multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

the berry esseen bound for student s statistic we prove the berry esseen bound for the student t statistic under the assumption of a third moment this bound coincides up to an absolute constant with the classical berry esseen bound for the mean in general the distribution of the student statistic converges to the standard normal distribution function at least as fast as the distribution of the mean and sometimes faster for example rates of convergence can be proved if the underlying distribution is in the domain of attraction of the normal law

extended kronecker summation for cluster treatment of lti systems with multiple delays a new procedure is presented for determining the kernel and the offspring hypersurfaces for general linear time invariant lti dynamics with multiple delays these hypersurfaces as they have very recently been introduced in a concept paper r sipahi and n olgac automatica 41 2005 pp 1413 1422 form the basis of the overriding paradigm which is called the cluster treatment of characteristic roots ctcr in fact these two sets of hypersurfaces exhaustively represent the locations in the domain of the delays where the system possesses at least one pair of imaginary characteristic roots to determine the kernel and offspring we use the extraordinary features of the extended kronecker summation operation in this paper the end result is that the infinite dimensional problem reduces to a finite dimensional one and preferably into an eigenvalue problem following the procedure described in this paper we are able to shorten the computational time considerably in determining these hypersurfaces we demonstrate these concepts via some example case studies one of the examples treats a 3 delay system for this case another interesting perspective called the building block is also utilized to display the kernel in three dimensional space in the domain of spectral delays

the bm l _ mathbf 1 norm density estimator process the notion of an l1 norm density estimator process indexed by a class of kernels is introduced then a functional central limit theorem and a glivenko cantelli theorem are established for this process while assembling the necessary machinery to prove these results a body of poissonization techniques and restricted chaining methods is developed which is useful for studying weak convergence of general processes indexed by a class of functions none of the theorems imposes any condition at all on the underlying lebesgue density f also somewhat unexpectedly the distribution of the limiting gaussian process does not depend on f

a consensus protocol under directed communications with two time delays and delay scheduling this paper studies a consensus protocol over a group of agents driven by second order dynamics the communication among members of the group is assumed to be directed and affected by two rationally independent time delays one in the position and the other in the velocity information channels these delays are unknown but considered to be constant and uniform throughout the system the stability of the consensus protocol is studied using a simplifying factorisation procedure and deploying the cluster treatment of characteristic roots ctcr paradigm this effort results in a unique depiction of the exact stability boundaries in the domain of the delays the ctcr requires the knowledge of the potential stability switching loci exhaustively within this domain the creation of these loci is an important contribution of this work it is done in a new surrogate coordinate system called the spectral delay space the relative stability of the system that is the speed to reach consensus is also investigated fo

stability criteria for certain third order delay differential equations in this paper we study the asymptotic stability of the zero solution of third order linear delay differential equations of the form y t p1y t p2y t q1y t q2y t v1y t v2y t where p1 p1 q1 q2 v1 and v2 are certain constants here 0 is a constant delay in proving our results we make use of pontryagin s theory for quasi polynomials

computation of the lyapunov matrix for periodic time delay systems and its application to robust stability analysis abstract a new procedure for computing the delay lyapunov matrix for periodic time delay systems that is based on the numerical solution of a partial differential equations pde system is presented the introduction of a new set of boundary conditions that are satisfied by the pde system allows us to propose a new methodology for computing the initial conditions required by the implemented numerical scheme the potential of the presented results is demonstrated by obtaining robust stability conditions depending on the delay lyapunov matrix with respect to the system parameters the delay and the frequency the theoretical results are applied to the widely known delayed mathieu equation

affine parameter estimation from the trace transform in this paper we assume that we are given the images of two segmented objects one of which may be an affinely distorted version of the other and wish to recover the values of the parameters of the affine transformation between the two images the images may also differ by the overall level of illumination the multiplicative constant of such difference may also be recovered we present a generic theoretical framework to solve this problem in terms of this framework other proposed methods may be interpreted we show how in this framework one can recover the affine parameters in a way that is robust to various effects such as occlusion and illumination variation the proposed method is generic enough to be applicable also to matching two images that do not depict the same scene or object

critical delays and polynomial eigenvalue problems in this work we present a new method to compute the delays of delay differential equations ddes such that the dde has a purely imaginary eigenvalue for delay differential equations with multiple delays the critical curves or critical surfaces in delay space that is the set of delays where the dde has a purely imaginary eigenvalue are parameterized we show how the method is related to other works in the field by treating the case where the delays are integer multiples of some delay value i e commensurate delays the parameterization is done by solving a quadratic eigenvalue problem which is constructed from the vectorization of a matrix equation and hence typically of large size for commensurate delay differential equations the corresponding equation is a polynomial eigenvalue problem as a special case of the proposed method we find a closed form for a parameterization of the critical surface for the scalar case we provide several examples with visualizations where the computation is done with some exploitation of the structure of eigenvalue problems

