edge location to subpixel values in digital imagery a new method for locating edges in digital data to subpixel values and which is invariant to additive and multiplicative changes in the data is presented for one dimensional edge patterns an ideal edge is fit to the data by matching moments it is shown that the edge location is related to the so called christoffel numbers also presented is the study of the effect of additive noise on edge location the method is extended to include two dimensional edge patterns where a line equation is derived to locate an edge this in turn is compared with the standard hueckel edge operator an application of the new edge operator as an edge detector is also provided and is compared with sobel and hueckel edge detectors in presence and absence of noise

mathematics for demosaicking digital color cameras sample the continuous color spectrum using three or more filters however each pixel represents a sample of only one of the color bands this arrangement is called a mosaic to produce a full resolution color image the recorded image must be processed to estimate the values of the pixels for all the other color bands this restoration process is often called demosaicking this paper uses stacked notation to represent the mosaicked image capture and derives the minimum mean square error mmse estimator for the demosaicked image by making common assumptions the restoration can be computed in a cost effective manner extensions to the linear method are proposed to allow adaptive behavior

subpixel edge detection of color images by principal axis analysis and moment preserving principle this paper discusses a new approach for detecting edges with sub pixel accuracy in color images using the principal axis analysis and the moment preserving principle first the principal axis of the color vectors in a three dimensional space is obtained analytically for each image block based on the projection scores the direction of the line edge is obtained by analyzing the three dimensional principal axis of a color image block next by preserving some spatial color moments of the pixels of each square block analytic formulas are derived to extract the edge feature experiments on both synthetic and real images show that the accuracy of the proposed method is comparable to other color edge detectors the proposed algorithm can be performed very fast for real time applications with no need for special hardware

subpixel edge localization and the interpolation of still images in this paper we present a nonlinear interpolation scheme for still image resolution enhancement the algorithm is based on a source model emphasizing the visual integrity of detected edges and incorporates a novel edge fitting operator that has been developed for this application a small neighborhood about each pixel in the low resolution image is first mapped to a best fit continuous space step edge the bilevel approximation serves as a local template on which the higher resolution sampling grid can then be superimposed where disputed values in regions of local window overlap are averaged to smooth errors the result is an image of increased resolution with noticeably sharper edges and in all tried cases lower mean squared reconstruction error than that produced by linear techniques

modeling edges at subpixel accuracy using the local energy approach in this paper we describe a new technique for id and 2d edge feature extraction to subpixel accuracy using edge models and the local energy approach a candidate edge is modeled as one of a number of parametric edge models and the fit is refined by a least squared error fitting technique

intrinsic analysis of statistical estimation the parametric statistical models with suitable regularity conditions have a natural riemannian manifold structure given by the information metric since the parameters are merely labels for the probability measures an inferential statement should be formulated through intrinsic objects invariant under reparametrizations in this context the estimators will be random objects valued on the manifold corresponding to the statistical model in spite of these considerations classical measures of an estimator s performance like the bias and the mean square error are clearly dependent on the statistical model parametrizations in this paper the authors work with extended notions of mean value and moments of random objects which take values on a hausdorff and connected manifold equipped with an affine connection in particular the riemannian manifold case is considered this extension is applied to the bias and the mean square error study in statistical point estimation theory under this approach an intrinsic version of the cramer rao lower bound is obtained a lower bound which depends on the intrinsic bias and the curvature of the statistical model for the mean square of the rao distance the invariant measure analogous to the mean square error further the behavior of the mean square of the rao distance of an estimator when conditioning with respect to a sufficient statistic is considered obtaining intrinsic versions of the rao blackwell and lehmann scheffe theorems asymptotic properties complete the study

binary tree based generic demosaicking algorithm for multispectral filter arrays in this paper we extend the idea of using mosaicked color filter array cfa in color imaging which has been widely adopted in the digital color camera industry to the use of multispectral filter array msfa in multispectral imaging the filter array technique can help reduce the cost achieve exact registration and improve the robustness of the imaging system however the extension from cfa to msfa is not straightforward first most cfas only deal with a few bands 3 or 4 within the narrow visual spectral region while the design of msfa needs to handle the arrangement of multiple bands more than 3 across a much wider spectral range second most existing cfa demosaicking algorithms assume the fixed bayer cfa and are confined to properties only existed in the color domain therefore they cannot be directly applied to multispectral demosaicking the main challenges faced in multispectral demosaicking is how to design a generic algorithm that can handle the more diversified msfa patterns and how to improve performance with a coarser spatial resolution and a less degree of spectral correlation in this paper we present a binary tree based generic demosaicking method two metrics are used to evaluate the generic algorithm including the root mean square error rmse for reconstruction performance and the classification accuracy for target discrimination performance experimental results show that the demosaicked images present low rmse less than 7 and comparable classification performance as original images these results support that msfa technique can be applied to multispectral imaging with unique advantages

