pairwise rotation invariant co occurrence local binary pattern designing effective features is a fundamental problem in computer vision however it is usually difficult to achieve a great tradeoff between discriminative power and robustness previous works shown that spatial co occurrence can boost the discriminative power of features however the current existing co occurrence features are taking few considerations to the robustness and hence suffering from sensitivity to geometric and photometric variations in this work we study the transform invariance ti of co occurrence features concretely we formally introduce a pairwise transform invariance pti principle and then propose a novel pairwise rotation invariant co occurrence local binary pattern pricolbp feature and further extend it to incorporate multi scale multi orientation and multi channel information different from other lbp variants pricolbp can not only capture the spatial context co occurrence information effectively but also possess rotation invariance we evaluate pricolbp comprehensively on nine benchmark data sets from five different perspectives e g encoding strategy rotation invariance the number of templates speed and discriminative power compared to other lbp variants furthermore we apply pricolbp to six different but related applications texture material flower leaf food and scene classification and demonstrate that pricolbp is efficient effective and of a well balanced tradeoff between the discriminative power and robustness

a new robust color image watermarking using local quaternion exponent moments abstract desynchronization attacks that cause displacement between embedding and detection are usually difficult for watermark to survive it is a challenging work to design a robust image watermarking scheme against desynchronization attacks especially for color host images in this paper we propose a robust color image watermarking scheme based on local quaternion exponent moments the proposed scheme has the following advantages 1 the stable and uniform color image feature points are extracted by the new color image detector in which the probability density gradient and color invariance model are used 2 the affine invariant local feature regions are constructed adaptively according to the variation of local probability density and 3 the effective quaternion exponent moments are derived and introduced to embed watermark in the color image which consider the correlation between different color channels experiments are carried out on a color image set of 100 images collected from internet and the preliminary results show that the proposed color image watermarking is not only invisible and robust against common image processing operations such as sharpening noise adding and jpeg compression but also robust against the desynchronization attacks

errata and comments on orthogonal moments based on exponent functions in this paper we show that the exponent fourier moments efms as defined in ref 1 are imprecise and the radial function of efms performs numerically unstable at last an improvement of exponent fourier moments iefms is given for avoiding the above problems experimental results also show the superiority of the proposed methods the imprecisions of exponent fourier moments efms are pointed out an improvement of exponent fourier moments iefms is proposed the iefms avoid the imprecisions of efms and performs much better than efms

mdghm surf this paper proposes a novel family of local feature descriptors a variant of the speed up robust features surf descriptor which is capable of demonstrably better performance the conventional surf descriptor is an efficient implementation of the sift descriptor although the surf descriptor can represent the nature of the underlying image pattern it is still sensitive to more complicated deformations such as large viewpoint and rotation changes to solve this problem our family of descriptors called mdghm surf is based on the modified discrete gaussian hermite moment mdghm which devises a movable mask to represent the local feature information of non square images whereas conventional surf uses first order derivatives mdghm surf uses mdghm which offers more feature information than first order derivative based local descriptors such as surf and sift consequently by redefining the conventional surf descriptor using mdghm mdghm surf can extract more distinctive features than conventional surf the results of evaluations conducted with six types of deformations indicate that our proposed method outperforms the matching accuracy of other surf related algorithms we propose a novel family of the surf descriptor to solve the sensitivity of the surf we redefine the surf using mdghm mdghm surf the mdghm offers more feature information than the first order derivative based surf the evaluations are conducted with six types of deformations and panoramic image generation the results indicate that our method outperforms other surf related algorithms

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

additive functional regression for densities as responses we propose and investigate additive density regression a novel additive functional regression model for situations where the responses are random distributions that can be viewed as random densiti

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

the fractional fourier transform and time frequency representations the functional fourier transform frft which is a generalization of the classical fourier transform was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community to which it may however be potentially useful the frft depends on a parameter spl alpha and can be interpreted as a rotation by an angle spl alpha in the time frequency plane an frft with spl alpha spl pi 2 corresponds to the classical fourier transform and an frft with spl alpha 0 corresponds to the identity operator on the other hand the angles of successively performed frfts simply add up as do the angles of successive rotations the frft of a signal can also be interpreted as a decomposition of the signal in terms of chirps the authors briefly introduce the frft and a number of its properties and then present some new results the interpretation as a rotation in the time frequency plane and the frft s relationships with time frequency representations such as the wigner distribution the ambiguity function the short time fourier transform and the spectrogram these relationships have a very simple and natural form and support the frft s interpretation as a rotation operator examples of frfts of some simple signals are given an example of the application of the frft is also given

