linearized multidimensional earth mover s distance gradient flows this paper presents the first framework capable of performing active contour segmentation using earth mover s distance emd to measure dissimilarity between multidimensional feature distributions emd is the best known and understood cross bin histogram distance measure and as such it allows for meaningful comparisons between distributions unlike bin to bin measures that only account for discrepancies on a bin to bin basis because emd is obtained with linear programming techniques its differential structure with respect to variations in bin weights as the active contour evolves is expressed through sensitivity analysis euler lagrange equations are then derived from the computed sensitivity at every iteration to produce gradient descent flows we validate our approach with color image segmentation in comparison with state of the art bhattacharyya bin to bin and 1d emd cross bin active contours some unique advantages of cross bin comparison are highlighted in our segmentation results better perceptual value and increased robustness with respect to the initialization

sharp l p bounds on spectral clusters for lipschitz metrics we establish l p bounds on l 2 normalized spectral clusters for self adjoint elliptic dirichlet forms with lipschitz coefficients in two dimensions we obtain best possible bounds for all 2 le p le infty up to logarithmic losses for 6 p le 8 in higher dimensions we obtain best possible bounds for a limited range of p

existence of solutions for a class of hemivariational inequality problems in this paper we are concerned with the existence of solutions for a class of hartman stampacchia type hemivariational inequalities by using the clarke generalized directional derivative and the galerkin approximation method two existence results of solutions for the generalized pseudomonotone mapping hemivariational inequality and elliptic hemivariational inequality are obtained

on measuring the distance between histograms abstract a distance measure between two histograms has applications in feature selection image indexing and retrieval pattern classification and clustering etc we propose a distance between sets of measurement values as a measure of dissimilarity of two histograms the proposed measure has the advantage over the traditional distance measures regarding the overlap between two distributions it takes the similarity of the non overlapping parts into account as well as that of overlapping parts we consider three versions of the univariate histogram corresponding to whether the type of measurement is nominal ordinal and modulo and their computational time complexities are b b and o b2 for each type of measurements respectively where b is the number of levels in histograms

carleman inequalities for the dirac and laplace operators and unique continuation on demontre les meilleures inegalites de type carleman possibles dans le cas de l operateur de dirac on obtient la propriete de prolongement unique pour d v ou v l loc r n 3n 2 2 n 3

nonextensive triangle equality and other properties of tsallis relative entropy minimization kullback leibler relative entropy has unique properties in cases involving distributions resulting from relative entropy minimization tsallis relative entropy is a one parameter generalization of kullback leibier relative entropy in the nonextensive thermostatistics in this paper we present the properties of tsallis relative entropy minimization and present some differences with the classical case in the representation of such a minimum relative entropy distribution we highlight the use of the q product an operator that has been recently introduced to derive the mathematical structure behind the tsallis statistics one of our main results is the generalization of triangle equality of relative entropy minimization to the nonextensive case

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

on the lp norm of spectral clusters for compact manifolds with boundary we use microlocal and paradifferential techniques to obtain l8 norm bounds for spectral clusters associated with elliptic second order operators on two dimensional manifolds with boundary the result leads to optimal lq bounds in the range 2 q for l2 normalized spectral clusters on bounded domains in the plane and more generally for two dimensional compact manifolds with boundary we also establish new sharp lq estimates in higher dimensions for a range of exponents qn q

optimal partitioning for classification and regression trees an iterative algorithm that finds a locally optimal partition for an arbitrary loss function in time linear in n for each iteration is presented the algorithm is a k means like clustering algorithm that uses as its distance measure a generalization of kullback s information divergence moreover it is proven that the globally optimal partition must satisfy a nearest neighbour condition using divergence as the distance measure these results generalize similar results of l breiman et al 1984 to an arbitrary number of classes or regression variables and to an arbitrary number of bills experimental results on a text to speech example are provided and additional applications of the algorithm including the design of variable combinations surrogate splits composite nodes and decision graphs are suggested

the earth mover s distance as a metric for image retrieval we investigate the properties of a metric between two distributions the earth mover s distance emd for content based image retrieval the emd is based on the minimal cost that must be paid to transform one distribution into the other in a precise sense and was first proposed for certain vision problems by peleg werman and rom for image retrieval we combine this idea with a representation scheme for distributions that is based on vector quantization this combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods the emd is based on a solution to the transportation problem from linear optimization for which efficient algorithms are available and also allows naturally for partial matching it is more robust than histogram matching techniques in that it can operate on variable length representations of the distributions that avoid quantization and other binning problems typical of histograms when used to compare distributions with the same overall mass the emd is a true metric in this paper we focus on applications to color and texture and we compare the retrieval performance of the emd with that of other distances

