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

on the unification of line processes outlier rejection and robust statistics with applications in early vision the modeling of spatial discontinuities for problems such as surface recovery segmentation image reconstruction and optical flow has been intensely studied in computer vision while line process models of discontinuities have received a great deal of attention there has been recent interest in the use of robust statistical techniques to account for discontinuities this paper unifies the two approaches to achieve this we generalize the notion of a line process to that of an analog outlier process and show how a problem formulated in terms of outlier processes can be viewed in terms of robust statistics we also characterize a class of robust statistical problems for which an equivalent outlier process formulation exists and give a straightforward method for converting a robust estimation problem into an outlier process formulation we show how prior assumptions about the spatial structure of outliers can be expressed as constraints on the recovered analog outlier processes and how traditional continuation methods can be extended to the explicit outlier process formulation these results indicate that the outlier process approach provides a general framework which subsumes the traditional line process approaches as well as a wide class of robust estimation problems examples in surface reconstruction image segmentation and optical flow are presented to illustrate the use of outlier processes and to show how the relationship between outlier processes and robust statistics can be exploited an appendix provides a catalog of common robust error norms and their equivalent outlier process formulations

weighted repeated median smoothing and filtering we propose weighted repeated median filters and smoothers for robust nonparametric regression in general and for robust online signal extraction from time series in particular the new methods allow us to remove outlying sequences and to preserve discontinuities shifts in the underlying regression function the signal in the presence of local linear trends suitable weighting of the observations according to their distances in the design space reduces the bias arising from nonlinearities and improves the efficiency using larger bandwidths while still distinguishing long term shifts from outlier sequences other localized robust regression techniques like s m and mm estimators as well as weighted l 1 regression are examined for comparison

clique descriptor of affine invariant regions for robust wide baseline image matching assuming that the image distortion between corresponding regions of a stereo pair of images with wide baseline can be approximated as an affine transformation if the regions are reasonably small recent image matching algorithms have focused on affine invariant region ir detection and its description to increase the robustness in matching however the distinctiveness of an intensity based region descriptor tends to deteriorate when an image includes homogeneous texture or repetitive pattern to address this problem we investigated the geometry of a local ir cluster also called a clique and propose a new clique based image matching method in the proposed method the clique of an ir is estimated by delaunay triangulation in a local affine frame and the hausdorff distance is adopted for matching an inexact number of multiple descriptor vectors we also introduce two adaptively weighted clique distances where the neighbour distance in a clique is appropriately weighted according to characteristics of the local feature distribution experimental results show the clique based matching method produces more tentative correspondences than variants of the sift based method

root properties and convergence rates of median filters median filters are a special class of ranked order filters used for smoothing signals repeated application of the filter on a quantized signal of finite length ultimately results in a sequence termed a root signal which is invariant to additional passes of the median filter in this paper the theory is developed both for determining the cardinality of the root signal space of arbitrary window width filters applied to signals with any number of quantization levels and for counting or estimating the number of passes required to produce a root for binary signals

the resistant line and related regression methods abstract in a bivariate x y scatterplot the three group resistant line is that line for which the median residual in each outer third of the data ordered on x is zero it was proposed by tukey as an exploratory method resistant to outliers in x and y and suited to hand calculation a dual plot representation of the procedure yields a fast convergent algorithm nonparametric confidence intervals for the slope consistency influence function and asymptotic normality results monte carlo results show that small sample efficiencies exceed their asymptotic values in important cases both breakdown and efficiency are adequate for exploratory work replacing medians by other m estimators of location increases efficiency substantially without affecting breakdown or computational complexity the method thus combines bounded influence and acceptable efficiency with conceptual and computational simplicity

asymmetric correlation a noise robust similarity measure for template matching we present an efficient and noise robust template matching method based on asymmetric correlation asc the asc similarity function is invariant to affine illumination changes and robust to extreme noise it correlates the given non normalized template with a normalized version of each image window in the frequency domain we show that this asymmetric normalization is more robust to noise than other cross correlation variants such as the correlation coefficient direct computation of asc is very slow as a dft needs to be calculated for each image window independently to make the template matching efficient we develop a much faster algorithm which carries out a prediction step in linear time and then computes dfts for only a few promising candidate windows we extend the proposed template matching scheme to deal with partial occlusion and spatially varying light change experimental results demonstrate the robustness of the proposed asc similarity measure compared to state of the art template matching methods

