point correspondence by a new third order graph matching algorithm the correspondence between point sets is a fundamental problem in pattern recognition which is often formulated and solved by graph matching in this paper we propose to solve the correspondence problem by a new third order graph matching algorithm compared with some previous hyper graph matching algorithms the proposed one achieves considerable memory reduction and is applicable to both undirected and directed graphs specifically the correspondence is formulated by the matching between adjacency tensors encoding the third order structural information of each graph which is then transformed to be a tractable matrix form two types of gradient based optimization methods the graduated nonconvexity and concavity procedure gnccp and graduated assignment ga algorithm are generalized to solve the problem comparative experiments with state of the art algorithms on both synthetic and real data witness the effectiveness of the proposed method highlightsan adjacency tensor based third order graph matching algorithm is proposed it enjoys a much lower storage complexity than affinity tensor based high order algorithms instead of spectral decomposition based optimization it adopts gradient based optimization experiments on synthetic and real world data witness its state of the art performance

symmetry aware graph matching visual symmetry encodes middle to high level geometric information and plays an important role in many computer vision applications not much effort however has been devoted to utilize symmetry information for graph matching in this paper we propose a new framework for symmetry aware graph matching in the context of image matching in the framework we first define symmetry matrices to characterize the geometric symmetry relation among image features and then develop two methods to discover such symmetry after that we design general strategies to boost graph matching algorithms with symmetry constraints and apply these strategies to several state of the art algorithms for evaluation the proposed symmetry aware graph matching algorithms are first applied to two datasets involving clear symmetry patterns a recently proposed architecture image set and a dental panoramic radiograph collection the results clearly demonstrate the benefits of using symmetry information an experiment is also conducted on a dataset where symmetry is less obvious the results show that our strategies still achieve better of similar performance compared with state of the arts highlightsit is the first time symmetry constraints that are introduced into graph matching the symmetry aware graph matching improves the matching performance a new dataset with annotation for evaluating graph matching is constructed

optimal controllers and output feedback stabilization abstract in this paper the output feedback stabilizability problem is explored in terms of control lyapunov functions sufficient conditions for stabilization are provided for a certain class of systems by means of output feedback stabilizers that can be obtained from an optimization problem our main results extends those developed in 31 and generalize a theorem due to sontag 23

convergence properties of the softassign quadratic assignment algorithm the softassign quadratic assignment algorithm is a discrete time continuous state synchronous updating optimizing neural network while its effectiveness has been shown in the traveling salesman problem graph matching and graph partitioning in thousands of simulations its convergence properties have not been studied here we construct discrete time lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction which show convergence to a fixed point the combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization

efficient high order matching we present a computational approach to high order matching of data sets in rd those are matchings based on data affinity measures that score the matching of more than two pairs of points at a time high order affinities are represented by tensors and the matching is then given by a rank one approximation of the affinity tensor and a corresponding discretization our approach is rigorously justified by extending zass and shashua s hypergraph matching to high order spectral matching this paves the way for a computationally efficient dual marginalization spectral matching scheme we also show that based on the spectral properties of random matrices affinity tensors can be randomly sparsified while retaining the matching accuracy our contributions are experimentally validated by applying them to synthetic as well as real data sets

a graduated assignment algorithm for graph matching a graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise by combining graduated nonconvexity two way assignment constraints and sparsity large improvements in accuracy and speed are achieved its low order computational complexity o lm where l and m are the number of links in the two graphs and robustness in the presence of noise offer advantages over traditional combinatorial approaches the algorithm not restricted to any special class of graph is applied to subgraph isomorphism weighted graph matching and attributed relational graph matching to illustrate the performance of the algorithm attributed relational graphs derived from objects are matched then results from twenty five thousand experiments conducted on 100 mode random graphs of varying types graphs with only zero one links weighted graphs and graphs with node attributes and multiple link types are reported no comparable results have been reported by any other graph matching algorithm before in the research literature twenty five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated

multi graph matching via affinity optimization with graduated consistency regularization this paper addresses the problem of matching common node correspondences among multiple graphs referring to an identical or related structure this multi graph matching problem involves two correlated components i the local pairwise matching affinity across pairs of graphs ii the global matching consistency that measures the uniqueness of the pairwise matchings by different composition orders previous studies typically either enforce the matching consistency constraints in the beginning of an iterative optimization which may propagate matching error both over iterations and across graph pairs or separate affinity optimization and consistency enforcement into two steps this paper is motivated by the observation that matching consistency can serve as a regularizer in the affinity objective function especially when the function is biased due to noises or inappropriate modeling we propose composition based multi graph matching methods to incorporate the two aspects by optimizing the affinity score meanwhile gradually infusing the consistency we also propose two mechanisms to elicit the common inliers against outliers compelling results on synthetic and real images show the competency of our algorithms

