local time stepping in runge kutta discontinuous galerkin finite element methods applied to the shallow water equations abstract large geophysical flows often encompass both coarse and highly resolved regions approximating these flows using shock capturing methods with explicit time stepping gives rise to a courant friedrichs lewy cfl time step constraint even if the refined regions are sparse they can restrict the global cfl condition to very small time steps vastly increasing computational effort over the whole domain one method to cope with this problem is to use locally varying time steps over the domain these are also referred to as multi rate methods in the ode literature ideally such methods must be conservative accurate and easy to implement in this study we derive a second order local time stepping procedure within a runge kutta discontinuous galerkin rkdg framework to solve the shallow water equations this procedure is based on previous first order work of the second author and collaborator kirby 1 2 3 as we are interested in both coastal and overland flows due to e g rainfall wetting and drying is incorporated into the model numerical results are shown which verify the accuracy and efficiency of the approach compared to using a globally defined cfl time step and the application of the method to rainfall runoff scenarios

an adaptive uniformly convergent numerical method for a semilinear singular perturbation problem a singularly perturbed semilinear two point boundary value problem is considered without any restriction on its turning points a difference scheme is presented for solving this problem on an arbitrary locally quasi uniform mesh it is shown that the solution of the scheme is first order accurate uniformly in the perturbation parameter in a discrete l 1 norm numerical results are presented for an adaptive method based on the scheme

some computational aspects of discrete orthonormal moments discrete orthogonal moments have several computational advantages over continuous moments however when the moment order becomes large discrete orthogonal moments such as the tchebichef moments tend to exhibit numerical instabilities this paper introduces the orthonormal version of tchebichef moments and analyzes some of their computational aspects the recursive procedure used for polynomial evaluation can be suitably modified to reduce the accumulation of numerical errors the proposed set of moments can be used for representing image shape features and for reconstructing an image from its moments with a high degree of accuracy

uniformly convergent difference schemes for singularly perturbed parabolic diffusion convection problems without turning points we consider first the initial boundary value problem for the parabolic equation varepsilon y xx a x t y x b x t y d x t y t f x t on 0 1 0 t where 0 0 b 0 andd 0 bounds ony and its derivatives are obtained under certain compatibility assumptions on the data we examine a family of difference schemes for this problem which is exponentially fitted in thex variable and uses classical differencing in thet variable on rectangular grids which are arbitrarily spaced in both thex andt directions under a courant friedrichs lewy type condition the errors at the grid points are shown to be bounded byc h k whereh k is the maximum mesh width in thex t direction andc is a constant independent of h andk the corresponding result for a two point boundary value problem is also derived

pointwise error estimates for a streamline diffusion finite element scheme pointwise error estimates for a streamline diffusion scheme for solving a model convection dominated singularly perturbed convection diffusion problem are given these estimates improve pointwise error estimates obtained by johnson et al 5

moment computation for objects with spline curve boundary a new approach is proposed for computation of area and geometric moments for a plane object with a spline curve boundary the explicit formulae are obtained for area and low order moment calculation the complexity of calculation depends on the moment order spline degree and the number of control points used in spline representation the formulae proposed use the advantage that the sequence of spline control points is cyclic it allowed us to reduce substantially the number of summands in them the formulae might be useful in different applications where it is necessary to perform measurements for shapes with a smooth boundary

invariant image recognition by zernike moments the problem of rotation scale and translation invariant recognition of images is discussed a set of rotation invariant features are introduced they are the magnitudes of a set of orthogonal complex moments of the image known as zernike moments scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments a systematic reconstruction based method for deciding the highest order zernike moments required in a classification problem is developed the quality of the reconstructed image is examined through its comparison to the original one the orthogonality property of the zernike moments which simplifies the process of image reconstruction make the suggest feature selection approach practical features of each order can also be weighted according to their contribution to the reconstruction process the superiority of zernike moment features over regular moments and moment invariants was experimentally verified

a comment on translation and scale invariants of tchebichef moments by hongqing zhu pattern recognition 40 2007 25302542 it points out wrong claim made by hongqing zhu 2007 it corrects this error by developing and using charlier moment the proposed charlier moment is a novel category the aim of the present comment is to point out wrong claim made by hongqing zhu 2007 on the computation of scaling invariants of tchebichef moments we also proposed a novel discrete orthogonal moments namely charlier moments and demonstrate that the scaling invariants of the charlier moments can be computed by using the method mentioned in the article of hongqing zhu 2007 experimental results show that our inference is correct

image analysis by tchebichef moments this paper introduces a new set of orthogonal moment functions based on the discrete tchebichef polynomials the tchebichef moments can be effectively used as pattern features in the analysis of two dimensional images the implementation of the moments proposed in this paper does not involve any numerical approximation since the basis set is orthogonal in the discrete domain of the image coordinate space this property makes tchebichef moments superior to the conventional orthogonal moments such as legendre moments and zernike moments in terms of preserving the analytical properties needed to ensure information redundancy in a moment set the paper also details the various computational aspects of tchebichef moments and demonstrates their feature representation capability using the method of image reconstruction

image analysis by krawtchouk moments a new set of orthogonal moments based on the discrete classical krawtchouk polynomials is introduced the krawtchouk polynomials are scaled to ensure numerical stability thus creating a set of weighted krawtchouk polynomials the set of proposed krawtchouk moments is then derived from the weighted krawtchouk polynomials the orthogonality of the proposed moments ensures minimal information redundancy no numerical approximation is involved in deriving the moments since the weighted krawtchouk polynomials are discrete these properties make the krawtchouk moments well suited as pattern features in the analysis of two dimensional images it is shown that the krawtchouk moments can be employed to extract local features of an image unlike other orthogonal moments which generally capture the global features the computational aspects of the moments using the recursive and symmetry properties are discussed the theoretical framework is validated by an experiment on image reconstruction using krawtchouk moments and the results are compared to that of zernike pseudo zernike legendre and tchebyscheff moments krawtchouk moment invariants are constructed using a linear combination of geometric moment invariants an object recognition experiment shows krawtchouk moment invariants perform significantly better than hu s moment invariants in both noise free and noisy conditions

translation and scale invariants of tchebichef moments discrete orthogonal moments such as tchebichef moments have been successfully used in the field of image analysis however the invariance property of these moments has not been studied mainly due to the complexity of the problem conventionally the translation and scale invariant functions of tchebichef moments can be obtained either by normalizing the image or by expressing them as a linear combination of the corresponding invariants of geometric moments in this paper we present a new approach that is directly based on tchebichef polynomials to derive the translation and scale invariants of tchebichef moments both derived invariants are unchanged under image translation and scale transformation the performance of the proposed descriptors is evaluated using a set of binary characters examples of using the tchebichef moments invariants as pattern features for pattern classification are also provided

invariant description and retrieval of planar shapes using radon composite features this paper proposes a novel feature based invariant descriptor termed radon composite features rcfs for planar shapes instead of analyzing shapes directly in the spatial domain some shape features are extracted from the radon transform plane using statistical and spectral analysis the proposed method overcomes the drawbacks of existing shape representation techniques since it accomplishes the invariances to common geometrical transformations without any normalization process which usually causes inaccuracies a novel hierarchical strategy with rcfs can achieve low complexity and coarse to fine retrieval and perform accurately when retrieving shapes while remaining robust against variations experiments demonstrate that rcf provides a higher degree of discrimination as compared with several state of the art approaches

a unified methodology for computing accurate quaternion color moments and moment invariants in this paper a general framework for computing accurate quaternion color moments and their corresponding invariants is proposed the proposed unified scheme arose by studying the characteristics of different orthogonal polynomials these polynomials are used as kernels in order to form moments the invariants of which can easily be derived the resulted scheme permits the usage of any polynomial like kernel in a unified and consistent way the resulted moments and moment invariants demonstrate robustness to noisy conditions and high discriminative power additionally in the case of continuous moments accurate computations take place to avoid approximation errors based on this general methodology the quaternion tchebichef krawtchouk dual hahn legendre orthogonal fourier mellin pseudo zernike and zernike color moments and their corresponding invariants are introduced a selected paradigm presents the reconstruction capability of each moment family whereas proper classification scenarios evaluate the performance of color moment invariants