a new method for computing delay margins for stability of linear delay systems this note is concerned with stability properties of linear time invariant delay systems we consider delay systems of retarded type modeled both as a high order scalar differential difference equation and as a set of first order differential difference equations expressed in state space form we provide a computational method that can be used to compute a delay interval such that the system under consideration is stable for all delay values that lie in the computed interval this method requires computing only the eigenvalues and generalized eigenvalues of certain constant matrices and it can be implemented efficiently based on this method we further state a simple necessary and sufficient condition concerning stability independent of delay for each of the two types of the models

self normalized large deviations let x x n n geq 1 be a sequence of independent and identically distributed random variables the classical cramer chernoff large deviation states that lim n to infty n 1 ln p sum i 1 n x i n geq x ln rho x if and only if the moment generating function of x is finite in a right neighborhood of zero this paper uses n p 1 p v n p n p 1 p sum i 1 n x i p 1 p p 1 as the normalizing constant to establish a self normalized large deviation without any moment conditions a self normalized moderate deviation that is the asymptotic probability of p s n v n p geq x n for x n o n p 1 p is also found for any x in the domain of attraction of a normal or stable law as a consequence a precise constant in the self normalized law of the iterated logarithm of griffin and kuelbs is obtained applications to the limit distribution of self normalized sums the asymptotic probability of the t statistic as well as to the erdos renyi shepp law of large numbers are also discussed

towards a universal self normalized moderate deviation this paper is an attempt to establish a universal moderate deviation for self normalized sums of independent and identically distributed random variables without any moment condition the exponent term in the moderate deviation is specified when the distribution is in the centered feller class an application to the law of the iterated logarithm is given

a new lkf approach to stability analysis of linear systems with uncertain delays in this paper we analyze the asymptotic stability of linear systems with multiple uncertain delays assuming the nominal delays to be constant with possible zero or nonzero values we apply the simple lyapunov krasovskii functional lkf with the derivative prescribed as a negative definite quadratic form of the current state of a system we combine this functional with some integral bound for the derivative of the functional along the solutions of an uncertain system what provides the novelty of approach this bound consists of an essential integral part and some bounded expression the fact is that the positiveness of the essential part provides itself the stability of a system the study is based on recent works where the functional was shown to admit a quadratic lower bound on some special set of functions though it is only known to have a local cubic one on the set of arbitrary functions the derived stability condition is much simpler than most ones obtained by lkfs and outlined in the literature it constitutes an algebraic inequality for delay perturbations based on the so called lyapunov matrix and converges to a necessary and sufficient condition in some sense

necessary stability conditions for delay systems with multiple pointwise and distributed delays necessary stability conditions for linear systems with multiple pointwise and distributed delays are presented new properties that connect the lyapunov delay matrix and the fundamental matrix of these systems are instrumental in proving that these conditions depend exclusively on the lyapunov delay matrix the result is illustrated by some examples

image registration using log polar mappings for recovery of large scale similarity and projective transformations this paper describes a novel technique to recover large similarity transformations rotation scale translation and moderate perspective deformations among image pairs we introduce a hybrid algorithm that features log polar mappings and nonlinear least squares optimization the use of log polar techniques in the spatial domain is introduced as a preprocessing module to recover large scale changes e g at least four fold and arbitrary rotations although log polar techniques are used in the fourier mellin transform to accommodate rotation and scale in the frequency domain its use in registering images subjected to very large scale changes has not yet been exploited in the spatial domain in this paper we demonstrate the superior performance of the log polar transform in featureless image registration in the spatial domain we achieve subpixel accuracy through the use of nonlinear least squares optimization the registration process yields the eight parameters of the perspective transformation that best aligns the two input images extensive testing was performed on uncalibrated real images and an array of 10 000 image pairs with known transformations derived from the corel stock photo library of royalty free photographic images

an exact method for the stability analysis of time delayed linear time invariant lti systems a general class of linear time invariant systems with time delay is studied recently they attracted considerable interest in the systems and control community the complexity arises due to the exponential type transcendental terms in their characteristic equation the transcendentality brings infinitely many characteristic roots which are cumbersome to elaborate as evident from the literature a number of methodologies have been suggested with limited ability to assess the stability in the parametric domain of time delay this study offers an exact structured and robust methodology to bring a closure to the question at hand ultimately we present a unique explicit analytical expression in terms of the system parameters which not only reveals the stability regions pockets in the domain of time delay but it also declares the number of unstable characteristic roots at any given pocket the method starts with the determination of all possible purely imaginary resonant characteristic roots for any positive time delay to achieve this a simplifying substitution is used for the transcendental terms in the characteristic equation it is proven that the number of such resonant roots for a given dynamics is finite each one of these roots is created by infinitely many time delays which are periodically distributed an interesting property is also claimed next that the root crossing directions at these locations are invariant with respect to the delay and dependent only on the crossing frequency these two unique findings facilitate a simple and practical stability method which is the highlight of the work