on the strongly damped wave equation we prove the existence of the universal attractor for the strongly damped semilinear wave equation in the presence of a quite general nonlinearity of critical growth when the nonlinearity is subcritical we prove the existence of an exponential attractor of optimal regularity having a basin of attraction coinciding with the whole phase space as a byproduct the universal attractor is regular and of finite fractal dimension moreover we carry out a detailed analysis of the asymptotic behavior of the solutions in dependence of the damping coefficient

decentralized measurement feedback stabilization of large scale systems via control vector lyapunov functions abstract this paper studies the problem of decentralized measurement feedback stabilization of nonlinear interconnected systems as a natural extension of the recent development on control vector lyapunov functions the notion of output control vector lyapunov function ocvlf is introduced for investigating decentralized measurement feedback stabilization problems sufficient conditions on local stabilizability are discussed which are based on the proposed notion of ocvlf it is shown that a decentralized controller for a nonlinear interconnected system can be constructed using these conditions under an additional vector dissipation like condition to illustrate the proposed method two examples are given

one dimensional random attractor and rotation number of the stochastic damped sine gordon equation abstract this paper is devoted to the study of the asymptotic dynamics of the stochastic damped sine gordon equation with homogeneous neumann boundary condition it is shown that for any positive damping and diffusion coefficients the equation possesses a random attractor and when the damping and diffusion coefficients are sufficiently large the random attractor is a one dimensional random horizontal curve regardless of the strength of noise hence its dynamics is not chaotic it is also shown that the equation has a rotation number provided that the damping and diffusion coefficients are sufficiently large which implies that the solutions tend to oscillate with the same frequency eventually and the so called frequency locking is successful

damped sine gordon equations with non homogeneous dirichlet boundary conditions abstract in this paper we give a new well posedness result for the damped sine gordon equations with non homogeneous dirichlet boundary conditions in a weaker sense by using the method of transposition

an approximate sine gordon equation and its traveling wave solution in n 1 dimensional space in this paper we apply the painleve analysis to the study of an approximate sine gordon equation and obtain the traveling solitary wave solution in n 1 dimensional space explicitly which is significantly different from one which is found in our last work the technique described herein can also be applied to other nonlinear evolution equations such as the kdv type equation and the nonlinear schrodinger equation in higher dimensional space

new algorithms for 2d and 3d point matching pose estimation and correspondence abstract a fundamental open problem in computer vision determining pose and correspondence between two sets of points in space is solved with a novel fast robust and easily implementable algorithm the technique works on noisy 2d or 3d point sets that may be of unequal sizes and may differ by non rigid transformations using a combination of optimization techniques such as deterministic annealing and the softassign which have recently emerged out of the recurrent neural network statistical physics framework analog objective functions describing the problems are minimized over thirty thousand experiments on randomly generated points sets with varying amounts of noise and missing and spurious points and on hand written character sets demonstrate the robustness of the algorithm

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

a probabilistic graph based framework for plug and play multi cue visual tracking in this paper we propose a novel approach for integrating multiple tracking cues within a unified probabilistic graph based markov random fields mrfs representation we show how to integrate temporal and spatial cues encoded by unary and pairwise probabilistic potentials as the inference of such high order mrf models is known to be np hard we propose an efficient spectral relaxation based inference scheme the proposed scheme is exemplified by applying it to a mixture of five tracking cues and is shown to be applicable to wider sets of cues this paves the way for a modular plug and play tracking framework that can be easily adapted to diverse tracking scenarios the proposed scheme is experimentally shown to compare favorably with contemporary state of the art schemes and provides accurate tracking results

image segmentation via probabilistic graph matching this paper presents an unsupervised and semi automatic image segmentation approach where we formulate the segmentation as an inference problem based on unary and pairwise assignment probabilities computed using low level image cues the inference is solved via a probabilistic graph matching scheme which allows rigorous incorporation of low level image cues and automatic tuning of parameters the proposed scheme is experimentally shown to compare favorably with contemporary semi supervised and unsupervised image segmentation schemes when applied to contemporary state of the art image sets

