application of the karhunen loeve procedure for the characterization of human faces the use of natural symmetries mirror images in a well defined family of patterns human faces is discussed within the framework of the karhunen loeve expansion this results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix without increasing the complexity of the calculation the resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average

fusion of color local spatial and global frequency information for face recognition this paper presents a novel face recognition method by means of fusing color local spatial and global frequency information specifically the proposed method fuses the multiple features derived from a hybrid color space the gabor image representation the local binary patterns lbp and the discrete cosine transform dct of the input image the novelty of this paper is threefold first a hybrid color space the rc rq color space is constructed by combining the r component image of the rgb color space and the chromatic component images c r and q of the yc bc r and yiq color spaces respectively the rc rq hybrid color space whose component images possess complementary characteristics enhances the discriminating power for face recognition second three effective image encoding methods are proposed for the component images in the rc rq hybrid color space to extract features i a patch based gabor image representation for the r component image ii a multi resolution lbp feature fusion scheme for the c r component image and iii a component based dct multiple face encoding for the q component image finally at the decision level the similarity matrices generated using the three component images in the rc rq hybrid color space are fused using a weighted sum rule experiments on the face recognition grand challenge frgc version 2 experiment 4 show that the proposed method improves face recognition performance significantly in particular the proposed method achieves the face verification rate roc iii curve of 92 43 at the false accept rate of 0 1 compared to the frgc baseline performance of 11 86 face verification rate at the same false accept rate

kernels regularization and differential equations many common machine learning methods such as support vector machines or gaussian process inference make use of positive definite kernels reproducing kernel hilbert spaces gaussian processes and regularization operators in this work these objects are presented in a general unifying framework and interrelations are highlighted with this in mind we then show how linear stochastic differential equation models can be incorporated naturally into the kernel framework and vice versa many kernel machines can be interpreted in terms of differential equations we focus especially on ordinary differential equations also known as dynamical systems and it is shown that standard kernel inference algorithms are equivalent to kalman filter methods based on such models in order not to cloud qualitative insights with heavy mathematical machinery we restrict ourselves to finite domains implying that differential equations are treated via their corresponding finite difference equations

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

face recognition using the discrete cosine transform an accurate and robust face recognition system was developed and tested this system exploits the feature extraction capabilities of the discrete cosine transform dct and invokes certain normalization techniques that increase its robustness to variations in facial geometry and illumination the method was tested on a variety of available face databases including one collected at mcgill university the system was shown to perform very well when compared to other approaches

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

analytical inversion of symmetric tridiagonal matrices in this paper we present an analytical formula for the inversion of symmetrical tridiagonal matrices the result is of relevance to the solution of a variety of problems in mathematics and physics as an example the formula is used to derive an exact analytical solution for the one dimensional discrete poisson equation with dirichlet boundary conditions

fusion of local normalization and gabor entropy weighted features for face identification face recognition is one of the most extensively studied topics in image analysis because of its wide range of possible applications such as in surveillance access control content based video search human computer interaction electronic advertisement and more face identification is a one to n matching problem where a captured face is compared to n samples in a database in this work we propose two new methods for face identification the first one combines entropy like weighted gabor features with the local normalization of gabor features the second fuses the entropy like weighted gabor features at the score level with the local binary pattern lbp applied to the magnitude lgbp and phase lgxp components of the gabor features we used the feret ar and frgc 2 0 databases to test and compare our results with those previously published results on these databases show significant improvement relative to previously published results reaching the best performance on the feret and ar databases our methods also showed significant robustness to slight pose variations we tested the proposed methods assuming noisy eye detection to check their robustness to inexact face alignment results show that the proposed methods are robust to errors of up to 3 pixels in eye detection highlightswe propose an entropy weighted strategy over selected gabor features we fuse local normalization with gabor features to improve face identification fusion of different features improve face identification relative to cases with no fusion our results are compared advantageously on several international face databases we tested our methods with variable illumination gesticulation pose and occlusion

bounds for entries of the inverse matrix of a tridiagonal matrix inequalities for the moduli of entries of the inverse matrix of a tridiagonal matrix are obtained these results are applicable to a relatively large family of matrices which occur in many branches of numerical analysis applied mathematics and engineering

