on the order of stable compensators abstract by means of two typical examples it is shown that in general the minimal order of a stabilizing stable compensator may not be bounded in terms of the plant order such bounds can only be given in the special case of plants with at most one right half plane zero implications for the simultaneous stabilization problem are elucidated

optimal diagonal scaling for infinity norm optimization abstract a solution is presented for the previously unsolved diagonally scaled multivariable infinity norm optimization problem of minimizing d s a s s x s d 1 s over the set of stable minimum phase diagonal d s and stable x s this problem is of central importance in the synthesis of feedback control laws for robust stability and insensitivity in the presence of structured plant uncertainty the result facilitates the design of feedback controllers which optimize the excess stability margin 3 or equivalently the structured singular value 4 of diagonally perturbed feedback systems

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

principal warps thin plate splines and the decomposition of deformations the decomposition of deformations by principal warps is demonstrated the method is extended to deal with curving edges between landmarks this formulation is related to other applications of splines current in computer vision how they might aid in the extraction of features for analysis comparison and diagnosis of biological and medical images in indicated

efficient image retrieval through vantage objects we describe a new indexing structure for general image retrieval that relies solely on a distance function giving the similarity between two images for each image object in the database its distance to a set of m predetermined vantage objects is calculated the m vector of these distances specifies a point in the m dimensional vantage space the database objects that are similar in terms of the distance function to a given query object can be determined by means of an efficient nearest neighbor search on these points we demonstrate the viability of our approach through experimental results obtained with two image databases one consisting of about 5200 raster images of stamps the other containing about 72 000 hieroglyphic polylines

the generalization of the r transform for invariant pattern representation the beneficial properties of the radon transform make it a useful intermediate representation for the extraction of invariant features from pattern images for the purpose of indexing matching this paper revisits the problem of radon image utilization with a generic view on a popular radon transform based transform and pattern descriptor the r transform and r signature bringing in a class of transforms and descriptors spatially describing patterns at all directions and at different levels while maintaining the beneficial properties of the conventional r transform and r signature the domain of this class which is delimited due to the existence of singularities and the effect of sampling quantization and additive noise is examined moreover the ability of the generic r transform to encode the dominant directions of patterns is also discussed adding to the robustness to additive noise of the generic r signature the stability of dominant direction encoding by the generic r transform and the superiority of the generic r signature over existing invariant pattern descriptors on grayscale and binary noisy datasets have been confirmed by experiments

robustness of shape descriptors to incomplete contour representations with inspiration from psychophysical researches of the human visual system we propose a novel aspect and a method for performance evaluation of contour based shape recognition algorithms regarding their robustness to incompleteness of contours we use complete contour representations of objects as a reference training set incomplete contour representations of the same objects are used as a test set the performance of an algorithm is reported using the recognition rate as a function of the percentage of contour retained we call this evaluation procedure the icr test we consider three types of contour incompleteness viz segment wise contour deletion occlusion and random pixel depletion as an illustration the robustness of two shape recognition algorithms to contour incompleteness is evaluated these algorithms use a shape context and a distance multiset as local shape descriptors qualitatively both algorithms mimic human visual perception in the sense that recognition performance monotonously increases with the degree of completeness and that they perform best in the case of random depletion and worst in the case of occluded contours the distance multiset method performs better than the shape context method in this test framework

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

new mathematical and algorithmic schemes for pattern classification with application to the identification of writers of important ancient documents abstract in this paper a novel approach is introduced for classifying curves into proper families according to their similarity first a mathematical quantity we call plane curvature is introduced and a number of propositions are stated and proved proper similarity measures of two curves are introduced and a subsequent statistical analysis is applied first the efficiency of the curve fitting process has been tested on 2 shapes datasets of reference next the methodology has been applied to the very important problem of classifying 23 byzantine codices and 46 ancient inscriptions to their writers thus achieving correct dating of their content the inscriptions have been attributed to ten individual hands and the byzantine codices to four writers