critical frequencies and parameters for linear delay systems a lyapunov matrix approach abstract a new method based on recent results concerning the construction of the lyapunov matrix of delay systems reveals conditions under which the characteristic function has a root s 0 such that s 0 is also a root as the pure imaginary roots which are crucial in the stability analysis of time delay systems are of that type this method gives rise to a novel approach for the delay independent and delay dependent stability analyses of systems with delay that are multiple of a basic delay distributed delays and of a class of neutral type time delay systems a number of examples are given to illustrate the approach and to show its strength

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

video orbits of the projective group a simple approach to featureless estimation of parameters we present direct featureless methods for estimating the eight parameters of an exact projective homographic coordinate transformation to register pairs of images together with the application of seamlessly combining a plurality of images of the same scene resulting in a single image or new image sequence of greater resolution or spatial extent the approach is exact for two cases of static scenes 1 images taken from the same location of an arbitrary three dimensional 3 d scene with a camera that is free to pan tilt rotate about its optical axis and zoom or 2 images of a flat scene taken from arbitrary locations the featureless projective approach generalizes interframe camera motion estimation methods that have previously used a camera model which lacks the degrees of freedom to exactly characterize such phenomena as camera pan and tilt and or which have relied upon finding points of correspondence between the image frames the featureless projective approach which operates directly on the image pixels is shown to be superior in accuracy and the ability to enhance the resolution the proposed methods work well on image data collected from both good quality and poor quality video under a wide variety of conditions sunny cloudy day night these new fully automatic methods are also shown to be robust to deviations from the assumptions of static scene and no parallax

analytic solution of a delay differential equation arising in cost functionals for systems with distributed delays the solvability of a delay differential equation arising in the construction of quadratic cost functionals i e lyapunov functionals for a linear time delay system with a constant and a distributed delay is investigated we present a delay free auxiliary ordinary differential equation system with algebraically coupled split boundary conditions which characterizes the solutions of the delay differential equation and is used for solution synthesis a spectral property of the time delay system yields a necessary and sufficient condition for existence and uniqueness of solutions to the auxiliary system equivalently the delay differential equation the result is a tractable analytic solution framework to the delay differential equation

stability and bifurcations of equilibria in a multiple delayed differential equation the influence of multiple negative delayed feedback loops on the stability of a single action mechanism are considered a characteristic equation for the linearized stability of the equilibrium is completely analyzed as a function of two parameters describing a delay in one loop and a ratio of the gains in the two feedback loops the bifurcations occurring as the linear stability is lost are analyzed by the construction of a centre manifold in particular the nature of hopf and more degenerate higher codimension bifurcations are explicitly determined

linear systems with commensurate time delays stability and stabilization independent of delay notions of exponential stability independent of delay and stabilizability independent of delay are developed for the class of delay differential systems of the retarded type with commensurate time delays various criteria for exponential stability independent of delay with a given order are specified in terms of matrices whose entries are functions of a single real parameter and polynomials in one variable whose coefficients are functions of a single real parameter sufficient conditions and a necessary condition based on local stabilizability are given for stabilizability independent of delay using state feedback with commensurate time delays constructive methods for determining a stabilizing feedback are also presented the last part of the paper deals with a standard type of observer and regulator with the requirement that the closed loop system be stable independent of delay

critical effects of the polarity change in delayed states within an lti dynamics with multiple delays this note concerns the polarity inversion of the delayed states in linear time invariant multiple time delay systems lti mtds to start with for such systems the assessment of asymptotic stability is complicated due to the infinite dimensionality introduced by the delays it is shown that the mentioned polarity inversion influences the respective delay dependent stability maps in interesting ways there are some intriguing invariant characteristics and correspondences between the original and inverted systems which form the primary contributions of this note these findings are shown to be the enabling features to relate the stability maps of the two systems the cluster treatment of characteristic roots ctcr paradigm is utilized to identify these features an example case study is provided to illustrate the claims