a divide and conquer method for unitary and orthogonal eigenproblems leth n xn be a unitary upper hessenberg matrix whose eigenvalues and possibly also eigenvectors are to be determined we describe how this eigenproblem can be solved by a divide and conquer method in which the matrixh is split into two smaller unitary upper hessenberg matricesh 1 andh 2 by a rank one modification ofh the eigenproblems forh 1 andh 2 can be solved independently and the solutions of these smaller eigenproblems define a rational function whose zeros on the unit circle are the eigenvalues ofh the eigenvector ofh can be determined from the eigenvalues ofh and the eigenvectors ofh 1 andh 2 the outlined splitting of unitary upper hessenberg matrices into smaller such matrices is carried out recursively this gives rise to a divide and conquer method that is suitable for implementation on a parallel computer whenh n xn is orthogonal the divide and conquer scheme simplifies and is described separately our interest in the orthogonal eigenproblem stems from applications in signal processing numerical examples for the orthogonal eigenproblem conclude the paper

inversion of tridiagonal matrices this paper presents a simple algorithm for inverting nonsymmetric tridiagonal matrices that leads immediately to closed forms when they exist ukita s theorem is extended to characterize the class of matrices that have tridiagonal inverses

analytical inversion of general periodic tridiagonal matrices in this paper we present an analytical forms for the inversion of general periodic tridiagonal matrices and provide some very simple analytical forms which immediately lead to closed formulae for some special cases such as symmetric or perturbed toeplitz for both periodic and non periodic tridiagonal matrices an efficient computational algorithm for finding the inverse of any general periodic tridiagonal matrices from the analytical form is given it is suited for implementation using computer algebra systems such as maple matlab macsyma and mathematica an example is also given to illustrate the algorithm

hierarchical ensemble of global and local classifiers for face recognition in the literature of psychophysics and neurophysiology many studies have shown that both global and local features are crucial for face representation and recognition this paper proposes a novel face recognition method which exploits both global and local discriminative features in this method global features are extracted from the whole face images by keeping the low frequency coefficients of fourier transform which we believe encodes the holistic facial information such as facial contour for local feature extraction gabor wavelets are exploited considering their biological relevance after that fisher s linear discriminant fld is separately applied to the global fourier features and each local patch of gabor features thus multiple fld classifiers are obtained each embodying different facial evidences for face recognition finally all these classifiers are combined to form a hierarchical ensemble classifier we evaluate the proposed method using two large scale face databases feret and frgc version 2 0 experiments show that the results of our method are impressively better than the best known results with the same evaluation protocol

free circle actions with contractible orbits on symplectic manifolds we prove that closed symplectic four manifolds do not admit any smooth free circle actions with contractible orbits without assuming that the actions preserve the symplectic forms in higher dimensions such actions by symplectomorphisms do exist and we give explicit examples based on the constructions of fgm

symplectic and poisson geometry on b manifolds abstract let m 2 n be a poisson manifold with poisson bivector field we say that m is b poisson if the map n m 2 n t m intersects the zero section transversally on a codimension one submanifold z m this paper will be a systematic investigation of such poisson manifolds in particular we will study in detail the structure of m in the neighborhood of z and using symplectic techniques define topological invariants which determine the structure up to isomorphism we also investigate a variant of de rham theory for these manifolds and its connection with poisson cohomology

non symbolic algorithms for the inversion of tridiagonal matrices a representation for the entries of the inverse of general tridiagonal matrices is based on the determinants of their principal submatrices it enables us to introduce through the linear recurrence relations satisfied by such determinants a simple algorithm for the entries of the inverse of any tridiagonal nonsingular matrix reduced as well as unreduced the numerical approach is preserved here without invoking the symbolic computation for tridiagonal diagonally dominant matrices a scaling transformation on the recurrences allows us to give another algorithm to avoid overflow and underflow

a fast and reliable numerical solver for general bordered k tridiagonal matrix linear equations to improve on the shortcomings observed in symbolic algorithms introduced recently for related matrices a reliable numerical solver is proposed for computing the solution of the matrix linear equation a x b the n n matrix coefficient a is a nonsingular bordered k tridiagonal matrix the particular structure of a is exploited through an incomplete or full givens reduction depending on the singularity of its associated k tridiagonal matrix then adapted back substitution and sherman morrison s formula can be applied specially the inverse of the matrix a is computed moreover for a wide range of matrices a the solution of the vector linear equation a x b can be computed in o n time numerical comparisons illustrate the results

integrability of lie brackets in this paper we present the solution to a longstanding problem of differential geometry lie s third theorem for lie algebroids we show that the integrability problem is controlled by two computable obstructions as applications we derive explain and improve the known integrability results we establish integrability by local lie groupoids we clarify the smoothness of the poisson sigma model for poisson manifolds and we describe other geometrical applications

