refined moment calculation using image block representation this paper deals with effective calculation of moments of binary images recently spiliotis and mertzios see ibid vol 7 p 1609 15 nov 1998 published a method based on image block representation ibr we propose a refinement of their method which yields exact results and performs even more effectively

projective invariants of co moments of 2d images functions of moments of 2d images that are invariant under some changes are important in image analysis and pattern recognition one of the most basic changes to a 2d image is geometric change two images of the same plane taken from different viewpoints are related by a projective transformation unfortunately it is well known that geometric moment invariants for projective transformations do not exist in general yet if we generalize the standard definition of the geometric moments and utilize some additional information from the images certain type of projective invariants of 2d images can be derived this paper first defines co moment as a moment like function of image that contains two reference points then a set of functions of co moments that is invariant under general projective transformations is derived the invariants are simple and in explicit form experimental results validated the mathematical derivations

fast computation of tchebichef moments for binary and grayscale images discrete orthogonal moments have been recently introduced in the field of image analysis it was shown that they have better image representation capability than the continuous orthogonal moments one problem concerning the use of moments as feature descriptors is the high computational cost which may limit their application to the problems where the online computation is required in this paper we present a new approach for fast computation of the 2 d tchebichef moments by deriving some properties of tchebichef polynomials and using the image block representation for binary images and intensity slice representation for grayscale images a fast algorithm is proposed for computing the moments of binary and grayscale images the theoretical analysis shows that the computational complexity of the proposed method depends upon the number of blocks of the image thus it can speed up the computational efficiency as far as the number of blocks is smaller than the image size

real time computation of two dimensional moments on binary images using image block representation this work presents a new approach and an algorithm for binary image representation which is applied for the fast and efficient computation of moments on binary images this binary image representation scheme is called image block representation since it represents the image as a set of nonoverlapping rectangular areas the main purpose of the image block representation process is to provide an efficient binary image representation rather than the compression of the image the block represented binary image is well suited for fast implementation of various processing and analysis algorithms in a digital computing machine the two dimensional 2 d statistical moments of the image may be used for image processing and analysis applications a number of powerful shape analysis methods based on statistical moments have been presented but they suffer from the drawback of high computational cost the real time computation of moments in block represented images is achieved by exploiting the rectangular structure of the blocks

pattern recognition by affine moment invariants abstract the paper deals with moment invariants which are invariant under general affine transformation and may be used for recognition of affine deformed objects our approach is based on the theory of algebraic invariants the invariants from second and third order moments are derived and shown to be complete the paper is a significant extension and generalization of recent works several numerical experiments dealing with pattern recognition by means of the affine moment invariants as the features are described

generalized dual hahn moment invariants in this work we introduce a generalized expression of the weighted dual hahn moment invariants up to any order and for any value of their parameters in order for the proposed invariants to be formed the weighted dual hahn moments up to any order and for any value of their parameters are expressed as a linear combination of geometric ones for this reason a formula expressing the nth degree dual hahn polynomial for any value of its parameters as a linear combination of monomials c r x r is proved in addition a recurrent relation for the fast computation of the aforementioned monomials coefficients c r is also given moreover normalization aspects of the generalized weighted dual hahn moment invariants are discussed while a modification of them is proposed in order to avoid their numerical instabilities finally experimental results and classification scenarios including datasets of natural scenes evaluate the proposed methodology

korn s inequalities for piecewise h 1 vector fields korn s inequalities for piecewise h 1 vector fields are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

grad div stablilization for stokes equations in this paper a stabilizing augmented lagrangian technique for the stokes equations is studied the method is consistent and hence does not change the continuous solution we show that this stabilization improves the well posedness of the continuous problem for small values of the viscosity coefficient we analyze the influence of this stabilization on the accuracy of the finite element solution and on the convergence properties of the inexact uzawa method

an efficient algorithm for computation of shape moments from run length codes or chain codes abstract moments are very useful for shape analysis zero to third order moments have been used for computer vision applications such as shape recognition and orientation they can serve for composition of the well known moment invariants used as desirable features as well as for the detection of the location and the principal axis direction of a shape the shape is often represented by a binary image and its moments can be obtained by use of fast algorithms considering the shape as a discrete point array in this paper a new algorithm based on the double integral formulation is presented the shape is considered as a continuous region and the contribution of boundary points is used for fast computation of shape moments this method can be used to calculate moments from either the run length codes or the chain codes of shape

on the accuracy of the rotation form in simulations of the navier stokes equations the rotation form of the navier stokes equations nonlinearity is commonly used in high reynolds number flow simulations it was pointed out by a few authors and not widely known apparently that it can also lead to a less accurate approximate solution than the usual email protected u form we give a different explanation of this effect related to i resolution of the bernoulli pressure and ii the scaling of the coupling between velocity and pressure error with respect to the reynolds number we show analytically that i the difference between the two nonlinearities is governed by the difference in the resolution of the bernoulli and kinematic pressures and ii a simple linear grad div stabilization ameliorates much of the bad scaling of the velocity error with respect to re the rotation form does have superior conservation properties to the alternatives and it appears to be amenable to more efficient preconditioners thus the rotational form with grad div stabilization is a promising method we also give experiments that show bad velocity approximation is tied to poor pressure resolution in either form

an efficient algorithm for computing moments on a block representation of a grey scale image computing lower order moments is important in image processing suppose the input grey image with size nxn has been compressed into the block representation where the number of blocks is k commonly k

a high order discontinuous galerkin method for 2d incompressible flows in this paper we introduce a high order discontinuous galerkin method for two dimensional incompressible flow in the vorticity stream function formulation the momentum equation is treated explicitly utilizing the efficiency of the discontinuous galerkin method the stream function is obtained by a standard poisson solver using continuous finite elements there is a natural matching between these two finite element spaces since the normal component of the velocity field is continuous across element boundaries this allows for a correct upwinding gluing in the discontinuous galerkin framework while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability the method is efficient for inviscid or high reynolds number flows optimal error estimates are proved and verified by numerical experiments

pattern recognition with moment invariants a comparative study and new results abstract moment invariants have been proposed as pattern sensitive features in classification and recognition applications in this paper the authors present a comprehensive study of the effectiveness of different moment invariants in pattern recognition applications by considering two sets of data handwritten numerals and aircrafts the authors also present a detailed study of zernike and pseudo zernike moment invariants including a new procedure for deriving the moment invariants in addition the authors introduce a new normalization scheme that reduces the large dynamic range of these invariants as well as implicit redundancies in these invariants based on a comprehensive study with both handwritten numerals and aircraft data the authors show that the new method of deriving zernike moment invariants along with the new normalization scheme yield the best overall performance even when the data are degraded by additive noise

fast computation of separable two dimensional discrete invariant moments for image classification in this paper we present a new set of bivariate discrete orthogonal polynomials based on the product of meixner s discrete orthogonal polynomials by tchebichef s krawtchouk s and hahn s discrete orthogonal polynomials this set of bivariate discrete orthogonal polynomials is used to define three new types of discrete orthogonal moments as meixner tchebichef moments meixner krawtchouk moments and meixner hahn moments we also present an approach to accelerate the computation of these moments by using the image block representation for binary images and image slice representation for gray scale images a novel set of meixner tchebichef invariant moments meixner krawtchouk invariant moments and meixner hahn invariant moments is also derived these invariant moments are derived algebraically from the geometric invariant moments and their computation is accelerated using an image representation scheme the proposed algorithms are tested using several well known computer vision datasets including moment s invariability and pattern recognition the performance of these invariant moments used as pattern features for a pattern classification is compared with the shape descriptors of hu legendre tchebichef krawtchouk krawtchouk hahn and tchebichef hahn invariant moments the texture descriptors and the color descriptors for four different databases new set of bivariate discrete orthogonal polynomials separable two dimensional discrete invariant moments improving the performance of image classification acceleration of computational time of discrete orthogonal invariant moments

a new family of stable mixed finite elements for the 3d stokes equations a natural mixed element approach for the stokes equations in the velocity pressure formulation would approximate the velocity by continuous piecewise polynomials and would approximate the pressure by discontinuous piecewise polynomials of one degree lower however many such elements are unstable in 2d and 3d this paper is devoted to proving that the mixed finite elements of this p k p k 1 type when k 3 satisfy the stability condition the babuska brezzi inequality on macro tetrahedra meshes where each big tetrahedron is subdivided into four subtetrahedra this type of mesh simplifies the implementation since it has no restrictions on the initial mesh the new element also suits the multigrid method