angular radon spectrum for rotation estimation abstract this paper presents a robust method for rotation estimation of planar point sets using the angular radon spectrum ars given a gaussian mixture model gmm representing the point distribution the ars is a continuous function derived from the radon transform of such distribution the ars characterizes the orientation of a point distribution by measuring its alignment w r t a pencil of parallel lines by exploting its translation and angular shift invariance the rotation angle between two point sets can be estimated through the correlation of the corresponding spectra beside its definition the novel contributions of this paper include the efficient computation of the ars and of the correlation function through their fourier expansion and a new algorithm for assessing the rotation between two point sets moreover experiments with standard benchmark datasets assess the performance of the proposed algorithm and other state of the art methods in presence of noisy and incomplete data

diffusion approximation and computation of the critical size this paper is devoted to the mathematical definition of the extrapolation length which appears in the diffusion approximation to obtain this result we describe the spectral properties of the transport equation and we show how the diffusion approximation is related to the computation of the critical size the paper also contains some simple numerical examples and some new results for the milne problem introduction the computation of the critical size and the diffusion approximation for the transport equation have been closely related and this is due to the following facts first the computation of the critical size is much easier for the diffusion approximation than for the original transport equation second for the critical size one can consider a host media x nxq with x0 given and 17 a positive number the problem of the critical size is then reduced to the computation of the parameter zj it turns out that when the transport operator is almost conservative the critical value of the parameter 17 is large and it is exactly for this range of value that the diffusion approximation is accurate on the other hand the physical boundary condition for the diffusion approxi mation is of the form

object matching with hierarchical skeletons the skeleton of an object provides an intuitive and effective abstraction which facilitates object matching and recognition however without any human interaction traditional skeleton based descriptors and matching algorithms are not stable for deformable objects specifically some fine grained topological and geometrical features would be discarded if the skeleton was incomplete or only represented significant visual parts of an object moreover the performance of skeleton based matching highly depends on the quality and completeness of skeletons in this paper we propose a novel object representation and matching algorithm based on hierarchical skeletons which capture the shape topology and geometry through multiple levels of skeletons for object representation we reuse the pruned skeleton branches to represent the coarse and fine grained shape topological and geometrical features moreover this can improve the stability of skeleton pruning without human interaction we also propose an object matching method which considers both global shape properties and fine grained deformations by defining singleton and pairwise potentials for similarity computation between hierarchical skeletons our experiments attest our hierarchical skeleton based method a significantly better performance than most existing shape based object matching methods on six datasets achieving a 99 21 bulls eye score on the mpeg7 shape dataset highlightsit represents the coarse and fine grained shape topological and geometrical features it improves the stability of skeleton pruning without human interaction it considers both global and fine shape properties by different potential functions it achieves a better performance than most existing methods on six datasets experiments attest our method a better performance than most related approaches we achieve a 99 21 bulls eye score on the mpeg7 shape dataset

shape matching and modeling using skeletal context shape is a significant visual clue for human perception and shape models show considerable promise as a basis for extracting objects from images this paper proposes a novel approach for shape matching and modeling using the symmetry characterization of shape interior and the spatial relationships of shape structures based on the representative skeletal features we develop a mechanism to generate a coarse segment matching between different instances of an object additionally the natural correspondence of skeletal branches to sequential segments along the shape curves is employed in the matching process to avoid false correspondences across different segments point matches within the corresponding segments are then obtained by solving a constrained assignment problem the validation of the proposed approach is illustrated on various data sets in the presence of considerable deformation and occlusion and the results are compared with those of popular approaches we also demonstrate the performance of our method on biological objects for shape modeling showing better models than those obtained by the state of the art shape modeling approaches

