ciarlet raviart mixed finite element approximation for an optimal control problem governed by the first bi harmonic equation the ciarlet raviart mixed finite element approximation is constructed to solve the constrained optimal control problem governed by the first bi harmonic equation the optimality conditions consisting of the state and the co state equations is derived also the a priori error estimates are analyzed in the analysis of the a priori error estimates the improved convergent rate of the higher order than existed results is proved some numerical experiments are performed to confirm the theoretical analysis for the a priori error estimate

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

finite element methods for maxwell s transmission eigenvalues the transmission eigenvalue problem plays a critical role in the theory of qualitative methods for inhomogeneous media in inverse scattering theory efficient computational tools for transmission eigenvalues are needed to motivate improvements to theory and more importantly are parts of inverse algorithms for estimating material properties in this paper we propose two finite element methods to compute a few lowest maxwell s transmission eigenvalues which are of interest in applications since the discrete matrix eigenvalue problem is large sparse and in particular non hermitian due to the fact that the problem is neither elliptic nor self adjoint we devise an adaptive method which combines the arnoldi iteration and estimation of transmission eigenvalues exact transmission eigenvalues for balls are derived and used as a benchmark numerical examples are provided to show the viability of the proposed methods and to test the accuracy of recently derived inequalities for transmission eigenvalues

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

generalized low energy expansion formula for green s function of the fokker planck equation the frequency expansion formula for the one dimensional fokker planck equation derived in a previous paper is generalized to an expansion formula for arbitrary powers of the green s function based on this expansion the small frequency behavior of the green s function is studied for the cases where the potential v x tends to infinity at both x and x

symmetry classification and exact solutions of the kramers equation the complete classification of lie symmetries for the kramers equation is described group invariance under infinitesimal transformations is used to generate a wide class of exact solutions some of the known solutions are obtained as particular cases the general results can also be used to solve some types of moving boundary problems we researched some q conditional symmetry properties of this equation

surface signatures an orientation independent free form surface representation scheme for the purpose of objects registration and matching this paper introduces anew free form surface representation scheme for the purpose of fast and accurate registration and matching accurate registration of surfaces is a common task in computer vision the proposed representation scheme captures the surface curvature information seen from certain points and produces images called surface signatures at these points matching signatures of different surfaces enables the recovery of the transformation parameters between these surfaces we propose using template matching to compare the signature images to enable partial matching another criterion the overlap ratio is used this representation scheme can be used as a global representation of the surface as well as a local one and performs near real time registration we show that the signature representation can be used to recover scaling transformation as well as matching objects in 3d scenes in the presence of clutter and occlusion applications presented include free form object matching multimodal medical volumes registration and dental teeth reconstruction from intraoral images

effective implementation of the weak galerkin finite element methods for the biharmonic equation abstract the weak galerkin wg methods have been introduced in mu et al 2013 2014 14 for solving the biharmonic equation the purpose of this paper is to develop an algorithm to implement the wg methods effectively this can be achieved by eliminating local unknowns to obtain a global system with significant reduction of size in fact this reduced global system is equivalent to the schur complements of the wg methods the unknowns of the schur complement of the wg method are those defined on the element boundaries the equivalence of the wg method and its schur complement is established the numerical results demonstrate the effectiveness of this new implementation technique

precision range image registration using a robust surface interpenetration measure and enhanced genetic algorithms this paper addresses the range image registration problem for views having low overlap and which may include substantial noise the current state of the art in range image registration is best represented by the well known iterative closest point icp algorithm and numerous variations on it although this method is effective in many domains it nevertheless suffers from two key limitations it requires prealignment of the range surfaces to a reasonable starting point and it is not robust to outliers arising either from noise or low surface overlap this paper proposes a new approach that avoids these problems to that end there are two key novel contributions in this work a new hybrid genetic algorithm ga technique including hill climbing and parallel migration combined with a new robust evaluation metric based on surface interpenetration up to now interpenetration has been evaluated only qualitatively we define the first quantitative measure for it because they search in a space of transformations ga are capable of registering surfaces even when there is low overlap between them and without need for prealignment the novel ga search algorithm we present offers much faster convergence than prior ga methods while the new robust evaluation metric ensures more precise alignments even in the presence of significant noise than mean squared error or other well known robust cost functions the paper presents thorough experimental results to show the improvements realized by these two contributions