reference values obtained by kernel based estimation of quantile regressions in this paper we study the problem of estimating non parametrically a quantile regression curve as it applies to computing reference values we propose an automatic procedure that uses a symmetrized nearest neighbor kernel estimator of conditional distributions we also discuss ways of measuring the dispersion of quantile regression estimator one is based on the asymptotic distribution of such quantiles while the other relies on the bootstrap method the results of a small simulation study show that the methods of the paper perform rather well even in a situation where a good parametric solution is available as an example we analyze a small part of a data set that was collected to establish reference values for blood velocity in different parts of the umbilical cord of human fetuse as they grow toward birth

projective moment invariants the paper is devoted to the moment invariants with respect to projective transform it has been a common belief that such invariants do not exist we show that projective moment invariants exist in a form of infinite series containing moments with positive as well as negative indices

fractional cosine sine and hartley transforms in previous papers the fourier transform ft has been generalized into the fractional fourier transform frft the linear canonical transform lct and the simplified fractional fourier transform sfrft because the cosine sine and hartley transforms are very similar to the ft it is reasonable to think they can also be generalized by the similar way we introduce several new transforms they are all the generalization of the cosine sine or hartley transform we first derive the fractional cosine sine and hartley transforms frct frst frht they are analogous to the frft then we derive the canonical cosine and sine transforms cct cst they are analogous to the lct we also derive the simplified fractional cosine sine and hartley transforms sfrct sfrst sfrht they are analogous to the sfrft and have the advantage of real input real output we also discuss the properties digital implementation and applications e g the applications for filter design and space variant pattern recognition of these transforms the transforms introduced in this paper are very efficient for digital implementation we can just use one half or one fourth of the real multiplications required for the frft and lct to implement them when we want to process even odd or pure real imaginary functions we can use these transforms instead of the frft and lct besides we also show that the frct frst cct cst and sfrct sfrst are also useful for the one sided t spl isin 0 spl infin signal processing

order preserving nonparametric regression with applications to conditional distribution and quantile function estimation in some regression problems we observe a response yti to level t of a treatment applied to an individual with level xi of a given characteristic where it has been established that response is monotone increasing in the level of the treatment a related problem arises when estimating conditional distributions where the raw data are typically independent and identically distributed pairs xi zi and yti denotes the proportion of zi s that do not exceed t we expect the regression means gt x e yti xi x to enjoy the same order relation as the responses that is gt gs whenever s t this requirement is necessary to obtain bona fide conditional distribution functions for example if we estimate gt by passing a linear smoother through each dataset t xi yti 1 i n then the order preserving property is guaranteed if and only if the smoother has nonnegative weights however in such cases the estimators generally have high levels of boundary bias on the other hand the order preser

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

quantile smoothing splines summary although nonparametric regression has traditionally focused on the estimation of conditional mean functions nonparametric estimation of conditional quantile functions is often of substantial practical interest we explore a class of quantile smoothing splines defined as solutions to

an adaptive composite quantile approach to dimension reduction sufficient dimension reduction li 1991 has long been a prominent issue in multivariate nonparametric regression analysis to uncover the central dimension reduction space we propose in this paper an adaptive composite quantile approach compared to existing methods 1 it requires minimal assumptions and is capable of revealing all dimension reduction directions 2 it is robust against outliers and 3 it is structure adaptive thus more efficient asymptotic results are proved and numerical examples are provided including a real data analysis

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

blur invariants constructed from arbitrary moments this paper deals with moment invariants with respect to image blurring it is mainly a reaction to the works of zhang and chen recently published in these transactions we present a general method on how to construct blur invariants from arbitrary moments and show that it is no longer necessary to separately derive the invariants for each polynomial basis we show how to discard dependent terms in blur invariants definition and discuss a proper implementation of the invariants in orthogonal bases using recurrent relations an example for legendre moments is given

a zernike moment phase based descriptor for local image representation and matching a local image descriptor robust to the common photometric transformations blur illumination noise and jpeg compression and geometric transformations rotation scaling translation and viewpoint is crucial to many image understanding and computer vision applications in this paper the representation and matching power of region descriptors are to be evaluated a common set of elliptical interest regions is used to evaluate the performance the elliptical regions are further normalized to be circular with a fixed size the normalized circular regions will become affine invariant up to a rotational ambiguity here a new distinctive image descriptor to represent the normalized region is proposed which primarily comprises the zernike moment zm phase information an accurate and robust estimation of the rotation angle between a pair of normalized regions is then described and used to measure the similarity between two matching regions the discriminative power of the new zm phase descriptor is compared with five major existing region descriptors sift gloh pca sift complex moments and steerable filters based on the precision recall criterion the experimental results involving more than 15 million region pairs indicate the proposed zm phase descriptor has generally speaking the best performance under the common photometric and geometric transformations both quantitative and qualitative analyses on the descriptor performances are given to account for the performance discrepancy first the key factor for its striking performance is due to the fact that the zm phase has accurate estimation accuracy of the rotation angle between two matching regions second the feature dimensionality and feature orthogonality also affect the descriptor performance third the zm phase is more robust under the nonuniform image intensity fluctuation finally a time complexity analysis is provided

