qaplib a quadratic assignment problem library abstract after a short introduction into quadratic assignment problems we give a library of problem instances for the quadratic assignment problem the examples are listed y authors in alphabetical order

subset algebra lift operators for 0 1 integer programming we extend the sherali adams lovasz schrijver balas ceria cornuejols and lasserre lift and project methods for 0 1 optimization by considering liftings to subset algebras our methods yield polynomial time algorithms for solving a relaxation of a set covering problem at least as strong as that given by the set of all valid inequalities with small coefficients and more generally all valid inequalities where the right hand side is not very large relative to the positive coefficients in the left hand side applied to generalizations of vertex packing problems our methods yield in polynomial time relaxations that have unbounded rank using for example the n operator

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

solving lift and project relaxations of binary integer programs we propose a method for optimizing the lift and project relaxations of binary integer programs introduced by lovasz and schrijver in particular we study both linear and semidefinite relaxations the key idea is a restructuring of the relaxations which isolates the complicating constraints and allows for a lagrangian approach we detail an enhanced subgradient method and discuss its efficient implementation computational results illustrate that our algorithm produces tight bounds more quickly than state of the art linear and semidefinite solvers

bounds for the quadratic assignment problem using the bundle method semidefinite programming sdp has recently turned out to be a very powerful tool for approximating some np hard problems the nature of the quadratic assignment problem qap suggests sdp as a way to derive tractable relaxations we recall some sdp relaxations of qap and solve them approximately using a dynamic version of the bundle method the computational results demonstrate the efficiency of the approach our bounds are currently among the strongest ones available for qap we investigate their potential for branch and bound settings by looking also at the bounds in the first levels of the branching tree

a filter bank for the directional decomposition of images theory and design the authors introduce a directionally oriented 2 d filter bank with the property that the individual channels may be critically sampled without loss of information the passband regions of the component filters are wedge shaped and thus provide directional information it is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed the authors discuss the theory for directional decomposition and reconstruction in addition implementation issues are addressed where realizations based on both recursive and nonrecursive filters are considered

a nonlinear programming algorithm for solving semidefinite programs via low rank factorization in this paper we present a nonlinear programming algorithm for solving semidefinite programs sdps in standard form the algorithm s distinguishing feature is a change of variables that replaces the symmetric positive semidefinite variable x of the sdp with a rectangular variable r according to the factorization x rr t the rank of the factorization i e the number of columns of r is chosen minimally so as to enhance computational speed while maintaining equivalence with the sdp fundamental results concerning the convergence of the algorithm are derived and encouraging computational results on some large scale test problems are also presented

general tensor discriminant analysis and gabor features for gait recognition traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis lda because of the undersample problem usp the dimensionality of the feature space is much higher than the number of training samples motivated by the successes of the two dimensional lda 2dlda for face recognition we develop a general tensor discriminant analysis gtda as a preprocessing step for lda the benefits of gtda compared with existing preprocessing methods such as the principal components analysis pca and 2dlda include the following 1 the usp is reduced in subsequent classification by for example lda 2 the discriminative information in the training tensors is preserved and 3 gtda provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of gtda converges whereas that of 2dlda does not we use human gait recognition to validate the proposed gtda the averaged gait images are utilized for gait representation given the popularity of gabor function based image decompositions for image understanding and object recognition we develop three different gabor function based image representations 1 gabord is the sum of gabor filter responses over directions 2 gabors is the sum of gabor filter responses over scales and 3 gaborsd is the sum of gabor filter responses over scales and directions the gabord gabors and gaborsd representations are applied to the problem of recognizing people from their averaged gait images a large number of experiments were carried out to evaluate the effectiveness recognition rate of gait recognition based on first obtaining a gabor gabord gabors or gaborsd image representation then using gdta to extract features and finally using lda for classification the proposed methods achieved good performance for gait recognition based on image sequences from the university of south florida usf humanid database experimental comparisons are made with nine state of the art classification methods in gait recognition

computational experience with stable set relaxations we investigate relaxations for the maximum stable set problem based on the lovasz number vartheta g as an initial upper bound we strengthen this relaxation by adding two classes of cutting planes odd circuit and triangle inequalities we present computational results using this tighter model on many classes of graphs

