decay rate dependent conditions for exponential stability of stochastic neutral systems with markovian jumping parameters abstract this note studies the problem of decay rate dependent exponential stability for neutral stochastic delay systems with markovian jumping parameters first by introducing an operator d x t i as well as a novel lyapunov krasovskii functional sufficient conditions for exponential stability of system with a decay rate are obtained second the results are extended to the robust exponential estimates for uncertain neutral stochastic delay systems with markovian jumping parameters finally numerical examples are provided to show the effectiveness of the proposed results

beyond diffusion process nss is proposed to replace the role of diffusion process to capture the geometry of the underlying manifold in shape and image retrieval nss is more precise than diffusion process and more robust to noise nss is computed more efficiently than diffusion process and it no longer needs an iterative process to guarantee the retrieval precision we obtain state of the art retrieval performance on several benchmark datasets measuring the similarity between two instances reliably shape or image is a challenging problem in shape and image retrieval in this paper a simple yet effective method called neighbor set similarity nss is proposed which is superior to both traditional pairwise similarity and diffusion process nss makes full use of contextual information to capture the geometry of the underlying manifold and obtains a more precise measure than the original pairwise similarity moreover based on nss we propose a powerful fusion process to utilize the complementarity of different descriptors to further enhance the retrieval performance the experimental results on mpeg 7 shape dataset n s image dataset and orl face dataset demonstrate the effectiveness of the proposed method in addition the time complexity of nss is much lower than diffusion process which suggests that nss is more suitable for large scale image retrieval than diffusion process

shape retrieval using hierarchical total bregman soft clustering in this paper we consider the family of total bregman divergences tbds as an efficient and robust distance measure to quantify the dissimilarity between shapes we use the tbd based l1 norm center as the representative of a set of shapes and call it the t center first we briefly present and analyze the properties of the tbds and t centers following our previous work in 1 then we prove that for any tbd there exists a distribution which belongs to the lifted exponential family lef of statistical distributions further we show that finding the maximum a posteriori map estimate of the parameters of the lifted exponential family distribution is equivalent to minimizing the tbd to find the t centers this leads to a new clustering technique namely the total bregman soft clustering algorithm we evaluate the tbd t center and the soft clustering algorithm on shape retrieval applications our shape retrieval framework is composed of three steps 1 extraction of the shape boundary points 2 affine alignment of the shapes and use of a gaussian mixture model gmm 2 3 4 to represent the aligned boundaries and 3 comparison of the gmms using tbd to find the best matches given a query shape to further speed up the shape retrieval algorithm we perform hierarchical clustering of the shapes using our total bregman soft clustering algorithm this enables us to compare the query with a small subset of shapes which are chosen to be the cluster t centers we evaluate our method on various public domain 2d and 3d databases and demonstrate comparable or better results than state of the art retrieval techniques

quadratic stability and stabilization of uncertain linear discrete time systems with state delay abstract this paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete time systems with state delay the system under consideration involves state time delay and time varying norm bounded parameter uncertainties appearing in all the matrices of the state space model necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities respectively a robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities two examples are presented to demonstrate the effectiveness of the proposed approach

c 1 cubic splines on powell sabin triangulations a bivariate c 1 cubic spline space on a triangulation with powell sabin refinement which extends the well known c 1 quadratic spline space and has a nested structure is introduced a construction of a locally supported basis that forms a partition of unity is presented based on choosing particular triangles and line segments in the domain further it is shown how these objects can be determined in order to obtain nonnegative basis functions under a natural restriction on the powell sabin refinement geometrically intuitive b spline representation is proposed which makes these splines a useful tool for cagd applications

the burbea rao and bhattacharyya centroids we study the centroid with respect to the class of information theoretic burbea rao divergences that generalize the celebrated jensen shannon divergence by measuring the non negative jensen difference induced by a strictly convex and differentiable function although those burbea rao divergences are symmetric by construction they are not metric since they fail to satisfy the triangle inequality we first explain how a particular symmetrization of bregman divergences called jensen bregman distances yields exactly those burbea rao divergences we then proceed by defining skew burbea rao divergences and show that skew burbea rao divergences amount in limit cases to compute bregman divergences we then prove that burbea rao centroids can be arbitrarily finely approximated by a generic iterative concave convex optimization algorithm with guaranteed convergence property in the second part of the paper we consider the bhattacharyya distance that is commonly used to measure overlapping degree of probability distributions we show that bhattacharyya distances on members of the same statistical exponential family amount to calculate a burbea rao divergence in disguise thus we get an efficient algorithm for computing the bhattacharyya centroid of a set of parametric distributions belonging to the same exponential families improving over former specialized methods found in the literature that were limited to univariate or diagonal multivariate gaussians to illustrate the performance of our bhattacharyya burbea rao centroid algorithm we present experimental performance results for k means and hierarchical clustering methods of gaussian mixture models