robust shape similarity retrieval based on contour segmentation polygonal multiresolution and elastic matching in this paper we are going to present a novel shape similarity retrieval algorithm that can be used to match and recognize 2d objects the match process uses a new multi resolution polygonal shape descriptor that is invariant to scale rotation and translation the shape descriptor equally segments the contour of any shape regardless of its complexity and captures three features around its center including the distance and slope relative to the center all parameters are normalized relative to the max values the novel shape matching algorithm uses the shape descriptor and applies it by linearly scanning a stored set of shapes and measuring the similarity using elastic comparisons of shape segments similarity measurement is achieved by the sum of differences distance measure the multi resolution segmentation provides flexibility for applications that have different time and space requirements while maintaining high accuracy results and the elastic matching adds an advantage when matching partially occluded shapes we applied our algorithms on many test databases including the mpeg 7 shape core experiment and achieved the highest result reported with a score of 84 33 for the mpeg 7 part b similarity test

a drift collision balance for a boltzmann poisson system in bounded domains we consider a low density approximation to a boltzmann poisson system for electrons in a semiconductor in regimes where strong forcing balances the collision terms we compute the hydrodynamics corresponding to this regime by the chapman enskog method and by a closure of moment equations as well in both cases we obtain reaction diffusion systems with anisotropic diffusions and convection coefficients that depend on the spatial derivatives of the anisotropic diffusion in the case of a relaxation collision operator there is a recursion formula such that this self consistent closure computes all the moments at all orders in the expanding parameter the recursion procedure can be applied to field dependent relaxation time approximations yielding a velocity saturated mobility in addition we discuss boundary conditions for both the distribution function and the moments these nonequilibrium hydrodynamical regimes have been observed in the modeling of submicron doped semiconductor silicon devices and nume

shape classification using the inner distance part structure and articulation are of fundamental importance in computer and human vision we propose using the inner distance to build shape descriptors that are robust to articulation and capture part structure the inner distance is defined as the length of the shortest path between landmark points within the shape silhouette we show that it is articulation insensitive and more effective at capturing part structures than the euclidean distance this suggests that the inner distance can be used as a replacement for the euclidean distance to build more accurate descriptors for complex shapes especially for those with articulated parts in addition texture information along the shortest path can be used to further improve shape classification with this idea we propose three approaches to using the inner distance the first method combines the inner distance and multidimensional scaling mds to build articulation invariant signatures for articulated shapes the second method uses the inner distance to build a new shape descriptor based on shape contexts the third one extends the second one by considering the texture information along shortest paths the proposed approaches have been tested on a variety of shape databases including an articulated shape data set mpeg7 ce shape 1 kimia silhouettes the eth 80 data set two leaf data sets and a human motion silhouette data set in all the experiments our methods demonstrate effective performance compared with other algorithms

distance learning for similarity estimation in this paper we present a general guideline to find a better distance measure for similarity estimation based on statistical analysis of distribution models and distance functions a new set of distance measures are derived from the harmonic distance the geometric distance and their generalized variants according to the maximum likelihood theory these measures can provide a more accurate feature model than the classical euclidean and manhattan distances we also find that the feature elements are often from heterogeneous sources that may have different influence on similarity estimation therefore the assumption of single isotropic distribution model is often inappropriate to alleviate this problem we use a boosted distance measure framework that finds multiple distance measures which fit the distribution of selected feature elements best for accurate similarity estimation the new distance measures for similarity estimation are tested on two applications stereo matching and motion tracking in video sequences the performance of boosted distance measure is further evaluated on several benchmark data sets from the uci repository and two image retrieval applications in all the experiments robust results are obtained based on the proposed methods

3d shape matching via two layer coding view based 3d shape retrieval is a popular branch in 3d shape analysis owing to the high discriminative property of 2d views however many previous works do not scale up to large 3d shape databases we propose a two layer coding tlc framework to conduct shape matching much more efficiently the first layer coding is applied to pairs of views represented as depth images the spatial relationship of each view pair is captured with so called eigen angle which is the planar angle between the two views measured at the center of the 3d shape prior to the second layer coding the view pairs are divided into subsets according to their eigen angles consequently view pairs that differ significantly in their eigen angles are encoded with different codewords which implies that spatial arrangement of views is preserved in the second layer coding the final feature vector of a 3d shape is the concatenation of all the encoded features from different subsets which is used for efficient indexing directly tlc is not limited to encode the local features from 2d views but can be also applied to encoding 3d features exhaustive experimental results confirm that tlc achieves state of the art performance in both retrieval accuracy and efficiency

