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

mixed finite elements for second order elliptic problems in three variables two families of mixed finite elements one based on simplices and the other on cubes are introduced as alternatives to the usual raviart thomas nedelec spaces these spaces are analogues of those introduced by brezzi douglas and marini in two space variables error estimates inl2 andh s are derived

a non iterative probabilistic method for contextual correspondence matching abstract in this paper we develop a framework for non iterative structural matching using contextual information it is based on bayesian reasoning and involves the explicit modelling of the binary relations between the objects the difference between this and previously developed theories of the kind lies in the assumption that the binary relations used are derivable from the unary measurements that refer to individual objects this leads to a non iterative formula for probabilistic reasoning which is amenable to real time implementation and produces good results the theory is demonstrated using two applications one on stereo matching of linear features and the other on automatic map registration the breaking points of the theory are also identified experimentally and the situations under which the proposed algorithm is applicable are discussed

mixed finite element methods on nonmatching multiblock grids we consider mixed finite element methods for second order elliptic equations on nonmatching multiblock grids a mortar finite element space is introduced on the nonmatching interfaces we approximate in this mortar space the trace of the solution and we impose weakly a continuity of flux condition a standard mixed finite element method is used within the blocks optimal order convergence is shown for both the solution and its flux moreover at certain discrete points superconvergence is obtained for the solution and also for the flux in special cases computational results using an efficient parallel domain decomposition algorithm are presented in confirmation of the theory

mortar multiscale finite element methods for stokes darcy flows we investigate mortar multiscale numerical methods for coupled stokes and darcy flows with the beavers joseph saffman interface condition the domain is decomposed into a series of subdomains coarse grid of either stokes or darcy type the subdomains are discretized by appropriate stokes or darcy finite elements the solution is resolved locally in each coarse element on a fine scale allowing for non matching grids across subdomain interfaces coarse scale mortar finite elements are introduced on the interfaces to approximate the normal stress and impose weakly continuity of the normal velocity stability and a priori error estimates in terms of the fine subdomain scale h h and the coarse mortar scale h h are established for fairly general grid configurations assuming that the mortar space satisfies a certain inf sup condition several examples of such spaces in two and three dimensions are given numerical experiments are presented in confirmation of the theory

superconvergence for rectangular mixed finite elements in this paper we prove superconvergence error estimates for the vector variable for mixed finite element approximations of second order elliptic problems for the rectangular finite elements of raviart and thomas 19 and for those of brezzi et al 4 we prove that the distance inl 2 between the approximate solution and a projection of the exact one is of higher order than the error itself this result is exploited to obtain superconvergence at gaussian points and to construct higher order approximations by a local postprocessing

kronecker product graph matching abstract in this paper the interpolator based kronecker product graph matching ibkpgm algorithm for performing attributed graph matching is presented the ibkpgm algorithm is based on the kronecker product graph matching kpgm formulation this new formulation incorporates a general approach to a wide class of graph matching problems based on attributed graphs allowing the structure of the graphs to be based on multiple sets of attributes salient features of the ibkpgm algorithm are that no assumption is made about the adjacency structure of the graphs to be matched and that the explicit calculation of compatibility values between all vertices of the reference and input graphs as well as between all edges of the reference and input graphs are avoided

quadrilateral h div finite elements we consider the approximation properties of quadrilateral finite element spaces of vector fields defined by the piola transform extending results previously obtained for scalar approximation the finite element spaces are constructed starting with a given finite dimensional space of vector fields on a square reference element which is then transformed to a space of vector fields on each convex quadrilateral element via the piola transform associated to a bilinear isomorphism of the square onto the element for affine isomorphisms a necessary and sufficient condition for approximation of order r 1 in l2 is that each component of the given space of functions on the reference element contain all polynomial functions of total degree at most r in the case of bilinear isomorphisms the situation is more complicated and we give a precise characterization of what is needed for optimal order l2 approximation of the function and of its divergence as applications we demonstrate degradation of the convergence order on quadrilateral meshes as compared to rectangular meshes for some standard finite element approximations of h div we also derive new estimates for approximation by quadrilateral raviart thomas elements requiring less regularity and propose a new quadrilateral finite element space which provides optimal order approximation in h div finally we demonstrate the theory with numerical computations of mixed and least squares finite element approximations of the solution of poisson s equation