efficient and accurate computation of geometric moments on gray scale images a novel algorithm that permits the fast and accurate computation of geometric moments on gray scale images is presented in this paper the proposed algorithm constitutes an extension of the ibr algorithm introduced in the past which was applicable only for binary images a new image representation scheme the isr intensity slice representation which represents a gray scale image as an expansion of several two level images of different intensity values enables the partially application of the ibr algorithm to each image component moreover using the resulted set of image blocks the geometric moments computation can be accelerated through appropriate computation schemes

a unified framework of continuous and discontinuous galerkin methods for solving the incompressible navier stokes equation abstract in this paper we propose a unified numerical framework for the time dependent incompressible navier stokes equation which yields the h 1 h div conforming and discontinuous galerkin methods with the use of different viscous stress tensors and penalty terms for pressure robustness under minimum assumption on galerkin spaces the semi and fully discrete stability is proved when a family of implicit runge kutta methods are used for time discretization furthermore we present a unified discussion on the penalty term numerical experiments are presented to compare our schemes with classical schemes in the literature in both unsteady and steady situations it turns out that our scheme is competitive when applied to well known benchmark problems such as taylor green vortex kovasznay flow potential flow lid driven cavity flow and the flow around a cylinder

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

decomposition of binary images a survey and comparison we present an overview of the most important methods that decompose an arbitrary binary object into a union of rectangles we describe a run length encoding and its generalization decompositions based on quadtrees on mathematical morphology on the distance transform and a theoretically optimal decomposition based on a maximal matching in bipartite graphs we compare their performance in image compression in moment computation and in linear filtering we show that the choice is always a compromise between the complexity and time memory consumption we give advice how to select an appropriate method in particular cases

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

singular continuous spectra and discrete wave packet dynamics asymptotic estimates which relate the diffusion of wave packets on discrete lattices to hausdorff dimensions of the local density of states are discussed

novel moment invariants for improved classification performance in computer vision applications a novel set of moment invariants based on the krawtchouk moments are introduced in this paper these moment invariants are computed over a finite number of image intensity slices extracted by applying an innovative image representation scheme the image slice representation isr method based on this technique an image is decomposed to a several non overlapped intensity slices which can be considered as binary slices of certain intensity this image representation gives the advantage to accelerate the computation of image s moments since the image can be described in a number of homogenous rectangular blocks which permits the simplification of the computation formulas the moments computed over the extracted slices seem to be more efficient than the corresponding moments of the same order that describe the whole image in recognizing the pattern under processing the proposed moment invariants are exhaustively tested in several well known computer vision datasets regarding their rotation scaling and translation rst invariant recognition performance by resulting to remarkable outcomes

high order exactly divergence free hybrid discontinuous galerkin methods for unsteady incompressible flows abstract in this paper we present an efficient discretization method for the solution of the unsteady incompressible navier stokes equations based on a high order hybrid discontinuous galerkin formulation the crucial component for the efficiency of the discretization method is the distinction between stiff linear parts and less stiff non linear parts with respect to their temporal and spatial treatment exploiting the flexibility of operator splitting time integration schemes we combine two spatial discretizations which are tailored for two simpler sub problems a corresponding hyperbolic transport problem and an unsteady stokes problem for the hyperbolic transport problem a spatial discretization with an upwind discontinuous galerkin method and an explicit treatment in the time integration scheme is rather natural and allows for an efficient implementation the treatment of the stokes part involves the solution of linear systems in this case a discretization with hybrid discontinuous galerkin methods is better suited we consider such a discretization for the stokes part with two important features h div conforming finite elements to guarantee exactly divergence free velocity solutions and a projection operator which reduces the number of globally coupled unknowns we present the method discuss implementational aspects and demonstrate the performance on two and three dimensional benchmark problems

fast algorithm for the computation of moment invariants abstract moment invariants have been used as feature descriptors in a variety of object recognition applications when assuming a continuous image function moments calculated using a double integral formulation are invariant to variations in translation rotation and size of the object however due to the recursive nature of the calculations and the limited speed of microprocessors the moments were not computable in real time in this paper we present fast invariant moment computations using the delta method as a means of scene representation this method computes moments of contiguous images by using the contribution of each line rather than individual pixel

grad div stabilization and subgrid pressure models for the incompressible navier stokes equations in this paper the grad div stabilization for the incompressible navier stokes finite element approximations is considered from two different viewpoints i as a variational multiscale approach for the pressure subgrid modeling and ii as a stabilization procedure of least square type some new error estimates for the linearized problem with the grad div stabilization are proved with the help of norms induced by the pressure schur complement operator we discuss the stabilization parameter choice arising in the frameworks of least square and multiscale methods and consider assumptions which allow to relate both approaches

a low order galerkin finite element method for the navier stokes equations of steady incompressible flow a stabilization issue and iterative methods a galerkin finite element method is considered to approximate the incompressible navier stokes equations together with iterative methods to solve a resulting system of algebraic equations this system couples velocity and pressure unknowns thus requiring a special technique for handling we consider the navier stokes equations in velocity kinematic pressure variables as well as in velocity bernoulli pressure variables the latter leads to the rotation form of nonlinear terms this form of the equations plays an important role in our studies a consistent stabilization method is considered from a new view point theory and numerical results in the paper address both the accuracy of the discrete solutions and the effectiveness of solvers and a mutual interplay between these issues when particular stabilization techniques are applied 2002 published by elsevier science b v

stokes complexes and the construction of stable finite elements with pointwise mass conservation two families of conforming finite elements for the two dimensional stokes problem are developed guided by two discrete smoothed de rham complexes which we coin stokes complexes we show that the finite element pairs are inf sup stable and also provide pointwise mass conservation on very general triangular meshes

a locally conservative ldg method for the incompressible navier stokes equations in this paper a new local discontinuous galerkin method for the incompressible stationary navier stokes equations is proposed and analyzed four important features render this method unique its stability its local conservativity its high order accuracy and the exact satisfaction of the incompressibility constraint although the method uses completely discontinuous approximations a globally divergence free approximate velocity in h div is obtained by simple element by element post processing optimal error estimates are proven and an iterative procedure used to compute the approximate solution is shown to converge this procedure is nothing but a discrete version of the classical fixed point iteration used to obtain existence and uniqueness of solutions to the incompressible navier stokes equations by solving a sequence of oseen problems numerical results are shown which verify the theoretical rates of convergence they also confirm the independence of the number of fixed point iterations with respect to the discretization parameters finally they show that the method works well for a wide range of reynolds numbers

a unified methodology for the efficient computation of discrete orthogonal image moments a novel methodology is proposed in this paper to accelerate the computation of discrete orthogonal image moments the computation scheme is mainly based on a new image representation method the image slice representation isr method according to which an image can be expressed as the outcome of an appropriate combination of several non overlapped intensity slices this image representation decomposes an image into a number of binary slices of the same size whose pixels come in two intensities black or any other gray level value therefore the image block representation can be effectively applied to describe the image in a more compact way once the image is partitioned into intensity blocks the computation of the image moments can be accelerated as the moments can be computed by using decoupled computation forms the proposed algorithm constitutes a unified methodology that can be applied to any discrete moment family in the same way and produces similar promising results as has been concluded through a detailed experimental investigation

a connection between scott vogelius and grad div stabilized taylor hood fe approximations of the navier stokes equations this article studies two methods for obtaining excellent mass conservation in finite element computations of the navier stokes equations using continuous velocity fields with a particular mesh construction the scott vogelius element pair has recently been shown to be inf sup stable and have optimal approximation properties while also providing pointwise mass conservation we present herein the first numerical tests of this element pair for the time dependent navier stokes equations we also prove that the limit of the grad div stabilized taylor hood solutions to the navier stokes problem converges to the scott vogelius solution as the stabilization parameter tends to infinity that is we provide theoretical justification that choosing the grad div parameter large does not destroy the solution numerical tests are provided which verify the theory and show how both scott vogelius and grad div stabilized taylor hood with large stabilization parameter elements can provide accurate results with excellent mass conservation for navier stokes approximations

on the convergence rate of grad div stabilized taylor hood to scott vogelius solutions for incompressible flow problems abstract it was recently proven in case et al 2010 2 that under mild restrictions grad div stabilized taylor hood solutions of navier stokes problems converge to the scott vogelius solution of that same problem however even though the analytical rate was only shown to be 1 2 where is the stabilization parameter the computational results suggest the rate may be improvable to 1 we prove herein the analytical rate is indeed 1 and extend the result to other incompressible flow problems including leray and mhd numerical results are given that verify the theory