exploring the relationship between max cut and stable set relaxations the max cut and stable set problems are two fundamental hard problems in combinatorial optimization it has been known for a long time that any instance of the stable set problem can be easily transformed into a max cut instance moreover laurent poljak rendl and others have shown that any convex set containing the cut polytope yields via a suitable projection a convex set containing the stable set polytope we review this work and then extend it in the following ways we show that the rounded version of certain positive semidefinite inequalities for the cut polytope imply via the same projection a surprisingly large variety of strong valid inequalities for the stable set polytope these include the clique odd hole odd antihole web and antiweb inequalities and various inequalities obtained from these via sequential lifting we also examine a less general class of inequalities for the cut polytope which we call odd clique inequalities and show that they are in general much less useful for generating valid inequalities for the stable set polytope as well as being of theoretical interest these results have algorithmic implications in particular we obtain as a by product a polynomial time separation algorithm for a class of inequalities which includes all web inequalities

the contourlet transform an efficient directional multiresolution image representation the limitations of commonly used separable extensions of one dimensional transforms such as the fourier and wavelet transforms in capturing the geometry of image edges are well known in this paper we pursue a true two dimensional transform that can capture the intrinsic geometrical structure that is key in visual information the main challenge in exploring geometry in images comes from the discrete nature of the data thus unlike other approaches such as curvelets that first develop a transform in the continuous domain and then discretize for sampled data our approach starts with a discrete domain construction and then studies its convergence to an expansion in the continuous domain specifically we construct a discrete domain multiresolution and multidirection expansion using nonseparable filter banks in much the same way that wavelets were derived from filter banks this construction results in a flexible multiresolution local and directional image expansion using contour segments and thus it is named the contourlet transform the discrete contourlet transform has a fast iterated filter bank algorithm that requires an order n operations for n pixel images furthermore we establish a precise link between the developed filter bank and the associated continuous domain contourlet expansion via a directional multiresolution analysis framework we show that with parabolic scaling and sufficient directional vanishing moments contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves finally we show some numerical experiments demonstrating the potential of contourlets in several image processing applications

connections between semidefinite relaxations of the max cut and stable set problems we describe links between a recently introduced semidefinite relaxation for the max cut problem and the well known semidefinite relaxation for the stable set problem underlying the lovasz s theta function it turns out that the connection between the convex bodies defining the semidefinite relaxations mimics the connection existing between the corresponding polyhedra we also show how the semidefinite relaxations can be combined with the classical linear relaxations in order to obtain tighter relaxations

dual geometric neighbor embedding for image super resolution with sparse tensor neighbors embedding ne technology has proved its efficiency in single image super resolution sisr however image patches do not strictly follow the similar structure in the low resolution and high resolution spaces consequently leading to a bias to the image restoration in this paper considering that patches are a set of data with multiview characteristics and spatial organization we advance a dual geometric neighbor embedding dgne approach for sisr in dgne multiview features and local spatial neighbors of patches are explored to find a feature spatial manifold embedding for images we adopt a geometrically motivated assumption that for each patch there exists a small neighborhood in which only the patches that come from the same feature spatial manifold will lie approximately in a low dimensional affine subspace formulated by sparse neighbors in order to find the sparse neighbors a tensor simultaneous orthogonal matching pursuit algorithm is advanced to realize a joint sparse coding of feature spatial image tensors some experiments are performed on realizing a 3x amplification of natural images and the recovered results prove its efficiency and superiority to its counterparts

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

primal dual path following algorithms for semidefinite programming this paper deals with a class of primal dual interior point algorithms for semidefinite programming sdp which was recently introduced by kojima shindoh and hara siam j optim 7 1997 pp 86 125 these authors proposed a family of primal dual search directions that generalizes the one used in algorithms for linear programming based on the scaling matrix x1 2s 1 2 they study three primal dual algorithms based on this family of search directions a short step path following method a feasible potential reduction method and an infeasible potential reduction method however they were not able to provide an algorithm which generalizes the long step path following algorithm introduced by kojima mizuno and yoshise progress in mathematical programming interior point and related methods n megiddor ed springer verlag berlin new york 1989 pp 29 47 in this paper we characterize two search directions within their family as being unique solutions of systems of linear equations in symmetric variables based on this characterization we present a simplified polynomial convergence proof for one of their short step path following algorithms and for the first time a polynomially convergent long step path following algorithm for sdp which requires an extra sqrt n factor in its iteration complexity order as compared to its linear programming counterpart where n is the number of rows or columns of the matrices involved

a lift and project cutting plane algorithm for mixed 0 1 programs we propose a cutting plane algorithm for mixed 0 1 programs based on a family of polyhedra which strengthen the usual lp relaxation we show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point this cut is found through the solution of a linear program that has about twice the size of the usual lp relaxation a lifting step is used to reduce the size of the lp s needed to generate the cuts an additional strengthening step suggested by balas and jeroslow is then applied we report our computational experience with a preliminary version of the algorithm this approach is related to the work of balas on disjunctive programming the matrix cone relaxations of lovasz and schrijver and the hierarchy of relaxations of sherali and adams