a posteriori error estimates for the mortar mixed finite element method several a posteriori error estimators for mortar mixed finite element discretizations of elliptic equations are derived a residual based estimator provides optimal upper and lower bounds for the pressure error an efficient and reliable estimator for the velocity and mortar pressure error is also derived which is based on solving local element problems in a higher order space the interface flux jump term that appears in the estimators can be used as an indicator for driving an adaptive process for the mortar grids only

mixed finite elements for elliptic problems with tensor coefficients as cell centered finite differences we present an expanded mixed finite element approximation of second order elliptic problems containing a tensor coefficient the mixed method is expanded in the sense that three variables are explicitly approximated namely the scalar unknown the negative of its gradient and its flux the tensor coefficient times the negative gradient the resulting linear system is a saddle point problem in the case of the lowest order raviart thomas elements on rectangular parallelepipeds we approximate this expanded mixed method by incorporating certain quadrature rules this enables us to write the system as a simple cell centered finite difference method requiring the solution of a sparse positive semidefinite linear system for the scalar unknown for a general tensor coefficient the sparsity pattern for the scalar unknown is a 9 point stencil in two dimensions and 19 points in three dimensions existing theory shows that the expanded mixed method gives optimal order approximations in the l 2 and h s norms and superconvergence is obtained between the l 2 projection of the scalar variable and its approximation we show that these rates of convergence are retained for the finite difference method if h denotes the maximal mesh spacing then the optimal rate is o h the superconvergence rate o h 2 is obtained for the scalar unknown and rate o h 3 2 for its gradient and flux in certain discrete norms moreover the full o h 2 is obtained in the strict interior of the domain computational results illustrate these theoretical results

relaxation matching techniques a comparison many different relaxation schemes have been proposed for image analysis tasks we have developed a general matching procedure for comparing semantic network descriptions of images and we have implemented a variety of relaxation techniques an automatic segmentation and description system is used to produce the image representations so that the matching procedures must cope with variations in feature values missing objects and possible multiple matches this environment is used to test different relaxation matching schemes under a variety of conditions the best performance of those we compared in terms of the number of iterations and the number of errors is for the gradient based optimization approach of faugeras and price the related optimization approach of hummel and zucker performed almost as well with differences primarily in difficult matches i e where much of the evidence is against the match for instance poor segmentations the product combination rule proposed by peleg was extremely fast indeed too fast to work when global context is needed the classical rosenfeld hummel and zucker method is included for historical comparisons and performed only adequately producing fewer correct matches and taking more iterations

symbolic graph matching with the em algorithm abstract this paper describes how relational graph matching can be effected using the expectation and maximisation algorithm according to this viewpoint matching is realised as a two step iterative em like process firstly updated symbolic matches are located so as to minimise the divergence between the model and data graphs secondly with the updated matches to hand probabilities describing the affinity between nodes in the model and data graphs may be computed the probability distributions underpinning this study are computed using a simple model of uniform matching errors as a result the expected likelihood function is defined over a family of exponential distributions of hamming distance we evaluate our matching method and offer comparison with both mean field annealing and quadratic assignment

a surface based approach to 3 d object recognition using a mean field annealing neural network abstract three dimensional 3 d object recognition identifies objects in an input image using a modelbase we present a 3 d object recognition system in which a symbolic description of the object is generated from the input range data in terms of the visible surface patches the segmented surface representation of an object is regarded as a graph in which nodes contain the information about the individual surface patches whereas links represent the relationships between them such as connectivity object recognition is achieved by matching the object graph of a scene with the model graph of a modelbase in the proposed approach a mean field annealing mfa neural network nn is employed as a constraint satisfaction network in which an energy function robust to occlusion is proposed for effective matching the energy level is at its minimum when the optimal match is achieved simulation results with synthetic and real range images having various occlusion rates are presented to show the effectiveness of the proposed algorithm

matching invariant to translations rotations and scale changes abstract an optimization approach to invariant matching is proposed in this approach an object or a pattern is invariantly represented by an object centred description called an attributed relational structure ars embedding invariant properties and relations between the primitives of the pattern such as line segments and points noise effect is taken into account such that a scene can consist of noisy sub parts of a model the matching is then to find the optimal mapping between the arss of the scene and the model a gain functional is formulated to measure the goodness of fit and is to be maximized by using the relaxation labelling method experiments are shown to illustrate the matching algorithm and to demonstrate that the approach is truly invariant to arbitrary translations rotations and scale changes under noise