computable elastic distances between shapes we dene distances between geometric curves by the square root of the minimal energy required to transform one curve into the other the energy is formally dened from a left invariant riemannian distance on an innite dimensional group acting on the curves which can be explicitly computed the obtained distance boils down to a variational problem for which an optimal matching between the curves has to be computed an analysis of the distance when the curves are polygonal leads to a numerical procedure for the solution of the variational problem which can eciently be implemented as illustrated by experiments 1 1 generalities the problem of matching two objects together is very impor tant in computer vision and shape recognition in many cases recognition is based on shapes outlines with the help of some suitably designed distance a general principle is to associate with any pair o1 o 2 of objects to be compared a measure of discrepancy d o1 o 2 the recognition of an observed object o may be done by nding from a dictionary of templates the previously recorded object otemp for which d o otemp is minimal clearly the denition of the distance is the crucial step of the method and much research has been done in this direction we shall not try here to provide a review of the huge literature existing on the subject see for example 17 but rather focus on methods related to deformable templates with which we are directly concerned instead of basing recognition on a nite collection of points of interest primitives taken from the outline of an object corners inflexion points etc which is a popular way of handling the problem our purpose is to base the comparison on the whole outline considered as a plane curve the distance we shall dene incorporates some deformation energy between the curves the approach as we will see turns out to be intrinsic and robust to usual euclidean transformations the method is related to the wide literature on snakes 14 7 21 etc in the way that our distance corresponds to some continuous process of deformation of one curve into another it is also related to papers on elastic matching such as 8 however we provide an elastic matching algorithm which is based on a true distance between intrinsic properties of the shapes taking into account possible invariance to scaling or euclidean transformations in the case they are required from this point of view our results are indebted to the seminal work of grenander on group theory applied to pattern recognition cf 10 and 11 in particular see also 1 2 12 another source of inspiration may come from mathematical physics since we are going to look to the path process of lowest energy which deforms one object into

semi supervised kernel mean shift clustering mean shift clustering is a powerful nonparametric technique that does not require prior knowledge of the number of clusters and does not constrain the shape of the clusters however being completely unsupervised its performance suffers when the original distance metric fails to capture the underlying cluster structure despite recent advances in semi supervised clustering methods there has been little effort towards incorporating supervision into mean shift we propose a semi supervised framework for kernel mean shift clustering skms that uses only pairwise constraints to guide the clustering procedure the points are first mapped to a high dimensional kernel space where the constraints are imposed by a linear transformation of the mapped points this is achieved by modifying the initial kernel matrix by minimizing a log det divergence based objective function we show the advantages of skms by evaluating its performance on various synthetic and real datasets while comparing with state of the art semi supervised clustering algorithms

on an estimate of the decay rate for stable linear delay systems in this paper it is shown that for a certain class of stable linear delay systems we can obtain an estimate of the decay rate of the solution by a simple computation

total bregman divergence and its applications to dti analysis divergence measures provide a means to measure the pairwise dissimilarity between objects e g vectors and probability density functions pdfs kullback leibler kl divergence and the square loss sl function are two examples of commonly used dissimilarity measures which along with others belong to the family of bregman divergences bd in this paper we present a novel divergence dubbed the total bregman divergence tbd which is intrinsically robust to outliers a very desirable property in many applications further we derive the tbd center called the t center using the l1 norm for a population of positive definite matrices in closed form and show that it is invariant to transformation from the special linear group this t center which is also robust to outliers is then used in tensor interpolation as well as in an active contour based piecewise constant segmentation of a diffusion tensor magnetic resonance image dt mri additionally we derive the piecewise smooth active contour model for segmentation of dt mri using the tbd and present several comparative results on real data

fast and robust 2d shape extraction using discrete point sampling and centerline grouping in complex images this paper initially develops the discrete point sampling operator s concept model and parameters that we have previously proposed and makes its belt shaped regions in a discrete point sampling map more salient and appropriate for centerline extraction the cross sectional features of these belt shaped regions are then analyzed and seven types of feature points are defined to facilitate descriptions of such features based on these feature points a three level detection system is proposed including feature points line segments and centerlines to extract centerlines from the belt shaped regions eight basic types of centerlines and five types of relationships among the centerlines are defined by computational geometry algorithms and gestalt laws are used to cluster them into groupings if some prior information about a desired shape is available retrieval grouping may be carried out by a discrete point sampling map the purpose of which is to find centerlines by best matching with prior information discrete point sampling effectually overcomes the influences of interference from noise textures and uneven illumination and greatly reduces the difficulty of centerline extraction centerline clustered groupings and retrieval grouping can offer a strong anti interference ability with nonlinear deformations such as articulation and occlusion this method can extract large scale complex shapes combined of lines and planes from complex images the wheel location results of noise test and other shape extraction experiments show that our method has a strong capability to persist with nonlinear deformations