statistical shape analysis clustering learning and testing using a differential geometric treatment of planar shapes we present tools for 1 hierarchical clustering of imaged objects according to the shapes of their boundaries 2 learning of probability models for clusters of shapes and 3 testing of newly observed shapes under competing probability models clustering at any level of hierarchy is performed using a minimum variance type criterion and a markov process statistical means of clusters provide shapes to be clustered at the next higher level thus building a hierarchy of shapes using finite dimensional approximations of spaces tangent to the shape space at sample means we implicitly impose probability models on the shape space and results are illustrated via random sampling and classification hypothesis testing together hierarchical clustering and hypothesis testing provide an efficient framework for shape retrieval examples are presented using shapes and images from eth surrey and amcom databases

two sided tangential interpolation with real rational units in h the problem of computing units in rh that satisfy ball gohberg rodman two sided tangential interpolation conditions over the open right half complex plane is considered we first show that every unit in rh can be written up to left multiplication by an orthogonal matrix as a finite product of positive real functions in rh with invertible value at this factorization is used to recast interpolation conditions on units as coupled positive real interpolation problems for the factors an algebraic necessary and sufficient condition for the existence of solutions and a parameterization of all solutions when one exists are given we introduce a multivariable parity interlacing property for left interpolation data and present an algorithm to compute units the algorithm involves a line search and is guaranteed to terminate in a finite number of operations when the data set has parity interlacing property as an application strong stabilization of lti plants is discussed a procedure to construct a stable stabilizing controller is given the results are illustrated with a simple mimo example a necessary and sufficient condition characterizing all real rational units that satisfy tangential interpolation conditions is given an algorithm to compute units for left interpolation is presented

path similarity skeleton graph matching this paper proposes a novel graph matching algorithm and applies it to shape recognition based on object silhouettes the main idea is to match skeleton graphs by comparing the geodesic paths between skeleton endpoints in contrast to typical tree or graph matching methods we do not consider the topological graph structure our approach is motivated by the fact that visually similar skeleton graphs may have completely different topological structures the proposed comparison of geodesic paths between endpoints of skeleton graphs yields correct matching results in such cases the skeletons are pruned by contour partitioning with discrete curve evolution which implies that the endpoints of skeleton branches correspond to visual parts of the objects the experimental results demonstrate that our method is able to produce correct results in the presence of articulations stretching and contour deformations

small gain stability conditions for linear systems with time varying delays abstract in this paper we show that a variety of stability conditions both existing and new can be derived for linear systems subject to time varying delays in a unified manner in the form of scaled small gain conditions from a robust control perspective our development seeks to cast the stability problem as one of robust stability analysis and the resulting stability conditions are also reminiscent of robust stability bounds typically found in robust control theory the development is built on the well known conventional robust stability analysis requiring essentially no more than a straightforward application of the small gain theorem the derived conditions have conceptual appeal and they can be checked using standard robust control toolboxes

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

hyperbolic versus parabolic asymptotics in kinetic theory toward fluid dynamic models in this work we are interested in the hyperbolic limits in kinetic theory we propose a nonstandard scaling to be understood as a sort of intermediate hyperbolic limit which connects the macroscopic hyperbolic limiting behavior of the physical system with the microscopic properties usually obtained under parabolic scalings we present our main result by means of a general kinetic frame for the intermediate hyperbolic limit which covers some well known examples in kinetic theory vlasov poisson fokker planck systems and linear relaxation for boltzmann type equations in semiconductor theory among others we will also apply our methods to deal with the kac approach to boltzmann operators

computational macroscopic approximations to the one dimensional relaxation time kinetic system for semiconductors abstract we study comparisons of deterministic computational methods for one dimensional relaxation charged transport in submicron channel devices our analysis focuses on the appropriate macroscopic approximations under regimes associated to different devices with similar geometries we show when taking standard parameters corresponding to si devices that the kinetic one dimensional relaxation model can be approximated by a multi fluid domain decomposition technique that incorporates classical drift diffusion equations with corrections in the current in addition when considering physical dimensions corresponding to gaas devices the technique requires new hydrodynamics that we propose and compute our comparison involves detailed computations of local distribution function solution of the kinetic equation its first three moments compared with the computed fluid variables and the presentation of all corresponding current voltage characteristic curves