necessary stability conditions for linear delay systems we present necessary conditions for the exponential stability of linear systems with multiple delays they are expressed in terms of the delay lyapunov matrix of the lyapunov krasovskii functionals of complete type approach new properties of independent interest that establish connections of the system fundamental matrix with its lyapunov matrix are crucial elements of our proof we illustrate our work with a number of examples

complete stability robustness of third order lti multiple time delay systems a unique procedure is presented in this paper for a complete stability robustness of the third order lti multiple time delay systems lti mtds the uniqueness of the treatment is simply due to the fact that there is no comparable methodology presently in the literature the end result of this procedure is an exhaustive and precise determination of the stable regions in the domain of time delays the backbone of the method is a novel framework called the cluster treatment of characteristic roots ctcr ctcr is constructed over two fundamental propositions the first proposition claims the existence of a bounded number of so called kernel curves where the only imaginary characteristic roots occur the second proposition is on an interesting directional invariance property of the crossing tendencies of these imaginary roots for simplicity of conveyance and without loss of generality the number of time delays is taken as two in this document the new methodology is expandable to higher order dynamics with more time delays than two as the authors intend to demonstrate in future publications publications

lyapunov matrices for neutral time delay systems with exponential kernel abstract in this contribution we study the problem of finding a lyapunov matrix for neutral type systems with distributed delay and exponential kernel in previous works an attempt was made to reduce this problem to the computation of solutions to an auxiliary delay free system with boundary conditions in this paper we propose new boundary conditions allowing a significant extension of existing results it is established that the new auxiliary boundary value problem has a unique solution if and only if there exists a unique lyapunov matrix

a comparison of affine region detectors the paper gives a snapshot of the state of the art in affine covariant region detectors and compares their performance on a set of test images under varying imaging conditions six types of detectors are included detectors based on affine normalization around harris mikolajczyk and schmid 2002 schaffalitzky and zisserman 2002 and hessian points mikolajczyk and schmid 2002 a detector of maximally stable extremal regions proposed by matas et al 2002 an edge based region detector tuytelaars and van gool 1999 and a detector based on intensity extrema tuytelaars and van gool 2000 and a detector of salient regions proposed by kadir zisserman and brady 2004 the performance is measured against changes in viewpoint scale illumination defocus and image compression the objective of this paper is also to establish a reference test set of images and performance software so that future detectors can be evaluated in the same framework

efficient computation of characteristic roots of delay differential equations using lms methods we aim at the efficient computation of the rightmost stability determining characteristic roots of a system of delay differential equations the approach we use is based on the discretization of the time integration operator by a linear multistep lms method the size of the resulting algebraic eigenvalue problem is inversely proportional to the steplength we summarize theoretical results on the location and numerical preservation of roots furthermore we select nonstandard lms methods which are better suited for our purpose we present a new procedure that aims at computing efficiently and accurately all roots in any right half plane the performance of the new procedure is demonstrated for small and large scale systems of delay differential equations

the asymptotic stability of linear autonomous systems with commensurate time delays the asymptotic stability of linear systems with commensurate time delays is studied algorithms are given to check if a given system is asymptotically stable independent of delay or to determine the largest delay time the system can tolerate to preserve its asymptotic stability these algorithms are simple to apply since they require only to find the eigenvalues of two specially constructed matrices and some simple mathematical calculations

static output feedback stabilization necessary conditions for multiple delay controllers this note focuses on the static output feedback stabilization problem for a class of single input single output systems when the control law includes multiple distinct delays we are interested in giving necessary conditions for the existence of such stabilizing controllers illustrative examples second order system chain of integrators or chain of oscillators are presented and discussed

brief paper extraction of 3d stability switching hypersurfaces of a time delay system with multiple fixed delays stability switching hypersurfaces ssh of a general class of linear time invariant lti multiple time delay systems mtds are extracted the number of delays and system order n 0 in this problem are given but they are arbitrarily large hence the extraction of ssh becomes non trivial a novel and efficient procedure reveals the 3d projections of dimensional ssh without the need for finding the ssh in achieving this computation times required remain in the same order of magnitude independently of and n 0 case studies demonstrate the effectiveness of the approach

a generalization of kharitonov s theorem robust stability of interval plants the robust stability problem is considered for interval plants in the case of single input multioutput or single output multi input systems a necessary and sufficient condition for the robust stabilization of such plants is developed using a generalization of v l kharitonov s theorem 1978 the generalization given provides necessary and sufficient conditions for the stability of a family of polynomials delta s q sub 1 s p sub 1 s q sub m s p sub m s where the q sub i are fixed and the p sub i are interval polynomials the coefficients of which are regarded as a point in parameter space which varies within a prescribed box this generalization called the box theorem reduces the question of the stability of the box in parameter space to the equivalent problem of the stability of a prescribed set of line segments it is shown that for special classes of polynomials q sub i s the set of line segments collapses to a set of points and this version of the box theorem in turn reduces to kharitonov s original theorem

lyapunov matrices for a class of neutral type time delay systems a class of neutral type time delay systems is presented for which computation of lyapunov matrices is reduced to a solution of an auxiliary delay free system of linear differential matrix equations with a special set of two point boundary conditions