when does the positive semidefiniteness constraint help in lifting procedures we study the lift and project procedures of lovaisz and schrijver for 0 1 integer programming problems we prove that the procedure using the positive semidefiniteness constraint is not better than the one without it in the worst case various examples are considered we also provide geometric conditions characterizing when the positive semidefiniteness constraint does not help

adaptive image data hiding in edges using patched reference table and pair wise embedding technique reference table rt based embedding method embeds secret digits into pixel pairs under the guidance of a reference table most of the existing rt based methods either require elaborate conversions among different bases or have limited embedding capacity in this paper we use a patched reference table prt as a guide and propose a prt method to provide a better image quality and extendable embedding capacity we also exploit the concept of pixel value differencing pvd and propose another method prt pvd in the traditional pvd based methods the shape of the difference histograms of the stego images is significantly altered and thus vulnerable to some steganalyzers prt pvd adopts the prt method and uses a specially designed embedding sequence to preserve the difference histogram shape experimental results reveal that the proposed prt and prt pvd methods not only have better embedding efficiency over the existing methods but also are robust to detection by modern steganalysis tools

cones of matrices and set functions and 0 1 optimization it has been recognized recently that to represent a polyhedron as the projection of a higher dimensional but simpler polyhedron is a powerful tool in polyhedral combinatorics a general method is developed to construct higher dimensional polyhedra or in some cases convex sets whose projection approximates the convex hull of 0 1 valued solutions of a system of linear inequalities an important feature of these approximations is that one can optimize any linear objective function over them in polynomial time in the special case of the vertex packing polytope a sequence of systems of inequalities is obtained such that the first system already includes clique odd hole odd antihole wheel and orthogonality constraints in particular for perfect and many other graphs this first system gives the vertex packing polytope for various classes of graphs including t perfect graphs it follows that the stable set polytope is the projection of a polytope with a polynomial number of facets an extension o

on a representation of the matching polytope via semidefinite liftings we consider the relaxation of the matching polytope defined by the non negativity and degree constraints we prove that given an undirected graph on n nodes and the corresponding relaxation of the matching polytope n 2 iterations of the lovasz schrijver semidefinite lifting procedure are needed to obtain the matching polytope in the worst case we show that n 2 iterations of the procedure always suffice

on clifford s theorem for singular curves let c be a 2 connected projective curve either reduced with planar singularities or contained in a smooth algebraic surface and let s be a subcanonical cluster that is a zero dimensional scheme such that the space h 0 c iskc contains a generically invertible section under some general assumptions on s or c we show that h 0 c iskc pa c 1 deg s and if equality holds then either s is trivial or c is honestly hyperelliptic or 3 disconnected as a corollary we give a generalization of clifford s theorem for reduced curves with planar singularities

a new lift and project operator abstract in this paper we analyze the strength of split cuts in a lift and project framework we first observe that the lovasz schrijver and sherali adams lift and project operator hierarchies can be viewed as applying specific 0 1 split cuts to an appropriate extended formulation and demonstrate how to strengthen these hierarchies using additional split cuts more precisely we define a new operator that adds all 0 1 split cuts to the extended formulation for 0 1 mixed integer sets with k binary variables this new operator is guaranteed to obtain the integer hull in k 2 steps compared to k steps for the lovasz schrijver or the sherali adams operator we also present computational results on the stable set problem with our new operator

fractal analysis for reduced reference image quality assessment in this paper multifractal analysis is adapted to reduced reference image quality assessment rr iqa a novel rr qa approach is proposed which measures the difference of spatial arrangement between the reference image and the distorted image in terms of spatial regularity measured by fractal dimension an image is first expressed in log gabor domain then fractal dimensions are computed on each log gabor subband and concatenated as a feature vector finally the extracted features are pooled as the quality score of the distorted image using ell 1 distance compared with existing approaches the proposed method measures image quality from the perspective of the spatial distribution of image patterns the proposed method was evaluated on seven public benchmark data sets experimental results have demonstrated the excellent performance of the proposed method in comparison with state of the art approaches

maximum stable set formulations and heuristics based on continuous optimization the stability number g for a given graph g is the size of a maximum stable set in g the lovasz theta number provides an upper bound on g and can be computed in polynomial time as the optimal value of the lovasz semidefinite program in this paper we show that restricting the matrix variable in the lovasz semidefinite program to be rank one and rank two respectively yields a pair of continuous nonlinear optimization problems each having the global optimal value g we propose heuristics for obtaining large stable sets in g based on these new formulations and present computational results indicating the effectiveness of the heuristics