mallows type bounded influence regression trimmed means abstract the influence functions of the regression trimmed mean estimators proposed by koenker and bassett 1978 and welsh 1987 are bounded in the dependent variable space but not in the independent variable space this article follows the approach of mallows 1973 1975 and modifies these estimators so that the resulting estimators have bounded influence functions the large sample behavior of these estimators is studied and it is shown that they have the same asymptotic distribution the small sample behaviors of the ordinary regression and bounded influence regression trimmed means are then investigated by means of a monte carlo study and by applying the estimators to water salinity data see ruppert and carroll 1980 based on these results we conclude that one can potentially gain much by using bounded influence regression trimmed means over ordinary regression trimmed means however there does not seem to be a clear choice between the koenker bassett and welsh versions

two stage rank estimation of quantile index models abstract this paper estimates a class of models which satisfy a monotonicity condition on the conditional quantile function of the response variable this class includes as a special case the monotonic transformation model with the error term satisfying a conditional quantile restriction thus allowing for very general forms of conditional heteroscedasticity a two stage approach is adopted to estimate the relevant parameters in the first stage the conditional quantile function is estimated nonparametrically by the local polynomial estimator discussed in chaudhuri journal of multivariate analysis 39 1991a 246 269 annals of statistics 19 1991b 760 777 and cavanagh 1996 preprint in the second stage the monotonicity of the quantile function is exploited to estimate the parameters of interest by maximizing a rank based objective function the proposed estimator is shown to have desirable asymptotic properties and can then also be used for dimensionality reduction or to estimate the unknown structural function in the context of a transformation model

discriminative common vectors for face recognition in face recognition tasks the dimension of the sample space is typically larger than the number of the samples in the training set as a consequence the within class scatter matrix is singular and the linear discriminant analysis lda method cannot be applied directly this problem is known as the small sample size problem in this paper we propose a new face recognition method called the discriminative common vector method based on a variation of fisher s linear discriminant analysis for the small sample size case two different algorithms are given to extract the discriminative common vectors representing each person in the training set of the face database one algorithm uses the within class scatter matrix of the samples in the training set while the other uses the subspace methods and the gram schmidt orthogonalization procedure to obtain the discriminative common vectors then the discriminative common vectors are used for classification of new faces the proposed method yields an optimal solution for maximizing the modified fisher s linear discriminant criterion given in the paper our test results show that the discriminative common vector method is superior to other methods in terms of recognition accuracy efficiency and numerical stability

efficient bias corrected nonparametric spectral estimation summary we consider estimation of a spectral density at a particular frequency a linear model is developed based on the local second order behaviour of kernel spectral estimates and a second stage estimate is derived from this model the estimate is shown to be asymptotically more efficient than the kernel estimate with the optimal but unknown bandwidth whenever the smoothing parameter is chosen so that it oversmooths the kernel estimate a small sample simulation study shows good characteristics of the second stage estimate practical implementation is discussed through examples

regression rank scores and regression quantiles we show that regression quantiles which could be computed as solutions of a linear programming problem and the solutions of the corresponding dual problem which we call the regression rank scores generalize the duality of order statistics and of ranks from the location to the linear model noting this fact we study the regression quantile and regression rank score processes in the heteroscedastic linear regression model obtaining some new estimators and interesting comparisons with existing estimators

discrete fractional wavelet transform and its application to multiple encryption the fractional wavelet transform is a useful mathematical transformation that generalizes the most prominent tool in signal and image processing namely wavelet transform by rotation of signals in the time frequency plane the definition of discrete fractional wavelet transform is not reported yet in the literature therefore a definition of the discrete fractional wavelet transform is consolidated by discretizing continuous fractional wavelet transform in the proposed work possible applications of the transform are in transient signal processing image analysis image transmission biometrics image compression etc in this paper image transmission is chosen as the primary application and hence a novel encryption scheme is proposed for securing multiple images during communication and transmission over insecure channel the proposed multiple image encryption scheme is consolidated by fractional wavelet transform and chaotic maps first all the images are encrypted followed by their sharing the sharing process is done considering numerical techniques by making the sharing process a system of linear equations experimental results and security analysis demonstrate the efficiency and robustness of the proposed primary application

unitary equivalence of one parameter groups of toeplitz and composition operators abstract the composition operators on h 2 whose symbols are hyperbolic automorphisms of the unit disk fixing 1 comprise a one parameter group and the analytic toeplitz operators coming from covering maps of annuli centered at the origin whose radii are reciprocals also form a one parameter group using the eigenvectors of the composition operators and of the adjoints of the toeplitz operators a direct unitary equivalence is found between the restrictions to z h 2 of the group of toeplitz operators and the group of adjoints of these composition operators on the other hand it is shown that there is not a unitary equivalence of the groups of toeplitz operators and the adjoints of the composition operators on the whole of h 2 but there is a similarity between them