the stress conjugate to logarithmic strain abstract a stress s is said to be conjugate to a strain measure e if the inner product s e is the power per unit volume the logarithmic strain in u with u the right stretch tensor has been considered an interesting strain measure because of the relationship of its material time derivative ln u with the stretching tensor d in a previous article int j solids structures 22 1019 1032 1986 a formula for ln u was obtained in direct notation for the cases where the principal stretches are repeated as well as for the case where they are all distinct here the formula for ln u and the definition of conjugate stress are used to derive an explicit properly invariant expression for the stress conjugate to the logarithmic strain

interior superconvergence in mortar and non mortar mixed finite element methods on non matching grids we establish interior velocity superconvergence estimates for mixed finite element approximations of second order elliptic problems on non matching rectangular and quadrilateral grids both mortar and non mortar methods for imposing the interface conditions are considered in both cases it is shown that a discrete l 2 error in the velocity in a compactly contained subdomain away from the interfaces con1 2 higher than the error in the whole domain for the non mortar method we also establish pressure superconvergence which is needed in the velocity analysis numerical results are presented in confirmation of the theory

optimal encoding of graph homomorphism energy using fuzzy information aggregation operators abstract the attributed relational graph matching arg strategy is a well known approach to object pattern recognition in the past for the parallel solution of arg matching problem an overall objective function was constructed using linearly weighted information aggregation function and one set of parameter values was chosen for all models by trial and error for the parameters in the function in this paper the compatibility between every pair of model and scene attributes is interpreted as a fuzzy value and subsequently the nonlinear fuzzy information aggregation operators are used to fuse the information captured in the chosen attributes to learn the parameters in the fuzzy information aggregation operators the learning from samples strategy is used the learning of weight parameters is formulated as an optimisation problem and solved using the gradient projection algorithm based learning procedure the learning procedure implicitly evaluates ambiguity robustness and discriminatory power of the relational attributes chosen for graph matching and assigns weights appropriately to the chosen attributes the learning procedure also enables us to compute a distinct set of optimal parameters for every model to reflect the characteristics of the model so that the homomorphic arg matching problem can be optimally encoded in the energy function for the model experimental results are presented to illustrate effectiveness and necessity of the parameter estimation and learning procedures

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

on the theory of fourth order tensors and their applications in computational mechanics many problems concerned with the mathematical treatment of fourth order tensors still remain open in the literature in the present paper they will be considered in the framework of a complete theory involving a set of notations and definitions a tensor operation algebra differentiation rules eigenvalue problems applications of fourth order tensors to isotropic tensor functions and some other relevant aspects a tensor is understood to be an invariant quantity with respect to any co ordinate system transformation which justifies the use of absolute notation preferred in this work as a most important application field of fourth order tensors elastic moduli are formulated in a material and a spatial description and given for various hyperelastic material models

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

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

superconvergence of mixed finite element approximations over quadrilaterals a superconvergence result is established in this article for approximate solutions of second order elliptic equations by mixed finite element methods over quadrilaterals the superconvergence indicates an accuracy of cal o h k 2 for the mixed finite element approximation if the raviart thomas or brezzi douglas fortin marini elements of order k are employed with optimal error estimate of cal o h k 1 numerical experiments are presented to illustrate the theoretical result

nonlinear system identification based on a fock space framework a method is presented for the identification of a nonlinear dynamical system whose input output map is assumed to be a volterra series mapping inputs u belonging to l 2 i to outputs y in the sobolev space h n 2 i where i is a compact interval of the real line and n is a nonnegative integer the input output relation is denoted by y t v u t triangleq v t u t in i it is assumed also that a set of test input output pairs u j in l 2 i y j in h n 2 i j 1 cdots m are provided our system identification procedure is based on the construction of a reproducing kernel hilbert space namely a symmetric fock space f rho for the nonlinear functional v t the corresponding nonlinear operator v then belongs to a bochner space b n 2 we obtain the best estimate hat v of v based on the input output data in the form of a generalized inverse in b n 2 both the noncausal and causal versions of hat v are derived the concept of varepsilon causality which i