signatures versus histograms definitions distances and algorithms the aim of this paper is to present a new method to compare histograms the main advantage is that there is an important time complexity reduction with respect to the methods presented before this reduction is statistically and analytically demonstrated in the paper the distances between histograms that we presented are defined on a structure called signature which is a lossless representation of histograms moreover the type of the elements of the sets that the histograms represent are ordinal nominal and modulo we show that the computational cost of these distances is o z for the ordinal and nominal types and o z 2 for the modulo one z being the number of non empty bins of the histograms the computational cost of the algorithms presented in the literature depends on the number of bins of the histograms in most of the applications the obtained histograms are sparse then considering only the non empty bins drastically decreases the time consumption of the comparison the distances and algorithms presented in this paper are experimentally validated on the comparison of images obtained from public databases and positioning of mobile robots through the recognition of indoor scenes captured in a learning stage

hardy littlewood theory for semigroups soit t t t 0 un semi groupe symetrique sousmarkovien et soit n 2 alors on a les proprietes equivalentes a dim t t n b il existe c 2 0 s t t t f c 2 t n 2 f 1 f l 1 x t 0 en fait a b meme dans le cas n 2

general entropy criteria for inverse problems with applications to data compression pattern classification and cluster analysis minimum distance approaches are considered for the reconstruction of a real function from finitely many linear functional values an optimal class of distances satisfying an orthogonality condition analogous to that enjoyed by linear projections in hilbert space is derived these optimal distances are related to measures of distances between probability distributions recently introduced by c r rao and t k nayak 1985 and possess the geometric properties of cross entropy useful in speech and image compression pattern classification and cluster analysis several examples from spectrum estimation and image processing are discussed

a coarse to fine framework to efficiently thwart plagiarism this paper presents a systematic framework using multilevel matching approach for plagiarism detection pd a multilevel structure i e document paragraph sentence is used to represent each document in document and paragraph level we use traditional dimensionality reduction technique to project high dimensional histograms into latent semantic space the earth mover s distance emd instead of exhaustive matching is employed to retrieve relevant documents which enables us to markedly shrink the searching domain two pd algorithms are designed and implemented to efficiently flag the suspected plagiarized document sources we conduct extensive experimental verifications including document retrieval pd the study of the effects of parameters and the empirical study of the system response the results corroborate that the proposed approach is accurate and computationally efficient for performing pd

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

on existence and scattering with minimal regularity for semilinear wave equations abstract we prove existence and scattering results for semilinear wave equations with low regularity data we also determine the minimal regularity that is needed to ensure local existence and well posedness and we give counterexamples to well posedness more specifically we show that equations of the type u u p with initial data u u t in r n 1 r n have a local solution if p n and we construct counterexamples if p n the existence results rely on mixed norm space time estimates of strichartz type

function described graphs for modelling objects represented by sets of attributed graphs we present in this article the model function described graph fdg which is a type of compact representation of a set of attributed graphs ags that borrow from random graphs the capability of probabilistic modelling of structural and attribute information we define the fdgs their features and two distance measures between ags unclassified patterns and fdgs models or classes and we also explain an efficient matching algorithm two applications of fdgs are presented in the former fdgs are used for modelling and matching 3d objects described by multiple views whereas in the latter they are used for representing and recognising human faces described also by several views

minimum cross entropy spectral analysis the principle of minimum cross entropy minimum directed divergence minimum discrimination information minimum relative entropy is summarized discussed and applied to the classical problem of estimating power spectra given values of the autocorrelation function this new method differs from previous methods in its explicit inclusion of a prior estimate of the power spectrum and it reduces to maximum entropy spectral analysis as a special case the prior estimate can be viewed as a means of shaping the spectral estimator cross entropy minimization yields a family of shaped spectral estimators consistent with known autocorrelations results are derived in two equivalent ways once by minimizing the cross entropy of underlying probability densities and once by arguments concerning the cross entropy between the input and output of linear filters several example minimum cross entropy spectra are included