estimating conditional quantiles at the root of a regression function the robbins monro process x n 1 x n c n y n is a standard stochastic approximation method for estimating the root theta of an unknown regression function there is a vast literature on the convergence properties of x n to theta in practice one is also interested in the conditional distribution of the system under the sequential control when the control is set at theta or near theta this problem appears to have received no attention in the literature we introduce an estimator using methods of nonparametric conditional quantile estimation and derive its asymptotic properties

orthogonal variant moments features in image analysis moments are statistical measures used to obtain relevant information about a certain object under study e g signals images or waveforms e g to describe the shape of an object to be recognized by a pattern recognition system invariant moments e g the hu invariant set are a special kind of these statistical measures designed to remain constant after some transformations such as object rotation scaling translation or image illumination changes in order to e g improve the reliability of a pattern recognition system the classical moment invariants methodology is based on the determination of a set of transformations or perturbations for which the system must remain unaltered although very well established the classical moment invariants theory has been mainly used for processing single static images i e snapshots and the use of image moments to analyze images sequences or video from a dynamic point of view has not been sufficiently explored and is a subject of much interest nowadays in this paper we propose the use of variant moments as an alternative to the classical approach this approach presents clear differences compared to the classical moment invariants approach that in specific domains have important advantages the difference between the classical invariant and the proposed variant approach is mainly but not solely conceptual invariants are sensitive to any image change or perturbation for which they are not invariant so any unexpected perturbation will affect the measurements i e is subject to uncertainty on the contrary a variant moment is designed to be sensitive to a specific perturbation i e to measure a transformation not to be invariant to it and thus if the specific perturbation occurs it will be measured hence any unexpected disturbance will not affect the objective of the measurement confronting thus uncertainty furthermore given the fact that the proposed variant moments are orthogonal i e uncorrelated it is possible to considerably reduce the total inherent uncertainty the presented approach has been applied to interesting open problems in computer vision such as shape analysis image segmentation tracking object deformations and object motion tracking obtaining encouraging results and proving the effectiveness of the proposed approach

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

fractional order statistic approximation for nonparametric conditional quantile inference abstract using and extending fractional order statistic theory we characterize the o n 1 coverage probability error of the previously proposed hutson 1999 confidence intervals for population quantiles using l statistics as endpoints we derive an analytic expression for the n 1 term which may be used to calibrate the nominal coverage level to get o n 3 2 log n 3 coverage error asymptotic power is shown to be optimal using kernel smoothing we propose a related method for nonparametric inference on conditional quantiles this new method compares favorably with asymptotic normality and bootstrap methods in theory and in simulations code is provided for both unconditional and conditional inference

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

regression rank scores estimation in anocova in semiparametric anocova mixed effects models the role of regression rank scores in robust estimation of fixed effects parameters as well as covariate regression functionals is critically appraised and the relevant asymptotic theory is presented

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

estimation of the retransformed conditional mean in health care cost studies summary we propose a new approach for analyzing skewed and heteroscedastic health care cost data through regression of the conditional quantiles of the transformed cost using the appealing equivariance property of quantiles to monotone transformations we propose a distribution free estimator of the conditional mean cost on the original scale the proposed method is extended to a two part heteroscedastic model to account for zero costs commonly seen in health care cost studies simulation studies indicate that the proposed estimator has competitive and more robust performance than existing estimators in various heteroscedastic models

stable computation of higher order charlier moments for signal and image reconstruction abstract the computation of high order discrete orthogonal moments is very complex and unstable due to fluctuations in numerical polynomial values in this paper we will present new algorithms for the stable computation of high order discrete orthogonal charlier polynomials and moments these algorithms are based on the use of modified recurrence relations of charlier polynomials with respect to the order n and with respect to the variable x and on the use of the modified gram schmidt orthonormalization process gsop the algorithms in question allow the cancellation of terms that cause the numerical fluctuations of charlier polynomial values during the recursive calculations they also preserve the orthogonality property of high order charlier polynomials which enables an efficient analysis of large size bio signals and 2d 3d images therefore the simulation results prove the efficiency of the proposed algorithms when it comes to reconstructing large size bio signals and images