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

algebraic structure of diffusion and scattering in one dimension the one variable fokker planck equation is studied from an algebraic point of view diffusion in an external potential can be interpreted as a multiple scattering process a description of the one dimensional scattering in terms of boson operators is introduced and it is generalized to a form that does not depend on representation an expression for the green s function is derived in terms of generators of the osp 1 2 superalgebra it is shown that many seemingly different descriptions of the diffusion problem are just different representations of this general expression

discrete interpolation norms with applications we describe norm representations for interpolation spaces generated by finite dimensional subspaces of hilbert spaces these norms are products of integer and noninteger powers of the grammian matrices associated with the generating pair of spaces for the interpolation space we include a brief description of some of the algorithms which allow the efficient computation of matrix powers we consider in some detail the case of fractional sobolev spaces both for positive and negative indices together with applications arising in preconditioning techniques numerical experiments are included

mixed finite element analysis and numerical solitary solution for the rlw equation in this paper a mixed finite element mfe formulation is proposed for the 1 d regularized long wave rlw equation u t auu x delta u xxt 0 the existence of its mixed generalized solution and semidiscrete and fully discrete mixed finite element solutions is proved error estimates based on energy methods are given and finally results of numerical experiments comparing this formulation with a galerkin method based on cubic splines are also given

green s function of the fokker planck equation general formula of frequency expansion the one variable fokker planck equation is studied in its general form by means of an algebraic method an expression of the green s function is derived as an expansion in powers of the square root of frequency the expansion coefficient of arbitrary order is expressed as a functional of the potential in terms of integrals

a new p1 weak galerkin method for the biharmonic equation abstract a new weak galerkin wg finite element method is designed featuring in using the first order polynomial to approximate solution of biharmonic equation the proposed p 1 wg method achieves o h convergence in energy norm and o h 2 in l 2 norm in solving the biharmonic equation this is not possible for the traditional finite element method as the minimum polynomial degree is 2 in order to approximate the biharmonic equation numerical tests on various polygonal meshes verify the theory

sl 3 c structure of one dimensional schrodinger equation we present a new formalism for describing solutions of the one dimensional stationary schrodinger equation in terms of the lie group sl 3 c and its lie algebra in this formalism we obtain a universal expression for the green function which can be used in any representation of sl 3 c and also expressions for various quantities involving products of green functions specifically we introduce an infinite dimensional representation of sl 3 c that provides a natural description of multiple scattering of waves using this particular representation we can derive formulas which are useful for the analysis of the green function we present a new formalism for describing solutions of the one dimensional stationary schrodinger equation in terms of the lie group sl 3 c and its lie algebra in this formalism we obtain a universal expression for the green function which can be used in any representation of sl 3 c and also expressions for various quantities involving products of green functions specifically we introduce an infinite dimensional representation of sl 3 c that provides a natural description of multiple scattering of waves using this particular representation we can derive formulas which are useful for the analysis of the green function

the dual bootstrap iterative closest point algorithm with application to retinal image registration motivated by the problem of retinal image registration this paper introduces and analyzes a new registration algorithm called dual bootstrap iterative closest point dual bootstrap icp the approach is to start from one or more initial low order estimates that are only accurate in small image regions called bootstrap regions in each bootstrap region the algorithm iteratively 1 refines the transformation estimate using constraints only from within the bootstrap region 2 expands the bootstrap region and 3 tests to see if a higher order transformation model can be used stopping when the region expands to cover the overlap between images steps 1 and 3 the bootstrap steps are governed by the covariance matrix of the estimated transformation estimation refinement step 2 uses a novel robust version of the icp algorithm in registering retinal image pairs dual bootstrap icp is initialized by automatically matching individual vascular landmarks and it aligns images based on detected blood vessel centerlines the resulting quadratic transformations are accurate to less than a pixel on tests involving approximately 6000 image pairs it successfully registered 99 5 of the pairs containing at least one common landmark and 100 of the pairs containing at least one common landmark and at least 35 image overlap

using spin images for efficient object recognition in cluttered 3d scenes we present a 3d shape based object recognition system for simultaneous recognition of multiple objects in scenes containing clutter and occlusion recognition is based on matching surfaces by matching points using the spin image representation the spin image is a data level shape descriptor that is used to match surfaces represented as surface meshes we present a compression scheme for spin images that results in efficient multiple object recognition which we verify with results showing the simultaneous recognition of multiple objects from a library of 20 models furthermore we demonstrate the robust performance of recognition in the presence of clutter and occlusion through analysis of recognition trials on 100 scenes

structure of the reflection coefficient and the eigenvalue problem of the fokker planck equation structure of the reflection coefficient of the fokker planck equation is investigated asymptotic expressions of the reflection coefficient for small wavenumber low frequency and large wavenumber high frequency are presented as an application of this analysis a method for calculating the eigenvalues of the fokker planck equation is derived

icp registration using invariant features investigates the use of euclidean invariant features in a generalization of iterative closest point icp registration of range images pointwise correspondences are chosen as the closest point with respect to a weighted linear combination of positional and feature distances it is shown that under ideal noise free conditions correspondences formed using this distance function are correct more often than correspondences formed using the positional distance alone in addition monotonic convergence to at least a local minimum is shown to hold for this method when noise is present a method that automatically sets the optimal relative contribution of features and positions is described this method trades off the error in feature values due to noise against the error in positions due to misalignment experimental results suggest that using invariant features decreases the probability of being trapped in a local minimum and may be an effective solution for difficult range image registration problems where the scene is very small compared to the model

corners give problems when decoupling fourth order equations into second order systems decoupling a fourth order elliptic boundary value problem into a system of second order equations may give an alternative approach to obtaining a solution for the original problem the system approach is usually preferred for numerical methods since one may use piecewise linear finite elements to approximate a solution in this note we compare both settings for the plate equation and prove that for planar domains with corners the system approach may fail to produce the correct solution

diffusion in asymptotically logarithmic potentials behavior of solutions to the one dimensional fokker planck equation with potentials u x which diverge logarithmically as x is investigated through the analysis of the frequency component of the green s function it is shown that solutions of the equation decrease for large time t either logarithmically or as t where may take arbitrary positive value depending on a parameter

an efficient numerical scheme for the biharmonic equation by weak galerkin finite element methods on polygonal or polyhedral meshes this paper presents a new and efficient numerical algorithm for the biharmonic equation by using weak galerkin wg finite element methods the wg finite element scheme is based on a variational form of the biharmonic equation that is equivalent to the usual h 2 semi norm weak partial derivatives and their approximations called discrete weak partial derivatives are introduced for a class of discontinuous functions defined on a finite element partition of the domain consisting of general polygons or polyhedra the discrete weak partial derivatives serve as building blocks for the wg finite element method the resulting matrix from the wg method is symmetric positive definite and parameter free an error estimate of optimal order is derived in an h 2 equivalent norm for the wg finite element solutions error estimates in the usual l 2 norm are established yielding optimal order of convergence for all the wg finite element algorithms except the one corresponding to the lowest order i e piecewise quadratic elements some numerical experiments are presented to illustrate the efficiency and accuracy of the numerical scheme

error estimates of spectral legendre galerkin methods for the fourth order equation in one dimension we employ spectral legendre galerkin and mixed legendre galerkin approximations to solve the first bi harmonic equation in one dimension respectively by orthogonal properties of legendre polynomials we obtain an explicit a posteriori error indicator for spectral legendre galerkin methods furthermore in virtue of an auxiliary variable we present spectral mixed legendre galerkin methods and study the a priori estimate and a posteriori error indicator especially these indicators only depend on the expansions of the right hand item numerical examples are presented to verify our theoretical analysis

an iterative finite element method for approximating the biharmonic equation analyse et estimations d erreur d une methode a elements finis mixtes pour le modele biharmonique d une plaque a appui libre ou encastree

legendre galerkin spectral element method for the biharmonic equations and its applications abstract a spectral element method based on the legendre galerkin approximation is presented to solve the two dimensional biharmonic equations rigorous error analysis is carried out to establish the convergence of the method by constructing appropriate basis functions which satisfy the boundary conditions of the differential equations the discrete variational formulation is reduced to linear system with sparse and symmetric matrices which can be efficiently solved by a fast schur complement method accuracy test is provided to confirm the convergence rate of the theoretical results finally the proposed method is applied to calculate the displacement of an elastic plate under a uniform applied load and stream function of zero reynolds number flow in a driven cavity the results compare well with established results

c1 macroelements in adaptive finite element methods some interesting properties of composite basis functions for c1 macroelements are investigated including their use for constructing conforming c1 function spaces on non conforming adaptively refined meshes of particular interest is the classical cubic hsieh clough tocher 3 split triangle because of its simplicity and convergence properties in fourth order problems as compared with the powell sabin heindl 6 split and 12 split triangles a posteriori error indicators for adaptive refinement are developed numerical experiments demonstrate convergence rates and adaptive refinement performance based on a simplified error indicator is tested extensibility to analogous three dimensional tetrahedral elements is briefly discussed copyright 2006 john wiley sons ltd

replicator dynamics in the iterative process for accurate range image matching iterative algorithms are often used for range image matching in this paper we treat the iterative process of range image matching as a live biological system evolving from one generation to another whilst different generations of the population are regarded as range images captured at different viewpoints the iterative process is simulated using time the well known replicator equations in theoretical biology are then adapted to estimate the probabilities of possible correspondences established using the traditional closest point criterion to reduce the effect of image resolutions on the final results for efficient and robust overlapping range image matching the relative fitness difference rather than the absolute fitness difference is employed in the replicator equations in order to model the probability change of possible correspondences being real over successive iterations the fitness of a possible correspondence is defined as the negative of a power of its squared euclidean distance while the replicator dynamics penalize those individuals with low fitness they are further penalised with a parameter since distant points are often unlikely to represent their real replicators while the replicator equations assume that all individuals are equally likely to meet each other and thus treat them equally we penalise those individuals competing for the same points as their possible replicators the estimated probabilities of possible correspondences being real are finally embedded into the powerful deterministic annealing scheme for global optimization resulting in the camera motion parameters being estimated in the weighted least squares sense a comparative study based on real range images with partial overlap has shown that the proposed algorithm is promising for automatic matching of overlapping range images

a c1 virtual element method on polyhedral meshes abstract the purpose of the present paper is to develop c 1 virtual elements in three dimensions for linear elliptic fourth order problems motivated by the difficulties that standard conforming finite elements encounter in this framework we focus the presentation on the lowest order case the generalization to higher orders being briefly provided in the appendix the degrees of freedom of the proposed scheme are only 4 per mesh vertex representing function values and gradient values interpolation error estimates for the proposed space are provided together with a set of numerical tests to validate the method at the practical level

algebraic approach to scattering theory of the fokker planck equation the one variable fokker planck equation is studied in a scattering formalism scattering processes are represented by paths in one dimensional space and the paths are treated as algebraic objects that constitute infinite dimensional representations of sl 2 c various expressions for the scattering coefficients are derived in a systematic way by means of algebraic methods with considerations on symmetries

parameter extension for combined hybrid finite element methods and application to plate bending problems abstract based on a weighted average of the modified hellinger reissner principle and its dual the combined hybrid finite element chfe method was originally proposed with a combination parameter limited in the interval 0 1 in actual computation this parameter plays an important role in adjusting the energy error of discretization models in this paper a novel expression of the combined hybrid variational form is used to show the relationship between the resultant method and some galerkin least squares stabilized finite scheme for plate bending problems the choice of combination parameter is then extended to 0 0 1 existence uniqueness and convergence of the solution of discrete schemes are proved and the advantage of the parameter extension in computation is discussed as an application improvement of adini s rectangular element by the chfe approach is performed