a fast motion estimation algorithm based on the block sum pyramid in this correspondence a fast approach to motion estimation is presented the algorithm uses the block sum pyramid to eliminate unnecessary search positions it first constructs the sum pyramid structure of a block successive elimination is then performed hierarchically from the top level to the bottom level of the pyramid many search positions can be skipped from being considered as the best motion vector and thus the search complexity can be reduced the algorithm can achieve the same estimation accuracy as the full search block matching algorithm with much less computation time

motion estimation using statistical learning theory this paper describes a novel application of statistical learning theory slt to single motion estimation and tracking the problem of motion estimation can be related to statistical model selection where the goal is to select one correct motion model from several possible motion models given finite noisy samples slt also known as vapnik chervonenkis vc theory provides analytic generalization bounds for model selection which have been used successfully for practical model selection this paper describes a successful application of an slt based model selection approach to the challenging problem of estimating optimal motion models from small data sets of image measurements flow we present results of experiments on both synthetic and real image sequences for motion interpolation and extrapolation these results demonstrate the feasibility and strength of our approach our experimental results show that for motion estimation applications slt based model selection compares favorably against alternative model selection methods such as the akaike s fpe schwartz criterion sc generalized cross validation gcv and shibata s model selector sms the paper also shows how to address the aperture problem using slt based model selection for penalized linear ridge regression formulation

fast block matching algorithm based on the winner update strategy block matching is a widely used method for stereo vision visual tracking and video compression many fast algorithms for block matching have been proposed in the past but most of them do not guarantee that the match found is the globally optimal match in a search range this paper presents a new fast algorithm based on the winner update strategy which utilizes an ascending lower bound list of the matching error to determine the temporary winner two lower bound lists derived by using partial distance and by using minkowski s inequality are described the basic idea of the winner update strategy is to avoid at each search position the costly computation of the matching error when there exists a lower bound larger than the global minimum matching error the proposed algorithm can significantly speed up the computation of the block matching because 1 computational cost of the lower bound we use is less than that of the matching error itself 2 an element in the ascending lower bound list will be calculated only when its preceding element has already been smaller than the minimum matching error computed so far 3 for many search positions only the first several lower bounds in the list need to be calculated our experiments have shown that when applying to motion vector estimation for several widely used test videos 92 to 98 of operations can be saved while still guaranteeing the global optimality moreover the proposed algorithm can be easily modified either to meet the limited time requirement or to provide an ordered list of best candidate matches

a best upper bound for the 2 norm condition number of a matrix abstract let a be an n n nonsingular real or complex matrix the best possible upper bound for the ratio of the largest and smallest singular values of a using tr a a det a and n only is obtained a comparison with an earlier bound is given and the singular and nonsquare cases are included if all the eigenvalues of a are real and positive the best possible upper bound for the ratio of the largest and smallest eigenvalues of a involving tr a det a and n only is presented as well

cooperative robust estimation using layers of support we present an approach to the problem of representing images that contain multiple objects or surfaces rather than using an edge based approach to represent the segmentation of a scene we propose a multilayer estimation framework which uses support maps to represent the segmentation of the image into homogeneous chunks this support based approach can represent objects that are split into disjoint regions or have surfaces that are transparently interleaved our framework is based on an extension of robust estimation methods that provide a theoretical basis for support based estimation we use a selection criteria derived from the minimum description length principle to decide how many support maps to use in describing an image our method has been applied to a number of different domains including the decomposition of range images into constituent objects the segmentation of image sequences into homogeneous higher order motion fields and the separation of tracked motion features into distinct rigid body motions