large sample theory of intrinsic and extrinsic sample means on manifolds ii this article develops nonparametric inference procedures for estimation and testing problems for means on manifolds a central limit theorem for frechet sample means is derived leading to an asymptotic distribution theory of intrinsic sample means on riemannian manifolds central limit theorems are also obtained for extrinsic sample means w r t an arbitrary embedding of a differentiable manifold in a euclidean space bootstrap methods particularly suitable for these problems are presented applications are given to distributions on the sphere s d directional spaces real projective space rp n 1 axial spaces complex projective space cp k 2 planar shape spaces w r t veronese whitney embeddings and a three dimensional shape space 4 3

geometry based demosaicking demosaicking is a particular case of interpolation problems where from a scalar image in which each pixel has either the red the green or the blue component we want to interpolate the full color image state of the art demosaicking algorithms perform interpolation along edges but these edges are estimated locally we propose a level set based geometric method to estimate image edges inspired by the image in painting literature this method has a time complexity of o s where s is the number of pixels in the image and compares favorably with the state of the art algorithms both visually and in most relevant image quality measures

covariance subspace and intrinsic crame spl acute r rao bounds crame spl acute r rao bounds on estimation accuracy are established for estimation problems on arbitrary manifolds in which no set of intrinsic coordinates exists the frequently encountered examples of estimating either an unknown subspace or a covariance matrix are examined in detail the set of subspaces called the grassmann manifold and the set of covariance positive definite hermitian matrices have no fixed coordinate system associated with them and do not possess a vector space structure both of which are required for deriving classical crame spl acute r rao bounds intrinsic versions of the crame spl acute r rao bound on manifolds utilizing an arbitrary affine connection with arbitrary geodesics are derived for both biased and unbiased estimators in the example of covariance matrix estimation closed form expressions for both the intrinsic and flat bounds are derived and compared with the root mean square error rmse of the sample covariance matrix scm estimator for varying sample support k the accuracy bound on unbiased covariance matrix estimators is shown to be about 10 log 10 n k sup 1 2 db where n is the matrix order remarkably it is shown that from an intrinsic perspective the scm is a biased and inefficient estimator and that the bias term reveals the dependency of estimation accuracy on sample support observed in theory and practice the rmse of the standard method of estimating subspaces using the singular value decomposition svd is compared with the intrinsic subspace crame spl acute r rao bound derived in closed form by varying both the signal to noise ratio snr of the unknown p dimensional subspace and the sample support in the simplest case the crame spl acute r rao bound on subspace estimation accuracy is shown to be about p n p sup 1 2 1 2 snr sup 1 2 rad for p dimensional subspaces it is seen that the svd based method yields accuracies very close to the crame spl acute r rao bound establishing that the principal invariant subspace of a random sample provides an excellent estimator of an unknown subspace the analysis approach developed is directly applicable to many other estimation problems on manifolds encountered in signal processing and elsewhere such as estimating rotation matrices in computer vision and estimating subspace basis vectors in blind source separation

distances and riemannian metrics for multivariate spectral densities the paper is concerned with the practical problem of how to compare power spectral densities of multivariable time series for scalar time series several notions of distance divergences have been proposed and studied starting from the early 1970s while multivariable ones have only recently began to receive any attention in the paper two classes of divergence measures inspired by classical prediction theory are introduced these divergences naturally induce riemannian metrics on the cone of multivariable densities the metrics amount to the quadratic term in the divergence between infinitesimally close to each other power spectra for one of the two we provide explicit formulae for the corresponding geodesics and geodesic distance a close connection between the geometry of power spectra and the geometry of the fisher rao metric is noted

color demosaicking via directional linear minimum mean square error estimation digital cameras sample scenes using a color filter array of mosaic pattern e g the bayer pattern the demosaicking of the color samples is critical to the image quality this paper presents a new color demosaicking technique of optimal directional filtering of the green red and green blue difference signals under the assumption that the primary difference signals pds between the green and red blue channels are low pass the missing green samples are adaptively estimated in both horizontal and vertical directions by the linear minimum mean square error estimation lmmse technique these directional estimates are then optimally fused to further improve the green estimates finally guided by the demosaicked full resolution green channel the other two color channels are reconstructed from the lmmse filtered and fused pds the experimental results show that the presented color demosaicking technique outperforms the existing methods both in psnr measure and visual perception