a distortion measure for blocking artifacts in images based on human visual sensitivity a visual model that gives a distortion measure for blocking artifacts in images is presented given the original and reproduced image as inputs the model output is a numerical value that quantifies the visibility of blocking error in the reproduced image the model is derived based on the human visual sensitivity to horizontal and vertical edge artifacts that result from blocking psychovisual experiments have been carried out to measure the visual sensitivity to these artifacts in the experiments typical edge artifacts are shown to subjects and the sensitivity to them is measured with the variation of background luminance background activity edge length and edge amplitude synthetic test patterns are used as background images in the experiments the sensitivity measures thus obtained are used to estimate the model parameters the final model is tested on real images and the results show that the error visibility predicted by the model correlates well with the subjective ranking

on polyhedral approximations of the second order cone we demonstrate that a conic quadratic problem is polynomially reducible to linear programming we demonstrate this by constructing for every an lp program explicitly given in terms of e and the data of cqp with the following properties i the number dimx dimu of variables and the number dimp of constraints in lp do not exceed ii every feasible solutionx to cqp can be extended to a feasible solution x u to lp iii if x u is feasible for lp thenx satisfies the e relaxed constraints of cqp namely

applications of second order cone programming in a second order cone program socp a linear function is minimized over the intersection of an affine set and the product of second order quadratic cones socps are nonlinear convex problems that include linear and convex quadratic programs as special cases but are less general than semidefinite programs sdps several efficient primaldual interior point methods for socp have been developed in the last few years after reviewing the basic theory of socps we describe general families of problems that tan be recast as socps these include robust linear programming and robust leastsquares problems problems involving sums or maxima of norms or with convex hyperbolic constraints we discuss a variety of engineering applications such as filter design antenna array weight design truss design and grasping forte optimization in robotics we describe an efficient primaldual interior point method for solving socps which shares many of the features of primaldual interior point methods for linear program

a level 2 reformulation linearization technique bound for the quadratic assignment problem abstract this paper studies polyhedral methods for the quadratic assignment problem bounds on the objective value are obtained using mixed 0 1 linear representations that result from a reformulation linearization technique rlt the rlt provides different levels of representations that give increasing strength prior studies have shown that even the weakest level 1 form yields very tight bounds which in turn lead to improved solution methodologies this paper focuses on implementing level 2 we compare level 2 with level 1 and other bounding mechanisms in terms of both overall strength and ease of computation in so doing we extend earlier work on level 1 by implementing a lagrangian relaxation that exploits block diagonal structure present in the constraints the bounds are embedded within an enumerative algorithm to devise an exact solution strategy our computer results are notable exhibiting a dramatic reduction in nodes examined in the enumerative phase and allowing for the exact solution of large instances

ellipsoidal relaxations of the stable set problem theory and algorithms a new exact approach to the stable set problem is presented which attempts to avoid the pitfalls of existing approaches based on linear and semidefinite programming the method begins by constructing an ellipsoid that contains the stable set polytope and has the property that the upper bound obtained by optimizing over it is equal to the lovasz theta number this ellipsoid can then be used to construct useful convex relaxations of the stable set problem which can be embedded within a branch and bound framework extensive computational results are given which indicate the potential of the approach

interior point methods for the monotone semidefinite linear complementarity problem in symmetric matrices the sdlcp semidefinite linear complementarity problem in symmetric matrices introduced in this paper provides a unified mathematical model for various problems arising from systems and control theory and combinatorial optimization it is defined as the problem of finding a pair x y of n times n symmetric positive semidefinite matrices which lies in a given n n 1 2 dimensional affine subspace fc of sc 2 and satisfies the complementarity condition x bullet y 0 where sc denotes the n n 1 2 dimensional linear space of symmetric matrices and x bullet y the inner product of x and y the problem enjoys a close analogy with the lcp in the euclidean space in particular the central trajectory leading to a solution of the problem exists under the nonemptiness of the interior of the feasible region and a monotonicity assumption on the affine subspace fc the aim of this paper is to establish a theoretical basis of interior point methods with the use of newton directions toward the central trajectory for the monotone sdlcp