co transduction for shape retrieval in this paper we propose a new shape object retrieval algorithm namely co transduction the performance of a retrieval system is critically decided by the accuracy of adopted similarity measures distances or metrics in shape object retrieval ideally intraclass objects should have smaller distances than interclass objects however it is a difficult task to design an ideal metric to account for the large intraclass variation different types of measures may focus on different aspects of the objects for example measures computed based on contours and skeletons are often complementary to each other our goal is to develop an algorithm to fuse different similarity measures for robust shape retrieval through a semisupervised learning framework we name our method co transduction which is inspired by the co training algorithm given two similarity measures and a query shape the algorithm iteratively retrieves the most similar shapes using one measure and assigns them to a pool for the other measure to do a re ranking and vice versa using co transduction we achieved an improved result of 97 72 bull s eye measure on the mpeg 7 data set over the state of the art performance we also present an algorithm called tri transduction to fuse multiple input similarities and it achieved 99 06 on the mpeg 7 data set our algorithm is general and it can be directly applied on input similarity measures metrics it is not limited to object shape retrieval and can be applied to other tasks for ranking retrieval

robust exponential stability of uncertain systems with time varying delays focuses on the problem of robust exponential stability of a class of uncertain systems described by functional differential equations with time varying delays the uncertainties are assumed to be continuous time varying nonlinear and norm bounded sufficient conditions for robust exponential stability are given for both single and multiple delays cases

cluster ensembles a knowledge reuse framework for combining multiple partitions this paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings we first identify several application scenarios for the resultant knowledge reuse framework that we call cluster ensembles the cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information in addition to a direct maximization approach we propose three effective and efficient techniques for obtaining high quality combiners consensus functions the first combiner induces a similarity measure from the partitionings and then reclusters the objects the second combiner is based on hypergraph partitioning the third one collapses groups of clusters into meta clusters which then compete for each object to determine the combined clustering due to the low computational costs of our techniques it is quite feasible to use a supra consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation we evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios i where the original clusters were formed based on non identical sets of features ii where the original clustering algorithms worked on non identical sets of objects and iii where a common data set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution promising results are obtained in all three situations for synthetic as well as real data sets

macro elements and stable local bases for splines on powell sabin triangulations macro elements of arbitrary smoothness are constructed on powell sabin triangle splits these elements are useful for solving boundary value problems and for interpolation of hermite data it is shown that they are optimal with respect to spline degree and we believe they are also optimal with respect to the number of degrees of freedom the construction provides local bases for certain superspline spaces defined over powell sabin refinements these bases are shown to be stable as a function of the smallest angle in the triangulation which in turn implies that the associated spline spaces have optimal order approximation power

refinable c2 piecewise quintic polynomials on powell sabin 12 triangulations we present a construction of nested spaces of c 2 macro elements of degree 5 on triangulations of a polygonal domain obtained by uniform refinements of an initial triangulation and a powell sabin 12 split

smooth macro elements on powell sabin 12 splits macro elements of smoothness c r are constructed on powell sabin 12 splits of a triangle for all r 0 these new elements complement those recently constructed on powell sabin 6 splits and can be used to construct convenient superspline spaces with stable local bases and full approximation power that can be applied to the solution of boundary value problems and for interpolation of hermite data

solution estimates for linear differential equations with delay abstract in this paper we give explicit exponential estimates x t m e t t 0 where t t0 m 0 for solutions of a linear scalar delay differential equation x t k 1 m b k t x h k t f t t t 0 x t t t t 0 we consider two different cases when 0 corresponding to exponential stability and the case of in the first case together with the exponential estimate we also obtain an exponential stability test in the second case we get estimation for solution growth here both the coefficients and the delays are measurable not necessarily continuous

new exponential estimates for time delay systems this note considers the problem of exponential stability for time delay systems in terms of linear matrix inequalities a new sufficient condition for exponential stability is obtained based on this an improved upper bound of the decay rate can be easily calculated when time varying norm bounded parameter uncertainties appear a new sufficient condition for robust exponential stability of uncertain time delay systems is also provided the reduced conservatism of the proposed conditions is illustrated via two numerical examples