fast computation of legendre and zernike moments this paper presents recursive algorithms for fast computation of legendre and zernike moments of a grey level image intensity distribution for a binary image a contour integration method is developed for the evaluation of legendre moments using only the boundary information a method for recursive calculation of zernike polynomial coefficients is also given a square to circular image transformation scheme is introduced to minimize the computation involved in zernike moment functions the recursive formulae can also be used in inverse moment transforms to reconstruct the original image from moments the mathematical framework of the algorithms is given in detail and illustrated with binary and grey level images

numerical methods for time dependent convection diffusion equations abstract we examine a singularly perturbed linear parabolic initial boundary value problem in one space variable various finite difference schemes are derived for this problem using a semidiscrete petrov galerkin finite element method these schemes do not have a cell reynolds number restriction and are shown to be first order accurate uniformly in the perturbation parameter numerical results are also presented

on image analysis by moments research has been performed investigating the use of moments for pattern recognition in recent years the basic problem of the influence of discretization and noise on moment accuracy as object descriptors has been barely investigated in this paper the detailed error analysis involved in the moment method is discussed several new techniques to increase the accuracy and efficiency of moment descriptor are proposed we utilize these results for the problem of image reconstruction from the orthogonal legendre moments computed from discrete and noisy data the automatic selection of an optimal number of moments is also discussed

an affine invariant curve matching method for photo identification of marine mammals individual identification of marine mammals is of interest to marine biologists this paper aims at the recognition of the edges associated with marine mammals whose pictures are taken under affine transformations the introduced affine curve matching method uses the area of mismatch between a query and a database curve this area is obtained by optimally aligning the curves based on the minimum affine distance involving their distinguishing points the method is applied to databases of sea lions gray whales and dolphins and its performance is compared with two other affine curve matching methods the results show that the introduced curve matching approach outperforms the other approaches and thus further reduces the search time for identifying an individual the developed method is of general purpose as it can be used for other affine curve matching applications

finite element analysis of exponentially fitted lumped schemes for time dependent convection diffusion problems in the paper we consider a singularly perturbed linear parabolic initialboundary value problem in one space variable two exponential fitted schemes are derived for the problem using petrov galerkin finite element methods with various choices of trial and test spaces on rectangular meshes which are either arbitrary or slightly restricted we derive global energy norm andl 2 norm and locall error bounds which are uniform in the diffusion parameter numerical results are also persented

on the independence of rotation moment invariants abstract the problem of the independence and completeness of rotation moment invariants is addressed in this paper first a general method for constructing invariants of arbitrary orders by means of complex moments is described as a major contribution of the paper it is shown that for any set of invariants there exists a relatively small basis by means of which all other invariants can be generated the method how to construct such a basis and how to prove its independence and completeness is presented some practical impacts of the new results are mentioned at the end of the paper

translation invariants of zernike moments moment functions defined using a polar coordinate representation of the image space such as radial moments and zernike moments are used in several recognition tasks requiring rotation invariance however this coordinate representation does not easily yield translation invariant functions which are also widely sought after in pattern recognition applications this paper presents a mathematical framework for the derivation of translation invariants of radial moments defined in polar form using a direct application of this framework translation invariant functions of zernike moments are derived algebraically from the corresponding central moments both derived functions are developed for non symmetrical as well as symmetrical images they mitigate the zero value obtained for odd order moments of the symmetrical images vision applications generally resort to image normalization to achieve translation invariance the proposed method eliminates this requirement by providing a translation invariance property in a zernike feature set the performance of the derived invariant sets is experimentally confirmed using a set of binary latin and english characters

rotation scale and translation resilient watermarking for images many electronic watermarks for still images and video content are sensitive to geometric distortions for example simple rotation scaling and or translation rst of an image can prevent blind detection of a public watermark in this paper we propose a watermarking algorithm that is robust to rst distortions the watermark is embedded into a one dimensional 1 d signal obtained by taking the fourier transform of the image resampling the fourier magnitudes into log polar coordinates and then summing a function of those magnitudes along the log radius axis rotation of the image results in a cyclical shift of the extracted signal scaling of the image results in amplification of the extracted signal and translation of the image has no effect on the extracted signal we can therefore compensate for rotation with a simple search and compensate for scaling by using the correlation coefficient as the detection measure false positive results on a database of 10 000 images are reported robustness results on a database of 2000 images are described it is shown that the watermark is robust to rotation scale and translation in addition we describe tests examining the watermarks resistance to cropping and jpeg compression

fast algorithm for generation of moment invariants abstract moment invariants are important shape descriptors in computer vision the method of decomposing the trigonometric function is suggested to obtain various moment invariants based on this method the multi filter algorithm is introduced as an efficient way to generate large numbers of moment invariants a great deal of repeated computation on sub polynomial is avoided general explicit constructions of basic moment invariants are also provided furthermore the proposed magnitude normalized method makes invariants more stable and easier for classification

moments and moment invariants in the radon space radon transform has been acknowledged as the promising solution for image processing due to its high noise robustness and the ability of converting the rotation scaling and translation operations on a pattern image into translations and scaling in the radon image recently several transforms widely employed in signal processing have been introduced in images radon space for pattern recognition however moments and especially moment invariants in the radon space have not been thoroughly investigated in this paper we introduce a mathematical framework of constructing moments and moment invariants in the radon space first rotational moments which represent non orthogonal moments and legendre fourier moments which represent orthogonal moments are introduced in the radon space respectively on this basis we propose a method to obtain rotation scaling and translation as well as affine invariance of these moments in the radon space second we prove that the proposed moments in the radon space can be represented by a linear combination of classical geometric moments with this property the implementation time of the moments in the radon space can be significantly reduced and the recognition accuracy can also be greatly improved since no numerical approximation is involved theoretical and experimental analysis on invariant recognition accuracy noise robustness image blur distortion and computational time also shows the superiority of the proposed methods highlightsa framework of constructing moments and moment invariants in the radon space is introduced a method to obtain rst and affine invariance of moments in the radon space is proposed the implementation time of the proposed moments can be significantly reduced the recognition accuracy of the proposed moments can also be increased

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

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

translation and scale invariants of legendre moments abstract by convention the translation and scale invariant functions of legendre moments are achieved by using a combination of the corresponding invariants of geometric moments they can also be accomplished by normalizing the translated and or scaled images using complex or geometric moments however the derivation of these functions is not based on legendre polynomials this is mainly due to the fact that it is difficult to extract a common displacement or scale factor from legendre polynomials in this paper we introduce a new set of translation and scale invariants of legendre moments based on legendre polynomials the descriptors remain unchanged for translated elongated contracted and reflected non symmetrical as well as symmetrical images the problems associated with the vanishing of odd order legendre moments of symmetrical images are resolved the performance of the proposed descriptors is experimentally confirmed using a set of binary english chinese and latin characters in addition to this a comparison of computational speed between the proposed descriptors and the aforesaid geometric moments based method is also presented

3d image analysis by separable discrete orthogonal moments based on krawtchouk and tchebichef polynomials abstract in this paper we introduce new sets of separable discrete moments for 3d image analysis named tkkm tchebichef krawtchouk krawtchouk moments and ttkm tchebichef tchebichef krawtchouk moments firstly we present a detailed comparative study between the proposed separable 3d moments and the classical ones in terms of global feature extraction capability under noisy and noise free conditions also their local feature extraction ability is examined secondly our study investigates the ability of the proposed separable 3d moments in pattern recognition for this new sets of separable 3d discrete moment invariants are introduced the proposed rotation scaling and translation 3d moment invariants have been rigorously tested under different sets of mixed transforms the obtained results show that the representation capability in comparison with traditional krawtchouk and tchebichef moments has been significantly improved by using the new proposed 3d separable moments and can be highly useful in the field of 3d image analysis