A new derivation is presented for the least squares solution of the design problem of 2-D FIR filters by minimizing the Frobenius norm of the difference between the matrices of the ideal and actual frequency responses sampled at the points of a frequency grid. The mathematical approach is based on the singular value decomposition of two complex transformation matrices. Interestingly, the design...

According to the principle of transference, a compact three-dimensional representation of a rigid body kinematics is obtained by substituting dual for real numbers. This representation has recently been applied to robotics where in addition to its compactness, it allows to constitute the Jacobian matrix explicitly from the product of the dual transformation matrices with no additional computati...

The use of transformation matrices is common practice in both computer graphics and image processing, with applications also in similar fields like computer vision. The mathematics behind transformation matrices is simple and relies on basic linear algebra properties. Nevertheless, applying transformation matrices to real-life problems can sometimes be tricky, as there are numerous pitfalls one...

Chromatic adaptation transforms generally rely on a variant of the von Kries transformation method to account for changes in the LMS cone signals that occur when changing from one illuminant to another. Von Kries adaptation—also often referred to as the coefficient rule method or the diagonal transformation method—adjusts the 3 color channels by independent scale factors. Since there generally ...

Abstract. The objective of this paper is to enhance the parallelism of the tile bidiagonal transformation using tree reduction on multicore architectures. First introduced by Ltaief et. al [LAPACK Working Note #247, 2011], the bidiagonal transformation using tile algorithms with a two-stage approach has shown very promising results on square matrices. However, for tall and skinny matrices, the ...