sensitivity reduction by stable controllers for mimo infinite dimensional systems via the tangential nevanlinna pick interpolation we study the problem of finding a stable stabilizing controller that satisfies a desired sensitivity level for an mimo infinite dimensional system the systems we consider have finitely many simple transmission zeros in c but they are allowed to possess infinitely many poles in c we compute both upper and lower bounds of the minimum sensitivity achievable by a stable controller via the tangential nevanlinna pick interpolation we also obtain stable controllers attaining such an upper bound to illustrate the results we discuss a repetitive control system as an application of the proposed method

non rigid point set registration by preserving global and local structures in previous work on point registration the input point sets are often represented using gaussian mixture models and the registration is then addressed through a probabilistic approach which aims to exploit global relationships on the point sets for non rigid shapes however the local structures among neighboring points are also strong and stable and thus helpful in recovering the point correspondence in this paper we formulate point registration as the estimation of a mixture of densities where local features such as shape context are used to assign the membership probabilities of the mixture model this enables us to preserve both global and local structures during matching the transformation between the two point sets is specified in a reproducing kernel hilbert space and a sparse approximation is adopted to achieve a fast implementation extensive experiments on both synthesized and real data show the robustness of our approach under various types of distortions such as deformation noise outliers rotation and occlusion it greatly outperforms the state of the art methods especially when the data is badly degraded

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

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

an interpolation approach to multiobjective ℋ design a problem of practical importance is to find a linear controller that shapes the closed loop frequency responses in some desirable fashion when the magnitude of the target shapes is specified this problem may be cast as that of finding a controller such that several norms satisfy specified bounds in this paper we show that under suitable assumptions an exact solution to this multiobjective problem can be obtained the method we propose requires the solution to 1 a finite dimensional linear matrix inequality problem and 2 a standard single objective problem for a suitably constructed auxiliary plant we illustrate the results with a numerical example

shape representation and classification using the poisson equation we present a novel approach that allows us to reliably compute many useful properties of a silhouette our approach assigns for every internal point of the silhouette a value reflecting the mean time required for a random walk beginning at the point to hit the boundaries this function can be computed by solving poisson s equation with the silhouette contours providing boundary conditions we show how this function can be used to reliably extract various shape properties including part structure and rough skeleton local orientation and aspect ratio of different parts and convex and concave sections of the boundaries in addition to this we discuss properties of the solution and show how to efficiently compute this solution using multigrid algorithms we demonstrate the utility of the extracted properties by using them for shape classification and retrieval

robust symbolic representation for shape recognition and retrieval a new method for shape recognition and retrieval is proposed here the suggested algorithm is based on several steps the algorithm analyzes the contour of pairs of shapes their contours are recovered and represented by a pair of n points obtained by linear interpolation given two points p i and q j from the two shapes the cost of their matching is evaluated by using the shape context and by using dynamic programming the best matching between the point sets is obtained dynamic programming not only recovers the best matching but also identifies occlusions i e points in the two shapes which cannot be properly matched given the correspondence between the two point sets the two contours are aligned using procrustes analysis after alignment each contour is transformed into a string of symbols and a modified version of edit distance is used to compute the similarity between strings of symbols finally recognition and retrieval are obtained by a simple nearest neighbor procedure the algorithm has been tested on a large set of shape databases kimia mpeg 7 natural silhouette database gesture database marine database swedish leaf database diatom database eth 80 3d object database providing performances for both in recognition and in retrieval superior to most of previously proposed approaches

indexing hierarchical structures using graph spectra hierarchical image structures are abundant in computer vision and have been used to encode part structure scale spaces and a variety of multiresolution features in this paper we describe a framework for indexing such representations that embeds the topological structure of a directed acyclic graph dag into a low dimensional vector space based on a novel spectral characterization of a dag this topological signature allows us to efficiently retrieve a promising set of candidates from a database of models using a simple nearest neighbor search we establish the insensitivity of the signature to minor perturbation of graph structure due to noise occlusion or node split merge to accommodate large scale occlusion the dag rooted at each nonleaf node of the query votes for model objects that share that part effectively accumulating local evidence in a model dag s topological subspaces we demonstrate the approach with a series of indexing experiments in the domain of view based 3d object recognition using shock graphs