strong lift and project cutting planes for the stable set problem a great deal of research has been focusing since the early seventies on finding strong relaxations for the stable set problem polyhedral combinatorics techniques have been at first developed to strengthen the natural linear formulation afterward strong semidefinite programming relaxations have been deeply investigated nevertheless the resulting integer programming ip algorithms cannot be regarded as being quite successful in practice as most of the relaxations give rise to one out of two extreme situations either provide weak bounds at low computational cost or give good bounds sometimes excellent but too demanding to compute in this paper we present a method to bridge such a gap in particular a new lift and project relaxation is obtained by a problem specific variant of the lifting operator m k k by lovasz and schrijver combined with benders decomposition this yields strong cutting planes generated by solving a cut generating linear program an extensive computational experience shows that embedding these cuts in a branch and cut framework significantly reduces the size of the enumeration trees as well as the cpu times with respect to state of the art ip algorithms

second order cone programming second order cone programming socp problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the cartesian product of second order lorentz cones linear programs convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as socp problems as can many other problems that do not fall into these three categories these latter problems model applications from a broad range of fields from engineering control and finance to robust optimization and combinatorial optimization on the other hand semidefinite programming sdp that is the optimization problem over the intersection of an affine set and the cone of positive semidefinite matrices includes socp as a special case therefore socp falls between linear lp and quadratic qp programming and sdp like lp qp and sdp problems socp problems can be solved in polynomial time by interior point methods the computational effort per iteration required by these methods to solve socp problems is greater than that required to solve lp and qp problems but less than that required to solve sdp s of similar size and structure because the set of feasible solutions for an socp problem is not polyhedral as it is for lp and qp problems it is not readily apparent how to develop a simplex or simplex like method for socp while socp problems can be solved as sdp problems doing so is not advisable both on numerical grounds and computational complexity concerns for instance many of the problems presented in the survey paper of vandenberghe and boyd vb96 as examples of sdps can in fact be formulated as socps and should be solved as such in 2 3 below we give socp formulations for four of these examples the convex quadratically constrained quadratic programming qcqp problem problems involving fractional quadratic functions rutcor rutgers university e mail alizadeh rutcor rutgers edu research supported in part by the u s national science foundation grant ccr 9901991 ieor columbia university e mail gold ieor columbia edu research supported in part by the department of energy grant de fg02 92er25126 national science foundation grants dms 94 14438 cda 97 26385 and dms 01 04282

human visual weighted progressive image transmission a progressive image transmission scheme which combines transform coding with the human visual system hvs model is developed the adaptive transform coding of w h chen and c h smith 1977 is utilized to classify an image into four equally populated subblocks based on their ac energies the modulation transfer function mtf of the hvs model is obtained experimentally based on processing a number of test images a simplified technique for incorporating the mtf into the discrete cosine transform dct domain is utilized in the hierarchical image buildup the image is first reconstructed from the dc coefficients of all subblocks further transmission hierarchy of transform coefficients and consequent image buildup are dependent on their hvs weighted variances the hvs weighted reconstructed images are compared to the ones without any weighting at several stages the hvs weighted progressive image transmission results in perceptually higher quality images compared to the unweighted scheme

tighter linear and semidefinite relaxations for max cut based on the lovasz schrijver lift and project procedure we study how the lift and project method introduced by lovasz and schrijver siam j optim 1 1991 pp 166 190 applies to the cut polytope we show that the cut polytope of a graph can be found in k iterations if there exist k edges whose contraction produces a graph with no k5 minor therefore for a graph g with n ge 4 nodes with stability number alpha g n 4 iterations suffice instead of the m number of edges iterations required in general and under some assumption n alpha g 3 iterations suffice the exact number of needed iterations is determined for small n le 7 by a detailed analysis of the new relaxations if positive semidefiniteness is added to the construction then one finds in one iteration a relaxation of the cut polytope which is tighter than its basic semidefinite relaxation and than another one introduced recently by anjos and wolkowicz discrete appl math to appear we also show how the lovasz schrijver relaxations for the stable set polytope of g can be strengthened using the corresponding relaxations for the cut polytope of the graph g nabla obtained from g by adding a node adjacent to all nodes of g

reduced reference quality assessment based on the entropy of dwt coefficients of locally weighted gradient magnitudes perceptual image quality assessment iqa attempts to use computational models to estimate the image quality in accordance with subjective evaluations reduced reference iqa rriqa methods make use of partial information or features extracted from the reference image for estimating the quality of distorted images finding a balance between the number of rr features and accuracy of the estimated image quality is essential and important in iqa in this paper we propose a training free low cost rriqa method that requires a very small number of rr features six rr features the proposed rriqa algorithm is based on the discrete wavelet transform dwt of locally weighted gradient magnitudes we apply human visual system s contrast sensitivity and neighborhood gradient information to weight the gradient magnitudes in a locally adaptive manner the rr features are computed by measuring the entropy of each dwt subband for each scale and pooling the subband entropies along all orientations resulting in l rr features one average entropy per scale for an l level dwt extensive experiments performed on seven large scale benchmark databases demonstrate that the proposed rriqa method delivers highly competitive performance as compared with the state of the art rriqa models as well as full reference ones for both natural and texture images the matlab source code of redlog and the evaluation results are publicly available online at https http lab engineering asu edu ivulab software redlog