a moment based variational approach to tomographic reconstruction we describe a variational framework for the tomographic reconstruction of an image from the maximum likelihood ml estimates of its orthogonal moments we show how these estimated moments and their correlated error statistics can be computed directly and in a linear fashion from given noisy and possibly sparse projection data moreover thanks to the consistency properties of the radon transform this two step approach moment estimation followed by image reconstruction can be viewed as a statistically optimal procedure furthermore by focusing on the important role played by the moments of projection data we immediately see the close connection between tomographic reconstruction of nonnegative valued images and the problem of nonparametric estimation of probability densities given estimates of their moments taking advantage of this connection our proposed variational algorithm is based on the minimization of a cost functional composed of a term measuring the divergence between a given prior estimate of the image and the current estimate of the image and a second quadratic term based on the error incurred in the estimation of the moments of the underlying image from the noisy projection data we show that an iterative refinement of this algorithm leads to a practical algorithm for the solution of the highly complex equality constrained divergence minimization problem we show that this iterative refinement results in superior reconstructions of images from very noisy data as compared with the classical filtered back projection fbp algorithm

a performance evaluation of local descriptors in this paper we compare the performance of descriptors computed for local interest regions as for example extracted by the harris affine detector mikolajczyk k and schmid c 2004 many different descriptors have been proposed in the literature it is unclear which descriptors are more appropriate and how their performance depends on the interest region detector the descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations we compare shape context belongie s et al april 2002 steerable filters freeman w and adelson e setp 1991 pca sift ke y and sukthankar r 2004 differential invariants koenderink j and van doorn a 1987 spin images lazebnik s et al 2003 sift lowe d g 1999 complex filters schaffalitzky f and zisserman a 2002 moment invariants van gool l et al 1996 and cross correlation for different types of interest regions we also propose an extension of the sift descriptor and show that it outperforms the original method furthermore we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the sift based descriptors perform best moments and steerable filters show the best performance among the low dimensional descriptors

recognition of noisy subsequences using constrained edit distances let x be any unknown word from a finite dictionary h let u be any arbitrary subsequence of x we consider the problem of estimating x by processing y which is a noisy version of u we do this by defining the constrained edit distance between xh and y subject to any arbitrary edit constraint involving the number and type of edit operations to be performed an algorithm to compute this constrained edit distance has been presented although in general the algorithm has a cubic time complexity within the framework of our solution the algorithm possesses a quadratic time complexity recognition using the constrained edit distance as a criterion demonstrates remarkable accuracy experimental results which involve strings of lengths between 40 and 80 and which contain an average of 26 547 errors per string demonstrate that the scheme has about 99 5 percent accuracy

variability analysis of complex networks measures based on stochastic distances abstract complex networks can model the structure and dynamics of different types of systems it has been shown that they are characterized by a set of measures in this work we evaluate the variability of complex network measures face to perturbations and for this purpose we impose controlled perturbations and quantify their effect we analyze theoretical models random small world and scale free and real networks a collaboration network and a metabolic networks along with the shortest path length vertex degree local cluster coefficient and betweenness centrality measures in such an analysis we propose the use of three stochastic quantifiers the kullback leibler divergence and the jensen shannon and hellinger distances the sensitivity of these measures was analyzed with respect to the following perturbations edge addition edge removal edge rewiring and node removal all of them applied at different intensities the results reveal that the evaluated measures are influenced by these perturbations additionally hypotheses tests were performed to verify the behavior of the degree distribution to identify the intensity of the perturbations that leads to break this property

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

concerning the lp norm of spectral clusters for second order elliptic operators on compact manifolds in this paper we study the lp l2 mapping properties of a spectral projection operator for riemannian manifolds this operator is a generalization of the harmonic projection operator for spherical harmonics on s see c d sogge duke math j 53 1986 43 65 among other things we generalize the l2 restriction theorems of c fefferman e m stein and p tomas bull amer math sot 81 1975 477478 for the fourier transform in r to the setting of riemannian manifolds we obtain these results for the spectral projection operator as a corollary of a certain sobolev inequality involving d r2 for large r this sobolev inequality generalizes certain results for r of c kenig a ruiz and the author duke math j 55 1987 329 347 the main tools in the proof of the sobolev inequalities for riemannian manifolds are the hadamard parametrix cf l hbrmander acta mad 88 1968 341 370 and the analysis of linear partial differential equations vol iii springer verlag new york 1985 and oscillatory integral theorems of l carleson and p sjolin studia math 44 19x 287 299 and stein arm math stud 112 1986 307 357 0 1988 academic pnss iw

variable length signature for near duplicate image matching we propose a variable length signature for near duplicate image matching in this paper an image is represented by a signature the length of which varies with respect to the number of patches in the image a new visual descriptor viz probabilistic center symmetric local binary pattern is proposed to characterize the appearance of each image patch beyond each individual patch the spatial relationships among the patches are captured in order to compute the similarity between two images we utilize the earth mover s distance which is good at handling variable length signatures the proposed image signature is evaluated in two different applications i e near duplicate document image retrieval and near duplicate natural image detection the promising experimental results demonstrate the validity and effectiveness of the proposed variable length signature

comparable upper and lower bounds for boundary values of neumann eigenfunctions and tight inclusion of eigenvalues for smooth bounded domains in rn we prove upper and lower l2 bounds on the boundary data of neumann eigenfunctions and we prove quasiorthogonality of this boundary data in a spectral window the bounds are tight in the sense that both are independent of the eigenvalues this is achieved by working with an appropriate norm for boundary functions which includes a spectral weight that is a function of the boundary laplacian this spectral weight is chosen to cancel concentration at the boundary that can happen for whispering gallery type eigenfunctions these bounds are closely related to wave equation estimates due to tataru using this we bound the distance from an arbitrary helmholtz parameter e 0 to the nearest neumann eigenvalue in terms of boundary normal derivative data of a trial function u solving the helmholtz equation e u 0 this inclusion bound improves over previously known bounds by a factor of e5 6 analogously to a recently improved inclusion bound in the dirichlet case due to the first two authors finally we apply our theory to present an improved numerical implementation of the method of particular solutions for computation of neumann eigenpairs on smooth planar domains we show that the new inclusion bound improves the relative accuracy in a computed neumann eigenvalue around the 42000th from nine to fourteen digits with negligible extra numerical effort

periodic solutions for second order systems with not uniformly coercive potential abstract the existence and multiplicity of periodic solutions are obtained for the nonautonomous second order systems with locally coercive potential that is f t x as x for a e t in some positive measure subset of 0 t by using an analogy of egorov s theorem the properties of subadditive functions the least action principle and a three critical point theorem proposed by brezis and nirenberg

existence of a nontrivial solution for a class of hemivariational inequality problems at double resonance abstract in this paper we discuss a class of semilinear elliptic hemivariational inequality problems by using the nonsmooth minimax principle for locally lipschitz functions we establish the existence of a nontrivial solution for the semilinear elliptic hemivariational inequality problem where incomplete double resonance occurs at infinity between two distinct consecutive eigenvalues

existence of solutions for dirichlet elliptic problems with discontinuous nonlinearity abstract in this paper we concern with definite sign and sign changing solutions of a class of discontinuous problems by using the dual method we overcome the difficulty of non differentiability and obtain the existence results of definite sign solution and a sign changing solutions on the nehari manifold for the discontinuous problems some continuous results are extended to the discontinuous cases

concentration and lack of observability of waves in highly heterogeneous media we construct rapidly oscillating holder continuous coefficients for which the corresponding 1 dimensional wave equation lacks the classical observability property guaranteeing that the total energy of solutions may be bounded above by the energy localized in an open subset of the domain where the equation holds if the observation time is large enough the coefficients we build oscillate arbitrarily fast around two accumulation points this allows us to build quasi eigenfunctions for the corresponding eigenvalue problem that concentrate the energy away from the observation region as much as we wish this example may be extended to several space dimensions by separation of variables and illustrates why the well known controllability and dispersive properties for wave equations with smooth coefficients fail in the class of holder continuous coefficients in particular we show that for such coefficients no strichartz type estimate holds

entropy optimization of scale free networks robustness to random failures abstract many networks are characterized by highly heterogeneous distributions of links which are called scale free networks and the degree distributions follow p k ck we study the robustness of scale free networks to random failures from the character of their heterogeneity entropy of the degree distribution can be an average measure of a network s heterogeneity optimization of scale free networks robustness to random failures with average connectivity constant is equivalent to maximizing the entropy of the degree distribution by examining the relationship of the entropy of the degree distribution scaling exponent and the minimal connectivity we get the optimal design of scale free networks to random failures we conclude that the entropy of the degree distribution is an effective measure of network s resilience to random failures

cross entropy minimization given fully decomposable subset and aggregate constraints corresp the principle of maximum entropy and the principle of minimum cross entropy minimum directed divergence minimum discrimination information have been applied recently to problems in queuing theory and computer system performance modeling these information theoretic principles estimate probability distributions based on information in the form of known expected values in the case of queuing theory and computer system modeling the known expected values arise from rate balance equations this correspondence concerns situations in which the system state probabilities decompose into disjoint subsets and in which the known expected values are either expectations conditional on a specific subset or expectations involving aggregate subset probabilities new properties of minimum cross entropy distributions are derived and an efficient method of computing these distributions is derived computational examples are included in the case of queuing theory and computer system modeling the disjoint subsets correspond to internal device states and the aggregate probabilities correspond to overall device states the results here apply when one has both rate balance equations for device equilibrium involving internal device state probabilities as well as rate balance equations for system equilibrium involving aggregate device state probabilities

minimum cross entropy pattern classification and cluster analysis this paper considers the problem of classifying an input vector of measurements by a nearest neighbor rule applied to a fixed set of vectors the fixed vectors are sometimes called characteristic feature vectors codewords cluster centers models reproductions etc the nearest neighbor rule considered uses a non euclidean information theoretic distortion measure that is not a metric but that nevertheless leads to a classification method that is optimal in a well defined sense and is also computationally attractive furthermore the distortion measure results in a simple method of computing cluster centroids our approach is based on the minimization of cross entropy also called discrimination information directed divergence k l number and can be viewed as a refinement of a general classification method due to kullback the refinement exploits special properties of cross entropy that hold when the probability densities involved happen to be minimum cross entropy densities the approach is a generalization of a recently developed speech coding technique called speech coding by vector quantization

unique continuation and absence of positive eigenvalues for schrodinger operators on considere l operateur de laplace sur r n et une fonction v x sur un sous ensemble connexe ouvert de r n on montre que si n 3 une propriete de prolongement unique est vraie pour v l loc n 2 r n dans l espace de sobolev h loc 2 q r n avec q 2n n 2

asymptotic minimum discrimination information measure for asymptotically weakly stationary processes an explicit expression is derived for the minimum discrimination information mdi measure with respect to gaussian priors for sources characterized by their mean and by any principal leading block of their covariance matrix an explicit expression is provided for the mdi extension of the given partial covariance of the source with respect to a gaussian prior for zero mean sources and zero mean gaussian priors that are asymptotically weakly stationary aws processes it is shown that the asymptotic mdi measure equals half the itakura saito distortion measure between the asymptotic power spectral densities of the source and prior asymptotic mdi modelling of a given aws source by autoregressive and autoregressive moving average models which are aws models is considered and conditions are given for convergence of the sample covariance estimator of the source to the stationary covariance used in the modelling

content based image retrieval using color difference histogram this paper presents a novel image feature representation method namely color difference histograms cdh for image retrieval this method is entirely different from the existing histograms most of the existing histogram techniques merely count the number or frequency of pixels however the unique characteristic of cdhs is that they count the perceptually uniform color difference between two points under different backgrounds with regard to colors and edge orientations in l a b color space this method pays more attention to color edge orientation and perceptually uniform color differences and encodes color orientation and perceptually uniform color difference via feature representation in a similar manner to the human visual system the method can be considered as a novel visual attribute descriptor combining edge orientation color and perceptually uniform color difference as well as taking the spatial layout into account without any image segmentation learning processes or clustering implementation experimental results demonstrate that it is much more efficient than the existing image feature descriptors that were originally developed for content based image retrieval such as mpeg 7 edge histogram descriptors color autocorrelograms and multi texton histograms it has a strong discriminative power using the color texture and shape features while accounting for spatial layout

strichartz estimates for second order hyperbolic operators with nonsmooth coefficients ii in an earlier work we have proved some estimates of strichartz type for second order hyperbolic operators with c s coefficients for 0 s 1 here we improve these estimates and extend the range of s to 0 s 2 in particular for s 2 we obtain the full strichartz estimates

spectral cluster estimates for metrics of sobolev regularity we investigate spectral cluster estimates for compact manifolds equipped with a riemannian metric whose regularity is determined by its inclusion in a sobolev space of sufficiently high order the problem is reduced to obtaining l p estimates for the wave equation which are shown by employing wave packet techniques

addendum to concentration and lack of observability of waves in highly heterogeneous media in 1 we introduced a class of 1 d wave equations with rapidly oscillating holder continuous coefficients for which the classical boundary observability property fails we also established that these examples could be used to contradict strichartz type inequalities for the wave equation with low regularity coefficients the object of this addendum is to further analyze this issue as we will see the argument in 1 only provides sharp counter examples to the strichartz estimates when the coefficient belongs to l we carefully analyze these counter examples for holder continuous coefficients we also give a new application of our construction which shows that some eigenfunction estimates for elliptic operators due to sogge can fail when coefficients are not smooth enough

near duplicate document image matching a graphical perspective a near duplicate document image matching approach characterized by a graphical perspective is proposed in this paper document images are represented by graphs whose nodes correspond to the objects in the images consequently the image matching problem is then converted to graph matching to deal with the instability of object segmentation a multi granularity object tree is constructed for a document image each level in the tree corresponds to one possible object segmentation while different levels are characterized by various object granularities some graphs can be generated from the tree and the objects associated with each graph may be of different granularities two graphs with the maximum similarity are found from the multi granularity object trees of the two near duplicate document images which are to be matched the encouraging experimental results have demonstrated the effectiveness of the proposed approach

spectral cluster estimates for c 1 1 metrics in this paper we establish l p norm bounds for spectral clusters on compact manifolds under the assumption that the metric is c 1 1 precisely we show that the l p estimates proven by sogge in the case of smooth metrics hold under this limited regularity assumption it is known by examples of smith sogge that such estimates fail for c 1 metrics if 1

approximation theoretic derivation of logarithmic entropy principles for inverse problems and unique extension of the maximum entropy method to incorporate prior knowledge the minimum distance approach for reconstructing a positive function based on knowledge of finitely many linear functional values is examined two important classes of directed distances for signal processing and statistical inference are discussed by imposing conditions analogous to those satisfied by linear projections in hilbert space two logarithmic entropy principles are derived one of these involves the itakura saito distortion measure of communication theory and uniquely extends burg s maximum entropy method to incorporate prior knowledge the other uses the kullback leibler distance of statistics

bayes risk weighted vector quantization with posterior estimation for image compression and classification classification and compression play important roles in communicating digital information their combination is useful in many applications including the detection of abnormalities in compressed medical images in view of the similarities of compression and low level classification it is not surprising that there are many similar methods for their design because some of these methods are useful for designing vector quantizers it seems natural that vector quantization vq is explored for the combined goal we investigate several vq based algorithms that seek to minimize both the distortion of compressed images and errors in classifying their pixel blocks these algorithms are investigated with both full search and tree structured codes we emphasize a nonparametric technique that minimizes both error measures simultaneously by incorporating a bayes risk component into the distortion measure used for the design and encoding we introduce a tree structured posterior estimator to produce the class posterior probabilities required for the bayes risk computation in this design for two different image sources we demonstrate that this system provides superior classification while maintaining compression close or superior to that of several other vq based designs including kohonen s 1992 learning vector quantizer and a sequential quantizer classifier design

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

minimum cross entropy inversion spectrum analysis and classification introduction and discussion of possible geophysical applications abstract the principle of minimum cross entropy mce is a general method of inference about unknown probability densities given information in the form of constraints on expected values the background justification and properties of mce inversion are summarized briefly some recent applications in spectrum analysis and pattern classification are then summarized and some speculations on the application of mce to general inversion problems in geophysics are offered

optimizing controllability of complex networks by minimum structural perturbations to drive a large complex networked dynamical system toward some desired state using as few external signals as possible is a fundamental issue in the emerging field of controlling complex networks optimal control is referred to the situation where such a network can be fully controlled using only one driving signal we propose a general approach to optimizing the controllability of complex networks by judiciously perturbing the network structure the principle of our perturbation method is validated theoretically and demonstrated numerically for homogeneous and heterogeneous random networks and for different types of real networks as well the applicability of our method is discussed in terms of the relative costs of establishing links and imposing external controllers besides the practical usage of our approach its implementation elucidates interestingly the intricate relationship between certain structural properties of the network and its controllability

texture classification by modeling joint distributions of local patterns with gaussian mixtures texture classification generally requires the analysis of patterns in local pixel neighborhoods statistically the underlying processes are comprehensively described by their joint probability density functions jpdfs even for small neighborhoods however stable estimation of jpdfs by joint histograms jhsts is often infeasible since the number of entries in the jhst exceeds by far the number of pixels in a typical texture region moreover evaluation of distance functions between jhsts is often computationally prohibitive practically the number of entries in a jhst is therefore reduced by considering only two pixel patterns leading to 2d jhsts known as cooccurrence matrices or by quantization of the gray levels in local patterns to only two gray levels yielding local binary patterns lbps both approaches result in a loss of information we introduce here a framework for supervised texture classification which reduces or avoids this information loss local texture neighborhoods are first filtered by a filter bank without further quantization the jpdf of the filter responses is then described parametrically by gaussian mixture models gmms we show that the parameters of the gmms can be reliably estimated from small image regions moreover distances between the thus modelled jpdfs of different texture patterns can be computed efficiently in closed form from their model parameters we furthermore extend this texture descriptor to achieve full invariance to rotation we evaluate the framework for different filter banks on the brodatz texture set we first show that combining the lbp difference filters with the gmm based density estimator outperforms the classical lbp approach and its codebook extensions when replacing these rather elementary difference filters by the wavelet frame transform wft the performance of the framework on all 111 brodatz textures exceeds the one obtained more recently by spin image and rift descriptors by lazebnik et al

bounds for eigenfunctions of the laplacian on compact riemannian manifolds suppose that is an eigenfunction of with eigenvalue 0 it is proved that c1 n 14 2 where n is the dimension of m and c1 depends only upon a bound for the absolute value of the sectional curvature of m and a lower bound for the injectivity radius of m it is then shown that if m admits an isometric circle action and the metric is generic one has exceptional sequences of eigenfunctions satisfying the complementary bounds k c2 n 18k 2

properties of cross entropy minimization the principle of minimum cross entropy minimum directed divergence minimum discrimination information is a general method of inference about an unknown probability density when there exists a prior estimate of the density and new information in the form of constraints on expected values various fundamental properties of cross entropy minimization are proven and collected in one place cross entropy s well known properties as an information measure are extended and strengthened when one of the densities involved is the result of cross entropy minimization the interplay between properties of cross entropy minimization as an inference procedure and properties of cross entropy as an information measure is pointed out examples are included and general analytic and computational methods of finding minimum cross entropy probability densities are discussed

rate distortion speech coding with a minimum discrimination information distortion measure an information theory approach to the theory and practice of linear predictive coded lpc speech compression systems is developed it is shown that a traditional lpc system can be viewed as a minimum distortion or nearest neighbor system where the distortion measure is a minimum discrimination information between a speech process model and an observed frame of actual speech this distortion measure is used in an algorithm for computer aided design of block source codes subject to a fidelity criterion to obtain a 750 bits s speech compression system that resembles an lpc system but has a much lower rate a larger memory requirement and requires no on line lpc analysis quantitative and informal subjective comparisons are made among our system and lpc systems

region based hierarchical image matching this paper presents an approach to region based hierarchical image matching where given two images the goal is to identify the largest part in image 1 and its match in image 2 having the maximum similarity measure defined in terms of geometric and photometric properties of regions e g area boundary shape and color as well as region topology e g recursive embedding of regions to this end each image is represented by a tree of recursively embedded regions obtained by a multiscale segmentation algorithm this allows us to pose image matching as the tree matching problem to overcome imaging noise one to one many to one and many to many node correspondences are allowed the trees are first augmented with new nodes generated by merging adjacent sibling nodes which produces directed acyclic graphs dags then transitive closures of the dags are constructed and the tree matching problem reformulated as finding a bijection between the two transitive closures on dags while preserving the connectivity and ancestor descendant relationships of the original trees the proposed approach is validated on real images showing similar objects captured under different types of noise including differences in lighting conditions scales or viewpoints amidst limited occlusion and clutter

scaling and percolation in the small world network model in this paper we study the small world network model of watts and strogatz which mimics some aspects of the structure of networks of social interactions we argue that there is one nontrivial length scale in the model analogous to the correlation length in other systems which is well defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero giving a normal critical point in this limit this length scale governs the crossover from large to small world behavior in the model as well as the number of vertices in a neighborhood of given radius on the network we derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex vertex distance on the network and using series expansion and pad e approximants find an approximate analytic form for the scaling function we calculate the effective dimension of small world graphs and show that this dimension varies as a function of the length scale on which it is measured in a manner reminiscent of multifractals we also study the problem of site percolation on small world networks as a simple model of disease propagation and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms in epidemiological terms the point at which an epidemic occurs the typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph all our analytic results are confirmed by extensive numerical simulations of the model

scale and rotation invariant local binary pattern using scale adaptive texton and subuniform based circular shift this paper proposes an effective scale and rotation invariant local binary pattern lbp feature for texture classification a circular neighboring set of an image pixel is defined as a scale adaptive texton by taking into account the fundamental local structure property of the pixel the scale space of a texture image is derived by the laplacian of the gaussian and then employed to determine the optimal scale of each pixel reflecting the characteristic length of the corresponding structure and determining the radius of the scale adaptive texton different pixels have different optimal scales resulting in the scale invariance contrary to the traditional lbp features that usually ignore global spatial information the proposed method also defines subuniform patterns of each uniform pattern to improve the discrimination for each uniform pattern the subuniform pattern with the maximum statistical value is defined as the dominant orientation subuniform pattern it is moved to the first column and the others are circularly shifted experimental results demonstrate a good discrimination capability of the proposed scale and rotation invariant lbp in texture classification particularly the lbp based on the scale adaptive texton is promising to be powerful for texture description and scale invariant texture classification and the circular shift subuniform lbp can further improve the performance in the rotation invariant texture classification

steganalysis and payload estimation of embedding in pixel differences using neural networks in this paper a steganalysis technique is proposed for pixel value differencing method this steganographic method which is immune against conventional attacks performs the embedding in the difference of the values of pixel pairs therefore the histogram of the differences of an embedded image is different as compared with a cover image a number of characteristics are identified in the difference histogram that show meaningful alterations when an image is embedded five distinct multilayer perceptrons neural networks are trained to detect different levels of embedding every image is fed to all networks and a voting system categorizes the image as stego or cover the implementation results indicate 88 6 success in correct categorization of the test images that contained more than 20 embedding furthermore using a neural network an estimator is presented which gives an estimate of the amount of the mpvd embedding in an image implementation of the estimator showed an average accuracy of 88 3 in the estimation of the amount of embedding

a normalized levenshtein distance metric although a number of normalized edit distances presented so far may offer good performance in some applications none of them can be regarded as a genuine metric between strings because they do not satisfy the triangle inequality given two strings x and y over a finite alphabet this paper defines a new normalized edit distance between x and y as a simple function of their lengths x and y and the generalized levenshtein distance gld between them the new distance can be easily computed through gld with a complexity of o x cdot y and it is a metric valued in 0 1 under the condition that the weight function is a metric over the set of elementary edit operations with all costs of insertions deletions having the same weight experiments using the aesa algorithm in handwritten digit recognition show that the new distance can generally provide similar results to some other normalized edit distances and may perform slightly better if the triangle inequality is violated in a particular data set

evaluation of interest point detectors many different low level feature detectors exist and it is widely agreed that the evaluation of detectors is important in this paper we introduce two evaluation criteria for interest points repeatability rate and information content repeatability rate evaluates the geometric stability under different transformations information content measures the distinctiveness of features different interest point detectors are compared using these two criteria we determine which detector gives the best results and show that it satisfies the criteria well

on a relation between maximum likelihood classification and minimum relative entropy classification corresp maximum likelihood ml and minimum relative entropy mre minimum cross entropy classification of samples from an unknown probability density when the hypotheses comprise an exponential family are considered it is shown that ml and mre lead to the same classification nde and the result is illustrated in terms of a method for estimating covariance matrices recently developed by burg luenberger and wenger mre classification applies to the general case in which it cannot be assumed that the samples were generated by one of the hypothesis densities the common use of ml in this case is technically incorrect but the equivalence of mre and ml provides a theoretical justification

efficient color histogram indexing for quadratic form distance functions in image retrieval based on color the weighted distance between color histograms of two images represented as a quadratic form may be defined as a match measure however this distance measure is computationally expensive and it operates on high dimensional features o n we propose the use of low dimensional simple to compute distance measures between the color distributions and show that these are lower bounds on the histogram distance measure results on color histogram matching in large image databases show that prefiltering with the simpler distance measures leads to significantly less time complexity because the quadratic histogram distance is now computed on a smaller set of images the low dimensional distance measure can also be used for indexing into the database

a novel document similarity measure based on earth mover s distance in this paper we propose a novel measure based on the earth mover s distance emd to evaluate document similarity by allowing many to many matching between subtopics first each document is decomposed into a set of subtopics and then the emd is employed to evaluate the similarity between two sets of subtopics for two documents by solving the transportation problem the proposed measure is an improvement of the previous om based measure which allows only one to one matching between subtopics experiments have been performed on the tdt3 dataset to evaluate existing similarity measures and the results show that the emd based measure outperforms the optimal matching om based measure and all other measures in addition to the texttiling algorithm the sentence clustering algorithm is adopted for document decomposition and the experimental results show that the proposed emd based measure does not rely on the document decomposition algorithm and thus it is more robust than the om based measure

existence and multiplicity of solutions for semilinear hemivariational inequalities at resonance abstract in this paper we study semilinear hemivariational inequalities at resonance assuming a partially anticoercive nonsmooth potential we prove an existence and a multiplicity theorem the method of the proof is variational and in the multiplicity result we employ the nonsmooth local linking theorem