inference of segmented overlapping surfaces from binocular stereo presents an integrated approach to the derivation of scene descriptions from a pair of stereo images where the steps of feature correspondence and surface reconstruction are addressed within the same framework special attention is given to the development of a methodology with general applicability in order to handle the issues of noise lack of image features surface discontinuities and regions that are visible in one image only we adopt a tensor representation for the data and introduce a robust computational technique called tensor voting for information propagation the key contributions of this paper are twofold first we introduce saliency instead of correlation scores as the criterion to determine the correctness of matches and the integration of feature matching and structure extraction second our tensor representation and voting as a tool enables us to perform the complex computations associated with the formulation of the stereo problem in 3d at a reasonable computational cost we illustrate the steps on an example then provide results on both random dot stereograms and real stereo pairs all processed with the same parameter set

graph embedding in vector spaces by node attribute statistics graph based representations are of broad use and applicability in pattern recognition they exhibit however a major drawback with regards to the processing tools that are available in their domain graph embedding into vector spaces is a growing field among the structural pattern recognition community which aims at providing a feature vector representation for every graph and thus enables classical statistical learning machinery to be used on graph based input patterns in this work we propose a novel embedding methodology for graphs with continuous node attributes and unattributed edges the approach presented in this paper is based on statistics of the node labels and the edges between them based on their similarity to a set of representatives we specifically deal with an important issue of this methodology namely the selection of a suitable set of representatives in an experimental evaluation we empirically show the advantages of this novel approach in the context of different classification problems using several databases of graphs

discrete signal matching using coarse to fine wavelet basis functions in this paper we propose a matching algorithm to estimate accurate and dense displacements between two signals the displacements are characterized by a coarse to fine wavelet representation which is a linear combination of hierarchical basis functions developed by cai and wang siam numer anal 33 3 1996 937 the coarser scale basis function has larger support while the finer scale basis function has smaller support during the iterative minimization process the basis functions are utilized as large to small windows in selecting global to local regions for signal matching the estimated wavelet coefficients are then used to reconstruct the signal in a coarse to fine manner two sets of synthetic examples one with small displacement and the other with large displacements have been employed to illustrate the advantages of the wavelet based method this method has been applied to estimate the dense disparity between stereo images in several real examples and the results demonstrate its effectiveness

an innovative eigenvalue problem solver for free vibration of euler bernoulli beam by using the adomian decomposition method this paper deals with free vibration problems of euler bernoulli beam under various supporting conditions the technique we have used is based on applying the adomian decomposition method adm to our vibration problems doing some simple mathematical operations on the method we can obtain ith natural frequencies and mode shapes one at a time the computed results agree well with those analytical and numerical results given in the literature these results indicate that the present analysis is accurate and provides a unified and systematic procedure which is simple and more straightforward than the other modal analysis

a new analytical and numerical treatment for singular two point boundary value problems via the adomian decomposition method based on the adomian decomposition method a new analytical and numerical treatment is introduced in this research to investigate linear and non linear singular two point bvps the effectiveness of the proposed approach is verified by several linear and non linear examples

graph characterization via ihara coefficients the novel contributions of this paper are twofold first we demonstrate how to characterize unweighted graphs in a permutation invariant manner using the polynomial coefficients from the ihara zeta function i e the ihara coefficients second we generalize the definition of the ihara coefficients to edge weighted graphs for an unweighted graph the ihara zeta function is the reciprocal of a quasi characteristic polynomial of the adjacency matrix of the associated oriented line graph since the ihara zeta function has poles that give rise to infinities the most convenient numerically stable representation is to work with the coefficients of the quasi characteristic polynomial moreover the polynomial coefficients are invariant to vertex order permutations and also convey information concerning the cycle structure of the graph to generalize the representation to edge weighted graphs we make use of the reduced bartholdi zeta function we prove that the computation of the ihara coefficients for unweighted graphs is a special case of our proposed method for unit edge weights we also present a spectral analysis of the ihara coefficients and indicate their advantages over other graph spectral methods we apply the proposed graph characterization method to capturing graph class structure and clustering graphs experimental results reveal that the ihara coefficients are more effective than methods based on laplacian spectra

diffusion wavelet embedding a multi resolution approach for graph embedding in vector space abstract in this article we propose a multiscale method of embedding a graph into a vector space using diffusion wavelets at each scale we extract a detail subspace and a corresponding lower scale approximation subspace to represent the graph representative features are then extracted at each scale to provide a scale space description of the graph the lower scale is constructed using a super node merging strategy based on nearest neighbor or maximum participation and the new adjacency matrix is generated using vertex identification this approach allows the comparison of graphs where the important structural differences may be present at varying scales additionally this method can improve the differentiating power of the embedded vectors and this property reduces the possibility of cospectrality typical in spectral methods substantially the experimental results show that augmenting the features of abstract levels to the graph features increases the graph classification accuracies in different datasets

exact solutions of the generalized 2 1 dimensional nonlinear evolution equations via the modified simple equation method in this paper the modified simple equation method msem is applied to construct exact solutions of the generalized 2 1 dimensional nonlinear evolution equations nlees involving parameters via the 2 1 dimensional calogero bogoyavlenskii schiff cbs equation the 2 1 dimensional breaking soliton equation and the 2 1 dimensional bogoyavlenskii s breaking soliton equation the solitary wave solutions are derived from the exact solutions by assigning special values of the parameters