universal blind image quality assessment metrics via natural scene statistics and multiple kernel learning universal blind image quality assessment iqa metrics that can work for various distortions are of great importance for image processing systems because neither ground truths are available nor the distortion types are aware all the time in practice existing state of the art universal blind iqa algorithms are developed based on natural scene statistics nss although nss based metrics obtained promising performance they have some limitations 1 they use either the gaussian scale mixture model or generalized gaussian density to predict the nongaussian marginal distribution of wavelet gabor or discrete cosine transform coefficients the prediction error makes the extracted features unable to reflect the change in nongaussianity ng accurately the existing algorithms use the joint statistical model and structural similarity to model the local dependency ld although this ld essentially encodes the information redundancy in natural images these models do not use information divergence to measure the ld although the exponential decay characteristic edc represents the property of natural images that large small wavelet coefficient magnitudes tend to be persistent across scales which is highly correlated with image degradations it has not been applied to the universal blind iqa metrics and 2 all the universal blind iqa metrics use the same similarity measure for different features for learning the universal blind iqa metrics though these features have different properties to address the aforementioned problems we propose to construct new universal blind quality indicators using all the three types of nss i e the ng ld and edc and incorporating the heterogeneous property of multiple kernel learning mkl by analyzing how different distortions affect these statistical properties we present two universal blind quality assessment models nss global scheme and nss two step scheme in the proposed metrics 1 we exploit the ng of natural images using the original marginal distribution of wavelet coefficients 2 we measure correlations between wavelet coefficients using mutual information defined in information theory 3 we use features of edc in universal blind image quality prediction directly and 4 we introduce mkl to measure the similarity of different features using different kernels thorough experimental results on the laboratory for image and video engineering database ii and the tampere image database2008 demonstrate that both metrics are in remarkably high consistency with the human perception and overwhelm representative universal blind algorithms as well as some standard full reference quality indexes for various types of distortions

semidefinite programming relaxations for graph coloring and maximal clique problems the semidefinite programming formulation of the lovasz theta number does not only give one of the best polynomial simultaneous bounds on the chromatic number g or the clique number g of a graph but also leads to heuristics for graph coloring and extracting large cliques this semidefinite programming formulation can be tightened toward either g or g by adding several types of cutting planes we explore several such strengthenings and show that some of them can be computed with the same effort as the theta number we also investigate computational simplifications for graphs with rich automorphism groups

an interior point method for semidefinite programming we propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices

solving large scale semidefinite programs via an iterative solver on the augmented systems the search directions in an interior point method for large scale semidefinite programming sdp can be computed by applying a krylov iterative method to either the schur complement equation sce or the augmented equation both methods suffer from slow convergence as interior point iterates approach optimality numerical experiments have shown that a diagonally preconditioned conjugate residual method on the sce typically takes a huge number of steps to converge however it is difficult to incorporate cheap and effective preconditioners into the sce this paper proposes to apply the preconditioned symmetric quasi minimal residual psqmr method to a reduced augmented equation that is derived from the augmented equation by utilizing the eigenvalue structure of the interior point iterates numerical experiments on sdp problems arising from maximum clique and selected sdplib sdp library problems show that moderately accurate solutions can be obtained with a modest number of psqmr steps using the proposed preconditioned reduced augmented equation an sdp problem with 127600 constraints is solved in about 6 5 hours to an accuracy of 10 6 in relative duality gap