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

point matching under large image deformations and illumination changes to solve the general point correspondence problem in which the underlying transformation between image patches is represented by a homography a solution based on extensive use of first order differential techniques is proposed we integrate in a single robust m estimation framework the traditional optical flow method and matching of local color distributions these distributions are computed with spatially oriented kernels in the 5d joint spatial color space the estimation process is initiated at the third level of a gaussian pyramid uses only local information and the illumination changes between the two images are also taken into account subpixel matching accuracy is achieved under large projective distortions significantly exceeding the performance of any of the two components alone as an application the correspondence algorithm is employed in oriented tracking of objects

one dimensional mapping for estimating projective transformations in this paper the 1 d mapping is studied for estimating a general projective transformation between images first a ray model of image patches is proposed to convert a complex projective deformation of a patch in the cartesian space into two simple rigid shifts of radial lines in the log polar inverse polar space to capture these shifts via direct search two types of radial image line matching viz 1 d log polar mapping and 1 d inverse polar mapping are formally defined also the unique features of these shifts are analyzed then a novel two step mathematical framework is devised for transformation estimation in the first step the 1 d log polar mapping is applied to estimating four affine parameters via two alternative methods for simulated real images in the second step the 1 d inverse polar mapping is applied to estimating two projective parameters by a direct search combined with the two step line matching two translational parameters are also determined finally the performance of the framework is evaluated first in estimating a variety of projective transformations by comparing the estimates with their ground truths and between the two proposed methods and second in registering a wide range of challenging image pairs by comparing with a state of the art feature based method

bounds of imaginary spectra of lti systems in the domain of two of the multiple time delays the stability of linear time invariant lti systems with independent multiple time delays and the cluster treatment of characteristic roots ctcr paradigm are investigated from a new perspective it is known that for such systems all the imaginary characteristic roots can be detected completely on a small set of hypersurfaces in the domain of the delays sipahi and olgac 2006a they are called kernel hypersurfaces kh the complete description of kh is the only prerequisite for the ctcr stability assessment procedure as the number of delays increases however their evaluation becomes infeasible instead we present a procedure to extract the 2 d cross sections of these hypersurfaces in the domain of any two of the delays by fixing the remaining delays in the 2 delay domain of interest the exact upper and lower bounds of the imaginary spectra are determined for this a combination of half angle tangent representation of the characteristic equation and the dixon resultant theory is used as the main contributions of this paper the complete kh are obtained by sweeping the root crossing frequency in this interval using this knowledge ctcr creates the cross section of the stability map in the domain of the two arbitrarily selected delays we demonstrate the effectiveness of this methodology over an example case study with three independent delays and two commensurate ones

automatic panoramic image stitching using invariant features this paper concerns the problem of fully automated panoramic image stitching though the 1d problem single axis of rotation is well studied 2d or multi row stitching is more difficult previous approaches have used human input or restrictions on the image sequence in order to establish matching images in this work we formulate stitching as a multi image matching problem and use invariant local features to find matches between all of the images because of this our method is insensitive to the ordering orientation scale and illumination of the input images it is also insensitive to noise images that are not part of a panorama and can recognise multiple panoramas in an unordered image dataset in addition to providing more detail this paper extends our previous work in the area brown and lowe 2003 by introducing gain compensation and automatic straightening steps

imaginary characteristic roots of neutral systems with commensurate delays abstract this paper concentrates on stability analysis of neutral linear time invariant lti delay systems with multiple commensurate time delays a new numerical procedure is offered for the determination of purely imaginary characteristic roots of neutral delay systems which plays a crucial role in assessing the system stability based on simple linear algebra it is shown that the imaginary characteristic roots of such a system can be found by calculating the generalized eigenvalues of an associated matrix pair if the system is of retarded type we just need to determine the eigenvalues of a single matrix the results extend previously known work on neutral delay systems subject to a single delay for neutral systems subject to multiple commensurate delays in the light of the main result of this paper we present a new method to determine the largest first time delay interval for which a neutral delay system preserves its stability the paper is closed by showing numerical examples that illustrate the applicability and effectiveness of the proposed method

