study indicates that the proposed strategy may significantly reduce the mean inefficiency (miss rate) and operating cost at 27 and 32%, respectively, compared with other approaches at the expense of a small blocking rate.