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

a numerical method for kinetic semiconductor equations in the drift diffusion limit an asymptotic induced scheme for kinetic semiconductor equations with the diffusion scaling is developed the scheme is based on the asymptotic analysis of the kinetic semiconductor equation it works uniformly for all ranges of mean free paths the velocity discretization is done using quadrature points equivalent to a moment expansion method numerical results for different physical situations are presented

a numerical method for computing asymptotic states and outgoing distributions for kinetic linear half space problems linear half space problems can be used to solve domain decomposition problems between boltzmann and aerodynamic equations a new fast numerical method computing the asymptotic states and outgoing distributions for a linearized bgk half space problem is presented relations with the so called variational methods are discussed in particular we stress the connection between these methods and chapman enskog type expansions

shape classification by manifold learning in multiple observation spaces manifold learning is a non linear method with the aim of finding a constructive way to embed the data from a high dimensional space into a low dimensional one the improvement of shape classification is the major approach in this paper which is based on the continuity in feature space in accordance with the continuity in semantic one in this regard a non linear approach is employed to map the shape feature vectors to a new space while their semantics become similar with human opinion the euclidean distance between two feature vectors would be closed shapes are described by four contour based and region based techniques by the proposed method in other word they are described in four observation spaces furthermore a parameter space is learnt from multiple observation spaces based on fusion of dissimilarities in a supervised manner experimental results show the validity and efficiency of the proposed approach for shape classification over a variety of standard shape datasets

parameter free modelling of 2d shapes with ellipses our goal is to represent a given 2d shape with an automatically determined number of ellipses so that the total area covered by the ellipses is equal to the area of the original shape without any assumption or prior knowledge about the object structure to solve this interesting theoretical problem first we employ the skeleton of the 2d shape which provides important information on the parameters of the ellipses that could approximate the original shape for a given number of such ellipses the hard expectation maximisation em algorithm is employed to maximise the shape coverage under the equal area constraint different models i e solutions involving different numbers of ellipses are evaluated based on the akaike information criterion aic this considers a novel entropy based shape complexity measure that balances the model complexity and the model approximation error in order to minimise the aic criterion two variants are proposed and evaluated a the augmentative method that gradually increases the number of considered ellipses starting from a single one and b the decremental method that decreases the number of ellipses starting from a large automatically defined set the obtained quantitative results on more than 4000 2d shapes included in standard as well as in custom datasets quantify the performance of the proposed methods and illustrate that their solutions agree with human intuition highlights2d shape representation with an automatically determined number of ellipses we propose a novel definition of shape complexity that exploits the shape skeleton good balance between model complexity and shape coverage experiments on more than 4000 2d shapes show the effectiveness of the proposed methods the solutions proposed by aefa and defa seem to agree with human intuition

two sided interpolation for matrix functions with entries in the hardy space abstract the two sided lagrange sylvester interpolation problem is solved in the framework of h2 functions the extra hilbert space structure allows us to give self contained and independent arguments