a correction note on output feedback stabilization in a previous paper by the authors see ibid vol 35 no 8 p 951 4 1990 necessary and sufficient lyapunov like conditions for output feedback stabilisation of nonlinear systems were derived in this paper the authors point out an omission

dimension of the global attractor for strongly damped nonlinear wave equation the existence and estimate of the upper bound of the hausdorff dimension of the global attractor for the strongly damped nonlinear wave equation with the dirichlet boundary condition are considered by introducing a new norm in the phase space the gained hausdorff dimension decreases as the damping grows and remains small for large damping which conforms to physical intuition

graph matching with a dual step em algorithm this paper describes a new approach to matching geometric structure in 2d point sets the novel feature is to unify the tasks of estimating transformation geometry and identifying point correspondence matches unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the em algorithm according to our em framework the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters these gating probabilities measure the consistency of the matched neighborhoods in the graphs the recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log likelihood function we evaluate the technique on two real world problems

spectral symmetry analysis we present a spectral approach for detecting and analyzing rotational and reflectional symmetries in n dimensions our main contribution is the derivation of a symmetry detection and analysis scheme for sets of points irn and its extension to image analysis by way of local features each object is represented by a set of points s irn where the symmetry is manifested by the multiple self alignments of s the alignment problem is formulated as a quadratic binary optimization problem with an efficient solution via spectral relaxation for symmetric objects this results in a multiplicity of eigenvalues whose corresponding eigenvectors allow the detection and analysis of both types of symmetry we improve the scheme s robustness by incorporating geometrical constraints into the spectral analysis our approach is experimentally verified by applying it to 2d and 3d synthetic objects as well as real images

on the dimension of the global attractor for the damped sine gordon equation this article gives a more precise estimate on the dimension of the global attractor for the damped sine gordon equation the gained hausdorff dimension remains small for large damping which conforms to physics

consistency driven alternating optimization for multigraph matching a unified approach the problem of graph matching gm in general is nondeterministic polynomial complete and many approximate pairwise matching techniques have been proposed for a general setting in real applications it typically requires to find the consistent matching across a batch of graphs sequentially performing pairwise matching is prone to error propagation along the pairwise matching sequence and the sequences generated in different pairwise matching orders can lead to contradictory solutions motivated by devising a robust and consistent multiple gm model we propose a unified alternating optimization framework for multi gm in addition we define and use two metrics related to graphwise and pairwise consistencies the former is used to find an appropriate reference graph which induces a set of basis variables and launches the iteration procedure the latter defines the order in which the considered graphs in the iterations are manipulated we show two embodiments under the proposed framework that can cope with the nonfactorized and factorized affinity matrix respectively our multi gm model has two major characters 1 the affinity information across multiple graphs are explored in each iteration by fixing part of the matching variables via a consistency driven mechanism and 2 the framework is flexible to incorporate various existing pairwise gm solvers in an out of box fashion and also can proceed with the output of other multi gm methods the experimental results on both synthetic data and real images empirically show that the proposed framework performs competitively with the state of the art

the concave convex procedure the concave convex procedure cccp is a way to construct discrete time iterative dynamical systems that are guaranteed to decrease global optimization and energy functions monotonically this procedure can be applied to almost any optimization problem and many existing algorithms can be interpreted in terms of it in particular we prove that all expectation maximization algorithms and classes of legendre minimization and variational bounding algorithms can be reexpressed in terms of cccp we show that many existing neural network and mean field theory algorithms are also examples of cccp the generalized iterative scaling algorithm and sinkhorn s algorithm can also be expressed as cccp by changing variables cccp can be used both as a new way to understand and prove the convergence of existing optimization algorithms and as a procedure for generating new algorithms

a pocs based graph matching algorithm a novel projections onto convex sets pocs graph matching algorithm is presented two way assignment constraints are enforced without using elaborate penalty terms graduated nonconvexity or sophisticated annealing mechanisms to escape from poor local minima results indicate that the presented algorithm is robust and compares favorably to other well known algorithms