accurate calculation of zernike moments zernike moments zms are very effective global image descriptors which are used in many digital image processing applications the digitization process compromises the accuracy of the moments and therefore several of its properties are affected there are two major discretization errors namely the geometric error and numerical integration error in this paper we propose two new algorithms which eliminate these errors the first algorithm performs the exact computation of geometric moments gms over a unit disk and then uses gms to zms relationship to compute the latter this algorithm is computationally more expensive and it becomes numerically instable for higher order moments therefore we develop a second algorithm based on gaussian quadrature numerical integration the second algorithm reduces both the errors simultaneously and its accuracy increases as the degree of gaussian quadrature numerical integration increases the proposed algorithms are observed to provide very accurate zms which result in improved image reconstruction reduction in reconstruction error and improvement in rotation and scale invariance exhaustive experiments are provided to support improved accuracy of zms and time complexity analysis is performed for the existing and the proposed methods

weak convergence of k nn density and regression estimators with varying k and applications on considere le probleme sous une condition de lissite du second ordre dans le cas unidimensionnel

conditional empirical processes consider a sequence i xi yi i 1 of independent d 1 random vectors with common d f h text h left text x y right mathbb p left text x x y y right text left text x y right in mathbb r text d 1

exactly distribution free inference in instrumental variables regression with possibly weak instruments abstract this paper introduces a rank based test for the instrumental variables regression model that dominates the anderson rubin test in terms of finite sample size and asymptotic power in certain circumstances the test has correct size for any distribution of the errors with weak or strong instruments the test has noticeably higher power than the anderson rubin test when the error distribution has thick tails and comparable power otherwise like the anderson rubin test the rank tests considered here perform best relative to other available tests in exactly identified models

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

asymptotically optimal tests for conditional distributions let xl y1 xn yn be independent replicates of the random vector x y e rd m where x is rd valued and y is rm valued we assume that the conditional distribution p y e ix x qii of y given x x is a member of a parametrie family where the parameter space 0 is an open subset of rh with 0 e 0 under suitable regularity conditions we establish upper bounds for the power functions of asymptotic level a tests for the problem 0 against a sequence of contiguous alternatives as weil as asymptotically optimal tests which attain these bounds since the testing problem involves the joint density of x y as an infinite dimensional nuisance parameter its solution is not standard a monte carlo simulation exemplifies the influence of this nuisance parameter as a main tool we establish local asymptotic normality lan of certain poisson point processes which approximately describe our initial sampie

reference curves based on non parametric quantile regression reference curves which take time into account such as those for age are often required in medicine but simple systematic and efficient statistical methods for constructing them are lacking classical methods are based on parametric fitting polynomial curves semi parametric methods are also widely used especially in europe here we propose a new methodology for the estimation of reference intervals for data sets based on non parametric estimation of conditional quantiles the derived methods should be applicable to all clinical or more generally biological variables that are measured on a continuous quantitative scale as an example we analyse a data set collected to establish reference curves for biophysical properties of the skin of healthy french women the results are compared to those obtained with royston s polynomial parametric method and the semi parametric lms approach

l estimation for linear models abstract linear combinations of order statistics or l estimators have played an extremely important role in the development of robust methods for the one sample problem we suggest analogs of l estimators for the parameters of the linear model based on the p dimensional regression quantiles proposed by koenker and bassett 1978 a uniform bahadur type asymptotic representation of regression quantiles is established and this yields a general asymptotic theory of l estimators for the linear model a leading example of the proposed estimators is an analog of the trimmed mean trq which is asymptotically equivalent to the trimmed least squares estimator studied by ruppert and carroll 1980 but appears to be somewhat less sensitive to influential design observations this estimator is also asymptotically equivalent to the well known huber m estimator but offers the significant advantage that it is scale invariant we illustrate the methods by reconsidering a mid 18th century linear model analyzed b

specification analysis of linear quantile models this paper introduces a nonparametric test for the correct specification of a linear conditional quantile function over a continuum of quantile levels these tests may be applied to assess the validity of post estimation inferences regarding the effect of conditioning variables on the distribution of outcomes we show that the use of an orthogonal projection on the tangent space of nuisance parameters at each quantile index both improves power and facilitates the simulation of critical values via the application of a simple multiplier bootstrap procedure monte carlo evidence and an application to the empirical analysis of age earnings curves are included

a direct approach to inference in nonparametric and semiparametric quantile models we construct a generic confidence interval for a conditional quantile via the direct approach it avoids estimating the conditional density function of the dependent variable given the covariate and is asymptotically valid for any conditional quantile any conditional quantile estimator and any data structure provided that certain weak convergence of the conditional quantile process holds for the original quantile estimator we also construct a generic confidence band for the conditional quantile function across a range of covariate values by using yang stute estimator and two semiparametric quantile functions we demonstrate the flexibility and simplicity of the direct approach the advantages of our new confidence intervals are borne out in a simulation study