iteration schemes for the divide and conquer eigenvalue solver we propose globally convergent iteration schemes for updating the eigenvalues of a symmetric matrix after a rank 1 modification such calculations are the core of the divide and conquer technique for the symmetric tridiagonal eigenvalue problem we prove the superlinear convergence right from the start of our schemes which allows us to improve the complexity bounds of 3 the effectiveness of our algorithms is confirmed by numerical results which are reported and discussed

inversion of jacobi s tridiagonal matrix abstract this paper gives a simple algorithm for finding the explicit inverse of a general jacobi tridiagonal matrix a few illustrations are also provided to demonstrate the applicability of our algorithm

incremental learning of 3d dct compact representations for robust visual tracking visual tracking usually requires an object appearance model that is robust to changing illumination pose and other factors encountered in video many recent trackers utilize appearance samples in previous frames to form the bases upon which the object appearance model is built this approach has the following limitations 1 the bases are data driven so they can be easily corrupted and 2 it is difficult to robustly update the bases in challenging situations in this paper we construct an appearance model using the 3d discrete cosine transform 3d dct the 3d dct is based on a set of cosine basis functions which are determined by the dimensions of the 3d signal and thus independent of the input video data in addition the 3d dct can generate a compact energy spectrum whose high frequency coefficients are sparse if the appearance samples are similar by discarding these high frequency coefficients we simultaneously obtain a compact 3d dct based object representation and a signal reconstruction based similarity measure reflecting the information loss from signal reconstruction to efficiently update the object representation we propose an incremental 3d dct algorithm which decomposes the 3d dct into successive operations of the 2d discrete cosine transform 2d dct and 1d discrete cosine transform 1d dct on the input video data as a result the incremental 3d dct algorithm only needs to compute the 2d dct for newly added frames as well as the 1d dct along the third dimension which significantly reduces the computational complexity based on this incremental 3d dct algorithm we design a discriminative criterion to evaluate the likelihood of a test sample belonging to the foreground object we then embed the discriminative criterion into a particle filtering framework for object state inference over time experimental results demonstrate the effectiveness and robustness of the proposed tracker

restricted rank modification of the symmetric eigenvalue problem theoretical considerations the problem is considered how to obtain the eigenvalues and vectors of a matrix a vvt where a is a symmetric matrix with known spectral decomposition and vvt is a positive semidefinite matrix of low rank it is shown that the eigenvalues of a vvt can easily be located to any desired accuracy by means of the inertia of the matrix i vt a 1v the problem of determining the eigenvalues of a restricted to r v can be treated likewise

fusing local patterns of gabor magnitude and phase for face recognition gabor features have been known to be effective for face recognition however only a few approaches utilize phase feature and they usually perform worse than those using magnitude feature to investigate the potential of gabor phase and its fusion with magnitude for face recognition in this paper we first propose local gabor xor patterns lgxp which encodes the gabor phase by using the local xor pattern lxp operator then we introduce block based fisher s linear discriminant bfld to reduce the dimensionality of the proposed descriptor and at the same time enhance its discriminative power finally by using bfld we fuse local patterns of gabor magnitude and phase for face recognition we evaluate our approach on feret and frgc 2 0 databases in particular we perform comparative experimental studies of different local gabor patterns we also make a detailed comparison of their combinations with bfld as well as the fusion of different descriptors by using bfld extensive experimental results verify the effectiveness of our lgxp descriptor and also show that our fusion approach outperforms most of the state of the art approaches

kernel optimum nearly analytical discretization kond algorithm applied to parabolic and hyperbolic equations abstract two applications of the kernel optimum nearly analytical discretization kond algorithm to the parabolic and the hyperbolic type equations are presented in detail to lead to novel numerical schemes with very high numerical accuracy it is demonstrated numerically that the two dimensional kond p scheme for the parabolic type yields much less numerical error by over 2 3 orders measured quantitatively by the root mean square deviation from analytical solutions and reduces the cpu time to about 1 5 for a common numerical accuracy compared with the conventional explicit scheme of reference it is also demonstrated numerically that the kond h scheme for the hyperbolic type yields much less diffusive error and has fairly high stability for both of the linear and the nonlinear wave propagations compared with other conventional schemes origins of numerical errors in data processing in general numerical schemes are discussed