consensus analysis with large and multiple communication delays using spectral delay space concept in this study we consider the consensus problem for a group of second order agents interacting under a fixed undirected communication topology communication lines are affected by two rationally independent delays the first delay is assumed to be in the position information channels whereas the second delay is in the velocity information exchange the delays are assumed to be large and uniform throughout the entire network the stability analysis of such systems becomes quickly intractable as the number of agents increases and the delays enlarge to resolve this dilemma we first reduce the complexity of the problem dramatically by decomposing the characteristic equation of the system into a set of second order factors then we assess the stability of the resulting subsystems exactly and exhaustively in the domain of the time delays using the cluster treatment of characteristic roots ctcr paradigm ctcr requires the determination of all the potential stability switching loci in the domain of the d

stability analysis of time delay systems with incommensurate delays using positive polynomials we present a new stability condition for linear time delay systems tds with multiple incommensurate delays based on the rekasius substitution and positive polynomials the condition is checked by testing the positivity of multivariate polynomials in certain domains for this purpose we propose two alternative algorithms based on linear programming and sum of squares methods respectively the efficiency and accuracy of the algorithms is compared in an example to alternative stability conditions taken from the literature

combination of sign inverting and delay scheduling control concepts for multiple delay dynamics abstract in this paper we treat a novel combination of two controversial control concepts sign inverting control sic and delay scheduling ds for systems with multiple independent and large delays sic suggests the inversion of the control polarity and ds prolongs the existing delays the combined scheme functions with a single requirement that the union of the control schemes provides a larger stable operating region than each of its components does in the domain of the delays the critical knowledge that is needed to execute such a unified control strategy is the crisp description of these stable regions for each time delayed control scheme this need can be fulfilled using the recent cluster treatment of characteristic roots ctcr paradigm which establishes the stable regions exhaustively and non conservatively the resulting options in selecting operating modes render more robust control performance against much larger delay variations than each of the schemes we also investigate the disturbance rejection speeds within these enlarged stable regions in order to improve the control performance even further such multi faceted paradoxical combinations provide previously unexplored tools to control designers experimental validations of these novel concepts are presented on a simple setup with a single axis manipulator

lyapunov matrix based necessary and sufficient stability condition by finite number of mathematical operations for retarded type systems abstract a new necessary and sufficient exponential stability condition for systems with multiple delays is presented it is given in terms of a symmetric block matrix uniquely determined by the delay lyapunov matrix a notable feature is that the stability test requires a finite number of mathematical operations

linearly estimating all parameters of affine motion using radon transform fast and accurate motion estimation takes an important place in many fields of computer vision and image processing using radon transform to compute projections of the images along specified directions is an effective way to show the relationship between the 2d image object and its projections and estimate motions between the images all existing projection based motion estimation methods without the use of iteration have a severe defect that only five of the six affine parameters can be estimated there are some other methods that can estimate the six parameters but most of them are usually based on a certain iterative framework which is computationally intensive and sensitively dependent on the initial values in this paper a novel method based on radon transform is proposed to estimate all the six affine parameters directly the relationship in the projection domain between a pair of images connected by an affine motion is studied and a linear model is established by which all the six affine parameters can be directively found the employment of a hierarchical framework can produce more accurate results the experimental results reveal that the proposed method has a much better performance than the state of the art methods in this field

self normalized laws of the iterated logarithm on demontre une loi du logarithme itere qui generalise la version classique pour toutes les distributions dans la classe de feller pour cette demonstration l auteur utilise une auto normalisation convenable pour les sommes partielles de variables aleatoires independantes et identiquement distribuees un cas particulier de ces resultats s applique a toute distribution dans le domaine de l attraction d une certaine loi stable

lyapunov matrices for a class of time delay systems a class of distributed time delay systems is presented for which the problem of computation of lyapunov matrices is reduced to computation of solutions of an auxiliary two point boundary problem for a special delay free system of matrix equations

image registration by super curves we solve the 2 d affine image registration problem by curve matching and alignment our approach starts with a super curve which is formed by superimposing two affine related curves in one coordinate system we use b spline fusion technique to find a single b spline approximation of the super curve and a registration between the two curves simultaneously this approach achieves superior accuracy and efficiency in curve matching and alignment we then address the occlusion problem by finding partial match between the curves segmented using inflections and cusps which are affine invariant the combination of edge detection and curve alignment lead to accurate image registration

passage of levy processes across power law boundaries at small times we wish to characterise when a l e vy process x t crosses boundaries like t kappa kappa 0 in a one or two sided sense for small times t thus we enquire when limsup t downarrow 0 x t t kappa limsup t downarrow 0 x t t kappa and or liminf t downarrow 0 x t t kappa are almost surely a s finite or infinite necessary and sufficient conditions are given for these possibilities for all values of kappa 0 often for many values of kappa when the limsups are finite a s they are in fact zero as we show but the limsups may in some circumstances take finite nonzero values a s in general the process crosses one or two sided boundaries in quite different ways but surprisingly this is not so for the case kappa 1 2 an integral test is given to distinguish the possibilities in that case some results relating to other norming sequences for x and when x is centered at a nonstochastic function are also given