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

dimension of the global attractor for damped semilinear wave equations with critical exponent we obtain an estimate of the upper bound of the hausdorff dimension of the global attractor for damped semilinear wave equations with a critical exponent the obtained hausdorff dimension decreases as the damping grows for large damping

on the dimension of the global attractor for a damped semilinear wave equation with critical exponent we obtain in this paper a precise estimate of upper bound of the hausdorff dimension of the global attractor for a damped semilinear wave equation with critical exponent the obtained hausdorff dimension decreases as the damping grows and is uniformly bounded for large damping which conforms to physical intuition the obtained results generalize and correct the corresponding results obtained by zhou recently

improving shape retrieval by spectral matching and meta similarity we propose two computational approaches for improving the retrieval of planar shapes first we suggest a geometrically motivated quadratic similarity measure that is optimized by way of spectral relaxation of a quadratic assignment by utilizing state of the art shape descriptors and a pairwise serialization constraint we derive a formulation that is resilient to boundary noise articulations and nonrigid deformations this allows both shape matching and retrieval we also introduce a shape meta similarity measure that agglomerates pairwise shape similarities and improves the retrieval accuracy when applied to the mpeg 7 shape dataset in conjunction with the proposed geometric matching scheme we obtained a retrieval rate of 92 5

output feedback stabilization the stabilization of control systems using output feedback is addressed necessary and sufficient lyapunov conditions are established generalizing the artstein s stabilization theorem for linear control systems a necessary and sufficient lyapunov condition is provided for stabilization by means of a linear output feedback law

an algorithm for finding the most similar given sized subgraphs in two weighted graphs we propose a weighted common subgraph wcs matching algorithm to find the most similar subgraphs in two labeled weighted graphs wcs matching as a natural generalization of equal sized graph matching and subgraph matching has found wide applications in many computer vision and machine learning tasks in this brief wcs matching is first formulated as a combinatorial optimization problem over the set of partial permutation matrices then it is approximately solved by a recently proposed combinatorial optimization framework graduated nonconvexity and concavity procedure experimental comparisons on both synthetic graphs and real world images validate its robustness against noise level problem size outlier number and edge density

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

factorized graph matching graph matching gm is a fundamental problem in computer science and it plays a central role to solve correspondence problems in computer vision gm problems that incorporate pairwise constraints can be formulated as a quadratic assignment problem qap although widely used solving the correspondence problem through gm has two main limitations 1 the qap is np hard and difficult to approximate 2 gm algorithms do not incorporate geometric constraints between nodes that are natural in computer vision problems to address aforementioned problems this paper proposes factorized graph matching fgm fgm factorizes the large pairwise affinity matrix into smaller matrices that encode the local structure of each graph and the pairwise affinity between edges four are the benefits that follow from this factorization 1 there is no need to compute the costly in space and time pairwise affinity matrix 2 the factorization allows the use of a path following optimization algorithm that leads to improved optimization strategies and matching performance 3 given the factorization it becomes straight forward to incorporate geometric transformations rigid and non rigid to the gm problem 4 using a matrix formulation for the gm problem and the factorization it is easy to reveal commonalities and differences between different gm methods the factorization also provides a clean connection with other matching algorithms such as iterative closest point experimental results on synthetic and real databases illustrate how fgm outperforms state of the art algorithms for gm the code is available at http humansensing cs cmu edu fgm

on dimension of the global attractor for damped nonlinear wave equations in this paper we obtain a more precise estimate of upper bound of the hausdorff dimension of the global attractor for damped nonlinear wave equations with the dirichlet boundary condition the obtained hausdorff dimension decreases as the damping grows and is uniformly bounded for large damping which conforms to physical intuition

correspondence matching using kernel principal components analysis and label consistency constraints this paper investigates spectral approaches to the problem of point pattern matching we make two contributions first we consider rigid point set alignment here we show how kernel principal components analysis kernel pca can be effectively used for solving the rigid point correspondence matching problem when the point sets are subject to outliers and random position jitter specifically we show how the point proximity matrix can be kernelised and spectral correspondence matching transformed into one of kernel pca second we turn our attention to the matching of articulated point sets here we show label consistency constraints can be incorporated into definition of the point proximity matrix the new methods are compared to those of shapiro and brady and scott and longuet higgins together with multidimensional scaling we provide experiments on both synthetic data and real world data

dimension of kernel sections for damped nonautonomous wave equations with critical exponent in this paper by using the boundedness of kernel sections in higher regular space we obtain an uniform upper bound of hausdorff dimension of the kernel sections for damped nonautonomous wave equation when the nonlinearity has a critically growing exponent which improves the previous estimate of hausdorff dimension of the kernel sections

robust deformable and occluded object tracking with dynamic graph while some efforts have been paid to handle deformation and occlusion in visual tracking they are still great challenges in this paper a dynamic graph based tracker dgt is proposed to address these two challenges in a unified framework in the dynamic target graph nodes are the target local parts encoding appearance information and edges are the interactions between nodes encoding inner geometric structure information this graph representation provides much more information for tracking in the presence of deformation and occlusion the target tracking is then formulated as tracking this dynamic undirected graph which is also a matching problem between the target graph and the candidate graph the local parts within the candidate graph are separated from the background with markov random field and spectral clustering is used to solve the graph matching the final target state is determined through a weighted voting procedure according to the reliability of part correspondence and refined with recourse to a foreground background segmentation an effective online updating mechanism is proposed to update the model allowing dgt to robustly adapt to variations of target structure experimental results show improved performance over several state of the art trackers in various challenging scenarios

gnccp graduated nonconvexityand concavity procedure in this paper we propose the graduated nonconvexity and concavity procedure gnccp as a general optimization framework to approximately solve the combinatorial optimization problems defined on the set of partial permutation matrices gnccp comprises two sub procedures graduated nonconvexity which realizes a convex relaxation and graduated concavity which realizes a concave relaxation it is proved that gnccp realizes exactly a type of convex concave relaxation procedure ccrp but with a much simpler formulation without needing convex or concave relaxation in an explicit way actually gnccp involves only the gradient of the objective function and is therefore very easy to use in practical applications two typical related np hard problems partial graph matching and quadratic assignment problem qap are employed to demonstrate its simplicity and state of the art performance

structural graph matching using the em algorithm and singular value decomposition this paper describes an efficient algorithm for inexact graph matching the method is purely structural that is it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes we make two contributions 1 commencing from a probability distribution for matching errors we show how the problem of graph matching can be posed as maximum likelihood estimation using the apparatus of the em algorithm and 2 we cast the recovery of correspondence matches between the graph nodes in a matrix framework this allows one to efficiently recover correspondence matches using the singular value decomposition we experiment with the method on both real world and synthetic data here we demonstrate that the method offers comparable performance to more computationally demanding methods

a probabilistic approach to spectral graph matching spectral matching sm is a computationally efficient approach to approximate the solution of pairwise matching problems that are np hard in this paper we present a probabilistic interpretation of spectral matching schemes and derive a novel probabilistic matching pm scheme that is shown to outperform previous approaches we show that spectral matching can be interpreted as a maximum likelihood ml estimate of the assignment probabilities and that the graduated assignment ga algorithm can be cast as a maximum a posteriori map estimator based on this analysis we derive a ranking scheme for spectral matchings based on their reliability and propose a novel iterative probabilistic matching algorithm that relaxes some of the implicit assumptions used in prior works we experimentally show our approaches to outperform previous schemes when applied to exhaustive synthetic tests as well as the analysis of real image sequences

graph matching by simplified convex concave relaxation procedure the convex and concave relaxation procedure ccrp was recently proposed and exhibited state of the art performance on the graph matching problem however ccrp involves explicitly both convex and concave relaxations which typically are difficult to find and thus greatly limit its practical applications in this paper we propose a simplified ccrp scheme which can be proved to realize exactly ccrp but with a much simpler formulation without needing the concave relaxation in an explicit way thus significantly simplifying the process of developing ccrp algorithms the simplified ccrp can be generally applied to any optimizations over the partial permutation matrix as long as the convex relaxation can be found based on two convex relaxations we obtain two graph matching algorithms defined on adjacency matrix and affinity matrix respectively extensive experimental results witness the simplicity as well as state of the art performance of the two simplified ccrp graph matching algorithms

nonconforming quadrilateral finite element method for a class of nonlinear sine gordon equations nonconforming quadrilateral finite element method fem of the two dimensional nonlinear sine gordon equation is studied for semi discrete and crank nicolson fully discrete schemes respectively firstly we prove a special feature of a new arbitrary quadrilateral element named modified quasi wilson element i e the consistency error is of order o h 2 h denotes the mesh size in h 1 norm which leads to optimal order error estimate and superclose result with order o h 2 for the semi discrete scheme through a different approach from the existing literature secondly because the consistency error estimate of the new modified quasi wilson element can reach a staggering o h 3 order two orders higher than that of interpolation error the optimal order error estimates of crank nicolson fully discrete scheme are obtained on arbitrary quadrilateral meshes with ritz projection moreover a superclose result in h 1 norm is presented on generalized rectangular meshes by a new technique thirdly the global superconvergence results of h 1 norm for both semi discrete and fully discrete schemes are derived on rectangular meshes with interpolated postprocessing technique finally a numerical test is carried out to verify the theoretical analysis