composite finite elements of class ck let be a triangulation of d r2 with vertices a ai 1 i n and pkn d v ck d t v t pn where pn polynomials of total degree n for u cr d r k and v finite dimensional subspace of ck d we consider the hermite problem hk a v find v v d v ai d u ai 1 i n k this problem is solvable in v pkn d iff n 4k 1 enisek when v pkn d 3 where 3 is a subtriangulation of obtained by subdividing each t into 3 triangles the problem has a solution for n 4k 1 e g the c1 cubic hct triangle and a p27 triangle with 31 parameters when v pkn d 6 where 6 is a subtriangulation of obtained by subdividing each t into 6 triangles the problem has a solution for n 3k 1 e g the c1 quadratic ps triangle and a p25 triangle with 31 parameters in both cases the construction needs the partial derivatives d u ai for 2k 1 the domain d is assumed to be polygonal compact and connected

smooth macro elements based on clough tocher triangle splits summary macro elements of smoothness c r on clough tocher triangle splits are constructed for all r ge 0 these new elements are improvements on elements constructed in 11 in that disproving a conjecture made there certain unneeded degrees of freedom have been removed numerical experiments on hermite interpolation with the new elements are included

an efficient earth mover s distance algorithm for robust histogram comparison we propose emd l1 a fast and exact algorithm for computing the earth mover s distance emd between a pair of histograms the efficiency of the new algorithm enables its application to problems that were previously prohibitive due to high time complexities the proposed emd l1 significantly simplifies the original linear programming formulation of emd exploiting the l1 metric structure the number of unknown variables in emd l1 is reduced to o n from o n2 of the original emd for a histogram with n bins in addition the number of constraints is reduced by half and the objective function of the linear program is simplified formally without any approximation we prove that the emd l1 formulation is equivalent to the original emd with a l1 ground distance to perform the emd l1 computation we propose an efficient tree based algorithm tree emd tree emd exploits the fact that a basic feasible solution of the simplex algorithm based solver forms a spanning tree when we interpret emd l1 as a network flow optimization problem we empirically show that this new algorithm has an average time complexity of o n2 which significantly improves the best reported supercubic complexity of the original emd the accuracy of the proposed methods is evaluated by experiments for two computation intensive problems shape recognition and interest point matching using multidimensional histogram based local features for shape recognition emd l1 is applied to compare shape contexts on the widely tested mpeg7 shape data set as well as an articulated shape data set for interest point matching sift shape context and spin image are tested on both synthetic and real image pairs with large geometrical deformation illumination change and heavy intensity noise the results demonstrate that our emd l1 based solutions outperform previously reported state of the art features and distance measures in solving the two tasks

multivariate spline spaces in principle all of the properties and applications of multivariate spline functions can be derived from the basic theories in chapter 1 the expressions of the multivariate spline functions in 2 of chapter 1 are inconvenient to be applied directly because the expressions also rely on the solutions of the global conformality conditions so as to determine all the smooth cofactors

pre organizing shape instances for landmark based shape correspondence the major challenge in constructing a statistical shape model for a structure is shape correspondence which identifies a set of corresponded landmarks across a population of shape instances to accurately estimate the underlying shape variation both global or pairwise shape correspondence methods have been developed to automatically identify the corresponded landmarks for global methods landmarks are found by optimizing a comprehensive objective function that considers the entire population of shape instances while global methods can produce very accurate shape correspondence they tend to be very inefficient when the population size is large for pairwise methods all shape instances are corresponded to a given template independently therefore pairwise methods are usually very efficient however if the population exhibits a large amount of shape variation pairwise methods may produce very poor shape correspondence in this paper we develop a new method that attempts to address the limitations of global and pairwise methods in particular we first construct a shape tree to globally organize the population of shape instances by identifying similar shape instance pairs we then perform pairwise shape correspondence between such similar shape instances with high accuracy finally we combine these pairwise correspondences to achieve a unified correspondence for the entire population of shape instances we evaluate the proposed method by comparing its performance to five available shape correspondence methods and show that the proposed method achieves the accuracy of a global method with the efficiency of a pairwise method

bregman divergence bounds and universality properties of the logarithmic loss a loss function measures the discrepancy between the true values and their estimated fits for a given instance of data in classification problems a loss function is said to be proper if a minimizer of the expected loss is the true underlying probability we show that for binary classification the divergence associated with smooth proper and convex loss functions is upper bounded by the kullback leibler kl divergence to within a normalization constant this implies that by minimizing the logarithmic loss associated with the kl divergence we minimize an upper bound to any choice of loss from this set as such the logarithmic loss is universal in the sense of providing performance guarantees with respect to a broad class of accuracy measures importantly this notion of universality is not problem specific enabling its use in diverse applications including predictive modeling data clustering and sample complexity analysis generalizations to arbitary finite alphabets are also developed the derived inequalities extend several well known f divergence results