exact stability analysis of second order leaderless and leader follower consensus protocols with rationally independent multiple time delays abstract an investigation of double integrator agents with directed asymmetric consensus protocols and multiple rationally independent time delays is presented in this paper from two novel perspectives first we complement the group consensus literature on crucial stability analysis using a recent technique called the cluster treatment of characteristic roots ctcr for the first time on this class of time delayed systems the ctcr paradigm is pursued after a block diagonalization mode decoupling transformation on the system this treatment produces some unique stability tables for the dynamics in the space of the delays which are non conservative and exhaustive second a novel concept of spectral delay space is presented as an overture to the ctcr for the determination of the complete set of stability crossing switching hypersurfaces in the delay space examples are provided to display the strengths and efficiency of this new stability analysis mechanism

advanced clustering with frequency sweeping methodology for the stability analysis of multiple time delay systems a new methodology advanced clustering with frequency sweeping acfs is introduced for the stability analysis of the most general class of linear time invariant time delay systems with multiple delays acfs is a cross fertilization of algebraic geometry frequency sweeping technique and the root clustering paradigm and it can directly extract the 2 d cross sections of the stability views in any two delay domain in this domain acfs can also test the delay independent stability based on necessary and sufficient conditions and can compute for the delay dependent case the precise lower and upper bounds of the only parameter the frequency that acfs sweeps case studies that are prohibitive to analyze with the existing analytical methods are presented to demonstrate the strengths of the method

robust stability of time delay systems there are two fundamental results available when we study stability of a polynomial family that is described by convex polytope in the coefficient space the edge theorem and the theory based on the concept of convex directions many known results can be explained with these two results this paper deals with a generalization of this line of research to the case of quasipolynomials that are entire functions which include both degree of the independent variable and exponential functions the main objects of the paper are the developing of the concept of convex directions for quasipolynomials and exploiting this concept for construction of testing sets for quasipolynomial families one of the primary sources of motivation for the class of problems considered in this paper is derived from process control a typical problem formulation almost always includes a delay element in each subsystem process block when we interconnect a number of such blocks in a feedback system the study of robust stability involves quasipolynomials of the sort considered in this paper

lyapunov matrices for a class of time delay systems with piecewise constant kernel abstractin this contribution we study time delay systems with distributed delay whose kernel is piecewise constant it is shown that the problem of finding a lyapunov matrix for this class of time delay systems can be reduced to the computation of solutions to an auxiliary system of linear differential equations with boundary conditions the problem of solving the auxiliary system is then reduced to the solution of a system of linear algebraic equations it is established that the auxiliary system with boundary conditions admits a unique solution if and only if there exists a unique lyapunov matrix

optimal sign inverting control for time delayed systems a concept study with experiments an intriguing control logic sign inverting control sic is considered for control systems with delayed feedback it starts with a nominal control law formulated for non delayed case and simply inverts the sign of the control gains for some surprising benefits when used with the delays this operation sounds paradoxical as the sign inversion potentially harms the stability of the non delayed dynamics however sic with large delays may yield some complementary benefits to the nominal control logic from delay robustness perspective the main question we address in this paper is how to select the nominal control law so that such a contribution can be a feasible b optimal in some sense a structured methodology is proposed to achieve this starting with a linear quadratic regulator based controller a single scaling factor on the corresponding control gains is used for one dimensional optimisation experimental validation of the concept of this optimal sic procedure is also reported on a single axis

stability analysis for lti systems with multiple time delays using the bounds of its imaginary spectra abstract the stability of linear time invariant lti systems with multiple independent time delays and the cluster treatment of characteristic roots ctcr paradigm are investigated from a new perspective any delay composition that results in an imaginary characteristic root lies either on a small number of kernel hypersurfaces kh or their infinitely many offspring hypersurfaces oh the complete description of kh is the only prerequisite for the ctcr based stability assessment procedure as the number of delays increases however the determination of these kh becomes computationally costly instead we present a practical procedure to extract the 2 d cross sections of the kh set in the domain of the two arbitrarily selected delays first we determine the exact upper and lower bounds of the imaginary spectra in this 2 d cross section of interest this process starts with a half angle tangent representation of the characteristic equation followed by the dixon resultant operation based on the full knowledge of kh the ctcr paradigm creates the complete stability map in the domain of these two arbitrarily selected delays we demonstrate the effectiveness of this methodology over an example case study