an axisymmetric ordinary state based peridynamic model for linear elastic solids abstract in this study a new axisymmetric ordinary state based peridynamic pd model for axisymmetric problems of linear elastic solids is presented a fracture criterion based on the pd bond energy density is proposed adaptive dynamic relaxation adr method is adopted to obtain equilibrium solutions and a viable fictitious density of the model is derived and proven to be valid for implementation in the adr method performance and validity of the proposed axisymmetric pd model are demonstrated by three kinds of numerical problems i e compression tests pull out deformation and indentation fracture in the compression tests with focus on constant strain deformations the displacements predicted by the present model are compared with classical analytical solutions and the results show good agreements both m convergence and convergence behaviors under four influence functions are investigated and discussed based on a thorough error analysis in different compression cases the recovery of the poisson s ratios in the model is tested in detail as well the capability of capturing general non uniform axisymmetric deformation by the proposed model is verified in the pull out analysis the equilibrium displacement fields predicted by the present model agree very well with those by the finite element method the peridynamic evaluation of strains and stresses also show good match with the finite element ones the proposed fracture criterion is validated by the third example of indentation cracking which is compared with the available experimental data the model developed can effectively be used to analyze axisymmetric problems of linear elastic solids in the framework of the ordinary state based peridynamics

non ordinary state based peridynamic analysis of stationary crack problems an implicit implementation of the non ordinary state based peridynamics formulation for quasi static linearly elastic solids is presented emphasis is placed on assessing the accuracy of the numerical scheme in the vicinity of the crack front and other sources of stress concentration we also present a comparative study of methods used to control the zero energy modes inherent in the nonlocal definition of the strain tensor and reduce the spurious oscillations present particularly in regions of high strain gradients the accuracy of the peridynamics scheme including the impact of the lattice spacing and configuration is assessed by performing an analysis of the near tip stress and displacement fields k fields for 2d problems the manuscript also summarizes a verification study based on the classical 3d penny shaped crack problem and a validation study of a 3d notched fracture specimen

a linear receiver for direct sequence spread spectrum multiple access systems with antenna arrays and blind adaptation a linear receiver for direct sequence spread spectrum multiple access communication systems under the aperiodic random sequence model is considered the receiver consists of the conventional matched filter followed by a tapped delay line with the provision of incorporating the use of antenna arrays it has the ability of suppressing multiple access interference mai and narrowband interference in some weighted proportions as well as combining multipath components without explicit estimation of any channel conditions under some specific simplified channel models the receiver reduces to the minimum variance distortionless response beamformer the rake receiver a notch filter or an mai suppressor the interference rejection capability is made possible through a suitable choice of weights in the tapped delay line the optimal weights can be obtained by straightforward but computationally complex eigenanalysis in order to reduce the computational complexity a simple blind adaptive algorithm is also developed

asymptotically compatible schemes and applications to robust discretization of nonlocal models many problems in nature being characterized by a parameter are of interest both with a fixed parameter value and with the parameter approaching an asymptotic limit numerical schemes that are convergent in both regimes offer robust discretizations which can be highly desirable in practice the asymptotically compatible schemes studied in this paper meet such objectives for a class of parametrized problems an abstract mathematical framework is established rigorously here together with applications to the numerical solution of both nonlocal models and their local limits in particular the framework can be applied to nonlocal diffusion models and a general state based peridynamic system parametrized by the horizon radius recent findings have exposed the risks associated with some discretizations of nonlocal models when the horizon radius is proportional to the discretization parameter thus it is desirable to develop asymptotically compatible schemes for such models so as to offer robust numerical dis

fast algorithm for robust template matching with m estimators we propose a fast algorithm for speeding up the process of template matching that uses m estimators for dealing with outliers we propose a particular image hierarchy called the p pyramid that can be exploited to generate a list of ascending lower bounds of the minimal matching errors when a nondecreasing robust error measure is adopted then the set of lower bounds can be used to prune the search of the p pyramid and a fast algorithm is thereby developed in this paper this fast algorithm ensures finding the global minimum of the robust template matching problem in which a nondecreasing m estimator serves as an error measure experimental results demonstrate the effectiveness of our method

a generalized gaussian image model for edge preserving map estimation the authors present a markov random field model which allows realistic edge modeling while providing stable maximum a posterior map solutions the model referred to as a generalized gaussian markov random field ggmrf is named for its similarity to the generalized gaussian distribution used in robust detection and estimation the model satisfies several desirable analytical and computational properties for map estimation including continuous dependence of the estimate on the data invariance of the character of solutions to scaling of data and a solution which lies at the unique global minimum of the a posteriori log likelihood function the ggmrf is demonstrated to be useful for image reconstruction in low dosage transmission tomography