improved bound for complexity of matrix multiplication in 1968 strassen 16 described a method of multiplying two 2 2 matrices using only seven multiplications by applying it recursively it was shown that two n n matrices could be multiplied using o n operations in all where log2 7 2 81 this discovery led to a period of activity devoted to the improvement of this bound one can define an exponent of complexity which is in effect the smallest number such that two n n matrices can be multiplied using o n operations using an method of the type described by strassen a precise definition is given in 2 then strassen s result says that log2 7 so it is natural to wish to determine the true value of in the decade or so after 1978 several successive reductions in the upper bound for were achieved 2 3 6 8 10 12 14 17 leading to the bound 2 375477 obtained by coppersmith and winograd 7 it is an open question whether 2 we present a small improvement of the coppersmith winograd bound namely 2 3736897 which was first obtained in stothers 15 the proof uses an extension of the ideas of 7 and relies heavily on a combinatorial construction from 7 which depends on probabilistic arguments and a theorem of salem and spencer on sets of integers containing no three terms in arithmetical progression we have tried to organize the proof so that it is reasonably concise but also self contained to make it more accessible in the belief that at least parts of the argument may be of wider interest outside the algebraic complexity community to this end we derive the results we need from algebraic complexity theory in 2 which also contains general background material in 3 we present the essence of the combinatorial construction as a lemma which we subsequently apply several times we first apply it in 4 to recover the coppersmith winograd bound although our presentation is rather different the proof is essentially the same as that of 7 except for the proof of lemma 4 1 for which we give a somewhat simpler argument using 4 as preparation and motivation we obtain our new bound in 5 the argument is similar but more complicated and technical

illumination insensitive image representation via synergistic weighted center surround receptive field model and weber law a novel illumination insensitive texture feature descriptor weber synergistic center surround pattern is presented we model differential synergistic excitation pattern synergistic straight orientation pattern and synergistic diagonal orientation pattern we discuss different scale and direction weighted coefficients in detail we mine higher order spatial information of weighted wscp image representation under complex illumination condition is a great challenge in computer vision field motivated by weber law and synergistic center surround receipt field model we propose an illumination insensitive feature descriptor named as weber synergistic center surround pattern wscp including three components differential synergistic excitation pattern dsep synergistic straight orientation pattern ssop and synergistic diagonal orientation pattern sdop to further enhance the discriminative power of wscp we present a scale and orientation weighted wscp wwscp which fully considers the inner and outer layer pixels excitation distributions as well as their orientation information importance to acquire more discriminative and rich features we utilize the spatiograms to describe patterns instead of the conventional histograms which can obtain higher order spatial information in the final classification stage we present a novel distance measurement model called weighted similarity measurement model wsmm to improve classification accuracy by sufficiently utilizing the information contents and orientation distributions of each pattern extensive experimental comparisons between our methods and other state of the art methods are conducted on cmupie yale b yale b ext feret photex alot and rawfoot databases and performance results have verified the effectiveness and efficiency of our proposed methods on the robustness to illumination variations

eigenvalues of a symmetric tridiagonal matrix a divide and conquer approach the symmetric tridiagonal eigenproblem has been the topic of some recent work many methods have been advanced for the computation of the eigenvalues of such a matrix in this paper we present a divide and conquer approach to the computation of the eigenvalues of a symmetric tridiagonal matrix via the evaluation of the characteristic polynomial the problem of evaluation of the characteristic polynomial is partitioned into smaller parts which are solved and these solutions are then combined to form the solution to the original problem we give the update equations for the characteristic polynomial and certain auxiliary polynomials used in the computation furthermore this set of recursions can be implemented on a regulartree structure if the concurrency exhibited by this algorithm is exploited it can be shown that thetime for computation of all the eigenvalues becomeso nlogn instead ofo n2 as is the case for the approach where the order is increased by only one at every step we address the numerical problems associated with the use of the characteristic polynomial and present a numerically stable technique for the eigenvalue computation

analytical inversion of general tridiagonal matrices in this paper we give a complete analysis for general tridiagonal matrix inversion for both non block and block cases and provide some very simple analytical formulae which immediately lead to closed forms for some special cases such as symmetric or toeplitz tridiagonal matrices

the analytic inversion of any finite symmetric tridiagonal matrix we use the theory of orthogonal polynomials to write down explicit expressions for the polynomials of the first and second kind associated with a given infinite symmetric tridagonal matrix h the green s function is the inverse of the infinite symmetric tridiagonal matrix h zi by calculating the inverse of the finite symmetric tridiagonal matrix we can find the analytical form of the inverse of the finite symmetric tridiagonal matrix