convergent series solution of nonlinear equations abstract the author s decomposition method 1 provides a new efficient computational procedure for solving large classes of nonlinear and or stochastic equations these include differential equations containing polynomial exponential and trigonometric terms negative or irrational powers and product nonlinearities 2 also included are partial differential equations 3 delay differential equations 4 algebraic equations 5 and matrix equations 6 which describe physical systems essentially the method provides a systematic computational procedure for equations containing any nonlinear terms of physical significance the procedure depends on calculation of the author s a n a finite set of polynomials 1 13 in terms of which the nonlinearities can be expressed this paper shows important properties of the a n which ensure an accurate and computable convergent solution by the author s decomposition method 1 since the nonlinearities and or stochasticity which can be handled are quite general the results are potentially extremely useful for applications and make a number of common approximations such as linearization unnecessary

universal approximation using radial basis function networks there have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables some of these studies deal with cases in which the hidden layer nonlinearity is not a sigmoid this was motivated by successful applications of feedforward networks with nonsigmoidal hidden layer units this paper reports on a related study of radial basis function rbf networks and it is proved that rbf networks having one hidden layer are capable of universal approximation here the emphasis is on the case of typical rbf networks and the results show that a certain class of rbf networks with the same smoothing factor in each kernel node is broad enough for universal approximation

a new approach to the wave equation an application of the decomposition method abstract in the present paper the inhomogeneous wave equation is solved quickly easily and elegantly by adomian s decomposition method

analytical solution of the linear fractional differential equation by adomian decomposition method in this paper we consider the n term linear fractional order differential equation with constant coefficients and obtain the solution of this kind of fractional differential equations by adomian decomposition method with the equivalent transmutation we show that the solution by adomian decomposition method is the same as the solution by the green s function finally we illustrate our result with some examples

graph embedding using tree edit union in this paper we address the problem of how to learn a structural prototype that can be used to represent the variations present in a set of trees the prototype serves as a pattern space representation for the set of trees to do this we construct a super tree to span the union of the set of trees this is a chicken and egg problem since before the structure can be estimated correspondences between the nodes of the super tree and the nodes of the sample tree must be to hand we demonstrate how to simultaneously estimate the structure of the super tree and recover the required correspondences by minimizing the sum of the tree edit distances over pairs of trees subject to edge consistency constraints each node of the super tree corresponds to a dimension of the pattern space and for each tree we construct a pattern vector in which the elements of the weights corresponding to each of the dimensions of the super tree we perform pattern analysis on the set of trees by performing principal components analysis on the vectors the method is illustrated on a shape analysis problem involving shock trees extracted from the skeletons of 2d objects

generalised correlation for multi feature correspondence computing correspondences between pairs of images is fundamental to all structures from motion algorithms correlation is a popular method to estimate similarity between patches of images in the standard formulation the correlation function uses only one feature such as the gray level values of a small neighbourhood research has shown that different features such as colour edge strength corners texture measures work better under di0erent conditions we propose a framework of generalized correlation that can compute a real valued similarity measure using a feature vector whose components can be dissimilar the framework can combine the e0ects of di0erent image features such as multi spectral features edges corners texture measures etc into a single similarity measure in a 3exible manner additionally it can combine results of di0erent window sizes used for correlation with proper weighting for each relative importances of the features can be estimated from the image itself for accurate correspondence in this paper we present the framework of generalised correlation provide a few examples demonstrating its power as well as discuss the implementation issues 2002 published by elsevier science ltd on behalf of pattern recognition society

generalized assorted camera arrays robust cross channel registration and applications one popular technique for multimodal imaging is generalized assorted pixels gap where an assorted pixel array on the image sensor allows for multimodal capture unfortunately gap is limited in its applicability because of the need for multimodal filters that are amenable with semiconductor fabrication processes and results in a fixed multimodal imaging configuration in this paper we advocate for generalized assorted camera gac arrays for multimodal imaging i e a camera array with filters of different characteristics placed in front of each camera aperture the gac provides us with three distinct advantages over gap ease of implementation flexible application dependent imaging since filters are external and can be changed and depth information that can be used for enabling novel applications e g postcapture refocusing the primary challenge in gac arrays is that since the different modalities are obtained from different viewpoints there is a need for accurate and efficient cross channel registration traditional approaches such as sum of squared differences sum of absolute differences and mutual information all result in multimodal registration errors here we propose a robust cross channel matching cost function based on aligning normalized gradients which allows us to compute cross channel subpixel correspondences for scenes exhibiting nontrivial geometry we highlight the promise of gac arrays with our cross channel normalized gradient cost for several applications such as low light imaging postcapture refocusing skin perfusion imaging using color near infrared and hyperspectral imaging

robust matching cost function for stereo correspondence using matching by tone mapping and adaptive orthogonal integral image real world stereo images are inevitably affected by radiometric differences including variations in exposure vignetting lighting and noise stereo images with severe radiometric distortion can have large radiometric differences and include locally nonlinear changes in this paper we first introduce an adaptive orthogonal integral image which is an improved version of an orthogonal integral image after that based on matching by tone mapping and the adaptive orthogonal integral image we propose a robust and accurate matching cost function that can tolerate locally nonlinear intensity distortion by using the adaptive orthogonal integral image the proposed matching cost function can adaptively construct different support regions of arbitrary shapes and sizes for different pixels in the reference image so it can operate robustly within object boundaries furthermore we develop techniques to automatically estimate the values of the parameters of our proposed function we conduct experiments using the proposed matching cost function and compare it with functions employing the census transform supporting local binary pattern and adaptive normalized cross correlation as well as a mutual information based matching cost function using different stereo data sets by using the adaptive orthogonal integral image the proposed matching cost function reduces the error from 21 51 to 15 73 in the middlebury data set and from 15 9 to 10 85 in the kitti data set as compared with using the orthogonal integral image the experimental results indicate that the proposed matching cost function is superior to the state of the art matching cost functions under radiometric variation