on the constrained stochastic gradient algorithm model performance and improved version this paper discusses the constrained stochastic gradient csg algorithm used for controlling antenna arrays aiming to maximize the signal to interference plus noise ratio sinr in mobile communications firstly analytical expressions for the first moment of the weight vector and the sinr characteristic of the standard csg algorithm are derived for two interferer signals considering small step size conditions and assuming gaussian signal interference and noise from these model expressions the csg algorithm performance is assessed which predicts undesired behavior termed here unbalanced behavior pertaining to an unbalance between maximizing signal power and minimizing interference power when one or more interference angles of arrival are close to the signal angle of arrival and the angle of arrival spreads of the involved signals are small finally by using the model expressions an improved csg icsg algorithm is proposed to compensate the unbalanced behavior of the standard csg algorithm the accuracy of the proposed model and the effectiveness of the modified algorithm are assessed through numerical simulations

a nonparametric method for fitting a straight line to a noisy image in fitting a straight line to a noisy image the least squares method becomes highly unreliable either when the noise distribution is nonnormal or when it is contaminated by outliers the authors propose a nonparametric method the median of the intercepts to overcome these difficulties this method is free of assumptions about the noise distribution and insensitive to outliers and it does not require quantization of the parameter space thus unlike the hough transform its outcome does not depend on the bin size the method is efficient and its implementation does not involve practical difficulties such as local minima or poor convergence of iterative procedures

numerical experiments on the convergence properties of state based peridynamic laws and influence functions in two dimensional problems abstract peridynamics is widely used as the theoretical basis for numerical studies of fracture evolution propagation and behavior while the theory has been shown to converge to continuum mechanics in the theoretical limit its behavior as a discrete numerical approximation with respect to classic problems has not been shown in this study we use standard analytical solutions to thoroughly test the numerical accuracy and rate of convergence of the spatial discretization obtained by peridynamics we analyze the accuracy and rate of convergence of three different peridynamic constitutive responses of these two involve a state based dilation and the third is based on the estimation of the deformation gradient additionally we study the choice of the peridynamic influence function in each of the constitutive responses the peridynamic materials are solved in the linear elastic regime by solving a linear system of equations obtained by symbolically differentiating the force states we test the methods against standard constant strain solutions for uniaxial compression isotropic compression and simple shear we also apply the methods to a finite material with a pressurized thin crack using the westergaard s solution method to obtain an analytical displacement field for comparison the two dilation based peridynamic constitutive responses are found to only converge to one of the constant strain solutions while the deformation gradient based law converges in all cases with an appropriate choice of the influence functions we show that a cubic influence function is the best choice of those considered in all methods only the deformation gradient based model converges for all three linear deformation problems but is less accurate than the dilation based models for the thin crack problem because of instabilities we demonstrate an ad hoc smoothing technique based on the influence function that is able to alleviate these instabilities and improve the accuracy of the deformation gradient based model

adaptive generalized eigen pairs extraction algorithms and their convergence analysis the generalized hermitian eigenvalue problem ghep is of great use in modern signal processing compared with other methods neural network model based algorithms provide an efficient way to solve such problems online up to now a class of neural network model based generalized feature extraction algorithms have been reported in the literature however most existing noncoupled algorithms suffer from the so called speed stability problem in contrast coupled learning algorithms estimate the generalized eigenvector and generalized eigenvalue simultaneously in coupled manners therefore they can solve the speed stability problem and perform better than noncoupled algorithms in this paper we first propose a coupled generalized system which is obtained by using the newton s method and a novel generalized information criterion then based on this coupled generalized system we successfully obtain two coupled algorithms with normalization steps for minor principal generalized eigen pairs extraction and the technique of multiple generalized eigen pairs extraction is also introduced in this paper the convergence of the proposed algorithms is justified by deterministic discrete time ddt approach with the efficiency and feasibility validated by experimental results as well compared with similar work the proposed algorithms have lower computational complexity better numerical stability and higher estimation accuracy

robust image registration by increment sign correlation abstract a novel and robust statistic as a similarity measure for robust image registration is proposed the statistic is named as increment sign correlation because it is based on the average evaluation of incremental tendency of brightness in adjacent pixels it is formalized to be a binary distribution or a gaussian distribution for a large image size through statistical analysis and modeling by utilizing the proposed statistical model for example we can theoretically determine a reasonable value of threshold for verification of matching this sign correlation can also be proved to expectedly have the constant value 0 5 for any uncorrelated images to a template image and then the property of the constancy can be utilized to analyze the high robustness for occlusion the good performance for the case of saturation or highlight can also be proved through theoretical analysis and fundamental experiments a basic algorithm for image scanning search and registration over a large scene is represented with a technique for a fast version by the branch and bound approach many experimental evidences with real images are provided and discussed