exponential estimates for retarded time delay systems an lmi approach exponential estimates and sufficient conditions for the exponential stability of linear time delay systems are given the proof make use of lyapunov krasovskii functionals and the conditions are expressed in terms of linear matrix inequalities

shape vocabulary a robust and efficient shape representation for shape matching in this paper a learning based shape descriptor for shape matching is demonstrated formulated in a bag of words like framework the proposed method summarizes the local features extracted from certain shape to generate a integrated representation it contributes to the speed up of shape matching since the distance metric in the vector space analysis can be directly applied to compare the constructed global descriptors eliminating the time consuming stage of local feature matching similar to the philosophy in spatial pyramid matching a strategy for feature division is applied in the phase of encoded feature pooling and vocabulary learning which helps to construct a more discriminative descriptor incorporating both global and local information also a local contour based feature extraction method is designed for 2d shapes while significant properties of the local contours are inspected for the design of feature division rules the designed local feature extraction method and the feature division rules manage to reduce the variances of shape representation due to the changes in rotation in addition to 2d shape we also present a simple and natural method to extend the proposed method to the scenario of 3d shape representation the proposed shape descriptor is validated on several benchmark data sets for evaluating 2d and 3d shape matching algorithms and it is observed that the investigated shape descriptor maintains superior discriminative power as well as high time efficiency

a bayesian exemplar based approach to hierarchical shape matching this paper presents a novel probabilistic approach to hierarchical exemplar based shape matching no feature correspondence is needed among exemplars just a suitable pairwise similarity measure the approach uses a template tree to efficiently represent and match the variety of shape exemplars the tree is generated offline by a bottom up clustering approach using stochastic optimization online matching involves a simultaneous coarse to fine approach over the template tree and over the transformation parameters the main contribution of this paper is a bayesian model to estimate the a posteriori probability of the object class after a certain match at a node of the tree this model takes into account object scale and saliency and allows for a principled setting of the matching thresholds such that unpromising paths in the tree traversal process are eliminated early on the proposed approach was tested in a variety of application domains here results are presented on one of the more challenging domains real time pedestrian detection from a moving vehicle a significant speed up is obtained when comparing the proposed probabilistic matching approach with a manually tuned nonprobabilistic variant both utilizing the same template tree structure

a kernel classification framework for metric learning learning a distance metric from the given training samples plays a crucial role in many machine learning tasks and various models and optimization algorithms have been proposed in the past decade in this paper we generalize several state of the art metric learning methods such as large margin nearest neighbor lmnn and information theoretic metric learning itml into a kernel classification framework first doublets and triplets are constructed from the training samples and a family of degree 2 polynomial kernel functions is proposed for pairs of doublets or triplets then a kernel classification framework is established to generalize many popular metric learning methods such as lmnn and itml the proposed framework can also suggest new metric learning methods which can be efficiently implemented interestingly using the standard support vector machine svm solvers two novel metric learning methods namely doublet svm and triplet svm are then developed under the proposed framework experimental results show that doublet svm and triplet svm achieve competitive classification accuracies with state of the art metric learning methods but with significantly less training time

on c 2 quintic spline functions over triangulations of powell sabin s type abstract given a triangulation of a polygonal domain we find a refinemet of of by choosing t in a neighborhood of the center of the inscribed circle of each triangle of t connecting t to the vertices of the triangle t and connecting t to t if t shares an interior edge with t or to the midpoint e of any boundary edge e of t the resulting triangulation is a triangulation of powell sabin s type we investigate a c 2 quintic spline space s 5 2 whose elements are c 3 only at t s we give a dimension formula for this spline space show how to construct a locally supported basis display an interpolation scheme and prove that this spline space has the full approximation order

delay dependent robust h sub spl infin and l sub 2 l sub spl infin filtering for a class of uncertain nonlinear time delay systems this note presents delay dependent robust h sub spl infin and l sub 2 l sub spl infin filter designs for a class of nonlinear systems with multiple time varying delays in the state and parameter uncertainties residing in a polytope the nonlinearities are assumed to satisfy global lipschitz conditions attention is focused on the design of robust full order and reduced order filters guaranteeing a prescribed noise attenuation level in an h sub spl infin or l sub 2 l sub spl infin sense the admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