small time compactness and convergence behavior of deterministically and self normalised levy processes the first author s research was partially supported by arc grant dp0664603 the second author s research was partially supported by nsf grant dms 0503908

robust stability for time delay systems the edge theorem and graphical tests the robust stability problem is discussed for a class of uncertain delay systems where the characteristic equations involve a polytope p of quasi polynomials i e polynomials in one complex variable and exponential powers of the variable given a set d in the complex plane the goal is to find a constructive technique to verify whether all roots of every quasi polynomial in p belong to d that is to verify the d stability of p first it is demonstrated by counterexample that kharitonov s theorem does not hold for general delay systems next it is shown that under a mild assumption on the set d a polytope of quasi polynomials is d stable if and only if the edges of the polytope are d stable this extends the edge theorem for the d stability of a polytope of polynomials the third result gives a constructive graphical test for checking the d stability of a polytope of quasi polynomials which is especially simple when the set d is the open left half plane an application is given to demonstrate the power of the results

polynomial two parameter eigenvalue problems and matrix pencil methods for stability of delay differential equations several recent methods used to analyze asymptotic stability of delay differential equations ddes involve determining the eigenvalues of a matrix a matrix pencil or a matrix polynomial constructed by kronecker products despite some similarities between the different types of these so called matrix pencil methods the general ideas used as well as the proofs differ considerably moreover the available theory hardly reveals the relations between the different methods in this work a different derivation of various matrix pencil methods is presented using a unifying framework of a new type of eigenvalue problem the polynomial two parameter eigenvalue problem of which the quadratic two parameter eigenvalue problem is a special case this framework makes it possible to establish relations between various seemingly different methods and provides further insight in the theory of matrix pencil methods we also recognize a few new matrix pencil variants to determine dde stability finally the recognition of the new types of eigenvalue problem opens a door to efficient computation of dde stability

lucas kanade 20 years on a unifying framework since the lucas kanade algorithm was proposed in 1981 image alignment has become one of the most widely used techniques in computer vision applications range from optical flow and tracking to layered motion mosaic construction and face coding numerous algorithms have been proposed and a wide variety of extensions have been made to the original formulation we present an overview of image alignment describing most of the algorithms and their extensions in a consistent framework we concentrate on the inverse compositional algorithm an efficient algorithm that we recently proposed we examine which of the extensions to lucas kanade can be used with the inverse compositional algorithm without any significant loss of efficiency and which cannot in this paper part 1 in a series of papers we cover the quantity approximated the warp update rule and the gradient descent approximation in future papers we will cover the choice of the error function how to allow linear appearance variation and how to impose priors on the parameters

a unique methodology for the stability robustness of multiple time delay systems abstract the stability robustness is considered for linear time invariant lti systems with rationally independent multiple time delays against delay uncertainties the problem is known to be notoriously complex primarily because the systems are infinite dimensional due to delays multiplicity of the delays in this study complicates the analysis even further and rationally independent feature of the delays makes the problem prohibitively challenging as opposed to the tds with commensurate time delays where time delays are rationally related a unique framework is described for this broadly studied problem and the enabling propositions are proven we show that this procedure analytically reveals all possible stability regions exclusively in the space of the delays as an added strength it does not require the delay free system under consideration to be stable our methodology offers a resolution to this question which has been studied from variety of directions in the past four decades none of these respectable investigations can however deliver an exact and exhaustive robustness declaration from this stand point the new method has a unique contribution

registration of challenging image pairs initialization estimation and decision our goal is an automated 2d image pair registration algorithm capable of aligning images taken of a wide variety of natural and man made scenes as well as many medical images the algorithm should handle low overlap substantial orientation and scale differences large illumination variations and physical changes in the scene an important component of this is the ability to automatically reject pairs that have no overlap or have too many differences to be aligned well we propose a complete algorithm including techniques for initialization for estimating transformation parameters and for automatically deciding if an estimate is correct keypoints extracted and matched between images are used to generate initial similarity transform estimates each accurate over a small region these initial estimates are rank ordered and tested individually in succession each estimate is refined using the dual bootstrap icp algorithm driven by matching of multiscale features a three part decision criteria combining measurements of alignment accuracy stability in the estimate and consistency in the constraints determines whether the refined transformation estimate is accepted as correct experimental results on a data set of 22 challenging image pairs show that the algorithm effectively aligns 19 of the 22 pairs and rejects 99 8 percent of the misalignments that occur when all possible pairs are tried the algorithm substantially out performs algorithms based on keypoint matching alone