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Displaying 1-15 out of 15 total
A Coprime Blur Scheme for Data Security in Video Surveillance
Found in:
IEEE Transactions on Pattern Analysis and Machine Intelligence
By Christopher Thorpe, Feng Li, Zijia Li, Zhan Yu,David Saunders, Jingyi Yu
Issue Date:December 2013
pp. 3066-3072
This paper presents a novel coprime blurred pair (CBP) model to improve data security in camera surveillance. While most previous approaches have focused on completely encrypting the video stream, we introduce a spatial encryption scheme by strategically b...
A theory of Coprime Blurred Pairs
Found in:
Computer Vision, IEEE International Conference on
By Feng Li,Zijia Li,David Saunders, Jingyi Yu
Issue Date:November 2011
pp. 217-224
We present a new Coprime Blurred Pair (CBP) theory that may benefit a number of computer vision applications. A CBP is constructed by blurring the same latent image with two unknown kernels, where the two kernels are co-prime when mapped to bivariate polyn...
Numeric-symbolic exact rational linear system solver
Found in: Proceedings of the 36th international symposium on Symbolic and algebraic computation (ISSAC '11)
By B. David Saunders, Bryan S. Youse, David Harlan Wood
Issue Date:June 2011
pp. 305-312
An iterative refinement approach is taken to rational linear system solving. Such methods produce, for each entry of the solution vector, a rational approximation with denominator a power of 2. From this the correct rational entry can be reconstructed. Our...
Numerical techniques for computing the inertia of products of matrices of rational numbers
Found in: Proceedings of the 2007 international workshop on Symbolic-numeric computation (SNC '07)
By B. David Saunders, David Harlan Wood, John P. May
Issue Date:July 2007
pp. 125-132
Consider a rational matrix, particularly one whose entries have large numerators and denominators, but which is presented as a product of very sparse matrices with relatively small entries. We report on a numerical algorithm which computes the inertia of s...
A generalized class of polynomials that are hard to factor
Found in: Proceedings of the fourth ACM symposium on Symbolic and algebraic computation (SYMSAC '81)
By B. David Saunders, David R. Musser, Erich Kaltofen
Issue Date:August 1981
pp. 188-194
A class of univariate polynomials is defined which make the Berlekamp-Hensel factorization algorithm take an exponential amount of time. The class contains as subclasses the Swinnerton-Dyer polynomials discussed by Berlekamp and a subset of the cyclotomic ...
Fast computation of Smith forms of sparse matrices over local rings
Found in: Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation (ISSAC '12)
By Andy Novocin, B. David Saunders, Mark Giesbrecht, Mustafa Elsheikh
Issue Date:July 2012
pp. 146-153
We present algorithms to compute the Smith Normal Form of matrices over two families of local rings. The algorithms use the black-box model which is suitable for sparse and structured matrices. The algorithms depend on a number of tools, such as matrix ran...
Quadratic-time certificates in linear algebra
Found in: Proceedings of the 36th international symposium on Symbolic and algebraic computation (ISSAC '11)
By B. David Saunders, Erich L. Kaltofen, Michael Nehring
Issue Date:June 2011
pp. 171-176
We present certificates for the positive semidefiniteness of an n by n matrix A, whose entries are integers of binary length log
Large matrix, small rank
Found in: Proceedings of the 2009 international symposium on Symbolic and algebraic computation (ISSAC '09)
By B. David Saunders, Bryan S. Youse
Issue Date:July 2009
pp. 5-6
For the problem of computing the rank of a matrix we have a complexity result and a practical implementation, both of which apply best to the case of a matrix whose rank is substantially smaller than its order. First, matrix rank can be computed in essenti...
LinBox and future high performance computer algebra
Found in: Proceedings of the 2007 international workshop on Parallel symbolic computation (PASCO '07)
By B. David Saunders, Bruce W. Char, Bryan Youse
Issue Date:July 2007
pp. 102-103
Computer chip design is entering an era in which further increases in computational power will come by increased on-chip parallelism through multi-core architectures rather than by increasing clock speed. If high performance computer algebra tools are to b...
Efficient matrix rank computation with application to the study of strongly regular graphs
Found in: Proceedings of the 2007 international symposium on Symbolic and algebraic computation (ISSAC '07)
By David Saunders, John P. May, Zhendong Wan
Issue Date:July 2007
pp. 277-284
We present algorithms for computing the p-rank of integer matrices. They are designed to be particularly effective when p is a small prime, the rank is relatively low, and the matrix itself is large and dense and may exceed virtual memory space. Our motiva...
Smith normal form of dense integer matrices fast algorithms into practice
Found in: Proceedings of the 2004 international symposium on Symbolic and algebraic computation (ISSAC '04)
By David Saunders, Zhendong Wan
Issue Date:July 2004
pp. 274-281
We present a variation of the fast Monte Carlo algorithm of Eberly, Giesbrecht and Villard for computing the Smith form of an integer matrix. It is faster in practice, but with the same asymptotic complexity, and it also handles the singular case. Then we ...
Integer Smith form via the valence: experience with large sparse matrices from homology
Found in:
Proceedings of the 2000 international symposium on Symbolic and algebraic computation symbolic and algebraic computation (ISSAC '00)
By B. David Saunders, Gilles Villard, Jean-Guillaume Dumas
Issue Date:July 2000
pp. 95-105
We present a new algorithm to compute the Integer Smith normal form of large sparse matrices. We reduce the computation of the Smith form to independent, and therefore parallel, computations modulo powers of word-size primes. Consequently, the algorithm do...
On computing sparse shifts for univariate polynomials
Found in:
Proceedings of the international symposium on Symbolic and algebraic computation (ISSAC '94)
By B. David Saunders, Y. N. Lakshman
Issue Date:July 1994
pp. 108-113
Dixon's method for computing multivariate resultants by simultaneously eliminating many variables is reviewed. The method is found to be quite restrictive because often the Dixon matrix is singular, and the Dixon resultant vanished identically yielding no ...
APL microcomputer products (panel)
Found in:
Proceedings of the international conference on APL: APL and the future (APL '85)
By David Saunders, John C. Wilson, John D. Burger, John W. Myrna, Philip A. Van Cleave, Richard M. Smith, Richard S. Paulson
Issue Date:May 1985
pp. 456-459
This is a description of MEDCAT, a computer program which makes diagnoses, explains each step in its reasoning in response to questions, increases its knowledge and reasoning ability by conversing with expert physicians, and uses its logical and communicat...
An implementation of Kovacic's algorithm for solving second order linear homogeneous differential equations
Found in: Proceedings of the fourth ACM symposium on Symbolic and algebraic computation (SYMSAC '81)
By B. David Saunders
Issue Date:August 1981
pp. 105-108
Kovacic [3] has given an algorithm for the closed form solution of differential equations of the form ay" + by' + cy &equil; 0, where a, b, and c are rational functions with complex coefficients of the independent variable x. The algorithm provides a ...
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