sample mean versus sample frechet mean for combining complex wishart matrices a statistical study the space of covariance matrices is a non euclidean space the matrices form a manifold which if equipped with a riemannian metric becomes a riemannian manifold and recently this idea has been used for comparison and clustering of complex valued spectral matrices which at a given frequency are typically modeled as complex wishart distributed random matrices identically distributed sample complex wishart matrices can be combined via a standard sample mean to derive a more stable overall estimator however using the riemannian geometry their so called sample frechet mean can also be found we derive the expected value of the determinant of the sample frechet mean and the expected value of the sample frechet mean itself the population frechet mean is shown to be a scaled version of the true covariance matrix the risk under convex loss functions for the standard sample mean is never larger than for the frechet mean in simulations the sample mean also performs better for the estimation of an important functional derived from the estimated covariance matrix namely partial coherence

penrose demosaicking the penrose pixel layout an aperiodic pixel layout in rhombus penrose tiling has been shown to substantially outperform the existing square pixel layout in super resolution however it was tested only on grayscale images to study its performance on color images we have to reconstruct regular color images from penrose raw images i e images with only one color component at each penrose pixel resulting in the problem of demosaicking from penrose pixels penrose demosaicking is more difficult than regular demosaicking because none of the color components of the reconstructed regular color images are available therefore most of the traditional demosaicking methods do not apply we develop a sparse representation based method for penrose demosaicking extensive experiments show that penrose pixel layout outperforms regular pixel layouts in terms of both perceptual evaluation and s cielab the penrose pixel layout is unique among all irregular layouts because it is uniformly three colorable and it has only two pixel shapes thick and thin rhombi making its manufacturing relatively easy

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

integrable hierarchies of nonlinear difference difference equations and symmetries we construct the hierarchy of nonlinear difference difference equations associated with the discrete schrodinger spectral problem as examples of equations contained in this hierarchy we obtain the discrete time toda and volterra lattice equations in the case of the time discrete toda lattice we construct its lie point and generalized symmetries finally we present its backlund transformations and relate it to the already constructed symmetries

image compression by moment preserving edge detection abstract a new image compression algorithm based on a new edge detection technique is proposed a given image is compressed by dividing the image into non overlapping square blocks and coding the edge information in each non uniform block the edge feature in a given window is detected by applying the moment preserving principle to the image data the edge directions are approximated by multiples of 45 to speed up the direction process without introducing obvious distortion for a larger block size a more accurate model of a two step edge is employed in the detection process the proposed algorithm offers excellent reconstructed image quality agreeing with human perception high compression ratios and greatly reduced coding complexity the solution to the edge detection problem in a given block is also analytic the algorithm can be performed very fast for real time applications with no need for special hardware

the darboux backlund transformation without using a matrix representation we present a new method to construct soliton solutions for a large class of nonlinear systems which are associated with matrix spectral problems of high degree including a reduction of the lame equations and a generalized sine gordon system the spectral problems are represented in terms of clifford numbers then the solutions can be obtained in a straightforward way without using any matrix representation among the spectral problems under consideration is the dirac equation for a massless particle in the electromagnetic field and its generalizations

geometric methods for spectral analysis this paper explores a geometric framework for modeling nonstationary but slowly varying time series based on the assumption that short windowed power spectra capture their spectral character and that energy transference in the frequency domain has a physical significance the framework relies on certain notions of transportation distance and their respective geodesics to model possible nonparametric changes in the power spectral density with respect to time we discuss the relevance of this framework to applications in spectral tracking spectral averaging and speech morphing

detection of intensity changes with subpixel accuracy using laplacian gaussian masks we present a system that takes a gray level image as input locates edges with subpixel accuracy and links them into lines edges are detected by finding zero crossings in the convolution of the image with laplacian of gaussian log masks the implementation differs markedly from m i t s as we decompose our masks exactly into a sum of two separable filters instead of the usual approximation by a difference of two gaussians dog subpixel accuracy is obtained through the use of the facet model 1 we also note that the zero crossings obtained from the full resolution image using a space constant for the gaussian and those obtained from the 1 n resolution image with 1 n pixel accuracy and a space constant of n for the gaussian are very similar but the processing times are very different finally these edges are grouped into lines using the technique described in 2