quantile correlations and quantile autoregressive modeling in this article we propose two important measures quantile correlation qcor and quantile partial correlation qpcor we then apply them to quantile autoregressive qar models and introduce two valuable quantities the quantile autocorrelation function qacf and the quantile partial autocorrelation function qpacf this allows us to extend the box jenkins three stage procedure model identification model parameter estimation and model diagnostic checking from classical autoregressive models to quantile autoregressive models specifically the qpacf of an observed time series can be employed to identify the autoregressive order while the qacf of residuals obtained from the fitted model can be used to assess the model adequacy we not only demonstrate the asymptotic properties of qcor and qpcor but also show the large sample results of qacf qpacf and the quantile version of the box pierce test moreover we obtain the bootstrap approximations to the distributions of parameter estimators and p

computing kernel smoothed conditional quantiles from many observations abstract quantiles of a variable y conditional on another variable x when plotted against x can be a useful descriptive tool these plots give a quick impression of the functional form of the relation between x and the location spread and shape of the conditional distribution of y if several y are observed for each x then sample quantiles could be calculated for each x the resulting quantile plot may be quite noisy however and smoothing across x may be desired this article presents an algorithm that calculates kernel smoothed conditional quantiles with a cross validation choice of bandwidth for x it is computationally feasible for large data sets when x assumes a small number of values since it requires only one pass through the full data set the cross validation does not require a pass through the data because of simplifications arising from the l 1 loss function being based on absolute values the technique is illustrated by plotting the conditional quantiles of the net wealth of a sample of

semiparametrically efficient inference based on signs and ranks for median restricted models since the pioneering work of koenker and bassett 1978 econometric models involving median and quantile rather than the classical mean or conditional mean concepts have attracted much interest contrary to the traditional models where the noise is assumed to have mean zero median restricted models enjoy a rich group invariance structure in this paper we exploit this invariance structure in order to obtain semiparametrically efficient inference procedures for these models these procedures are based on residual signs and ranks and therefore insensitive to possible misspecification of the underlying innovation density yet semiparametrically efficient at correctly specified densities this latter combination is a definite advantage of these procedures over classical quasi likelihood methods the techniques we propose can be applied without additional technical difficulties to both cross sectional and time series models they do not require any explicit tangent space calculation nor any projections on these

analysis of least absolute deviation summary we develop a unified l 1 based analysis of variance type method for testing linear hypotheses like the classical l2 based analysis of variance the method is coordinate free in the sense that it is invariant under any linear transformation of the covariates or regression parameters moreover it allows singular design matrices and heterogeneous error terms a simple approximation using stochastic perturbation is proposed to obtain cut offvalues for the resulting test statistics both test statistics and distributional approximations can be computed using standard linear programming an asymptotic theory is derived for the method special cases of one and multi way analysis of variance and analysis of covariance models are worked out in detail the main results of this paper can be extended to general quantile regression extensive simulations show that the method works well in practical settings the method is also applied to a dataset from general social surveys

nonparametric models and methods for nonlinear analysis of covariance summary a fully nonparametric model for nonlinear analysis of covariance is proposed the term nonlinear means that the covariate influences the response in a possibly nonlinear and nonpolynomial fashion while the term fully nonparametric implies that the distributions for each factor level combination and covariate value are not restricted to comply with any parametric or semiparametric model the possibility of different shapes of covariate effect in different factor level combinations is also allowed this generality is useful whenever modelling assumptions such as proportional odds or linearity and homoscedasticity appear suspect in the context of this nonparametric model hypotheses of no main effect no interaction and no simple effect which adjust for the covariate values are defined and test statistics are developed both the response and the covariate are allowed to be ordinal the test statistics are based on averages over the covariate values of certain nadarayawatson type nonparametric regression quantities and asymptotically they have under their respective null hypotheses a central z2 distribution simulation results show that the statistics have good power properties the procedures are demonstrated on two real datasets

affine legendre moment invariants for image watermarking robust to geometric distortions geometric distortions are generally simple and effective attacks for many watermarking methods they can make detection and extraction of the embedded watermark difficult or even impossible by destroying the synchronization between the watermark reader and the embedded watermark in this paper we propose a new watermarking approach which allows watermark detection and extraction under affine transformation attacks the novelty of our approach stands on a set of affine invariants we derived from legendre moments watermark embedding and detection are directly performed on this set of invariants we also show how these moments can be exploited for estimating the geometric distortion parameters in order to permit watermark extraction experimental results show that the proposed watermarking scheme is robust to a wide range of attacks geometric distortion filtering compression and additive noise

on average derivative quantile regression for fixed 0 1 the quantile regression function gives the th quantile x in the conditional distribution of a response variable y given the value x x of a vector of covariates it can be used to measure the effect of covariates not only in the center of a population but also in the upper and lower tails a functional that summarizes key features of the quantile specific relationship between x and y is the vector of weighted expected values of the vector of partial derivatives of the quantile function x in a nonparametric setting can be regarded as a vector of quantile specific nonparametric regression coefficients in survival analysis models e g cox s proportional hazard model proportional odds rate model accelerated failure time model and in monotone transformation models used in regression analysis gives the direction of the parameter vector in the parametric part of the model can also be used to estimate the direction of the parameter vector in semiparametric single index models popular in econometrics we show that under suitable regularity conditions the estimate of obtained by using the locally polynomial quantile estimate of chaudhuri 1991a is n 1 2 consistent and asymptotically normal with asymptotic variance equal to the variance of the influence function of the functional we discuss how the estimate of can be used for model diagnostics and in the construction of a link function estimate in general single index models