frequency expansion method for the one dimensional fokker planck equation a frequency expansion method is formulated for the one variable fokker planck equation it is shown that this method is valid for potentials u x which diverge faster than log x or converge to a limit faster than any powers of x as x the analysis is based on the study of the reflection coefficients for the fokker planck equation expressions for the expansion coefficients of the reflection coefficients are also derived

fast and accurate surface alignment through an isometry enforcing game surface registration is often performed as a two step process a feature matching scheme is first adopted to find a coarse initial alignment between two meshes subsequently a refinement step which usually operates in the space of rigid motions is applied to reach an optimal registration with respect to pointwise distances between overlapping areas in this paper we propose a novel technique that allows to obtain an accurate surface registration in a single step without the need for an initial motion estimation the main idea of our approach is to cast the selection of correspondences between points on the surfaces in a game theoretic framework where a natural selection process allows matching points that satisfy a mutual rigidity constraint to thrive eliminating all the other correspondences this process yields a very robust inlier selection scheme that does not depend on any particular technique for selecting the initial strategies as it relies only on the global geometric compatibility between correspondences the practical effectiveness of the approach is confirmed by an extensive set of experiments and comparisons with state of the art techniques highlightswe introduce a novel pipeline for rigid surface alignment based on game theory the method allows to obtain accurate solutions without requiring an initial estimate we propose simple descriptors designed to be fast and effective within our pipeline we establish a relation between evolutionary stable states and optimal alignments the technique is efficient and outperforms the state of the art

automatic 3d free form shape matching using the graduated assignment algorithm three dimensional free form shape matching is a fundamental problem in both the machine vision and pattern recognition literatures however the automatic approach to 3d free form shape matching still remains open in this paper we propose using k closest points in the second view for the automatic 3d free form shape matching for the sake of computational efficiency the optimised k d tree is employed for the search of the k closest points since occlusion and appearance and disappearance of points almost always occur slack variables have to be employed explicitly modelling outliers in the process of matching then the relative quality of each possible point match is estimated using the graduated assignment algorithm leading the camera motion parameters to be estimated by the quaternion method in the weighted least squares sense the experimental results based on both synthetic data and real images without any pre processing show the effectiveness and efficiency of the proposed algorithm for the automatic matching of overlapping 3d free form shapes with either sparse or dense points

a high accuracy spectral method based on min max principle for biharmonic eigenvalue problems on a spherical domain abstract in this study we develop a high accuracy spectral method based on the min max principle for biharmonic eigenvalue problems in the spherical domain by analyzing the orthogonal spherical harmonic and approximation and using the min max principle we first deduce the error estimates of approximate eigenvalues then we construct an appropriate set of orthogonal spherical functions contained in h 0 2 and establish the matrix formulations for the discrete variational form whose mass matrix and stiff matrix are all sparse so that we can solve the numerical solutions efficiently finally we provide some numerical experiments to validate that the theoretical results are correct

robust error estimation in energy and balanced norms for singularly perturbed fourth order problems we consider singularly perturbed fourth order problems in two dimensions under assumptions on the structure of their solutions we construct layer adapted meshes and prove for a mixed method convergence and supercloseness in the associated energy norms as well as convergence in balanced norms

a mixed finite element method for the biharmonic equation we consider the mixed finite element approximation of the biharmonic problem on a smooth domain with either clamped or simply supported boundary conditions error estimates are proved for the ciarlet raviart formulation of the clamped plate problem and for a similar method for the simply supported plate problem

a stabilized mixed finite element method for the biharmonic equation based on biorthogonal systems abstract we propose a stabilized finite element method for the approximation of the biharmonic equation with a clamped boundary condition the mixed formulation of the biharmonic equation is obtained by introducing the gradient of the solution and a lagrange multiplier as new unknowns working with a pair of bases forming a biorthogonal system we can easily eliminate the gradient of the solution and the lagrange multiplier from the saddle point system leading to a positive definite formulation using a superconvergence property of a gradient recovery operator we prove an optimal a priori estimate for the finite element discretization for a class of meshes