homotopy perturbation method for solving sixth order boundary value problems in this paper we apply the homotopy perturbation method for solving the sixth order boundary value problems by reformulating them as an equivalent system of integral equations this equivalent formulation is obtained by using a suitable transformation the analytical results of the integral equations have been obtained in terms of convergent series with easily computable components several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method comparisons are made to confirm the reliability of the homotopy perturbation method we have also considered an example where the homotopy perturbation method is not reliable

depth based complexity traces of graphs in this paper we aim to characterize graphs in terms of a structural measure of complexity our idea is to decompose a graph into layered substructures of increasing size and then to measure the information content of these substructures to locate dominant substructures within a graph we commence by identifying a centroid vertex which has the minimum shortest path length variance to the remaining vertices for each graph a family of centroid expansion subgraphs is derived from the centroid vertex in order to capture dominant structural characteristics of the graph since the centroid vertex is identified through a global analysis of the shortest path length distribution the expansion subgraphs provide a fine representation of a graph structure we then show how to characterize graphs using depth based complexity traces here we explore two different strategies the first strategy is to measure how the entropies on the centroid expansion subgraphs vary with the increasing size of the subgraphs the second strategy is to measure how the entropy differences vary with the increasing size of the subgraphs we perform graph classification in the principal component space of the complexity trace vectors experiments on graph datasets abstracted from some bioinformatics and computer vision databases demonstrate the effectiveness and efficiency of the proposed graph complexity traces our methods are competitive to state of the art methods highlightswe identify a centroid vertex of a graph through its shortest path matrix we establish a family of expansion subgraphs of a graph from its centroid vertex we construct depth based complexity traces of a graph on its expansion subgraphs we evaluate the performance of our complexity traces on standard graph datasets we demonstrate the effectiveness and efficiency of the graph complexity traces

a new symbolic computational approach to singular initial value problems in the second order ordinary differential equations this paper presents a new symbolic algorithm to compute the singular initial value problem of second order ordinary differential equations using adomian decomposition method the algorithm has been implemented in the computer algebra system maple to facilitate the application of this method a number of examples are presented to demonstrate the computation efficiency of the program

a new iterative method to compute nonlinear equations the aim of this paper is to construct a new efficient iterative method to solve nonlinear equations the new method is based on the proposals of abbasbandy on improving the order of accuracy of newton raphson method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method applied mathematics and computation 145 2003 887 893 and on the proposals of babolian and biazar on improving the order of accuracy of adomian s decomposition method e babolian j biazar on the order of convergence of adomian method applied mathematics and computation 130 2002 383 387 the convergence of the new scheme is proved and at least the cubic order of convergence is established several examples are presented and compared to other methods showing the accuracy and fast convergence of this new method also it is shown in this paper that the modified adomian s method developed by babolian and biazar to solve nonlinear equations e babolian j biazar solution of nonlinear equations by modified adomian decomposition method applied mathematics and computation 132 2002 167 172 should be slightly modified due to the fact that convergence of adomian s method does not ensure convergence of the modified method an example illustrates this fact which unlike what is claimed by the authors does not converge with their method but with a simple different choice of the zero component becomes convergent

uncertainty propagation and the matching of junctions as feature groupings the interpretation of the 3d world from image sequences requires the identification and correspondences of key features in the scene we describe a robust algorithm for matching groupings of features related to the objects in the scene we consider the propagation of uncertainty from the feature detection stage through the grouping stage to provide a measure of uncertainty at the matching stage we focus upon indoor scenes and match junctions which are groupings of line segments that meet at a single point a model of the uncertainty in junction detection is described and the junction uncertainty under the epipolar constraint is determined junction correspondence is achieved through matching of each line segment associated with the junction a match likelihood is then derived based upon the detection uncertainties and then combined with information on junction topology to create a similarity measure a robust matching algorithm is proposed and used to match junctions between pairs of images the presented experimental results on real images show that the matching algorithm produces sufficiently reliable results for applications such as structure from motion

motion estimation with quadtree splines this paper presents a motion estimation algorithm based on a new multiresolution representation the quadtree spline this representation describes the motion field as a collection of smoothly connected patches of varying size where the patch size is automatically adapted to the complexity of the underlying motion the topology of the patches is determined by a quadtree data structure and both split and merge techniques are developed for estimating this spatial subdivision the quadtree spline is implemented using another novel representation the adaptive hierarchical basis spline and combines the advantages of adaptively sized correlation windows with the speedups obtained with hierarchical basis preconditioners results are presented on some standard motion sequences