optimization in model matching and perceptual organization we introduce an optimization approach for solving problems in computer vision that involve multiple levels of abstraction our objective functions include compositional and specialization hierarchies we cast vision problems as inexact graph matching problems formulate graph matching in terms of constrained optimization and use analog neural networks to perform the optimization the method is applicable to perceptual grouping and model matching preliminary experimental results are shown

a non mortar mixed finite element method for elliptic problems on non matching multiblock grids abstract we consider the approximation of second order elliptic equations on domains that can be described as a union of sub domains or blocks we assume that a grid is defined on each block independently so that the resulting grid over the entire domain need not be conforming i e match across the block boundaries several techniques have been developed to approximate elliptic equations on multiblock grids that utilize a mortar finite element space defined on the block boundary interface itself we define a mixed finite element method that does not use such a mortar space the method has an advantage in the case where adaptive local refinement techniques will be used in that there is no mortar grid to refine as is typical of mixed methods our method is locally conservative element by element it is also globally conservative across the block boundaries theoretical results show that the approximate solution converges at the optimal rate to the true solution we present computational results to illustrate and confirm the theory

computational aspects of the logarithmic strain space description abstract computational aspects of the logarithmic strain space description are discussed and compared with so called updated lagrangian descriptions the shortcomings of the latter are demonstrated on an analytical example of homogeneous finite distortion kinematics the numerical implementation and algorithms of the logarithmic strain space description with respect to the reference configuration are presented simulation results of two special purpose finite element programs which are based on the logarithmic strain space description are shown

a mortar finite element method using dual spaces for the lagrange multiplier the mortar finite element method allows the coupling of different discretization schemes and triangulations across subregion boundaries in the original mortar approach the matching at the interface is realized by enforcing an orthogonality relation between the jump and a modified trace space which serves as a space of lagrange multipliers in this paper this lagrange multiplier space is replaced by a dual space without losing the optimality of the method the advantage of this new approach is that the matching condition is much easier to realize in particular all the basis functions of the new method are supported in a few elements the mortar map can be represented by a diagonal matrix in the standard mortar method a linear system of equations must be solved the problem is considered in a positive definite nonconforming variational as well as an equivalent saddle point formulation

a new algorithm for subgraph optimal isomorphism abstract in this paper a new algorithm for subgraph isomorphism is proposed the main idea of the new algorithm is to decompose the graphs to be matched into smaller subgraphs the matching process is then done at the level of the decomposed subgraphs based on the concept of error correcting transformations the cost of matching two graphs is defined as the minimum of a weighted bipartite graph constructed from the decomposed subgraphs the average computational complexity of the proposed algorithm is found to be o n 4 the results of the application of the new algorithm show that the new technique is quite efficient and in many respects superior to similar existing techniques in the literature besides it overcomes most of the problems encountered in using tree search algorithms the new algorithm is also suitable for parallel processing implementation

elastic eigenstates in finite element modelling of large anisotropic elasticity abstract fe algorithm for large anisotropic hyper elastic deformations is presented this algorithm is based on the concept of the local reference configuration the spectral decomposition of the elastic modulus tensor into eigentensors of elastic deformations has been utilized in the constitutive equations some numerical results are also presented

an improved algorithm for relational distance graph matching one of the problems in computer vision is to give a computer a representation of a scene and recognize the objects in the scene and their spatial relationships this involves low level vision image processing mid level vision feature extraction and measurement and high level vision interpretation one important part of high level vision is relational matching the process of matching two relational descriptions of objects often for the purpose of object identification this paper presents an improvement of the original method by shapiro and haralick for solving the relational distance graph matching problem for unlabeled graphs on a parallel computer

superconvergence of the velocity along the gauss lines in mixed finite element methods superconvergence for the velocity along the gauss lines is derived for the mixed finite element method for the second order elliptic equation in rectangular domains these estimates are based on the rectangular finite elements of raviart thomas type

graph matching using a direct classification of node attendance abstract an algorithm has been developed that finds isomorphisms between both graphs and subgraphs the development is introduced in the object recognition problem domain the method isolates matching subgraphs finds a node to node mapping and reorders nodes thus permitting a direct comparison to be made between the resultant graphs the algorithm is of polynomial order it yields approximate results maintaining a performance level for subgraph isomorphisms at or above 95 under a wide variety of conditions and with varying levels of noise the performance on the full size comparisons associated with graph isomorphisms has been found to be 100 100 also under a variety of conditions performance metrics methods of testing and results are presented