on computing the maximal delay intervals for stability of linear delay systems this note is concerned with stability properties of linear time invariant delay systems the authors consider delay systems of both retarded and neutral types expressed in state space forms the author s main goal is to provide a computation oriented method for computing the maximal delay intervals over which the systems under consideration maintain stability the author s results show that this can be accomplished by computing the generalized eigenvalues of certain frequency dependent matrices based on these results the author also states a necessary and sufficient condition concerning stability independent of delay for each of the retarded and neutral systems the author s results can be readily implemented and appear suitable for analyzing systems with high dimensions and many delay units

memoryless h controller design for switched non linear systems with mixed time varying delays this article deals with the h control problem for a class of switched non linear systems with mixed time varying delays the novel features here are that the system in consideration is non linear perturbation with discrete and distributed delays the time varying delay is also involved in the observation output and the controllers to be designed satisfy some exponential stability constraints on the closed loop poles by using lyapunov razumikhin functional approach new sufficient conditions for the h control with exponential stability constraint are derived in terms of the solution of riccati type equations the approach allows for simultaneous computation of the two bounds that characterise the stability rate of the solution

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

sparse contextual activation for efficient visual re ranking in this paper we propose an extremely efficient algorithm for visual re ranking by considering the original pairwise distance in the contextual space we develop a feature vector called sparse contextual activation sca that encodes the local distribution of an image hence re ranking task can be simply accomplished by vector comparison under the generalized jaccard metric which has its theoretical meaning in the fuzzy set theory in order to improve the time efficiency of re ranking procedure inverted index is successfully introduced to speed up the computation of generalized jaccard metric as a result the average time cost of re ranking for a certain query can be controlled within 1 ms furthermore inspired by query expansion we also develop an additional method called local consistency enhancement on the proposed sca to improve the retrieval performance in an unsupervised manner on the other hand the retrieval performance using a single feature may not be satisfactory enough which inspires us to fuse multiple complementary features for accurate retrieval based on sca a robust feature fusion algorithm is exploited that also preserves the characteristic of high time efficiency we assess our proposed method in various visual re ranking tasks experimental results on princeton shape benchmark 3d object wm srhec07 3d competition yael data set b face mpeg 7 data set shape and ukbench data set image manifest the effectiveness and efficiency of sca

robust stabilization of uncertain t s fuzzy time delay systems with exponential estimates this paper deals with the problem of robust stabilization for uncertain takagi sugeno t s fuzzy systems with constant time delays the purpose is to design a state feedback fuzzy controller such that the closed loop system is robustly exponentially stable with a prescribed decay rate sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities lmis by using feasible solutions of these lmis desired fuzzy controllers are designed and their corresponding exponential estimates are given in addition the main results of this paper are explicitly dependent on the decay rate this enables one to design fuzzy controllers by freely selecting decay rates according to different practical conditions two numerical examples are provided finally to demonstrate the effectiveness of the proposed design methods

efficient 3d shape matching and retrieval using a concrete radialized spherical projection representation we present a 3d shape retrieval methodology based on the theory of spherical harmonics using properties of spherical harmonics scaling and axial flipping invariance is achieved rotation normalization is performed by employing the continuous principal component analysis along with a novel approach which applies pca on the face normals of the model the 3d model is decomposed into a set of spherical functions which represents not only the intersections of the corresponding surface with rays emanating from the origin but also points in the direction of each ray which are closer to the origin than the furthest intersection point the superior performance of the proposed methodology is demonstrated through a comparison against state of the art approaches on standard databases

bivariate spline spaces and minimal determining sets abstract the paper describes bivariate spline spaces and minimal determining sets shows applications of these concepts presents two new triangular finite elements describes public domain software for the analysis of spline spaces and concludes with a concise history of these subjects the software described in this paper is available on http www math utah edu alfeld mds that page also contains links to colored versions of the figures in this paper

exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays this paper is concerned with exponential estimates and stabilization for a class of uncertain singular systems with discrete and distributed delays a sufficient condition which does not only guarantee the exponential stability and admissibility but also gives the estimates of decay rate and decay coefficient is established in terms of the linear matrix inequality lmi technique and a new lyapunov krasovskii functional the estimating procedure is implemented by solving a set of lmis which can be checked easily by effective algorithms under the proposed condition the algebraic subsystems possess the same decay rate as the differential ones moreover a state feedback stabilizing controller which makes the closed loop system exponentially stable and admissible with a prescribed lower bound of the decay rate is designed numerical examples are provided to illustrate the effectiveness of the theoretical results

asymptotic and exponential stability of uncertain system with interval delay abstract this paper considers the problem of asymptotic and exponential stability analysis of the continuous system with interval time varying delay and uncertainties by constructing a new lyapunov krasovskii functional several delay range dependent conditions are derived in terms of the linear matrix inequalities lmis two novel integral equalities are employed to overcome the disadvantages of the methods in existing references the merits of the proposed criteria lie in the exponential stability being a free value and the less conservativeness finally some numerical examples are included to illustrate the effectiveness and the improvement of the proposed method

exponential stability of time delay systems via new weighted integral inequalities in this paper new weighted integral inequalities wiis are first derived based on jensen s integral inequalities in single and double forms it is theoretically shown that the newly derived inequalities in this paper encompass both the jensen inequality and its most recent improvement based on wirtinger s integral inequality the potential capability of wiis is demonstrated through applications to exponential stability analysis of some classes of time delay systems in the framework of linear matrix inequalities lmis the effectiveness and least conservativeness of the derived stability conditions using wiis are shown by various numerical examples

efficient shape matching using shape contexts we demonstrate that shape contexts can be used to quickly prune a search for similar shapes we present two algorithms for rapid shape retrieval representative shape contexts performing comparisons based on a small number of shape contexts and shapemes using vector quantization in the space of shape contexts to obtain prototypical shape pieces

a bivariate c1 cubic super spline space on powell sabin triangulation a bivariate c 1 cubic super spline is constructed on powell sabin type 1 split with the additional smoothness at vertices in the original triangulation being c 2 which permits the hermite interpolation up to the second order partial derivatives exactly on all the vertices in the original triangulation the locally supported dual basis and computational details using derivatives around each vertex are given

macro elements and stable local bases for splines on clough tocher triangulations macro elements of arbitrary smoothness are constructed on clough tocher triangle splits these elements can be used for solving boundary value problems or for interpolation of hermite data and are shown to be optimal with respect to spline degree we conjecture they are also optimal with respect to the number of degrees of freedom the construction provides local bases for certain superspline spaces defined over clough tocher refinements of arbitrary triangulations these bases are shown to be stable as a function of the smallest angle in the triangulation which in turn implies that the associated spline spaces have optimal order approximation power

on super splines and finite elements super splines are spaces of multivariate splines consisting of piecewise polynomials defined on triangulations where the degree of smoothness enforced at the vertices is larger than the degree of smoothness enforced across the edges dimension formulae for super spline spaces are established and the construction of explicit bases of locally supported splines is presented in addition it is shown that many classical finite element spaces can be interpreted as super spline spaces providing a link between spline theory and the highly applicable finite element theory

robust point set registration using gaussian mixture models in this paper we present a unified framework for the rigid and nonrigid point set registration problem in the presence of significant amounts of noise and outliers the key idea of this registration framework is to represent the input point sets using gaussian mixture models then the problem of point set registration is reformulated as the problem of aligning two gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized we show that the popular iterative closest point icp method and several existing point set registration methods in the field are closely related and can be reinterpreted meaningfully in our general framework our instantiation of this general framework is based on the the l2 distance between two gaussian mixtures which has the closed form expression and in turn leads to a computationally efficient registration algorithm the resulting registration algorithm exhibits inherent statistical robustness has an intuitive interpretation and is simple to implement we also provide theoretical and experimental comparisons with other robust methods for point set registration

a delay dependent approach to robust h sub spl infin filtering for uncertain discrete time state delayed systems a delay dependent approach to robust h sub spl infin filtering is proposed for linear discrete time uncertain systems with multiple delays in the state the uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed h sub spl infin noise attenuation level the proposed filter design methodology incorporates some recently appeared results such as moon s new version of the upper bound for the inner product of two vectors and de oliveira s idea of parameter dependent stability which greatly reduce the overdesign introduced in the derivation process in addition to the full order filtering problem the challenging reduced order case is also addressed by using different linearization procedures both full and reduced order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies

h spl infin output feedback controller design for linear systems with time varying delayed state this paper considers the h spl infin controller design problem for linear systems with time varying delays in states the authors obtain sufficient conditions for the existence of h spl infin controllers in terms of three linear matrix inequalities lmis these sufficient conditions are dependent on the maximum value of the time derivative of time varying delay furthermore they briefly explain how to construct such controllers from the positive definite solutions of their lmis and give an example

learning context sensitive shape similarity by graph transduction shape similarity and shape retrieval are very important topics in computer vision the recent progress in this domain has been mostly driven by designing smart shape descriptors for providing better similarity measure between pairs of shapes in this paper we provide a new perspective to this problem by considering the existing shapes as a group and study their similarity measures to the query shape in a graph structure our method is general and can be built on top of any existing shape similarity measure for a given similarity measure a new similarity is learned through graph transduction the new similarity is learned iteratively so that the neighbors of a given shape influence its final similarity to the query the basic idea here is related to pagerank ranking which forms a foundation of google web search the presented experimental results demonstrate that the proposed approach yields significant improvements over the state of art shape matching algorithms we obtained a retrieval rate of 91 61 percent on the mpeg 7 data set which is the highest ever reported in the literature moreover the learned similarity by the proposed method also achieves promising improvements on both shape classification and shape clustering

comments on on an estimate of the delay rate for stable linear delay systems it is shown that an estimate of the decay rate of a class of stable linear delay systems can be obtained without solving the transcendental equation and is in addition less restrictive than that given by mori et al 1982

3d model retrieval using probability density based shape descriptors we address content based retrieval of complete 3d object models by a probabilistic generative description of local shape properties the proposed shape description framework characterizes a 3d object with sampled multivariate probability density functions of its local surface features this density based descriptor can be efficiently computed via kernel density estimation kde coupled with fast gauss transform the non parametric kde technique allows reliable characterization of a diverse set of shapes and yields descriptors which remain relatively insensitive to small shape perturbations and mesh resolution density based characterization also induces a permutation property which can be used to guarantee invariance at the shape matching stage as proven by extensive retrieval experiments on several 3d databases our framework provides state of the art discrimination over a broad and heterogeneous set of shape categories

divergence function duality and convex analysis from a smooth strictly convex function rn r a parametric family of divergence function d may be introduced d x y 4 1 2 1 2 x 1 2 y 1 2x 1 2y for x y int dom rn and for r with d 1 defined through taking the limit of each member is shown to induce an independent riemannian metric as well as a pair of dual connections which are generally nonflat except for 1 in the latter case d 1 reduces to the nonparametric bregman divergence which is representable using and its convex conjugate and becomes the canonical divergence for dually flat spaces amari 1982 1985 amari nagaoka 2000 this formulation based on convex analysis naturally extends the information geometric interpretation of divergence functions eguchi 1983 to allow the distinction between two different kinds of duality referential duality and representational duality when applied to not necessarily normalized probability densities the concept of conjugated representations of densities is introduced so that connections defined on probability densities embody both referential and representational duality and are hence themselves bidual when restricted to a finite dimensional affine submanifold the natural parameters of a certain representation of densities and the expectation parameters under its conjugate representation form biorthogonal coordinates the alpha representation indexed by now 1 1 is shown to be the only measure invariant representation the resulting two parameter family of divergence functionals d 1 1 1 1 induces identical fisher information but bidual alpha connection pairs it reduces in form to amari s alpha divergence family when 1 or when 1 but to the family of jensen difference rao 1987 when 1

jensen bregman logdet divergence with application to efficient similarity search for covariance matrices covariance matrices have found success in several computer vision applications including activity recognition visual surveillance and diffusion tensor imaging this is because they provide an easy platform for fusing multiple features compactly an important task in all of these applications is to compare two covariance matrices using a dis similarity function for which the common choice is the riemannian metric on the manifold inhabited by these matrices as this riemannian manifold is not flat the dissimilarities should take into account the curvature of the manifold as a result such distance computations tend to slow down especially when the matrix dimensions are large or gradients are required further suitability of the metric to enable efficient nearest neighbor retrieval is an important requirement in the contemporary times of big data analytics to alleviate these difficulties this paper proposes a novel dissimilarity measure for covariances the jensen bregman logdet divergence jbld this divergence enjoys several desirable theoretical properties and at the same time is computationally less demanding compared to standard measures utilizing the fact that the square root of jbld is a metric we address the problem of efficient nearest neighbor retrieval on large covariance datasets via a metric tree data structure to this end we propose a k means clustering algorithm on jbld we demonstrate the superior performance of jbld on covariance datasets from several computer vision applications

integration of stochastic models by minimizing α divergence when there are a number of stochastic models in the form of probability distributions one needs to integrate them mixtures of distributions are frequently used but exponential mixtures also provide a good means of integration this letter proposes a one parameter family of integration called integration which includes all of these well known integrations these are generalizations of various averages of numbers such as arithmetic geometric and harmonic averages there are psychophysical experiments that suggest that integrations are used in the brain the divergence between two distributions is defined which is a natural generalization of kullback leibler divergence and hellinger distance and it is proved that integration is optimal in the sense of minimizing divergence the theory is applied to generalize the mixture of experts and the product of experts to the mixture of experts the predictive distribution is also stated in the bayesian framework