signal matching through scale space given a collection of similar signals that have been deformed with respect to each other the general signal matching problem is to recover the deformation we formulate the problem as the minimization of an energy measure that combines a smoothness term and a similarity term the minimization reduces to a dynamic system governed by a set of coupled first order differential equations the dynamic system finds an optimal solution at a coarse scale and then tracks it continuously to a fine scale among the major themes in recent work on visual signal matching have been the notions of matching as constrained optimization of variational surface reconstruction and of coarse to fine matching our solution captures these in a precise succinct and unified form results are presented for one dimensional signals a motion sequence and a stereo pair

matching two perspective views a computational approach to image matching is described it uses multiple attributes associated with each image point to yield a generally overdetermined system of constraints taking into account possible structural discontinuities and occlusions in the algorithm implemented intensity edgeness and cornerness attributes are used in conjunction with the constraints arising from intraregional smoothness field continuity and discontinuity and occlusions to compute dense displacement fields and occlusion maps along the pixel grids the intensity edgeness and cornerness are invariant under rigid motion in the image plane in order to cope with large disparities a multiresolution multigrid structure is employed coarser level edgeness and cornerness measures are obtained by blurring the finer level measures the algorithm has been tested on real world scenes with depth discontinuities and occlusions a special case of two view matching is stereo matching where the motion between two images is known the algorithm can be easily specialized to perform stereo matching using the epipolar constraint

new exact traveling wave solutions of the 4 1 dimensional fokas equation abstract in this paper two distinct methods are applied to look for exact traveling wave solutions of the 4 1 dimensional nonlinear fokas equation namely the modified simple equation method msem and the extended simplest equation method esem some new exact traveling wave solutions involving some parameters are obtained the solitary wave solutions can be extracted by assigning special values of these parameters the obtained solutions show the simplicity and efficiency of the used approaches that can be applied for nonlinear equations as well as linear ones

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

exact solutions for the generalized klein gordon equation via a transformation and exp function method and comparison with adomian s method in this paper a suitable transformation and a so called exp function method are used to obtain different types of exact solutions for the generalized klein gordon equation these exact solutions are in full agreement with the previous results obtained in refs sirendaoreji auxiliary equation method and new solutions of klein gordon equations chaos solitons fractals 31 4 2007 943 950 huiqun zhang extended jacobi elliptic function expansion method and its applications communications in nonlinear science and numerical simulation 12 5 2007 627 635 one of these exact solutions is compared with the approximate solutions obtained by the modified decomposition method accurate numerical results for a wider range of time are obtained after using different types of adm pade approximation our results show that the exp function method is very effective in finding exact solutions for the problem considered while the modified decomposition method is very powerful in finding numerical solutions with good accuracy for nonlinear pde without any need for a transformation or perturbation

backtrackless walks on a graph the aim of this paper is to explore the use of backtrackless walks and prime cycles for characterizing both labeled and unlabeled graphs the reason for using backtrackless walks and prime cycles is that they avoid tottering and can increase the discriminative power of the resulting graph representation however the use of such methods is limited in practice because of their computational cost in this paper we present efficient methods for computing graph kernels which are based on backtrackless walks in a labeled graph and whose worst case running time is the same as that of kernels based on random walks for clustering unlabeled graphs we construct feature vectors using ihara coefficients since these coefficients are related to the frequencies of prime cycles in the graph to efficiently compute the low order coefficients we present an o v 3 algorithm which is better than the o v 6 worst case running time of previously known algorithms in the experimental evaluation we apply the proposed method to clustering both labeled and unlabeled graphs the results show that using backtrackless walks and prime cycles instead of random walks can increase the accuracy of recognition

a new approach to nonlinear partial differential equations abstract the author s decomposition method for the solution of operator equations which may be nonlinear and or stochastic is generalized to multidimensional cases

implicit and explicit camera calibration theory and experiments by implicit camera calibration we mean the process of calibrating a camera without explicitly computing its physical parameters implicit calibration can be used for both three dimensional 3 d measurement and generation of image coordinates in this paper we present a new implicit model based on the generalized projective mappings between the image plane and two calibration planes the back projection and projection processes are modelled separately to ease the computation of distorted image coordinates from known world points a set of constraints of perspectivity is derived to relate the transformation parameters of the two calibration planes under the assumption of the radial distortion model we present a computationally efficient method for explicitly correcting the distortion of image coordinates in frame buffer without involving the computation of camera position and orientation by combining with any linear calibration techniques this method makes explicit the camera physical parameters extensive experimental comparison of our methods with the classic photogrammetric method and tsai s 1986 method in the aspects of 3 d measurement both absolute and relative errors the prediction of image coordinates and the effect of the number of calibration points is made using real images from 15 different depth values

psychophysical and computational studies towards a theory of human stereopsis psychophysical studies are described which pose a strong challenge to models of human stereopsis based on the processing of disparity information within independent spatial frequency tuned binocular channels these studies support instead the proposal that the processes of human binocular combination integrally relate the extraction of disparity information with the construction of raw primal sketch assertions this proposal implies global binocular combination rules using principles of figural continuity and cross channel correspondence to disambiguate local matches found independently within spatial frequency channels exploratory small scale computational experiments with stereo algorithms based on these rules are described and found to be successful in dealing with a variety of stereo inputs the constraints presented by objects which are exploited by these algorithms are discussed