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

new fractional order legendre fourier moments for pattern recognition applications abstract orthogonal moments enable computer based systems to discriminate between similar objects mathematicians proved that the orthogonal polynomials of fractional orders outperformed their corresponding counterparts in representing the fine details of a given function in this work novel orthogonal fractional order legendre fourier moments are proposed for pattern recognition applications the basis functions of these moments are defined and the essential mathematical equations for the recurrence relations orthogonality and the similarity transformations rotation and scaling are derived the proposed new fractional order moments are tested where their performance is compared with the existing orthogonal quaternion multi channel and fractional moments new descriptors were found to be superior to the existing ones in terms of accuracy stability noise resistance invariance to similarity transformations recognition rates and computational times

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

using zernike moments for the illumination and geometry invariant classification of multispectral texture we develop a method for recognizing color texture independent of rotation scale and illumination color texture is modeled using spatial correlation functions defined within and between sensor bands using a linear model for surface spectral reflectance with the same number of parameters as the number of sensor classes we show that illumination and geometry changes in the scene correspond to a linear transformation of the correlation functions and a linear transformation of their coordinates a several step algorithm that includes scale estimation and correlation moment computation is used to achieve the invariance the key to the method is the new result that illumination rotation and scale changes in the scene correspond to a specific transformation of correlation function zernike moment matrices these matrices can be estimated from a color image this relationship is used to derive an efficient algorithm for recognition the algorithm is substantiated using classification results on over 200 images of color textures obtained under various illumination conditions and geometric configurations

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

rota s universal operators and invariant subspaces in hilbert spaces a hilbert space operator is called universal in the sense of rota if every operator on the hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces we exhibit an analytic toeplitz operator whose adjoint is universal in the sense of rota and commutes with a quasi nilpotent injective compact operator with dense range in particular this new universal operator invites an approach to the invariant subspace problem that uses properties of operators that commute with the universal operator

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

invertible composition operators on hp abstract the weakly closed algebras generated by certain sets of composition operators are shown to be reflexive a structure theorem for invertible composition operators on h2 is obtained and used to show that such operators are reflexive the structure theorem shows that invertible hyperbolic composition operators are similar to cosubnormal operators built up from bilateral weighted shifts another consequence of the structure theorem is that the composition operators induced by hyperbolic disc automorphisms are universal thus the general invariant subspace problem for hilbert space operators is contained in the problem of determining the invariant subspace lattices of these operators

two step estimation of semiparametric censored regression models root n consistent estimators of the regression coecients in the linear censored regression model under conditional quantile restrictions on the error terms were pro posed by powell journal of econometrics 25 1984 303 325 32 1986a 143 155 while those estimators have desirable asymptotic properties under weak regularity conditions simulation studies have shown these estimators to exhibit a small sam ple bias in the opposite direction of the least squares bias for censored data this paper introduces two step estimators for these models which minimize convex objec tive functions and are designed to overcome thisnite sample bias the paper gives regularity conditions under which the proposed two step estimators are consistent and asymptotically normal a monte carlo study compares thenite sample behavior of the proposed methods with their one step counterparts 2001 elsevier science s a all rights reserved

testing for covariate effects in the fully nonparametric analysis of covariance model traditional inference questions in the analysis of covariance mainly focus on comparing different factor levels by adjusting for the continuous covariates which are believed to also exert a significant effect on the outcome variable testing hypotheses about the covariate effects although of substantial interest in many applications has received relatively limited study in the semiparametric nonparametric setting in the context of the fully nonparametric analysis of covariance model of akritas et al we propose methods to test for covariate main effects and covariate factor interaction effects the idea underlying the proposed procedures is that covariates can be thought of as factors with many levels the test statistics are closely related to some recent developments in the asymptotic theory for analysis of variance when the number of factor levels is large the limiting normal distributions are established under the null hypotheses and local alternatives by asymptotically approximating a new class

dct inspired feature transform for image retrieval and reconstruction scale invariant feature transform sift is effective for representing images in computer vision tasks as one of the most resistant feature descriptions to common image deformations however two issues should be addressed first feature description based on gradient accumulation is not compact and contains redundancies second multiple orientations are often extracted from one local region and therefore produce multiple descriptions which is not good for memory efficiency to resolve these two issues this paper introduces a novel method to determine the dominant orientation for multiple orientation cases named discrete cosine transform dct intrinsic orientation and a new dct inspired feature transform dift in each local region it first computes a unique dct intrinsic orientation via dct matrix and rotates the region accordingly and then describes the rotated region with partial dct matrix coefficients to produce an optimized low dimensional descriptor we test the accuracy and robustness of dift on real image matching afterward extensive applications performed on public benchmarks for visual retrieval show that using dct intrinsic orientation achieves performance on a par with sift but with only 60 of its features replacing the sift description with dift reduces dimensions from 128 to 32 and improves precision image reconstruction resulting from dift is presented to show another of its advantages over sift