a global local affinity graph for image segmentation construction of a reliable graph capturing perceptual grouping cues of an image is fundamental for graph cut based image segmentation methods in this paper we propose a novel sparse global local affinity graph over superpixels of an input image to capture both short and long range grouping cues and thereby enabling perceptual grouping laws including proximity similarity continuity and to enter in action through a suitable graph cut algorithm moreover we also evaluate three major visual features namely color texture and shape for their effectiveness in perceptual segmentation and propose a simple graph fusion scheme to implement some recent findings from psychophysics which suggest combining these visual features with different emphases for perceptual grouping in particular an input image is first oversegmented into superpixels at different scales we postulate a gravitation law based on empirical observations and divide superpixels adaptively into small medium and large sized sets global grouping is achieved using medium sized superpixels through a sparse representation of superpixels features by solving a ell 0 minimization problem and thereby enabling continuity or propagation of local smoothness over long range connections small and large sized superpixels are then used to achieve local smoothness through an adjacent graph in a given feature space and thus implementing perceptual laws for example similarity and proximity finally a bipartite graph is also introduced to enable propagation of grouping cues between superpixels of different scales extensive experiments are carried out on the berkeley segmentation database in comparison with several state of the art graph constructions the results show the effectiveness of the proposed approach which outperforms state of the art graphs using four different objective criteria namely the probabilistic rand index the variation of information the global consistency error and the boundary displacement error

a classification of well posed kinetic layer problems in the first part of this paper we study the half space boundary value problem for the boltzmann equation with an incoming distribution obtained when considering the boundary layer arising in the kinetic theory of gases as the mean free path tends to zero we linearize it about a drifting maxwellian and prove that as conjectured by cercignani 4 the problem is well posed when the drift velocity u exceeds the sound speed c but that one respectively four five additional conditions must be imposed when 0 u c respectively c u 0 and u c in the second part we show that the well posedness and the asymptotic behavior results for kinetic layers equations with prescribed incoming flux can be extended to more general and realistic boundary conditions

an algorithm for interpolation with units in h with applications to feedback stabilization abstract the problem of finding a unit in h i e an h function the inverse of which is also h which interpolates to given points in the right half plane has important applications in a number of feedback stabilization problems i e strong stabilization and simultaneous stabilization an algorithm for computing such interpolating units is presented which requires a lower degree unit than other available algorithms

improving skeletal shape abstraction using multiple optimal solutions shape abstraction is an important problem faced by researchers in many fields such as pattern recognition computer vision and industrial design a recently developed previous shape abstraction framework demirci et al 20 generates an abstracted shape based on the correspondences between the features of the input shapes where the correspondences are obtained using the first optimal solution of a well known transportation problem as the size of the feature space grows the possibility of having more than one optimal solution for the same problem increases considering the case where multiple optimal solutions exist for the same transportation problem we first rank all optimal solutions based on how much they preserve the local neighborhood relations in this paper instead of creating the abstracted shape using the first optimal solution as done by the previous work we create the abstracted shape using the highest ranked optimal solution with this new property more effective abstracted shapes are generated experimental evaluation of the framework demonstrates that the proposed approach compares favorably with the previous technique in a set of shape retrieval experiments for different datasets highlightsskeletal shape abstraction is reformulated as the transportation problem a distortion free graph embedding is used for a better representation all optimal solutions for the transportation problem are considered the optimal solution which most resembles the neighborhood relations is used experiments demonstrate the improved performance

perceptually motivated shape context which uses shape interiors in this paper we identify some of the limitations of current day shape matching techniques we provide examples of how contour based shape matching techniques cannot provide a good match for certain visually similar shapes to overcome this limitation we propose a perceptually motivated variant of the well known shape context descriptor we identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties we show that our method can easily be augmented with any other shape matching algorithm we also show from our experiments that the use of our descriptor can significantly improve the retrieval rates

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

shape similarity measure based on correspondence of visual parts a cognitively motivated similarity measure is presented and its properties are analyzed with respect to retrieval of similar objects in image databases of silhouettes of 2d objects to reduce influence of digitization noise as well as segmentation errors the shapes are simplified by a novel process of digital curve evolution to compute our similarity measure we first establish the best possible correspondence of visual parts without explicitly computing the visual parts then the similarity between corresponding parts is computed and aggregated we applied our similarity measure to shape matching of object contours in various image databases and compared it to well known approaches in the literature the experimental results justify that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions

recognize objects with three kinds of information in landmarks abstract object recognition is one of the most important tasks in computer vision domain and it has been extensively applied in many areas during the last three decades in this paper a method is proposed to recognize objects in shape spaces in which landmarks have three kinds of information i e landmarks position angle and feature vector by comparing angle and feature vector a landmark in an image can correspond with a few number of landmarks in another image then the pixel s positions of landmarks from two images are used to calculate the procrustean distance in a shape space if the value of the procrustean distance is smaller than a predefined threshold the two sets of landmarks will be considered to match each other applying the proposed method two dimensional objects including occluded objects can be recognized quickly

unit interpolation in h bounds of norm and degree of interpolants abstract this paper studies the problem of unit interpolation in h specifically bounds of the norm and degree of interpolants are obtained using the nevanlinna pick interpolation theory also simpler bounds are given using the poincare metric these results indicate that strong stabilization and simultaneous stabilization need a cautious approach if the system is ill conditioned in fact it is demonstrated that the degree of stable compensator is not bounded for the class of plants with fixed degree also an example shows that there is a class of plants for which the sensitivity can be made small only if unstable compensators are used

geometry based image retrieval in binary image databases in this paper a geometry based image retrieval system is developed for multiobject images we model both shape and topology of image objects using a structured representation called curvature tree ct the hierarchy of the ct reflects the inclusion relationships between the image objects to facilitate shape based matching triangle area representation tar of each object is stored at the corresponding node in the ct the similarity between two multiobject images is measured based on the maximum similarity subtree isomorphism mssi between their cts for this purpose we adopt a recursive algorithm to solve the mssi problem and a very effective dynamic programming algorithm to measure the similarity between the attributed nodes our matching scheme agrees with many recent findings in psychology about the human perception of multiobject images experiments on a database of 13 500 real and synthesized medical images and the mpeg 7 ce 1 database of 1 400 shape images have shown the effectiveness of the proposed method

affinity learning with diffusion on tensor product graph in many applications we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples often the pairwise similarities which are also called affinities are unreliable due to noise or due to intrinsic difficulties in estimating similarity values of the samples as observed in several recent approaches more reliable similarities can be obtained if the original similarities are diffused in the context of other data points where the context of each point is a set of points most similar to it compared to the existing methods our approach differs in two main aspects first instead of diffusing the similarity information on the original graph we propose to utilize the tensor product graph tpg obtained by the tensor product of the original graph with itself since tpg takes into account higher order information it is not a surprise that we obtain more reliable similarities however it comes at the price of higher order computational complexity and storage requirement the key contribution of the proposed approach is that the information propagation on tpg can be computed with the same computational complexity and the same amount of storage as the propagation on the original graph we prove that a graph diffusion process on tpg is equivalent to a novel iterative algorithm on the original graph which is guaranteed to converge after its convergence we obtain new edge weights that can be interpreted as new learned affinities we stress that the affinities are learned in an unsupervised setting we illustrate the benefits of the proposed approach for data manifolds composed of shapes images and image patches on two very different tasks of image retrieval and image segmentation with learned affinities we achieve the bull s eye retrieval score of 99 99 percent on the mpeg 7 shape dataset which is much higher than the state of the art algorithms when the data points are image patches the ncut with the learned affinities not only significantly outperforms the ncut with the original affinities but it also outperforms state of the art image segmentation methods

the milne problem for high field kinetic equations half space problems of the linear boltzmann equation with a constant driving force are considered such problems model boundary layers between kinetic zones and fluid zones described by a high field limit of the boltzmann equation existence uniqueness and asymptotic behavior of solutions are studied for positive and negative driving forces in the positive case the force field accelerates the particles and we show that the solution of the half space problem is determined only by the inflow data in contrast for negative forces the behavior at infinity has to be prescribed in order to insure uniqueness due to the nonvanishing forces the problem does not possess any entropy the existence and uniqueness issues are dealt with by supersolution techniques while the asymptotic behavior is analyzed by semiexplicit integration of the equations along the characteristics in the case of relaxation time approximation a fast numerical method for computing the asymptotic state method is presented and tested