surfaces from stereo integrating feature matching disparity estimation and contour detection an approach is described that integrates the processes of feature matching contour detection and surface interpolation to determine the three dimensional distance or depth of objects from a stereo pair of images integration is necessary to ensure that the detected surfaces are smooth surface interpolation takes into account detected occluding and ridge contours in the scene interpolation is performed within regions enclosed by these contours planar and quadratic patches are used as local models of the surface occluded regions in the image are identified and are not used for matching and interpolation a coarse to fine algorithm is presented that generates a multiresolution hierarchy of surface maps one at each level of resolution experimental results are given for a variety of stereo images

image registration using wavelet based motion model an image registration algorithm is developed to estimate dense motion vectors between two images using the coarse to fine wavelet based motion model this motion model is described by a linear combination of hierarchical basis functions proposed by cai and wang siam numer anal 33 3 937 970 1996 the coarser scale basis function has larger support while the finer scale basis function has smaller support with these variable supports in full resolution the basis functions serve as large to small windows so that the global and local information can be incorporated concurrently for image matching especially for recovering motion vectors containing large displacements to evaluate the accuracy of the wavelet based method two sets of test images were experimented using both the wavelet based method and a leading pyramid spline based method by szeliski et al international journal of computer vision 22 3 199 218 1996 one set of test images taken from barron et al international journal of computer vision 12 43 77 1994 contains small displacements the other set exhibits low texture or spatial aliasing after image blurring and contains large displacements the experimental results showed that our wavelet based method produced better motion estimates with error distributions having a smaller mean and smaller standard deviation

multilevel enhancement and detection of stereo disparity surfaces abstract the problem of stereo vision has been of increasing interest to the computer vision community over the past decade this paper presents a new computational framework for matching a pair of stereo images arising from viewing the same object from two different positions in contrast to previous work this approach formulates the matching problem as detection of a bright coherent disparity surface in a 3d image called the spatio disparity space sds image the sds images represents the goodness of each and every possible match a nonlinear filter is proposed for enhancing the disparity surface in the sds image and for suppressing the noise this filter is used to construct a hyperpyramid representation of the sds image then the disparity surface is detected using a coarse to fine control structure the proposed method is robust to photometric and geometric distortions in the stereo images and has a number of computational advantages it produces good results for complex scenes

fuzzy multilevel graph embedding structural pattern recognition approaches offer the most expressive convenient powerful but computational expensive representations of underlying relational information to benefit from mature less expensive and efficient state of the art machine learning models of statistical pattern recognition they must be mapped to a low dimensional vector space our method of explicit graph embedding bridges the gap between structural and statistical pattern recognition we extract the topological structural and attribute information from a graph and encode numeric details by fuzzy histograms and symbolic details by crisp histograms the histograms are concatenated to achieve a simple and straightforward embedding of graph into a low dimensional numeric feature vector experimentation on standard public graph datasets shows that our method outperforms the state of the art methods of graph embedding for richly attributed graphs highlights we propose an explicit graph embedding method we perform multilevel analysis of graph to extract global topological structural and attribute information we use homogeneity of subgraphs in graph for extracting topological structural details we encode numeric information by fuzzy histograms and symbolic information by crisp histograms our method outperforms graph embedding methods for richly attributed graphs

a numerical solution of the vibration equation using modified decomposition method abstract in the present paper the well known vibration equation for very large membrane with the help of powerful modification of adomian decomposition method proposed by wazwaz a reliable modification of adomian decomposition method applied mathematics and computation 102 1999 77 86 has been solved by using initial value the explicit solutions of the equation for different cases have been derived which accelerate the rapid convergence of the series solution the present method performs extremely well in terms of efficiency and simplicity numerical results for different particular cases of the problem are presented graphically

graph characteristics from the heat kernel trace graph structures have been proved important in high level vision since they can be used to represent structural and relational arrangements of objects in a scene one of the problems that arises in the analysis of structural abstractions of objects is graph clustering in this paper we explore how permutation invariants computed from the trace of the heat kernel can be used to characterize graphs for the purposes of measuring similarity and clustering the heat kernel is the solution of the heat equation and is a compact representation of the path length distribution on a graph the trace of the heat kernel is given by the sum of the laplacian eigenvalues exponentiated with time we explore three different approaches to characterizing the heat kernel trace as a function of time our first characterization is based on the zeta function which from the mellin transform is the moment generating function of the heat kernel trace our second characterization is unary and is found by computing the derivative of the zeta function at the origin the third characterization is derived from the heat content i e the sum of the elements of the heat kernel we show how the heat content can be expanded as a power series in time and the coefficients of the series can be computed using the laplacian spectrum we explore the use of these characterizations as a means of representing graph structure for the purposes of clustering and compare them with the use of the laplacian spectrum experiments with the synthetic and real world databases reveal that each of the three proposed invariants is effective and outperforms the traditional laplacian spectrum moreover the heat content invariants appear to consistently give the best results in both synthetic sensitivity studies and on real world object recognition problems

sinc galerkin method for solving nonlinear boundary value problems the sinc galerkin method is used to approximate solutions of nonlinear problems involving nonlinear second fourth and sixth order differential equations with homogeneous and nonhomogeneous boundary conditions the scheme is tested on four nonlinear problems the results demonstrate the reliability and efficiency of the algorithm developed

derivation of the adomian decomposition method using the homotopy analysis method abstract adomian decomposition method has been used intensively to solve nonlinear boundary and initial value problems it has been proved to be very efficient in generating series solutions of the problem under consideration under the assumption that such series solution exits however very little has been done to address the mathematical foundation of the method and its error analysis in this article the mathematical derivation of the method using the homotopy analysis method is presented in addition an error analysis is addressed as well as the convergence criteria

intensity and gradient based stereo matching using hierarchical gaussian basis functions we propose a stereo correspondence method by minimizing intensity and gradient errors simultaneously in contrast to conventional use of image gradients the gradients are applied in the deformed image space although a uniform smoothness constraint is imposed it is applied only to nonfeature regions to avoid local minima in the function minimization we propose to parameterize the disparity function by hierarchical gaussians both the uniqueness and the ordering constraints can be easily imposed in our minimization framework besides we propose a method to estimate the disparity map and the camera response difference parameters simultaneously experiments with various real stereo images show robust performances of our algorithm

stochastic stereo matching over scale a stochastic optimization approach to stereo matching is presented unlike conventional correlation matching and feature matching the method provides a dense array of disparities eliminating the need for interpolation first the stereo matching problem is defined in terms of finding a disparity map that satisfies two competing constraints 1 matched points should have similar image intensity and 2 the disparity map should vary as slowly as possible these constraints are interpreted as specifying the potential energy of a system of oscillators ground states are approximated by a new variant of simulated annealing which has two important features first the microcanonical ensemble is simulated using a new algorithm that is more efficient and more easily implemented than the familiar metropolis algorithm which simulates the canonical ensemble secondly it uses a hierarchical coarse to fine control structure employing gaussian or laplacian pyramids of the stereo images in this way quickly computed results at low resolutions are used to initialize the system at higher resolutions

information theoretic deformable registration using local image information we present a deformable registration algorithm for multi modality images based on information theoretic similarity measures at the scale of individual image voxels we derive analytical expressions for the mutual information the joint entropy and the sum of marginal entropies of two images over a small neighborhood in terms of image gradients using these expressions we formulate image registration algorithms maximizing local similarity over the whole image domain in an energy minimization framework this strategy produces highly elastic image alignment as the registration is driven by voxel similarities between the images the algorithms are easily implementable using the closed form expressions for the derivative of the optimization function with respect to the deformation and avoid estimation of joint and marginal probability densities governing the image intensities essential to conventional information theoretic image registration methods

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

adomian s method of decomposition critical review and examples of failure abstract adomian s method of decomposition is considered in application to initial boundary value problems for the one space dimensional spatially homogeneous heat conduction equation it is shown that the fundamental equation of the method is well defined only for certain restricted types of boundary conditions within the class of such boundary conditions examples are given such that the fundamental equation fails to have a unique solution and such that the sequence produced by iteration of this equation is divergent the latter is a counterexample to a published assertion of convergence

on product nonlinearities in stochastic differential equations the author s methods for solution of stochastic differential equations shown elsewhere to be applicable for nonlinear cases including polynomial exponential and trigonometric terms is shown to be applicable to product nonlinearities as well

a unified definition and computation of laplacian spectral distances abstract laplacian spectral kernels and distances e g biharmonic heat diffusion wave kernel distances are easily defined through a filtering of the laplacian eigenpairs they play a central role in several applications such as dimensionality reduction with spectral embeddings diffusion geometry image smoothing geometric characterisations and embeddings of graphs extending the results recently derived in the discrete setting 38 39 to the continuous case we propose a novel definition of the laplacian spectral kernels and distances whose approximation requires the solution of a set of inhomogeneous laplace equations their discrete counterparts are equivalent to a set of sparse symmetric and well conditioned linear systems which are efficiently solved with iterative methods finally we discuss the optimality of the laplacian spectrum for the approximation of the spectral kernels the relation between the spectral and green kernels and the stability of the spectral distances with respect to the evaluation of the laplacian spectrum and to multiple laplacian eigenvalues

pattern vectors from algebraic graph theory graph structures have proven computationally cumbersome for pattern analysis the reason for this is that before graphs can be converted to pattern vectors correspondences must be established between the nodes of structures which are potentially of different size to overcome this problem in this paper we turn to the spectral decomposition of the laplacian matrix we show how the elements of the spectral matrix for the laplacian can be used to construct symmetric polynomials that are permutation invariants the coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner we extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a hermitian property matrix that can be viewed as a complex analogue of the laplacian to embed the graphs in a pattern space we explore whether the vectors of invariants can be embedded in a low dimensional space using a number of alternative strategies including principal components analysis pca multidimensional scaling mds and locality preserving projection lpp experimentally we demonstrate that the embeddings result in well defined graph clusters our experiments with the spectral representation involve both synthetic and real world data the experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure the real world experiments show that the method can be used to locate clusters of graphs

numerical method for the solution of special nonlinear fourth order boundary value problems the sinc galerkin method is used to approximate solution of nonlinear problems this work deals with the sinc galerkin method for solving nonlinear fourth order differential equations with homogeneous and nonhomogeneous boundary conditions the scheme is tested on three nonlinear problems and a comparison with finite difference methods and fourth order multiderivative method is made it is shown that the sinc galerkin method yields better results

analytical approximations and pade approximants for volterra s population model in this paper an analytic approximation for volterra s model for population growth of a species in a closed system is presented the nonlinear integro differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation the series solution method and the decomposition method are implemented independently to the model and to a related ode the pade approximants that often show superior performance over series approximations are effectively used in the analysis to capture the essential behavior of the population u t of identical individuals

a quantum jensen shannon graph kernel for unattributed graphs in this paper we use the quantum jensen shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel in quantum mechanics the quantum jensen shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices we commence by computing the density matrix associated with a continuous time quantum walk over each graph being compared in particular we adopt the closed form solution of the density matrix introduced in rossi et al 2013 27 28 to reduce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly next we compare the mixed states represented by the density matrices using the quantum jensen shannon divergence with the quantum states for a pair of graphs described by their density matrices to hand the quantum graph kernel between the pair of graphs is defined using the quantum jensen shannon divergence between the graph density matrices we evaluate the performance of our kernel on several standard graph datasets from both bioinformatics and computer vision the experimental results demonstrate the effectiveness of the proposed quantum graph kernel highlightswe compute a density matrix for a graph using the continuous time quantum walk we compute the quantum jensen shannon divergence between graph density matrixes we define a quantum jensen shannon graph kernel using the quantum divergence we evaluate the performance of our quantum kernel on standard graph datasets we demonstrate the effectiveness of the proposed quantum kernel

parametric shape from shading by radial basis functions we present a new method of shape from shading by using radial basis functions to parameterize the object depth the radial basis functions are deformed by adjusting their centers widths and weights such that the intensity errors are minimized the initial centers and widths are arranged hierarchically to speed up convergence and to stabilize the solution although the smoothness constraint is used it can be eventually dropped out without causing instabilities in the solution an important feature of our parametric shape from shading method is that it offers a unified framework for integration of multiple sensory information we show that knowledge about surface depth and or surface normals anywhere in the image can be easily incorporated into the shape from shading process it is further demonstrated that even qualitative knowledge can be used in shape from shading to improve 3d reconstruction experimental comparisons of our method with several existing ones are made by using both synthetic and real images results show that our solution is more accurate than the others

the modified decomposition method applied to unsteady flow of gas through a porous medium in this paper an analytic solution for the unsteady flow of gas through a porous medium is constructed our approach rests on the recently developed modification of the adomian decomposition method the diagonal pade approximants are effectively used in the analysis to capture the essential behavior of y x and to determine the initial slope y 0 the proposed scheme avoids the complexity provided by using perturbation techniques

variational iteration method for unsteady flow of gas through a porous medium using he s polynomials and pade approximants in this paper we apply the variational iteration method using he s polynomials for finding the analytical solution of unsteady flow of gas through a porous medium the proposed method is an elegant combination of he s variational iteration and the homotopy perturbation methods the suggested algorithm is quite efficient and is practically well suited for use in such problems the proposed iterative scheme finds the solution without any discretization linearization or restrictive assumptions the diagonal pade approximants are effectively used in the analysis to capture the essential behavior of the solution and to determine the initial slope a clear advantage of this technique over the decomposition method is that no calculation of adomian s polynomials is needed

some np complete problems similar to graph isomorphism the graph isomorphism problem has so far resisted attempts at determining its complexity status it has not been shown to be np complete nor in p in this paper several altered or generalized versions of the isomorphism problem are presented and shown to be np complete one of these is the problem of determining whether a given graph has a fixed point free automorphism some speculation is made on the possible implications of these results on deciding the complexity status of isomorphism various classes and hierarchies of problems in np are discussed

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

symbolic implementation of the algorithm for calculating adomian polynomials in this paper a symbolic implementation code is developed of a technique proposed by wazwaz appl math comput 111 2000 53 for calculating adomian polynomials for nonlinear operators the algorithm proposed by him appl math comput 111 2000 53 offers a promising approach for calculating adomian polynomials for all forms of nonlinearity but it is not easy to implement due to its huge size of algebraic calculations complicated trigonometric terms and unique summation rules it is well known that the algebraic manipulation language such as mathematica is useful to facilitate such a hard computational work pattern matching capabilities peculiar feature of mathematica are used in index regrouping which is a key role in constructing adomian polynomials the computer algebra software mathematica is used to collect terms to their order and to simplify the terms the symbolic implementation code author developed appearing at appendix has the flexibility that may easily cover any length of adomian polynomial for many forms of nonlinear cases a nonlinear evolution equation is investigated in order to justify the availability of symbolic implementation code

spectral embedding of graphs in this paper we explore how to embed symbolic relational graphs with unweighted edges in a pattern space we adopt a graph spectral approach we use the leading eigenvectors of the graph adjacency matrix to define eigenmodes of the adjacency matrix for each eigenmode we compute vectors of spectral properties these include the eigenmode perimeter eigenmode volume cheeger number inter mode adjacency matrices and intermode edge distance we embed these vectors in a pattern space using two contrasting approaches the first of these involves performing principal or independent components analysis on the covariance matrix for the spectral pattern vectors the second approach involves performing multidimensional scaling on the l2 norm for pairs of pattern vectors we illustrate the utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2d images of 3d polyhedral objects two problems are investigated the first of these is the clustering of graphs representing distinct objects viewed from different directions the second is the identification of characteristic views of single objects these two studies reveal that both embedding methods result in well structured view spaces for graph data extracted from 2d views of 3d objects

inversion of nonlinear stochastic operators abstract the operator theoretic method adomian and malakian j math anal appl 76 1 1980 183 201 recently extended adomian s solutions of nonlinear stochastic differential equations g adomian stochastic systems analysis in applied stochastic processes nonlinear stochastic differential equations j math anal appl 55 1 1976 441 452 on the modeling and analysis of nonlinear stochastic systems in proceeding international conf on mathematical modeling vol 1 pp 29 40 to provide an efficient computational procedure for differential equations containing polynomial exponential and trigonometric nonlinear terms n y the procedure depends on the calculation of certain quantities an and bn this paper generalizes the calculation of the an and bn to much wider classes of nonlinearities of the form n y y essentially the method provides a systematic computational procedure for differential equations containing any nonlinear terms of physical significance this procedure depends on a recurrence rule from which explicit general formulae are obtained for the quantities an and bn for any order n in a convenient form this paper also demonstrates the significance of the iterative series decomposition proposed by adomian for linear stochastic operators in 1964 and developed since 1976 for nonlinear stochastic operators since both the nonlinear and stochastic behavior is quite general the results are extremely significant for applications processes need not for example be limited to either gaussian processes white noise or small fluctuations

approximate analytic solutions for a two dimensional mathematicalmodel of a packed bed electrode using the adomian decomposition method in this paper we solve a system of second order partial differential equations with non standard boundary conditions this system of equations is a mathematical model that describes distributions of the overpotential and reactant concentration in a working packed bed electrode for an electrochemical reactor to ensure the existence and uniqueness of the solutions for this model we choose standard instead of non standard boundary conditions and obtain approximate analytic solutions in the form of a series that rapidly converges using the adomian decomposition method the method is easily implemented using the symbol operations of scientific computational software such as matlab

the modified decomposition method and pade approximants for solving the thomas fermi equation in this paper we propose a new approach to develop a nonperturbative approximate solution for the thomas fermi equation this approach rests on the recently developed modification of the adomian decomposition method the initial slope of the thomas fermi potential y 0 is computed by converting the obtained series solution into several diagonal pade approximants the proposed scheme is presented in a general way so that it can be used in applied sciences

a learning approach to the two person decentralized team problem with incomplete information a learning approach to the two person decentralized team problem with incomplete information and with a 2x2 payoff matrix is considered it is shown that if the payoff matrix is unimodal there exists a proper choice of parameters of the learning algorithm that will ensure asymptotically an expected payoff as close to maximum payoff as desired it is shown that a team problem with multimodal payoff matrix gives rise to interesting class of open problems

a study of graph spectra for comparing graphs and trees the spectrum of a graph has been widely used in graph theory to characterise the properties of a graph and extract information from its structure it has also been employed as a graph representation for pattern matching since it is invariant to the labelling of the graph there are however a number of potential drawbacks in using the spectrum as a representation of a graph firstly more than one graph may share the same spectrum it is well known for example that very few trees can be uniquely specified by their spectrum secondly the spectrum may change dramatically with a small change structure there are a wide variety of graph matrix representations from which the spectrum can be extracted among these are the adjacency matrix combinatorial laplacian normalised laplacian and unsigned laplacian spectra can also be derived from the heat kernel matrix and path length distribution matrix the choice of matrix representation clearly has a large effect on the suitability of spectrum in a number of pattern recognition tasks in this paper we investigate the performance of the spectra as a graph representation in a variety of situations firstly we investigate the cospectrality of the various matrix representations over large graph and tree sets extending the work of previous authors we then show that the euclidean distance between spectra tracks the edit distance between graphs over a wide range of edit costs and we analyse the accuracy of this relationship we then use the spectra to both cluster and classify the graphs and demonstrate the effect of the graph matrix formulation on error rates these results are produced using both synthetic graphs and trees and graphs derived from shape and image data

efficient registration of stereo images by matching graph descriptions of edge segments we present a new approach to the stereo matching problem images are individually described by aneighborhood graph of line segments coming from a polygonal approximation of the contours the matching process is defined as the exploration of the largest components of adisparity graph built from the descriptions of the two images and is performed by an efficient prediction and propagation technique this approach was tested on a variety of man made environments and it appears to be fast and robust enough for mobile robot navigation and three dimensional part positioning applications

coined quantum walks lift the cospectrality of graphs and trees in this paper we explore how a spectral technique suggested by coined quantum walks can be used to distinguish between graphs that are cospectral with respect to standard matrix representations the algorithm runs in polynomial time and moreover can distinguish many graphs for which there is no subexponential time algorithm that is proven to be able to distinguish between them in the paper we give a description of the coined quantum walk from the field of quantum computing the evolution of the walk is governed by a unitary matrix we show how the spectrum of this matrix is related to the spectrum of the transition matrix of the classical random walk however despite this relationship the behaviour of the quantum walk is vastly different from the classical walk this leads us to define a new matrix based on the amplitudes of paths of the walk whose spectrum we use to characterise graphs we carry out three sets of experiments using this matrix representation firstly we test the ability of the spectrum to distinguish between sets of graphs that are cospectral with respect to standard matrix representation these include strongly regular graphs and incidence graphs of balanced incomplete block designs bibds secondly we test our method on all regular graphs on up to 14 vertices and all trees on up to 24 vertices this demonstrates that the problem of cospectrality is often encountered with conventional algorithms and tests the ability of our method to resolve this problem thirdly we use distances obtained from the spectra of s u 3 to cluster graphs derived from real world image data and these are qualitatively better than those obtained with the spectra of the adjacency matrix thus we provide a spectral representation of graphs that can be used in place of standard spectral representations far less prone to the problems of cospectrality