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

a hereditarily indecomposable mathcal l _ infty space that solves the scalar plus compact problem we construct a hereditarily indecomposable banach space with dual space isomorphic to l1 every bounded linear operator on this space is expressible as i k with a scalar and k compact

multi level dense descriptor and hierarchical feature matching for copy move forgery detection in this paper a multi level dense descriptor mldd extraction method and a hierarchical feature matching method are proposed to detect copy move forgery in digital images the mldd extraction method extracts the dense feature descriptors using multiple levels while the extracted dense descriptor consists of two parts the color texture descriptor and the invariant moment descriptor after calculating the mldd for each pixel the hierarchical feature matching method subsequently detects forgery regions in the input image first the pixels that have similar color textures are grouped together into distinctive neighbor pixel sets next each pixel is matched with pixels in its corresponding neighbor pixel set through its geometric invariant moments then the redundant pixels from previously generated matched pixel pairs are filtered out by the proposed adaptive distance and orientation based filtering method finally some morphological operations are applied to generate the final detected forgery regions experimental results show that the proposed scheme can achieve much better detection results compared with the existing state of the art cmfd methods even under various challenging conditions such as geometric transforms jpeg compression noise addition and down sampling

near infrared face recognition using zernike moments and hermite kernels this work proposes a novel face recognition method based on zernike moments zms and hermite kernels hks to cope with variations in facial expression changes in head pose and scale occlusions due to wearing eyeglasses and the effects of time lapse near infrared images are used to tackle the impact of illumination changes on face recognition and a combination of global and local features is utilized in the decision fusion step in the global part zms are used as a feature extractor and in the local part the images are partitioned into multiple patches and filtered patch wise with hks finally principal component analysis followed by linear discriminant analysis is applied to data vectors to generate salient features and decision fusion is applied on the feature vectors to properly combine both global and local features experimental results on casia nir and polyu nir face databases clearly show that the proposed method achieves significantly higher face recognition accuracy compared with existing methods

methods for estimating a conditional distribution function abstract motivated by the problem of setting prediction intervals in time series analysis we suggest two new methods for conditional distribution estimation the first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation it produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1 the second method involves an adjusted form of the nadaraya watson estimator it preserves the bias and variance properties of a class of second order estimators introduced by yu and jones but has the added advantage of always being a distribution itself our methods also have application outside the time series setting for example to quantile estimation for independent data this problem motivated the work of yu and jones

bivariate quantile smoothing splines it has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample we introduce bivariate quantile smoothing splines which belong to the space of bilinear tensor product splines as nonparametric estimators for the conditional quantile functions in a two dimensional design space the estimators can be computed by using standard linear programming techniques and can further be used as building blocks for conditional quantile estimations in higher dimensions for moderately large data sets we recommend penalized bivariate b splines as approximate solutions we use real and simulated data to illustrate the methodology proposed

ancova methods for heteroscedastic nonparametric regression models we consider an ancova design in which the relationship between the response yi and the covariate xi in cell factor level combination i satisfies the model yi mi xi i xi i where the error term i is assumed to be independent of xi and mi and i are respectively a smooth but unknown regression and scale function this model can be viewed as a generalization of the nonparametric ancova model of young and bowman as such it is a useful alternative for parametric or semiparametric ancova models whenever modeling assumptions such as proportional odds normality of the error terms linearity or homoscedasticity appear suspect we develop test statistics for the hypotheses of no main effects no interaction effects and no simple effects which adjust for the covariate values as defined by akritas arnold and du the asymptotic distribution of the test statistics is obtained its small sample behavior is studied by means of simulations and a real dataset is analyzed

kernel and nearest neighbor estimation of a conditional quantile let x 1 z 1 x 2 z 2 x n z n be iid as x z and for 0 p 1 let p x denote the conditional p quantile of z given x x i e p z p x x x p kernel and near est neighbor estimators of p x are proposed in order to study the asymptotics of these estimates bahadur type representations of the sample conditional quantiles are obtained these representations are used to examine the important issue of choosing the smoothing parameter by a local approach for a fixed x based on weak convergence of these estimators the results lead to asymptotic linear models which motivate certain estimators