integrability of poisson brackets we discuss the integration of poisson brackets motivated by our recent solution to the integrability problem for general lie brackets we give the precise obstructions to integrating poisson manifolds describing the integration as a symplectic quotient in the spirit of the poisson sigma model of cattaneo and felder for regular poisson manifolds we express the obstructions in terms of variations of symplectic areas improving on results of alcalde cuesta and hector we apply our results and our point of view to decide about the existence of complete symplectic realizations to the integrability of submanifolds of poisson manifolds and to the study of dual pairs morita equivalence and reduction

dct regularized extreme visual recovery here we study the extreme visual recovery problem in which over 90 of pixel values in a given image are missing existing low rank based algorithms are only effective for recovering data with at most 90 missing values thus we exploit visual data s smoothness property to help solve this challenging extreme visual recovery problem based on the discrete cosine transform dct we propose a novel dct regularizer that involves all pixels and produces smooth estimations in any view our theoretical analysis shows that the total variation regularizer which only achieves local smoothness is a special case of the proposed dct regularizer we also develop a new visual recovery algorithm by minimizing the dct regularizer and nuclear norm to achieve a more visually pleasing estimation experimental results on a benchmark image data set demonstrate that the proposed approach is superior to the state of the art methods in terms of peak signal to noise ratio and structural similarity

lie group valued moment maps we develop a theory of quasi hamiltonian g spaces for which the moment map takes values in the group g itself rather than in the dual of the lie algebra the theory includes counterparts of hamiltonian reductions the guillemin sternberg symplectic cro

tridiagonal test matrices for eigenvalue computations the clement or sylvesterkac matrix is a tridiagonal matrix with zero diagonal and simple integer entries its spectrum is known explicitly and consists of integers which makes it a useful test matrix for numerical eigenvalue computations we consider a new class of appealing two parameter extensions of this matrix which have the same simple structure and whose eigenvalues are also given explicitly by a simple closed form expression the aim of this paper is to present in an accessible form these new matrices and examine some numerical results regarding the use of these extensions as test matrices for numerical eigenvalue computations

lie poisson structure on some poisson lie groups poisson lie groups appeared in the work of drinfel d see e g drl dr2 as classical objects corresponding to quantum groups going in the other direction we may say that a poisson lie group is a group of symmetries of a phase space that are allowed to twist in a certain sense the symplectic or poisson structure the poisson structure on the group controls this twisting in a precise way quantizing both the phase space and the symmetries one may obtain a quantum group acting on a quantum phase space in recent work lu and ratiu lr used so called standard poisson structures on a compact semisimple lie group k and on its poisson dual k in order to give a new proof of the nonlinear convexity theorem of kostant ko their method is analogous to the famous symplectic proof of the linear convexity theorem given by atiyah a and guillemin and stemnberg gs the nonlinear convexity theorem like the linear one follows from a very general result on convexity of the image of the momentum map a gs however in lr it is applied not to a coadjoint orbit in t but to a symplectic leaf in k the main result of this paper is that the standard poisson structure on the poisson dual k to a compact semisimple poisson lie group k is actually isomorphic to the linear one on t this theorem seems to be related to some facts in the theory of quantum groups namely for generic q the universal enveloping algebra u t and its quantum deformation uq t are isomorphic as algebras though not as coalgebras of course since the quantum version is not cocommutative in particular there is a bijective correspondence between their representations a direct connection between our work and its quantum analogues though is still to be found the present work supplies a positive answer to question 5 1 in lr and strongly depends on that paper to simplify reading we keep the notations of lr wherever possible on one hand but give all necessary definitions on the other our work is also related to du in which the nonlinear convexity theorem is reduced to the linear one by a deformation argument not unlike the one that we use in 5 the paper is organized as follows in 2 we define poisson lie groups discuss

efficient computation of tridiagonal matrices largest eigenvalue abstract this paper proposes a method for a fast estimation of the largest eigenvalue of an asymmetric tridiagonal matrix the proposed method is based on the power method and the computation of the square of the original matrix the matrix square is computed through a proposed fast algorithm designed specifically for tridiagonal matrices implementations for compressed column ccs and compressed row storage crs formats are provided discussed and compared to a standard scientific library we investigate the roundoff numerical errors showing that the proposed method provides errors no greater than the usual power method we provide numerical results with simulations in c c implementation in order to demonstrate the effectiveness of the proposed method

on the variation in the cohomology of the symplectic form of the reduced phase space is called the momentum mapping of the hamiltonian t action given 1 1 the condition 1 2 just means that t acts along the fibers of j for the basic definitions and properties of non commutative hamiltonian group actions see am the results of this paper can easily be extended to hamiltonian actions of arbitrary compact connected lie groups by applying our results to the action of its maximal toms and using the equivariance of the momentum mapping for some more details see the remarks at the end of sect 2 we will assume throughout this paper that the momentum map is proper that is j i u is compact for each compact subset u of t now let r be a regular value of j that is t j tmm t is surjective for all meye j 1 4 then ye is a smooth submanifold of m compact because

the momentum map in poisson geometry every action on a poisson manifold by poisson diffeomorphisms lifts to a hamiltonian action on its symplectic groupoid which has a canonically defined momentum map we study various properties of this momentum map as well as its use in reduction

integration of twisted dirac brackets given a lie groupoid g over a manifold m we show that multiplicative 2 forms on g relatively closed with respect to a closed 3 form phi on m correspond to maps from the lie algebroid of g into t m satisfying an algebraic condition and a differential condition with respect to the phi twisted courant bracket this correspondence describes as a special case the global objects associated to phi twisted dirac structures as applications we relate our results to equivariant cohomology and foliation theory and we give a new description of quasi hamiltonian spaces and group valued momentum maps

nuclear norm based 2 dpca for extracting features from images the 2 d principal component analysis 2 dpca is a widely used method for image feature extraction however it can be equivalently implemented via image row based principal component analysis this paper presents a structured 2 d method called nuclear norm based 2 dpca n 2 dpca which uses a nuclear norm based reconstruction error criterion the nuclear norm is a matrix norm which can provide a structured 2 d characterization for the reconstruction error image the reconstruction error criterion is minimized by converting the nuclear norm based optimization problem into a series of f norm based optimization problems in addition n 2 dpca is extended to a bilateral projection based n 2 dpca n b2 dpca the virtue of n b2 dpca over n 2 dpca is that an image can be represented with fewer coefficients n 2 dpca and n b2 dpca are applied to face recognition and reconstruction and evaluated using the extended yale b cmu pie frgc and ar databases experimental results demonstrate the effectiveness of the proposed methods

trajectory space a dual representation for nonrigid structure from motion existing approaches to nonrigid structure from motion assume that the instantaneous 3d shape of a deforming object is a linear combination of basis shapes these bases are object dependent and therefore have to be estimated anew for each video sequence in contrast we propose a dual approach to describe the evolving 3d structure in trajectory space by a linear combination of basis trajectories we describe the dual relationship between the two approaches showing that they both have equal power for representing 3d structure we further show that the temporal smoothness in 3d trajectories alone can be used for recovering nonrigid structure from a moving camera the principal advantage of expressing deforming 3d structure in trajectory space is that we can define an object independent basis this results in a significant reduction in unknowns and corresponding stability in estimation we propose the use of the discrete cosine transform dct as the object independent basis and empirically demonstrate that it approaches principal component analysis pca for natural motions we report the performance of the proposed method quantitatively using motion capture data and qualitatively on several video sequences exhibiting nonrigid motions including piecewise rigid motion partially nonrigid motion such as a facial expressions and highly nonrigid motion such as a person walking or dancing

a fast numerical algorithm for the inverse of a tridiagonal and pentadiagonal matrix in the current paper we present a computationally efficient algorithm for obtaining the inverse of a tridiagonal matrix and a pentadiogonal matrix few conditions are required and the algorithm is suited for implementation using computer algebra systems

symplectic groupoids and poisson manifolds on definit la notion de groupoide symplectique on donne la variete de poisson de ce groupoide symplectique on presente une construction

a parallel algorithm for computing the eigenvalues of a symmetric tridiagonal matrix a parallel algorithm called polysection is presented for computing the eigenvalues of a symmetric tridiagonal matrix the method is based on a quadratic recurrence in which the characteristic polynomial is constructed on a binary tree from polynomials whose degree doubles at each level intervals that contain exactly one zero are determined by the zeros of polynomials at the previous level which ensures that different processors compute different zeros the signs of the polynomials at the interval endpoints are determined a priori and used to guarantee that all zeros are found the use of finite precision arithmetic may result in multiple zeros however in this case the intervals coalesce and their number determines exactly the multiplicity of the zero for an n x n matrix the eigenvalues can be determined in o log squared n time with n squared processors and o n time with n processors the method is compared with a parallel variant of bisection that requires o n squared time on a single processor o n time with n processors and o log n time with n squared processors