color filter array demosaicking using high order interpolation techniques with a weighted median filter for sharp color edge preservation demosaicking is an estimation process to determine missing color values when a single sensor digital camera is used for color image capture in this paper we propose a number of new methods based on the application of taylor series and cubic spline interpolation for color filter array demosaicking to avoid the blurring of an edge interpolants are first estimated in four opposite directions so that no interpolation is carried out across an edge a weighted median filter whose filter coefficients are determined by a classifier based on an edge orientation map is then used to produce an output from the four interpolants to preserve edges using the proposed methods the original color can be faithfully reproduced with minimal amount of color artifacts even at edges

multicomponent integrable reductions in the kadomtsev petviashvilli hierarchy new types of reductions of the kadomtsev petviashvili kp hierarchy are considered on the basis of sato s approach within this approach the kp hierarchy is represented by infinite sets of equations for potentials u2 u3 of pseudodifferential operators and their eigenfunctions and adjoint eigenfunctions the kp hierarchy was studied under constraints of the following type ni 1 i i x s x where s x are symmetries for the kp equation and i i i i are eigenfunctions with eigenvalue i it is shown that for the first three cases 2 3 4 these constraints give rise to hierarchies of 1 1 dimensional commuting flows for the variables u2 1 n 1 n bi hamiltonian structures for the new hierarchies are presented

detecting boundaries in a vector field a vector gradient approach is proposed to detect boundaries in multidimensional data with multiple attributes a vector field it is used to extend a gradient edge detector to color images the statistical effects of noise on the distribution of the amplitudes and directions of the vector gradient are characterized the noise behavior of the l sub 2 norm of the scalar gradients is also characterized for comparison when the attribute components are highly correlated as is often the case in color images use of the vector gradient shows a small gain in signal to noise ratio over that of the l sub 2 norm of the scalar gradients this small gain may or may not be significant depending on other measures an edge detector uses to deal with noise

darboux covariant equations of von neumann type and their generalizations lax pairs with operator valued coefficients which are explicitly connected by means of an additional condition are considered this condition is proved to be covariant with respect to the darboux transformation of a general form nonlinear equations arising from the compatibility condition of the lax pairs in the matrix case include in particular nahm equations and volterra bogoyavlenskii and toda lattices the examples of other one two and multi field lattice equations are also presented

fusion of color edge detection and color quantization for color image watermarking using principal axes analysis in the past few years many gray level image watermarking schemes have been proposed although the extension to the color case is rare and regularly accomplished by marking the image luminance or by processing each color channel separately this paper presents a new color image watermarking scheme that combines color edge detection and color quantization using principal axes analysis in three dimensional color space the watermark is hidden within the data by modifying a subset of carefully selected edge points to resist both geometric distortion and signal processing attacks experimental results show the robustness of the proposed scheme to resist common attacks

clustering with prim s sequential representation of minimum spanning tree we investigate mst based algorithms aiming to detect three types of clusters an inconsistent edge is found to dominate two subtrees at its two end vertices prim s sequential representation of mst is proposed and studied two psr mst based clustering schemes are developed experiments on some data sets show their effectiveness and efficiency minimum spanning tree mst has been proven to be a powerful tool for performing cluster analysis in this paper prim s sequential representation of mst psr mst is introduced to solve clustering problems after investigating the characteristics of mst based clustering algorithms it is found that inconsistent edges in an mst dominate two subtrees at their two end vertices meanwhile an edge which is longer than the neighbors on its two sides in a psr mst is discovered to dominate two subtrees at its two end vertices with these findings we propose two psr mst based clustering schemes with one being a hierarchical scheme and the other being a k partition method which requests users to specify only number of clusters the experimental results obtained on some synthetic and real world data sets show that the core procedure of the new clustering schemes finding inconsistent edges from a psr mst is effective moreover the k partition method based on psr mst is observed to outperform all the other compared algorithms in terms of clustering quality and time complexity

demosaicing by successive approximation in this paper we present a fast and high performance algorithm for color filter array cfa demosaicing cfa demosaicing is formulated as a problem of reconstructing correlated signals from their downsampled versions with an opposite phase the major contributions of this work include 1 a new iterative demosaicing algorithm in the color difference domain and 2 a spatially adaptive stopping criterion for suppressing color misregistration and zipper artifacts in the demosaiced images we have compared the proposed demosaicing algorithm with two current state of the art techniques reported in the literature ours outperforms both of them on demosaicing performance and computational cost

rapid and brief communication color edge detection using the minimal spanning tree in this study the edge detection task in vector valued images is examined as a clustering problem using samples within a data window the minimal spanning tree mst provides the ordering of multivariate observations and facilitates the identification of similar classes the edge detector parameters like edge strength type and orientation are subsequently determined from the clustered data experiments and comparisons are performed revealing the enhanced performance of the proposed approach

monotonic properties of the least squares mean we settle an open problem of several years standing by showing that the least squares mean for positive definite matrices is monotone for the usual loewner order indeed we show this is a special case of its appropriate generalization to partially ordered complete metric spaces of nonpositive curvature our techniques extend to establish other basic properties of the least squares mean such as continuity and joint concavity moreover we introduce a weighted least squares mean and derive our results in this more general setting

a class of integrable lattices and kp hierarchy we introduce a class of integrable l field first order lattices together with corresponding lax equations these lattices may be represented as a consistency condition for auxiliary linear systems defined on sequences of formal dressing operators this construction provides a simple way to build lattice miura transformations between one field lattice and l field l 2 ones we show that the lattices pertained to by the above class are in some sense compatible with kp flows and define the chains of constrained kadomtsev petviashvili lax operators

r matrix approach to lattice integrable systems an r matrix formalism is applied to the construction of the integrable lattice systems and their bi hamiltonian structure miura like gauge transformations between the hierarchies are also investigated in the end the ladder of linear maps between generated hierarchies is established and described

mathematics of dispersive water waves a commuting hierarchy of dispersive water wave equations makes a three hamiltonian system which belongs to a general class of nonstandard integrable systems whose theory is developed the modified water wave hierarchy is a bi hamiltonian system its modification bifurcates the water wave hierarchy and the hierarchies of the korteweg de vries and the modified korteweg de vries equations as well as the classical miura map are given new representations through various specializations of nonstandard systems

adaptive homogeneity directed demosaicing algorithm a cost effective digital camera uses a single image sensor applying alternating patterns of red green and blue color filters to each pixel location a way to reconstruct a full three color representation of color images by estimating the missing pixel components in each color plane is called a demosaicing algorithm this paper presents three inherent problems often associated with demosaicing algorithms that incorporate two dimensional 2 d directional interpolation misguidance color artifacts interpolation color artifacts and aliasing the level of misguidance color artifacts present in two images can be compared using metric neighborhood modeling the proposed demosaicing algorithm estimates missing pixels by interpolating in the direction with fewer color artifacts the aliasing problem is addressed by applying filterbank techniques to 2 d directional interpolation the interpolation artifacts are reduced using a nonlinear iterative procedure experimental results using digital images confirm the effectiveness of this approach

subpixel measurements using a moment based edge operator recent results in precision measurements using computer vision are presented an edge operator based on two dimensional spatial moments is given the operator can be implemented for virtually any size of window and has been shown to locate edges in digitized images to a twentieth of a pixel this accuracy is unaffected by additive or multiplicative changes to the data values the precision is achieved by correcting for many of the deterministic errors caused by nonideal edge profiles using a lookup table to correct the original estimates of edge orientation and location this table is generated using a synthesized edge which is located at various subpixel locations and various orientations the operator is extended to accommodate nonideal edge profiles and rectangularly sampled pixels the technique is applied to the measurement of imaged machined metal parts theoretical and experimental noise analyses show that the operator has relatively small bias in the presence of noise

an algebraic method to construct the darboux matrix we present an effective procedure to construct the 1 soliton darboux matrix our approach based on the zakharov shabat mikhailov s dressing method is especially useful in the case of non canonical normalization and for non isospectral linear problems the construction is divided into two steps first we represent a given linear problem as a system of some algebraic constraints on two matrices in this context we introduce and discuss invariants of the darboux matrix second we derive the darboux matrix demanding that it preserves the algebraic constraints in particular we consider in details the restrictions imposed by various reduction groups on the form of the darboux matrix

algebraic construction of the darboux matrix revisited we present algebraic construction of darboux matrices for 1 1 dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case we discuss different approaches to the darboux backlund transformation based on different dependences of the darboux matrix polynomial sum of partial fractions or the transfer matrix form we derive symmetric n soliton formulae in the general case the matrix spectral parameter and dressing actions in loop groups are also discussed we describe reductions to twisted loop groups unitary reductions the matrix lax pair for the kdv equation and reductions of chiral models harmonic maps to su n and to grassmann spaces we show that in the kdv case the nilpotent darboux matrix generates the binary darboux transformation the paper is intended as a review of known results usually presented in a novel context but some new results are included as well e g general compact formulae for n soliton surfaces and linear and bilinear constraints on the nonisospectral lax pair matrices which are preserved by darboux transformations

color image processing by using binary quaternion moment preserving thresholding technique this paper presents a new moment preserving thresholding technique called the binary quaternion moment preserving bqmp thresholding for color image data based on representing color data by the quaternions the statistical parameters of color data can be expressed through the definition of quaternion moments analytical formulas of the bqmp thresholding can thus be determined by using the algebra of the quaternions the computation time for the bqmp thresholding is of order of the data size by using the bqmp thresholding quaternion moment based operators are designed for the application of color image processing such as color image compression multiclass clustering of color data and subpixel color edge detection the experimental results show that the proposed operator for color image compression can have output picture quality acceptable to human eyes in addition the proposed edge operator can detect the color edge at the subpixel level therefore the proposed bqmp thresholding can be used as a tool for color image processing

primary consistent soft decision color demosaicking for digital cameras patent pending color mosaic sampling schemes are widely used in digital cameras given the resolution of ccd sensor arrays the image quality of digital cameras using mosaic sampling largely depends on the performance of the color demosaicking process a common problem with existing color demosaicking algorithms is an inconsistency of sample interpolations in different primary color channels which is the cause of the most objectionable color artifacts to cure the problem we propose a new primary consistent soft decision framework pcsd of color demosaicking in the pcsd framework we make multiple estimates of a missing color sample under different hypotheses on edge or texture directions the estimates are made via a primary consistent interpolation meaning that all three primary components of a color are interpolated in the same direction the final estimate of a color sample is obtained by testing different interpolation hypotheses in the reconstructed full resolution color image and selecting the best via an optimal statistical decision or inference process a concrete color demosaicking method of the pcsd framework is presented this new method eliminates certain types of color artifacts of existing color demosaicking methods extensive experimental results demonstrate that the pcsd approach can significantly improve the image quality of digital cameras in both subjective and objective measures in some instances our gain over the competing methods can be as much as 7db

color edge detection using vector order statistics a method is proposed whereby a color image is treated as a vector field and the edge information carried directly by the vectors is exploited a class of color edge detectors is defined as the minimum over the magnitudes of linear combinations of the sorted vector samples from this class a specific edge detector is obtained and its performance characteristics studied results of a quantitative evaluation and comparison to other color edge detectors using pratt s 1991 figure of merit and an artificially generated test image are presented edge detection results obtained for real color images demonstrate the efficiency of the detector

efficient minimax estimation of a class of high dimensional sparse precision matrices estimation of the covariance matrix and its inverse the precision matrix in high dimensional situations is of great interest in many applications in this paper we focus on the estimation of a class of sparse precision matrices which are assumed to be approximately inversely closed for the case that the dimensionality p can be much larger than the sample size n which is fundamentally different from the classical case that p n different in nature from state of the art methods that are based on penalized likelihood maximization or constrained error minimization based on the truncated neumann series representation we propose a computationally efficient precision matrix estimator that has a computational complexity of o p3 we prove that the proposed estimator is consistent in probability and in l2 under the spectral norm moreover its convergence is shown to be rate optimal in the sense of minimax risk we further prove that the proposed estimator is model selection consistent by establishing a convergence result under the entry wise norm simulations demonstrate the encouraging finite sample size performance and computational advantage of the proposed estimator the proposed estimator is also applied to a real breast cancer data and shown to outperform existing precision matrix estimators

on the construction of monopoles we show that any self dual su 2 monopole may be constructed either by ward s twistor method or nahm s use of the adhm construction the common factor in both approaches is an algebraic curve whose jacobian is used to linearize the non linear ordinary differential equations which arise in nahm s method we derive the non singularity condition for the monopole in terms of this curve and apply the result to prove the regularity of axially symmetric solutions

heterogeneity projection hard decision color interpolation using spectral spatial correlation this paper presents a novel heterogeneity projection hard decision hphd color interpolation procedure for reproduction of bayer mosaic images the proposed algorithm aims to estimate the optimal interpolation direction and perform hard decision interpolation in which each pixel only needs to be interpolated once a new heterogeneity projection scheme based on a novel spectral spatial correlation concept is proposed to estimate the best interpolation direction directly from the original mosaic image using the proposed heterogeneity projection scheme a hard decision rule can be decided before performing the interpolation the advantage of this scheme is that it provides an efficient way for decision based algorithms to generate improved results using fewer computations compared with three recently reported demosaicing techniques gunturk s lu s and li s methods the proposed hphd outperforms all of them in both psnr values and s cielab deltaeab measures by utilizing 25 natural images from kodak photocd

determining hysteresis thresholds for edge detection by combining the advantages and disadvantages of thresholding methods hysteresis is an important technique for edge detection but the unsupervised determination of its parameters is not an easy problem in this paper we propose a method for unsupervised determination of hysteresis thresholds using the advantages and disadvantages of two thresholding methods the basic idea of our method is to look for the best hysteresis thresholds in a set of candidates first the method finds a subset and a overset of the unknown edge points set then it determines the best edge map with the measure 2 compared with a general method to determine the parameters of an edge detector our method performs well and is less computationally complex the basic idea of our method can be generalized to other pattern recognition problems

an edge sensing generic demosaicing algorithm with application to image resampling in this paper we introduce a new demosaicing algorithm that can be used for various sensor images captured by digital cameras equipped with various red green blue color filter arrays our algorithm enhances the universal demosaicing algorithm of lukac et al by defining a new spectral interpolation model that exploits not only the information on the color of pixels but also the relative distance between neighboring pixels within an image moreover we include an edge detection model that makes our algorithm adaptive and reduces the presence of color shifts and artifacts a series of tests has been made on images of the kodak database and our algorithm performs better than the universal demosaicing algorithm with regard to both subjective and objective evaluation the versatility of our demosaicing algorithm is also highlighted through an application to the issue of color image resampling and we obtain conclusive experimental results

moment preserving corner detection abstract a new corner detection method based on the principle of preserving gray and mass moments is proposed for each circular region in a digital image bilevel thresholding based on gray moment preserving is used first to transform the blurred subimage in the region into a binary picture two approximate boundary points on the circumference of the thresholded circular region are obtained next by simple traversal an approximate corner point is estimated from the geometric relation between the centroid and the three vertices of the triangular lamina formed by the corner pattern within the circular region these points are then used as an initial guess for solving a system of nonlinear equations that are constructed by preserving the area and the three mass moments of the partial object lamina within the circular region more accurate corner boundary points can finally be determined from which not only the location but also the orientation as well as the angle of the corner can be computed experimental results show the effectiveness of the proposed method

a constrained l1 minimization approach to sparse precision matrix estimation this article proposes a constrained l1 minimization method for estimating a sparse inverse covariance matrix based on a sample of n iid p variate random variables the resulting estimator is shown to have a number of desirable properties in particular the rate of convergence between the estimator and the true s sparse precision matrix under the spectral norm is when the population distribution has either exponential type tails or polynomial type tails we present convergence rates under the elementwise l norm and frobenius norm in addition we consider graphical model selection the procedure is easily implemented by linear programming numerical performance of the estimator is investigated using both simulated and real data in particular the procedure is applied to analyze a breast cancer dataset and is found to perform favorably compared with existing methods

distances and riemannian metrics for spectral density functions we introduce a differential geometric structure for spectral density functions of discrete time random processes this is quite analogous to the riemannian structure of information geometry which is used to study perturbations of probability density functions and which is based on the fisher information metric herein we introduce an analogous riemannian metric which we motivate with a problem in prediction theory it turns out that this problem also provides a prediction theoretic interpretation to the itakura distortion measure which relates to our metric geodesies and geodesic distances are characterized in closed form and hence the geodesic distance between two spectral density functions provides an explicit intrinsic pseudo metric on the cone of density functions certain other distortion measures that involve generalized means of spectral density functions are shown to lead to the same riemannian metric finally an alternative riemannian metric is introduced which is motivated by an analogous problem involving smoothing instead of prediction

darboux integrable nonlinear liouville von neumann equation a new form of a binary darboux transformation is used to generate analytical solutions of a nonlinear liouville von neumann equation general theory is illustrated by explicit examples

demosaicing of color filter array captured images using gradient edge detection masks and adaptive heterogeneity projection without demosaicing processing this paper first proposes a new approach to extract more accurate gradient edge information on mosaic images directly next based on spectral spatial correlation a novel adaptive heterogeneity projection with proper mask size for each pixel is presented combining the extracted gradient edge information and the adaptive heterogeneity projection values a new edge sensing demosaicing algorithm is presented based on 24 popular testing images experimental results demonstrated that our proposed high quality demosaicing algorithm has the best image quality performance when compared with several recently published algorithms

constraints of the kadomtsev petviashvili hierarchy for the kadomtsev petviashvili kp hierarchy constructed in terms of the famous sato theory a k constraint is proposed that leads the hierarchy to the nonlinear system involving a finite number of dynamical coordinates the eigenvalue problem of the k constrained system is naturally obtained from the linear system of the kp hierarchy which takes the form of kth order polynomial coupled with a first order one thus we are able to derive the correspondent lax pair recursion operator bi hamiltonian structures and conserved quantities the constraints for the bkp hierarchy are also sketched

computing the karcher mean of symmetric positive definite matrices we present and analyze an iterative method for approximating the karcher mean of a set ofn n positive denite

multivariate image similarity in the compressed domain using statistical graph matching we address the problem of image similarity in the compressed domain using a multivariate statistical test for comparing color distributions our approach is based on the multivariate wald wolfowitz test a nonparametric test that assesses the commonality between two different sets of multivariate observations using some pre selected feature attributes the similarity measure provides a comprehensive estimate of the match between different images based on graph theory and the notion of minimal spanning tree mst feature extraction is directly provided from the jpeg discrete cosine transform dct domain without involving full decompression or inverse dct based on the zig zag scheme a novel selection technique is introduced that guarantees image s enhanced invariance to geometric transformations to demonstrate the performance of the proposed method the application on a diverse collection of images has been systematically studied in a query by example image retrieval task experimental results show that a powerful measure of similarity between compressed images can emerge from the statistical comparison of their pattern representations

improved direction estimation for di zenzo s multichannel image gradient operator gradient estimation is one of the most important tasks in image video processing for multichannel images a classical and widely used gradient method is di zenzo s gradient operator which is based on the measure of squared local contrast variation of multichannel images however up to now the indetermination of di zenzo s gradient direction has not been well solved which results in errors occurring in most of the subsequent studies in which di zenzo s vector gradient is used in this paper this problem is solved thoroughly furthermore the ranges of the values that the gradient angle should take in various cases are also analyzed as an application in color image processing a color version of canny edge detector is implemented by introducing the new gradient estimator to the traditional grayscale image canny operator the experimental results indicate that the improved di zenzo s gradient operator is currently one of the best color gradient estimators and outperforms other state of the art color image gradient methods the improved multichannel gradient operator not only provides accurate gradient estimation but also is efficient and easy to implement

noise robust color edge detector using gradient matrix and anisotropic gaussian directional derivative matrix in this paper a noise robust color edge detector using gradient matrix and anisotropic gaussian directional derivative andd matrix is proposed in order to alleviate the conflict between high edge resolution and noise robustness in the color canny detector where the isotropic gaussian kernels and gradient matrix of the r g b components are used the andds of the three components of a color image are arranged into the andd matrix from its singular value decomposition svd the andd based color edge strength map cesm is constructed and is relevant to the pixelwise optimal fusion of the andds of the three components in the sense of color edge enhancement the merits and defects of the andd based cesm and gradient based cesm are contrasted to show their complementarity in color edge detection the two cesms are fused to develop a new color edge detector it is compared with the color canny detector and two recent color edge detectors the results show that the proposed detector attains better detection performance for noiseless and noisy color images corrupted by white gaussian noise or impulsive noise of small percentage a color edge detector using gradient matrix and andd matrix is proposed the svd of the andd matrix is used to determine cesm and cesd of a color image the new detector has both high edge resolution and noise robustness it attains better performance than the two existing color edge detectors

efficient reversible data hiding for color filter array images a reversible data hiding algorithm which uses prediction errors in the color difference domain for mosaic images with the bayer color filter array cfa is proposed furthermore the proposed algorithm can be extended to deal with the digital time delay and integration dtdi mosaic images and lukac and plataniotis lp mosaic images experimental results on cfa dtdi and lp mosaic images demonstrate that the proposed algorithm can achieve high embedding capacity while maintaining good image quality

edge junction and corner detection using color distributions for over 30 years 1970 2000 researchers in computer vision have been proposing new methods for performing low level vision tasks such as detecting edges and corners one key element shared by most methods is that they represent local image neighborhoods as constant in color or intensity with deviations modeled as noise due to computational considerations that encourage the use of small neighborhoods where this assumption holds these methods remain popular the research presented models a neighborhood as a distribution of colors the goal is to show that the increase in accuracy of this representation translates into higher quality results for low level vision tasks on difficult natural images especially as neighborhood size increases we emphasize large neighborhoods because small ones often do not contain enough information we emphasize color because it subsumes gray scale as an image range and because it is the dominant form of human perception we discuss distributions in the context of detecting edges corners and junctions and we show results for each