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

coefficient strengthening a tool for reformulating mixed integer programs providing a good formulation is an important part of solving a mixed integer program we suggest measuring the quality of a formulation by whether it is possible to strengthen the coefficients of the formulation sequentially strengthening coefficients can then be used as a tool for improving formulations we believe this method could be useful for analyzing and producing tight formulations of problems that arise in practice we illustrate the use of the approach on a problem in production scheduling we also prove that coefficient strengthening leads to formulations with a desirable property if no coefficient can be strengthened then no constraint can be replaced by an inequality that dominates it the effect of coefficient strengthening is tested on a number of problems in computational experiments the strengthened formulations are compared to reformulations obtained by the preprocessor of a commercial software package for several test problems the formulations obtained by coefficient strengthening are substantially stronger than the formulations obtained by the preprocessor in particular we use coefficient strengthening to solve two difficult problems to optimality that have only recently been solved

wavelet based color image compression exploiting the contrast sensitivity function the visual efficiency of an image compression technique depends directly on the amount of visually significant information it retains by visually significant we mean information to which a human observer is most sensitive the overall sensitivity depends on aspects such as contrast color spatial frequency and so forth one important aspect is the inverse relationship between contrast sensitivity and spatial frequency this is described by the contrast sensitivity function csf in compression algorithms the csf can be exploited to regulate the quantization step size to minimize the visibility of compression artifacts existing csf implementations for wavelet based image compression use the same quantization step size for a large range of spatial frequencies this is a coarse approximation of the csf this paper presents two new techniques that implement the csf at significantly higher precision adapting even to local variations of the spatial frequencies within a decomposition subband the approaches can be used for luminance as well as color images for color perception three different csfs describe the sensitivity the implementation technique is the same for each color band implemented into the jpeg2000 compression standard the new techniques are compared to conventional csf schemes the proposed techniques turn out to be visually more efficient than previously published methods however the emphasis of this paper is on how the csf can be implemented in a precise and locally adaptive way and not on the superior performance of these techniques

on cuts and matchings in planar graphs we study the max cut problem in graphs not contractible tok5 and optimum perfect matchings in planar graphs we prove that both problems can be formulated as polynomial size linear programs

dual sparsity regularized sparse representation for single image super resolution row nonlocal similarity regularization term with l1 norm constraint is explored dual sparsity regularized sparse representation model is presented for sisr iterative shrinkage algorithm is extended to solve dual l1 norm constraints model recently by exploring the column nonlocal similarity prior among the sparse representation coefficients the column nonlocal similarity sparse representation models for solving the ill posed single image super resolution sisr problem are attracting more and more attention however these conventional models consider only the prior among nonlocal similar sparse representation coefficients and fail to consider the prior among all entries or rows of the sparse representation coefficient hence the modeling capability may be limited in fact if a cluster of similar representation coefficients is rearranged into a matrix in the sparse representation coefficient space the nonlocal similarity priors exist both among columns and rows using the row nonlocal similarity prior a row nonlocal similarity regularization term with l1 norm constraint is explored by introducing it to the conventional column nonlocal similarity sparse representation model we present a dual sparsity regularized sparse representation dsrsr model a surrogate function based iterative shrinkage algorithm is introduced to effectively solve the proposed model extensive experiments on sisr demonstrate that the presented model can effectively reconstruct the edge structures and suppress the noise achieving convincing improvement over many state of the art example based methods in terms of psnr ssim and visual quality

the volume algorithm producing primal solutions with a subgradient method we present an extension to the subgradient algorithm to produce primal as well as dual solutions it can be seen as a fast way to carry out an approximation of dantzig wolfe decomposition this gives a fast method for producing approximations for large scale linear programs it is based on a new theorem in linear programming duality we present successful experience with linear programs coming from set partitioning set covering max cut and plant location

adjoint divisors on algebraic curves abstract let c be a numerically connected curve lying on a smooth algebraic surface we show that if a is an ample invertible sheaf satisfying some technical numerical hypotheses then c a is normally generated as a corollary we show that the sheaf c 2 on a numerically connected curve c of arithmetic genus pa 3 is normally generated if c is ample and does not exist a subcurve b c such that pa b 1 b c b

image quality assessment based on a degradation model we model a degraded image as an original image that has been subject to linear frequency distortion and additive noise injection since the psychovisual effects of frequency distortion and noise injection are independent we decouple these two sources of degradation and measure their effect on the human visual system we develop a distortion measure dm of the effect of frequency distortion and a noise quality measure nqm of the effect of additive noise the nqm which is based on peli s 1990 contrast pyramid takes into account the following 1 variation in contrast sensitivity with distance image dimensions and spatial frequency 2 variation in the local luminance mean 3 contrast interaction between spatial frequencies 4 contrast masking effects for additive noise we demonstrate that the nonlinear nqm is a better measure of visual quality than peak signal to noise ratio psnr and linear quality measures we compute the dm in three steps first we find the frequency distortion in the degraded image second we compute the deviation of this frequency distortion from an allpass response of unity gain no distortion finally we weight the deviation by a model of the frequency response of the human visual system and integrate over the visible frequencies we demonstrate how to decouple distortion and additive noise degradation in a practical image restoration system

recent advances in the solution of quadratic assignment problems the quadratic assignment problem qap is notoriously difficult for exact solution methods in the past few years a number of long open qaps including those posed by steinberg 1961 nugent et al 1968 and krarup 1972 were solved to optimality for the first time the solution of these problems has utilized both new algorithms and novel computing structures we describe these developments as well as recent work which is likely to result in the solution of even more difficult instances

image quality assessment based on multiscale geometric analysis reduced reference rr image quality assessment iqa has been recognized as an effective and efficient way to predict the visual quality of distorted images the current standard is the wavelet domain natural image statistics model wnism which applies the kullback leibler divergence between the marginal distributions of wavelet coefficients of the reference and distorted images to measure the image distortion however wnism fails to consider the statistical correlations of wavelet coefficients in different subbands and the visual response characteristics of the mammalian cortical simple cells in addition wavelet transforms are optimal greedy approximations to extract singularity structures so they fail to explicitly extract the image geometric information e g lines and curves finally wavelet coefficients are dense for smooth image edge contours in this paper to target the aforementioned problems in iqa we develop a novel framework for iqa to mimic the human visual system hvs by incorporating the merits from multiscale geometric analysis mga contrast sensitivity function csf and the weber s law of just noticeable difference jnd in the proposed framework mga is utilized to decompose images and then extract features to mimic the multichannel structure of hvs additionally mga offers a series of transforms including wavelet curvelet bandelet contourlet wavelet based contourlet transform wbct and hybrid wavelets and directional filter banks hwd and different transforms capture different types of image geometric information csf is applied to weight coefficients obtained by mga to simulate the appearance of images to observers by taking into account many of the nonlinearities inherent in hvs jnd is finally introduced to produce a noticeable variation in sensory experience thorough empirical studies are carried out upon the live database against subjective mean opinion score mos and demonstrate that 1 the proposed framework has good consistency with subjective perception values and the objective assessment results can well reflect the visual quality of images 2 different transforms in mga under the new framework perform better than the standard wnism and some of them even perform better than the standard full reference iqa model i e the mean structural similarity index and 3 hwd performs best among all transforms in mga under the framework

mammographic mass segmentation embedding multiple features in vector valued level set in ambiguous regions mammographic mass segmentation plays an important role in computer aided diagnosis systems it is very challenging because masses are always of low contrast with ambiguous margins connected with the normal tissues and of various scales and complex shapes to effectively detect true boundaries of mass regions we propose a feature embedded vector valued contour based level set method with relaxed shape constraint in particular we initially use the contour based level set method to obtain the initial boundaries on the smoothed mammogram as the shape constraint to prevent the contour leaking and meanwhile preserve the radiative characteristics of specific malignant masses afterward we relax the obtained shape constraint by analyzing possible valid regions around the initial boundaries the relaxed shape constraint is then used to design a novel stopping function for subsequent vector valued level set method since texture maps gradient maps and the original intensity map can reflect different characteristics of the mammogram we integrate them together to obtain more accurate segmentation by incorporating the new stopping function into the newly proposed feature embedded vector valued contour based level set method the experimental results suggest that the proposed feature embedded vector valued contour based level set method with relaxed shape constraint can effectively find ambiguous margins of the mass regions comparing against existing active contours methods the new scheme is more effective and robust in detecting complex masses

on the matrix cut rank of polyhedra lovasz and schrijver 1991 described a semidefinite operator for generating strong valid inequalities for the 0 1 vectors in a prescribed polyhedron among their results they showed that n iterations of the operator are sufficient to generate the convex hull of 0 1 vectors contained in a polyhedron in n space we give a simple example having chvatal rank 1 that meets this worst case bound of n we describe another example requiring n iterations even when combining the semidefinite and gomory chvatal operators this second example is used to show that the standard linear programming relaxation of a k city traveling salesman problem requires at least k 8 iterations of the combined operator this bound is best possible up to a constant factor as k 1 iterations suffice

an application of the lovasz schrijver m k k operator to the stable set problem although the lift and project operators of lovasz and schrijver have been the subject of intense study their m k k operator has received little attention we consider an application of this operator to the stable set problem we begin with an initial linear programming lp relaxation consisting of clique and non negativity inequalities and then apply the operator to obtain a stronger extended lp relaxation we discuss theoretical properties of the resulting relaxation describe the issues that must be overcome to obtain an effective practical implementation and give extensive computational results remarkably the upper bounds obtained are sometimes stronger than those obtained with semidefinite programming techniques

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed