unitary rotation of square pixellated images the unitary rotation of square pixellated images is based on the finite su 2 oscillator model which describes systems whose values for position momentum and energy are discrete and finite in a two dimensional position space this allows the construction of angular momentum states orthonormal and complete for which rotations are defined as multiplication by phases that carry the rotation angle the decomposition of a digital square images in terms of these angular momentum states determines a unitary hence invertible rotation of the image whose kernel can be computed as a four dimensional array of real numbers

an adjoint method for the inverse design of solidification processes with natural convection this paper presents a finite element algorithm based on the adjoint method for the design of a certain class of solidification processes in particular the paper addresses the design of directional solidification processes for pure materials such that a desired freezing front heat flux and growth velocity are achieved this is the first time that an infinite dimensional continuum adjoint formulation is obtained and implemented for the solution of such inverse design problems with moving boundaries and boussinesq incompressible flow the present design problem belongs to a category of inverse problems in which one is looking for the unknown conditions in part of the boundary while overspecified boundary conditions are supplied in another part of the boundary here the freezing interface the solidification design problem is mathematically posed as a whole time domain optimization problem the gradient of the cost functional is calculated using the solution of an appropriately defined continuous adjoint problem the minimization process is realized by the conjugate gradient method via the solutions of the direct adjoint and sensitivity sub problems the proposed methodology is demonstrated with the solidification of an initially superheated liquid aluminum confined in a square mold the non uniformity in the casting product in the direction of gravity due to the existence of natural convection in the melt is emphasized the inverse design problem is then posed as finding the appropriate spatial temporal variations of the boundary heat flux on the vertical mold walls that can eliminate or reduce the effects of convection on the freezing interface heat fluxes and growth velocity the numerical example demonstrates the accuracy and convergence of the adjoint formulation finally open related research design problems are discussed 1998 john wiley sons ltd

image quality assessment by discrete orthogonal moments this paper proposes a novel full reference quality assessment qa metric that automatically assesses the quality of an image in the discrete orthogonal moments domain this metric is constructed by representing the spatial information of an image using low order moments the computation up to fourth order moments is performed on each individual 8x8 non overlapping block for both the test and reference images then the computed moments of both the test and reference images are combined in order to determine the moment correlation index of each block in each order the number of moment correlation indices used in this study is nine next the mean of each moment correlation index is computed and thereafter the single quality interpretation of the test image with respect to its reference is determined by taking the mean value of the computed means of all the moment correlation indices the proposed objective metrics based on two discrete orthogonal moments tchebichef and krawtchouk moments are developed and their performances are evaluated by comparing them with subjective ratings on several publicly available databases the proposed discrete orthogonal moments based metric performs competitively well with the state of the art models in terms of quality prediction while outperforms them in terms of computational speed

image analysis using hahn moments this paper shows how hahn moments provide a unified understanding of the recently introduced chebyshev and krawtchouk moments the two latter moments can be obtained as particular cases of hahn moments with the appropriate parameter settings and this fact implies that hahn moments encompass all their properties the aim of this paper is twofold 1 to show how hahn moments as a generalization of chebyshev and krawtchouk moments can be used for global and local feature extraction and 2 to show how hahn moments can be incorporated into the framework of normalized convolution to analyze local structures of irregularly sampled signals

image analysis by bessel fourier moments in this paper we proposed a new set of moments based on the bessel function of the first kind named bessel fourier moments bfms which are more suitable than orthogonal fourier mellin and zernike moments for image analysis and rotation invariant pattern recognition compared with orthogonal fourier mellin and zernike polynomials of the same degree the new orthogonal radial polynomials have more zeros and these zeros are more evenly distributed the bessel fourier moments can be thought of as generalized orthogonalized complex moments theoretical and experimental results show that the bessel fourier moments perform better than the orthogonal fourier mellin and zernike moments ofmms and zms in terms of image reconstruction capability and invariant recognition accuracy in noise free noisy and smooth distortion conditions

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

comparison of finite element techniques for solidification problems the accuracies of the computed temperatures of a liquid in a corner region under freezing conditions are compared for various fixed grid finite element techniques using the analytical solution for this problem as a reference in the finite element formulation of the problem different time stepping schemes are compared the implicit euler backward algorithm combined with an iterative scheme and two three time level methods the lees algorithm and a dupont algorithm which are both applied as non iterative schemes furthermore different methods for handling the evolution of latent heat are examined an approximation method suggested by lemmon and one suggested by del giudice both using the enthalpy formulation as well as a fictitious heat flow method presented by rolph and bathe results of calculations performed with the consistent heat capacity matrix are compared with those performed with a lumped heat capacity matrix

image analysis by circularly semi orthogonal moments various types of circularly orthogonal moments have been widely used for image reconstruction and rotation invariant classification however they suffer from two errors namely numerical integration error and geometric error which affect their reconstruction capability and pattern recognition accuracy in this paper a novel category of circular moments named circularly semi orthogonal moments is proposed in the proposed moment a set of orthogonal basis functions modulated by a negative power exponential envelope is utilized as the radial basis function for a given degree n the radial basis function possesses more compact bandwidth less cutoff frequency and more zeros compared with the frequently used circularly orthogonal moments including zernike and orthogonal fourier mellin moments and so the circularly semi orthogonal moment calculated with the zeroth order approximation is more robust to numerical error than the frequently used circularly orthogonal moments furthermore the capability of the semi orthogonal moment to describe high spatial frequency components of images is relatively higher than that of the frequently used circularly orthogonal moments experimental results demonstrate that the semi orthogonal moments calculated with the zeroth order approximation perform better than the frequently used circularly orthogonal moments in terms of image reconstruction capability and invariant recognition accuracy in noise free noisy and smooth distortion conditions it is also shown that the proposed high order moments are more numerically stable than the circularly orthogonal moments a kind of circular moments named circularly semi orthogonal moment is proposed it outperforms in image reconstruction over the circularly orthogonal moments it performs better in invariant image recognition under noisy and smooth distortions

h model reduction for discrete time singular systems this paper investigates the problem of h sub infinity model reduction for linear discrete time singular systems without decomposing the original system matrices necessary and sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities lmis and a coupling non convex rank constraint set when these conditions are feasible an explicit parametrization of the desired reduced order models is given particularly a simple lmi condition without rank constraint is derived for the zeroth order h sub infinity approximation problem finally an illustrative example is provided to demonstrate the applicability of the proposed approach

on robust stability of singular systems with random abrupt changes this paper deals with the class of continuous time singular linear systems with markovian switching sufficient conditions on stochastic stability and robust stochastic stability are developed in the lmi setting the developed sufficient conditions are used to check if either the nominal or the uncertain systems are regular impulse free and stochastically stable or robust stochastically stable

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

comparison of image patches using local moment invariants we propose a new set of moment invariants based on krawtchouk polynomials for comparison of local patches in 2d images being computed from discrete functions these moments do not carry the error due to discretization unlike many orthogonal moments which usually capture global features krawtchouk moments can be used to compute local descriptors from a region of interest in an image this can be achieved by changing two parameters and hence shifting the center of interest region horizontally or vertically or both this property enables comparison of two arbitrary local regions we show that krawtchouk moments can be written as a linear combination of geometric moments so easily converted to rotation size and position independent invariants we also construct local hu based invariants using hu invariants and utilizing them on images localized by the weight function given in the definition of krawtchouk polynomials we give the formulation of local krawtchouk based and hu based invariants and evaluate their discriminative performance on local comparison of artificially generated test images

a functional optimization approach to an inverse magneto convection problem a formulation and an fem implementation for the solution of an ill posed inverse design magneto convection problem is proposed in particular an incompressible viscous electrically conducting liquid material occupying a given domain is considered convection is driven by buoyancy effects as well as a lorentz force generated due to the applied magnetic field thermal boundary conditions are only prescribed in the part h0 of the boundary in addition the temperature distribution is also prescribed in the part i of the boundary h1 where the heat flux is known i e i is a boundary with overspecified thermal boundary conditions the inverse magneto convection problem is posed as an optimization problem in l2 i 0 tmax for the calculation of the boundary heat flux qo x t with x t h0 0 tmax the optimization scheme minimizes the discrepancy m x t x t qo l2 i 0 tmax between the temperature x t qo calculated from the solution of a direct problem for each flux qo and the desired or measured temperature m x t on the boundary i the exact l2 gradient of the cost functional is obtained from appropriately defined adjoint fields the adjoint problem is defined from the sensitivity operators obtained by linearization of the equations governing the direct problem the standard supg pspg stabilized fem formulation for incompressible fluid flow simulation is here extended to thermo magnetically driven flows the proposed fem formulation is used for the calculation of the direct adjoint and sensitivity thermal fluid flow and electric potential fields the entire optimization algorithm is solved using the conjugate gradient method finally the method is demonstrated through the solution of a few inverse problems with known results the need for regularization is identified in one of the example problems with uniformly distributed random errors in the temperature data m x t and a h1 regularized formulation is introduced to obtain stable solutions finally the numerical results are elucidated and potential applications are addressed

singularity detection and processing with wavelets the mathematical characterization of singularities with lipschitz exponents is reviewed theorems that estimate local lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed it is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their lipschitz exponents the wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately the local frequency of such oscillations is measured from the wavelet transform modulus maxima it has been shown numerically that one and two dimensional signals can be reconstructed with a good approximation from the local maxima of their wavelet transform modulus as an application an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales in two dimensions the wavelet transform maxima indicate the location of edges in images

on the selection of 2d krawtchouk moments for face recognition sparse representation of images using orthogonal two dimensional krawtchouk moments 2d kcms for face recognition is motivated by their ability to capture region based higher order hidden nonlinear structures from discrete coordinates of finitely supported images and the invariance of affine transformations of these moments to common geometric distortions this paper presents the effectiveness of selecting the discriminatory set of kcms as the global and local face features as opposed to traditional features obtained from heuristic choice of fixed order moments or projection of the moments for recognizing an identity the selection of significantly sparse 2d kcm based features according to the proposed approach results in highly efficient face recognition method as compared to the other methods that use orthogonal moments such as the 2d zernike 2d tchebichef or 2d gaussian hermite experiments on challenging databases viz frgc and ck auc and comparisons with the well established projection texture and moment based methods indicate superior recognition performance in terms of mean accuracy and robustness of the proposed holistic or hybrid type discriminative kcm based method especially when sample sizes are small and the intraclass faces have significant variations due to expressions highlightshybrid type face recognition using discriminative selection of krawtchouk moments a comparative study of different moment based discriminative face features experiments on two challenging databases show superiority of the proposed selection fisher scoring is preferable to lda projection for moment based face recognition effective facial parts are identified for recognition of expression variant faces

on the reconstruction aspects of moment descriptors the problem of reconstruction of an image from discrete and noisy data by the method of moments is examined the set of orthogonal moments based on legendre polynomials is employed a general class of signal dependent noise models is taken into account an asymptotic expansion for the global reconstruction error is established this reveals mutual relationships between a number of moments the image smoothness sampling rate and noise model characteristics the problem of an automatic data driven section of an optimal number of moments is studied this is accomplished with the help of cross validation techniques

orthogonal moment operators for subpixel edge detection abstract a new approach to detect step edges with subpixel accuracy is presented the proposed approach is based on a set of orthogonal complex moments of the image known as zernike moments an ideal two dimensional 2d step edge is modeled in terms of four parameters the background gray level the step size the distance of the edge from the center of the mask and the orientation of the edge discrete zernike moments are used to obtain a total of three complex masks to compute all the edge parameters for subpixel detection for pixel level edge detection only two masks one real and one complex are required the theoretical analysis of the influence of noise on the location and the orientation of an edge is presented this analysis reveals that the accuracy of the proposed approach is virtually unaffected by the additive noise the technique is effective in detecting both the pixel level and subpixel level edges experimental results are presented to demonstrate the efficacy of the proposed technique

quaternion polar harmonic fourier moments for color images abstract this paper proposes quaternion polar harmonic fourier moments qphfm for color image processing and analyzes the properties of qphfm after extending chebyshev fourier moments chfm to quaternion chebyshev fourier moments qchfm comparison experiments including image reconstruction and color image object recognition on the performance of qphfm and quaternion zernike moments qzm quaternion pseudo zernike moments qpzm quaternion orthogonal fourier mellin moments qofmm qchfm and quaternion radial harmonic fourier moments qrhfm are carried out experimental results show qphfm can achieve an ideal performance in image reconstruction and invariant object recognition in noise free and noisy conditions in addition this paper discusses the importance of phase information of quaternion orthogonal moments in image reconstruction

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 coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

fast computation of geometric moments using a symmetric kernel this paper presents a novel set of geometric moments with symmetric kernel sgm obtained using an appropriate transformation of image coordinates by using this image transformation the computational complexity of geometric moments gm is reduced significantly through the embedded symmetry and separability properties in addition it minimizes the numerical instability problem that occurs in high order gm computation the novelty of the method proposed in this paper lies in the transformation of gm kernel from interval 0 to interval 1 1 the transformed gm monomials are symmetry at the origin of principal cartesian coordinate axes and hence possess symmetrical property the computational complexity of sgm is reduced significantly from order o n 4 using the original form of computation to order o n 3 for the proposed symmetry separable approach experimental results show that the percentage of reduction in computation time of the proposed sgm over the original gm is very significant at about 75 0 and 50 0 for square and non square images respectively furthermore the invariant properties of translation scaling and rotation in hu s moment invariants are maintained the advantages of applying sgm over gm in zernike moments computation in terms of efficient representation and computation have been shown through experimental results

numerical stability of fast computation algorithms of zernike moments abstract a detailed comparative study of the numerical stability of the recursive algorithms widely used to calculate the zernike moments of an image is presented in this paper while many papers introducing fast algorithms for the computation of zernike moments have been presented in the literature there is not any work studying the numerical behaviour of these methods these algorithms have been in the past compared to each other only according to their computational complexity without been given the appropriate attention as far as their numerical stability is concerned being the most significant part of the algorithms reliability the present contribution attempts to fill this gap in the literature since it mainly demonstrates that the usefulness of a recursive algorithm is defined not only by its low computational complexity but most of all by its numerical robustness this paper exhaustively compares some well known recursive algorithms for the computation of zernike moments and sets the appropriate conditions in which each algorithm may fall in an unstable state the experiments show that any of these algorithms can be unstable under some conditions and thus the need to develop more stable algorithms is of major importance

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

a fully integrated noise robust strategy for the identification of constitutive laws from digital images constitutive parameter identification has been greatly improved by the achievement of full field measurements in this context noise sensitivity has been shown to be of great importance it is crucial to incorporate noise sensitivity minimization in the design of robust identification procedures in this paper we investigate noise sensitivity reduction techniques for constitutive parameter identification based on finite element model updating after examining the existing strategies we propose a single step algorithm based on a mixed optical mechanical cost function the key point of this novel procedure is that no boundary conditions are needed a first example on a real case illustrates the advantages of the proposed methodology in terms of noise sensitivity a second example shows its capabilities to identify a non linear consitutive law copyright 2010 john wiley sons ltd

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

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

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

image analysis by generalized chebyshev fourier and generalized pseudo jacobi fourier moments in this paper we present two new sets named the generalized chebyshev fourier radial polynomials and the generalized pseudo jacobi fourier radial polynomials which are orthogonal over the unit circle these generalized radial polynomials are then scaled to define two new types of continuous orthogonal moments which are invariant to rotation the classical chebyshev fourier and pseudo jacobi fourier moments are the particular cases of the proposed moments with parameter 0 the relationships among the proposed two generalized radial polynomials and jacobi polynomials shift jacobi polynomials and the hypergeometric functions are derived in detail and some interesting properties are discussed two recursive methods are developed for computing radial polynomials so that it is possible to improve computation speed and to avoid numerical instability simulation results are provided to validate the proposed moment functions and to compare their performance with previous works highlightspaper presents two generalized radial polynomials that are orthogonal over the unit circle paper constructs two new generalized descriptors using the scaled radial polynomials two recursive strategies for the computation of proposed radial polynomials are presented the proposed polynomials are related to jacobi shift jacobi polynomials and hypergeometric functions the distribution of zeroes of the proposed polynomials can be controlled by free parameter

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

dynamic displacement field reconstruction through a limited set of measurements application to plates abstract the paper presents a procedure for the identification of the full field dynamic response of a structure from a limited set of experimental measurements an iterative technique based on modal decomposition maps the displacement field of the vibrating structure by using experimental data in conjunction with the numerical model of the considered structure algebraic relationships between experimental measurements and equivalent modal loads allow the identification of the full field dynamic response from few experimental data this procedure is detailed for a plate structure subjected to a harmonic concentrated load

a numerical recipe for accurate image reconstruction from discrete orthogonal moments recursive procedures used for sequential calculations of polynomial basis coefficients in discrete orthogonal moments produce unreliable results for high moment orders as a result of error accumulation this paper demonstrates accurate reconstruction of arbitrary size images using full order orders as large as the image size tchebichef and krawtchouk moments by calculating polynomial coefficients directly from their definition formulas in hypergeometric functions and by creating lookup tables of these coefficients off line an arbitrary precision calculator is used to achieve greater numerical range and precision than is possible with software using standard 64 bit ieee floating point arithmetic this reconstruction scheme is content and noise independent

moment based local image watermarking via genetic optimization a totally optimized image watermarking methodology that manages to enhance its local behaviour by applying the krawtchouk moments is presented through this paper the introduced technique is making use of a simple genetic algorithm in order to optimize the set of parameters that significantly influences the locality properties alongside with the overall performance of the watermarking procedure herein the watermarking process is tackled as an optimization procedure in this context the appropriate set of configuration parameters is being searched for ensuring high quality watermarked images and low bit error rates at the extraction stage for this purpose several traditional and newly introduced image quality measures are used in order to quantify the influence of the examined set of parameters as far as the quality of the watermarked image and the accuracy of the extracted watermark are concerned the proposed method produces watermarked images of high quality and ensures high detection rates under several non geometric attacks by using less prior knowledge at the detector s side extensive experiments have shown that by handling the watermarking process as an optimization problem more robust and accurate watermarking schemes can be derived

image analysis by fractional order orthogonal moments orthogonal moments play an important role in image analysis and other similar applications however existing orthogonal moments are restricted to integer order and little investigation of non integer order orthogonal moments has been conducted to date in this paper a general framework of real order orthogonal moments also known as fractional order orthogonal moments is proposed in this general framework fractional order orthogonal moments can be defined in cartesian and polar coordinate systems shifted legendre polynomials are implemented in this paper to investigate the properties of fractional order orthogonal moments a series of experiments are performed which demonstrate that fractional order orthogonal moments are not only capable of region of interest roi feature extraction but also have potential for image reconstruction and face recognition and have high noise robustness in invariant image recognition

image analysis by modified legendre moments in the paper a new set of orthogonal moments based on the modified legendre polynomials is introduced three properties of the modified legendre polynomials which are orthogonality orthogonal invariance and the characteristic that an interval on the center of 1 1 covers more zeros than do that on the edge of 1 1 are discussed detailedly the orthogonality of the proposed moments ensures minimal information redundancy in a moment set the orthogonal invariance of the proposed polynomials makes the proposed moments have the property of translation invariance and the third property ensures that the modified legendre moments have superior feature representation capabilities over legendre moments in analyzing small images for small images the description by the modified legendre moments is better than that by the legendre moments and the chebyshev moments in terms of image reconstruction errors theoretical and experimental measures of performance are carried out to investigate the image representation capabilities of the proposed moments for images and noisy images the computational aspects of the moments using recurrence integral symmetry and translation invariance are also discussed experimental results are shown

shape features and finite element model updating from full field strain data finite element model updating is an inverse problem based on measured structural outputs in this case maximum principal strain measured using digital image correlation full field responses in the form of strain maps contain valuable information for model updating but within large volumes of highly redundant data in this paper shape descriptors based on zernike polynomials having the properties of orthogonality and rotational invariance are shown to be powerful decomposition kernels for defining the shape or map of the strain distribution a square plate with a circular hole subject to a uniaxial tensile load is considered and effective shape features are constructed using a set of modified zernike polynomials the modification includes the application of a decaying weighting function to the zernike polynomials so that high strain magnitudes around the hole are well represented the gram schmidt process is then used to ensure orthogonality for the obtained decomposition kernels over the domain of the specimen i e excluding the hole results show that only a very small number of zernike moment descriptors are necessary and sufficient to represent the full field data the onset of yielding may be quantified using the descriptors furthermore model updating of nonlinear elasto plastic material properties is carried out using the zernike moment descriptors derived from full field strain measurements

moving finite elements i we present new and general numerical methods for dealing with problems whose solutions develop sharp transition layers or near shocks these methods allow many nodes automatically to concentrate in the critical regions and move with them for clarity of exposition we concentrate on the space of piecewise linear functions with movable nodes with burgers equation as our test equation but the generalization to much more general spaces and equations including even certain previous moving vorticity blobs of the first author and s doss for the navier stokes equations becomes clear in this paper we present the theoretical and computational details of our scheme along with computational trial runs for burgers equation showing that the nodes do concentrate sharply and move with the shocks as desired the conclusiveness of these preliminary numerical trials is marred somewhat by the fact that we never successfully debugged a newton s method for our implicit stiff ode solver and were thus limited to ver

two dimensional unsteady solidification problem calculated by using the boundary fitted coordinate system abstract using the boundary fitted coordinate system we calculate the unsteady solidification problem the model for calculation is constructed of cylindrical coordinates with a symmetrical axis the gauss seidel scheme with second order accuracy of time and space is used as a solution method for the governing equations and the boundary fitted coordinate system enables us to calculate the moving interface easily the numerical results are compared with the analysis of a one dimensional unsteady solidification problem and are in good agreement with it from the calculations we find a simple form of the crystal growth rate

finite dimensional calculus we discuss topics related to finite dimensional calculus in the context of finite dimensional quantum mechanics the truncated heisenberg weyl algebra is called a taa algebra after tekin aydin and arik who formulated it in terms of orthofermions it is shown how to use a matrix approach to implement analytic representations of the heisenberg weyl algebra in univariate and multivariate settings we provide examples for the univariate case krawtchouk polynomials are presented in detail including a review of krawtchouk polynomials that illustrates some curious properties of the heisenberg weyl algebra as well as presenting an approach to computing krawtchouk expansions from a mathematical perspective we are providing indications as to how to implement infinite terms rota s finite operator calculus

efficient legendre moment computation for grey level images legendre orthogonal moments have been widely used in the field of image analysis because their computation by a direct method is very time expensive recent efforts have been devoted to the reduction of computational complexity nevertheless the existing algorithms are mainly focused on binary images we propose here a new fast method for computing the legendre moments which is not only suitable for binary images but also for grey level images we first establish a recurrence formula of one dimensional 1d legendre moments by using the recursive property of legendre polynomials as a result the 1d legendre moments of order p l p l p 0 can be expressed as a linear combination of l p 1 1 and l p 2 0 based on this relationship the 1d legendre moments l p 0 can thus be obtained from the arrays of l 1 a and l 0 a where a is an integer number less than p to further decrease the computation complexity an algorithm in which no multiplication is required is used to compute these quantities the method is then extended to the calculation of the two dimensional legendre moments l p q we show that the proposed method is more efficient than the direct method

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

on the accuracy of zernike moments for image analysis we give a detailed analysis of the accuracy of zernike moments in terms of their discretization errors and the reconstruction power it is found that there is an inherent limitation in the precision of computing the zernike moments due to the geometric nature of a circular domain this is explained by relating the accuracy issue to a celebrated problem in analytic number theory of evaluating the lattice points within a circle

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

image reconstruction from continuous gaussian hermite moments implemented by discrete algorithm the problem of image reconstruction from its statistical moments is particularly interesting to researchers in the domain of image processing and pattern recognition compared to geometric moments the orthogonal moments offer the ability to recover much more easily the image due to their orthogonality which allows reducing greatly the complexity of computation in the phase of reconstruction since the 1980s various orthogonal moments such as legendre moments zernike moments and discrete tchebichef moments have been introduced early or late to image reconstruction in this paper another set of orthonormal moments the gaussian hermite moments based on hermite polynomials modulated by a gaussian envelope is proposed to be used for image reconstruction especially the paper s focus is on the determination of the optimal scale parameter and the improvement of the reconstruction result by a post processing which make gaussian hermite moments be useful and comparable with other moments for image reconstruction the algorithms for computing the values of the basis functions moment computation and image reconstruction are also given in the paper as well as a brief discussion on the computational complexity the experimental results and error analysis by comparison with other moments show a good performance of this new approach

residual minimization least squares method for inverse heat conduction abstract a numerical method is systematically developed for resolving an inverse heat conduction problem in the presence of noisy discrete data this paper illustrates the effect of imposing constraints on the unknown function of interest a volterra integral equation of the first kind is derived and used as the starting point for residual minimization least squares methodology symbolic manipulation is exploited for purposes of augmenting the computational methodology preliminary indications suggest that the imposition of physical constraints on the system drastically reduces the level of mathematical sophistication needed for accurately approximating the unknown function of interest these constraints are actually available in many design studies or from models which are derived by physical processes

the adjoint method for an inverse design problem in the directional solidification of binary alloys this paper presents a systematic procedure based on the adjoint method for solving a class of inverse directional alloy solidification design problems in which a desired growth velocityvfis achieved under stable growth conditions to the best of our knowledge this is the first time that a continuum adjoint formulation is proposed for the solution of an inverse problem with simultaneous heat and mass transfer thermo solutal convection and phase change in this paper the interfacial stability is considered to imply a sharp solid liquid freezing interface this condition is enforced using the constitutional undercooling criterion in the form of an inequality constraint between the thermal and solute concentration gradients gandgc respectively at the freezing front the main unknowns of the design problem are the heating and or cooling boundary conditions on the mold walls the inverse design problem is formulated as a functional optimization problem the cost functional is defined by the square of thel2norm of the deviation of the freezing interface temperature from the temperature corresponding to thermodynamic equilibrium a continuum adjoint system is derived to calculate the adjoint temperature concentration and velocity fields such that the gradient of the cost functional can be expressed analytically the cost functional minimization process is realized by the conjugate gradient method via the finite element method solutions of the continuum direct sensitivity and adjoint problems the developed formulation is demonstrated with an example of designing the directional solidification of a binary aqueous solution in a rectangular mold such that a stable vertical interface advances from left to right with a desired growth velocity

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

vibration mode shape recognition using image processing abstract currently the most widely used method for comparing mode shapes from finite elements and experimental measurements is the modal assurance criterion mac which can be interpreted as the cosine of the angle between the numerical and measured eigenvectors however the eigenvectors only contain the displacement of discrete coordinates so that the mac index carries no explicit information on shape features new techniques based upon the well developed philosophies of image processing ip and pattern recognition pr are considered in this paper the zernike moment descriptor zmd fourier descriptor fd and wavelet descriptor wd are the most popular shape descriptors due to their outstanding properties in ip and pr these include 1 for the zmd rotational invariance expression and computing efficiency ease of reconstruction and robustness to noise 2 for the fd separation of the global shape and shape details by low and high frequency components respectively invariance under geometric transformation 3 for the wd multi scale representation and local feature detection once a shape descriptor has been adopted the comparison of mode shapes is transformed to a comparison of multidimensional shape feature vectors deterministic and statistical methods are presented the deterministic problem of measuring the degree of similarity between two mode shapes possibly one from a vibration test and the other from a finite element model may be carried out using pearson s correlation similar shape feature vectors may be arranged in clusters separated by euclidian distances in the feature space in the statistical analysis we are typically concerned with the classification of a test mode shape according to clusters of shape feature vectors obtained from a randomised finite element model the dimension of the statistical problem may often be reduced by principal component analysis then in addition to the euclidian distance the mahalanobis distance defining the separation of the test point from the cluster in terms of its standard deviation becomes an important measure bayesian decision theory may be applied to formally minimise the risk of misclassification of the test shape feature vector in this paper the zmd is applied to the problem of mode shape recognition for a circular plate results show that the zmd has considerable advantages over the traditional mac index when identifying the cyclically symmetric mode shapes that occur in axisymmetric structures at identical frequencies mode shape recognition of rectangular plates is carried out by the fd also the wd is applied to the problem of recognising the mode shapes in the thin and thick regions of a plate with different thicknesses it shows the benefit of using the wd to identify mode shapes having both local and global components the comparison and classification of mode shapes using ip and pr provides a toolkit to complement the conventional mac approach the selection of a particular shape descriptor and classification method will depend upon the problem in hand and the experience of the analyst

image representation using separable two dimensional continuous and discrete orthogonal moments this paper addresses bivariate orthogonal polynomials which are a tensor product of two different orthogonal polynomials in one variable these bivariate orthogonal polynomials are used to define several new types of continuous and discrete orthogonal moments some elementary properties of the proposed continuous chebyshev gegenbauer moments cgm gegenbauer legendre moments glm and chebyshev legendre moments clm as well as the discrete tchebichef krawtchouk moments tkm tchebichef hahn moments thm krawtchouk hahn moments khm are presented we also detail the application of the corresponding moments describing the noise free and noisy images specifically the local information of an image can be flexibly emphasized by adjusting parameters in bivariate orthogonal polynomials the global extraction capability is also demonstrated by reconstructing an image using these bivariate polynomials as the kernels for a reversible image transform comparisons with the known moments are performed and the results show that the proposed moments are useful in the field of image analysis furthermore the study investigates invariant pattern recognition using the proposed three moment invariants that are independent of rotation scale and translation and an example is given of using the proposed moment invariants as pattern features for a texture classification application

a 3d shape retrieval framework supporting multimodal queries this paper presents a unified framework for 3d shape retrieval the method supports multimodal queries 2d images sketches 3d objects by introducing a novel view based approach able to handle the different types of multimedia data more specifically a set of 2d images multi views are automatically generated from a 3d object by taking views from uniformly distributed viewpoints for each image a set of 2d rotation invariant shape descriptors is produced the global shape similarity between two 3d models is achieved by applying a novel matching scheme which effectively combines the information extracted from the multi view representation the experimental results prove that the proposed method demonstrates superior performance over other well known state of the art approaches

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

reconstruction of tomographic images from limited range projections using discrete radon transform and tchebichef moments this paper presents an image reconstruction method for x ray tomography from limited range projections it makes use of the discrete radon transform and a set of discrete orthogonal tchebichef polynomials to define the projection moments and the image moments by establishing the relationship between these two sets of moments we show how to estimate the unknown projections from known projections in order to improve the image reconstruction simulation results are provided in order to validate the method and to compare its performance with some existing algorithms

unified approach to simulation on deforming elements with application to phase change problems abstract several different approaches to simulation on deforming finite elements are shown to generate the same weighted residuals formulation for the evolution of the dependent variables control of node motion by means of mesh stretching in two dimensions is illustrated in the context of phase change problems simulation of problems with large phase boundary excursions shows good agreement with analytic solutions

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

finite element model updating from full field vibration measurement using digital image correlation abstract the comparison of structural responses e g natural frequencies and mode shapes between predictions and measurements is an important step in finite element fe model updating full field measurement techniques such as high speed cameras with digital image correlation dic algorithms provide detailed global displacement data it is necessary to compress huge amounts of full field data before implementing the comparison procedures image processing and pattern recognition techniques offer effective ways of doing this image decomposition using integral transformation is one of the most common procedures it is found that appropriate selection or construction of the transformation kernels usually generates succinct and effective shape feature terms thus the discrepancies between the geometric mode shapes may be assessed by using distance measures between the shape feature vectors in the present study vibration mode shapes of a composite panel are measured by a dic system and predicted by a fe model succinct and effective shape features of the full field mode shapes were obtained by employing the tchebichef moment descriptor mode shape discrepancies are clearly indicated by the resultant tchebichef features the fe model was then modified and updated results show that including only the shape features results in a better updated model than when natural frequencies only are used the most improved model was obtained when both natural frequencies and shape features are included in the updating routine

fast computation of krawtchouk moments the paper describes the calculation of the krawtchouk moments kms from an image which is a computationally demanding task we present two original methods that use the outputs of cascaded digital filters in deriving kms the first approach uses the digital filter outputs to form geometric moments gms and the kms are obtained via gms the second method uses a direct relationship to obtain kms from the digital filter outputs this is possible thanks to the formulation of krawtchouk polynomials in terms of binomial functions which are equivalent to the digital filter outputs in this study the performance of the proposed techniques is compared with other existing methods of kms calculation the experimental study shows that the first and the second proposed techniques perform 57 and 87 faster than the recurrence method for a real image of a size 128 128 pixels which performs a significant improvement

model updating using uncorrelated modes abstract fe model updating techniques are used to update dynamic fe models of structures in the light of modal test data iterative methods of model updating that update a set of chosen parameters of the model so as to reduce the difference between the natural frequencies and the mode shapes of the fe model and the corresponding quantities obtained through a modal test on the structure are probably the most widely used methods once experimental modal data has been identified a necessary prior step before updating can be carried out is that of establishing the correspondence between the fe model modes and the experimentally identified modes it is however experienced that many a times a situation is encountered where not all of the modes identified through an experiment can be correlated with certainty with those predicted by the fe model and some experimental modes may be left uncorrelated there could be several reasons for this lack of correlation as identified in the paper but the consequence is that such uncorrelated modes cannot be used in fe model updating using existing iterative methods based on modal data even when they form valid known pieces of information about the structure this is a disadvantage since it reduces the quantity of experimental data available for model updating and hence makes the updating process less effective in yielding an updated model that is a closer representation of the structure this paper identifies this as a limitation of the existing iterative methods of model updating based on modal data and puts forward a notion of fe model updating using uncorrelated modes the paper proposes a solution to overcome this limitation in the form of a new method of fe model updating that accepts both correlated as well as uncorrelated modes for updating this is in contrast to all the current iterative modal data based methods of model updating that are based on the assumption of availability of correlated mode pairs and hence cannot use uncorrelated mode shapes and corresponding natural frequencies in the updating process formulation of the proposed method is described followed by a couple of numerical examples based on a beam structure to validate the method the robustness of the method in the presence of simulated noise is also studied another numerical example of a more complex f shape structure is also presented the method is then validated though an experimental study the proposed method is found to successfully update an fe model yielding correct estimates of the updating parameters in the presence of uncorrelated modes

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

image reconstruction using various discrete orthogonal polynomials in comparison with dct abstract the energy compactness of various discrete orthogonal polynomials used as the basis functions in an image reconstruction kernel is being studied in this paper specifically the discrete cosine transform dct tchebichef krawtchouk hahn and poisson charlier these polynomials were being tested with a variety of grayscale images with and without block segmentation as a result we concluded that dct is still the best among all for smooth images and tchebichef is the best for rougher images krawtchouk would outperform tchebichef sometimes but hahn and poisson charlier performed badly overall moreover the weighted form of krawtchouk and hahn might be slightly superior to their original form but they create undesired blocking effects in block segmentation image reconstruction

geometrically invariant image watermarking using polar harmonic transforms this paper presents an invariant image watermarking scheme by introducing the polar harmonic transform pht which is a recently developed orthogonal moment method similar to zernike moment zm and pseudo zernike moment pzm approaches pht is defined on a circular domain the magnitudes of phts are invariant to image rotation and scaling furthermore the phts are free of numerical instability so they are more suitable for watermarking in this paper the invariant properties of phts are investigated during embedding a subset of the accurate phts are modified according to the binary watermark sequence then a compensation image is formatted by reconstructing the modified pht vector the final watermarked image is obtained by adding the compensation image to the original image in the decoder the watermark can be retrieved from the magnitudes of the phts directly experimental results illustrate that the proposed scheme outperforms zm pzm based schemes in terms of embedding capacity and watermark robustness and is also robust to both geometric and signal processing based attacks

a functional optimization formulation and implementation of an inverse natural convection problem abstract a formulation and a fem implementation for the solution of an ill posed inverse design natural convection problem is proposed in particular we consider an incompressible viscous liquid material occupying a given domain where convection is driven by buoyancy thermal boundary conditions are only prescribed in the part h 0 of the boundary in addition the temperature distribution is also prescribed in the part i of the boundary h 1 where the heat flux is known i e i is a boundary with over specified thermal boundary conditions the inverse convection problem is posed as an optimization problem in l 2 i 0 t max for the calculation of the boundary heat flux q o x t with x t h 0 0 t max the optimization scheme minimizes the discrepancy m x t x t q o l 2 1 0 t max between the temperature x t q o calculated from the solution of a direct problem for each flux q 0 and the measured or desired temperature m x t at the boundary i the gradient of the cost functional is obtained from the adjoint fields the adjoint problem is defined from the sensitivity operators obtained by linearization of the equations governing the direct problem the conjugate gradient method is employed to perform the optimization process the fem is used for the calculation of the direct adjoint and sensitivity thermal and fluid flow fields finally the method is demonstrated with the solution of some two dimensional inverse problems with known solutions the numerical results are discussed and future work with potential applications is addressed

quaternion moment and its invariants for color object classification moment invariants are important shape descriptors in computer vision in this study we propose new sets of quatemion moment descriptors for color image they are constructed in the quaternion framework and are an extension of complex moment invariants for grayscale images this is a useful tool in color image processing and color object recognition tasks that require the similarity invariance the advantage of the proposed quatemion moment invariants is that they can not only process color image in a holistic manner but also grayscale one in addition the computational complexity of the proposed method is much lower than the quaternion zernike moments defined in the polar coordinates an example of using the quaternion moment invariants as pattern features for a color object classification application is given theoretical and experimental results show that the proposed descriptors perform better than the other competing moment based methods c 2014 elsevier inc all rights reserved

orthogonal moment features for use with parametric and non parametric classifiers this research examines a variety of approaches for using two dimensional orthogonal polynomials for the recognition of handwritten arabic numerals it also makes use of parametric and non parametric statistical and neural network classifiers polynomials including legendre zernike and pseudo zernike are used to generate moment based features which are invariant to location size and optionally rotation an efficient method for computing the moments via geometric moments is presented a side effect of this method also yields scale invariance a new approach to location invariance using a minimum bounding circle is presented and a detailed analysis of the rotational properties of the moments is given data partitioning tests are performed to evaluate the various feature types and classifiers for rotational invariant character recognition the highest percentage of correctly classified characters was 91 7 and for non rotational invariant recognition it was 97 6 this compares with a previous effort using the same data and test conditions of 94 8 the techniques developed here should also be applicable to other areas of shape recognition

on the solution of an ill posed design solidification problem using minimization techniques in finite and infinite dimensional function spaces this paper provides a comparative study of two alternative methodologies for the solution of an inverse design solidification problem it is the one dimensional solidification problem of calculating the boundary heat flux history that achieves a desired freezing front velocity and desired heat fluxes at the freezing front the front velocity h t and flux history qms t on the solid side of the front control the obtained cast structure as such the potential applications of the proposed methods to the control of casting processes are enormous the first technique utilizes a finite dimensional approximation of the unknown boundary heat flux function q0 t the second technique uses the adjoint method to calculate in l2 the derivative of the cost functional tm t h t t q0 that expresses the square error between the calculated t h t t q0 and the given freezing front temperature tm both steepest descent sdm and conjugate gradient methods cgm are examined a front tracking fem technique is used for the discretization of the state space a detailed numerical analysis of the space and time discretization of the parameter and state spaces of the effect of the end condition of the adjoint problem and of other parameters in the solution are examined

pole assignment and controllability subspaces in descriptor systems the development by wonham and co workers of the concept of a controllability subspace and elucidation of its relationship with pole assignment have profoundly influenced the geometric control theory of state space systems this paper develops the corresponding theory for linear systems described by a mixture of algebraic and differential equations the proofs given use eigenstructure assignment and include necessary and sufficient conditions for the assignability of a given eigenstructure including the so called infinite eigenstructure this approach provides some simplifications of the state space theory such as an intrinsic characterization of controllability subspaces and a very general result concerning finite pole assignment in descriptor systems throughout care is taken to ensure the existence and uniqueness of classical solutions of the underlying differential equations which cannot be taken for granted

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed