Jorge Sastre

Face recognition using HOG-EBGM

This paper presents a new face recognition algorithm based on the well-known EBGM which replaces Gabor features by HOG descriptors. The recognition results show a better performance of our approach compared to other face recognition approaches using public available databases. This better performance is explained by the properties of HOG descriptors which are more robust to changes in illumination, rotation and small displacements, and to the higher accuracy of the face graphs obtained compared to classical Gabor-EBGM ones.

Precise eye localization using HOG descriptors

In this paper, we present a novel algorithm for precise eye detection. First, a couple of AdaBoost classifiers trained with Haar-like features are used to preselect possible eye locations. Then, a Support Vector Machine machine that uses Histograms of Oriented Gradients descriptors is used to obtain the best pair of eyes among all possible combinations of preselected eyes. Finally, we compare the eye detection results with three state-of-the-art works and a commercial software. The results show that our algorithm achieves the highest accuracy on the FERET and FRGCv1 databases, which is the most complete comparative presented so far.

Efficient orthogonal matrix polynomial based method for computing matrix exponential

The matrix exponential plays a fundamental role in the solution of differential systems which appear in different science fields. This paper presents an efficient method for computing matrix exponentials based on Hermite matrix polynomial expansions. Hermite series truncation together with scaling and squaring and the application of floating point arithmetic bounds to the intermediate results provide excellent accuracy results compared with the best acknowledged computational methods. A backward-error analysis of the approximation in exact arithmetic is given. This analysis is used to provide a theoretical estimate for the optimal scaling of matrices. Two algorithms based on this method have been implemented as MATLAB functions. They have been compared with MATLAB functions funm and expm obtaining greater accuracy in the majority of tests. A careful cost comparison analysis with expm is provided showing that the proposed algorithms have lower maximum cost for some matrix norm intervals. Numerical tests show that the application of floating point arithmetic bounds to the intermediate results may reduce considerably computational costs, reaching in numerical tests relative higher average costs than expm of only 4.43% for the final Hermite selected order, and obtaining better accuracy results in the 77.36% of the test matrices. The MATLAB implementation of the best Hermite matrix polynomial based algorithm has been made available online.

The growth of laguerre matrix polynomials on bounded intervals

Abstract Let A be a matrix in C r×r such that Re (z) > −1 2 for all the eigenvalues of A and let {π n ( A , 1 2 ) (x)} be the normalized sequence of Laguerre matrix polynomials associated with A. In this paper, it is proved that π n (A, 1 2 ) (x) = O(n α(A)/2 ln r−1 (n)) and π n+1 (A, 1 2 ) (x) − π n (A, 1 2 ) (x) = O(n (α(A)−1)/2 ln r−1 (n)) uniformly on bounded intervals, where α(A) = max{Re(z); z eigenvalue of A}.

Accurate matrix exponential computation to solve coupled differential models in engineering

The matrix exponential plays a fundamental role in linear systems arising in engineering, mechanics and control theory. This work presents a new scaling-squaring algorithm for matrix exponential computation. It uses forward and backward error analysis with improved bounds for normal and nonnormal matrices. Applied to the Taylor method, it has presented a lower or similar cost compared to the state-of-the-art Pade algorithms with better accuracy results in the majority of test matrices, avoiding Pades denominator condition problems.

Computing matrix functions arising in engineering models with orthogonal matrix polynomials

Trigonometric matrix functions play a fundamental role in the solution of second order differential equations. Hermite series truncation together with Paterson-Stockmeyer method and the double angle formula technique allow efficient computation of the matrix cosine. A careful error bound analysis of the Hermite approximation is given and a theoretical estimate for the optimal value of its parameters is obtained. Based on the ideas above, an efficient and highly-accurate Hermite algorithm is presented. A MATLAB implementation of this algorithm has also been developed and made available online. This implementation has been compared to other efficient state-ofthe-art implementations on a large class of matrices for different dimensions, obtaining higher accuracy and lower computational costs in the majority of cases.

Computing matrix functions solving coupled differential models

In this paper a modification of the method proposed in [E. Defez, L. Jodar, Some applications of Hermite matrix polynomials series expansions, Journal of Computational and Applied Mathematics 99 (1998) 105-117] for computing matrix sine and cosine based on Hermite matrix polynomial expansions is presented. An algorithm and illustrative examples demonstrate the performance of the new proposed method.

On the asymptotics of Laguerre matrix polynomials for large x and n

Abstract This work deals with the asymptotics of normalized Laguerre matrix polynomials of a complex matrix parameter for n / x = o ( 1 ) and x / n = O ( 1 ) as n → ∞ .

Asymptotics of the modified Bessel and the incomplete gamma matrix functions

In this paper, an asymptotic expression of the incomplete gamma matrix function and integral expressions of Bessel matrix functions are given. Results are applied to study the asymptotic behavior of the modified Bessel function.

High performance computing of the matrix exponential

This work presents a new algorithm for matrix exponential computation that significantly simplifies a Taylor scaling and squaring algorithm presented previously by the authors, preserving accuracy. A Matlab version of the new simplified algorithm has been compared with the original algorithm, providing similar results in terms of accuracy, but reducing processing time. It has also been compared with two state-of-the-art implementations based on Pade approximations, one commercial and the other implemented in Matlab, getting better accuracy and processing time results in the majority of cases.