adaptive normalized quasi newton algorithms for extraction of generalized eigen pairs and their convergence analysis the main contributions of this paper are to propose and analyze fast and numerically stable adaptive algorithms for the generalized hermitian eigenvalue problem ghep which arises in many signal processing applications first for given explicit knowledge of a matrix pencil we formulate two novel deterministic discrete time ddt systems for estimating the generalized eigen pair eigenvector and eigenvalue corresponding to the largest smallest generalized eigenvalue by characterizing a generalized eigen pair as a stationary point of a certain function the proposed ddt systems can be interpreted as natural combinations of the normalization and quasi newton steps for finding the solution second we present adaptive algorithms corresponding to the proposed ddt systems moreover we establish rigorous analysis showing that for a step size within a certain range the sequence generated by the ddt systems converges to the orthogonal projection of the initial estimate onto the generalized eigensubspace corresponding to the largest smallest generalized eigenvalue numerical examples demonstrate the practical applicability and efficacy of the proposed adaptive algorithms

multimodal genetic algorithms based algorithm for automatic point correspondence in this paper the problem of automatic determination of point correspondence between two images is formulated as a multimodal function optimization and the usefulness of genetic algorithms gas as a multimodal optimizer is explored initially a number of variations of gas capable of simultaneously discovering multiple extremes of an objective function are evaluated on a mathematical benchmark objective function with multiple unequal maxima the variation of the gas that performs best on the benchmark function in terms of the number of maxima discovered is selected for the determination of automatic point correspondence between two images the selected variation of the gas involves an iterative procedure for the formation of a genetic population of individuals or chromosomes each individual encodes the position of a point of interest on one of the available images as well as parameters of a local transformation that generates the position of the corresponding point on the other image the proposed algorithm aims to discover individuals that corresponds to local maxima of an objective function that measures the similarity between patches of the two images when the gas based multimodal optimization algorithm terminates pairs of corresponding points between the two images are obtained that can be used for the generation of a dense deformation field by means of the thin plate splines model the proposed algorithm is applied to 2d medical images dental and retinal images under known transformations similarity and elastic transformation and is also assessed on medical images with unknown transformations computer tomography transverse slices the proposed algorithm is compared against the iterative closest point icp algorithm and a well known non rigid registration algorithm based on free form deformations ffd using various quantitative criteria the obtained results indicate that in case of known similarity transformations the proposed multimodal gas based algorithm and the icp algorithm present equivalent performance whereas the ffd algorithm is clearly outperformed in the case of known sinousoidal deformations the proposed multimodal gas based and the ffd algorithm achieve equivalent performance and clearly outperform the icp algorithm finally in the case of unknown elastic deformations the proposed gas based algorithm appears to perform marginally better than the ffd algorithm whereas it clearly outperforms the icp algorithm

convergence analysis of a deterministic discrete time system of feng s mca learning algorithm the convergence of minor component analysis mca algorithms is an important issue with bearing on the use of these methods in practical applications this correspondence studies the convergence of feng s mca learning algorithm via a corresponding deterministic discrete time ddt system some sufficient convergence conditions are obtained for feng s mca learning algorithm with constant learning rate simulations are carried out to illustrate the theory

robust voxel similarity metrics for the registration of dissimilar single and multimodal images in this paper we develop data driven registration algorithms relying on pixel similarity metrics that enable an accurate subpixel rigid registration of dissimilar single or multimodal 2d 3d images gross dissimilarities are handled by considering similarity measures related to robust m estimators in particular a novel robust similarity metric is proposed for comparing multimodal images the proposed robust similarity metrics are compared to the most popular standard similarity metrics on synthetic as well as on real world image pairs showing gross dissimilarities three case studies are considered the registration of single modal and multimodal 3d medical images the matching of multispectral remotely sensed images and the registration of intensity and range images the proposed robust similarity measures compare favourably with the standard non robust techniques

asymptotics of reweighted estimators of multivariate location and scatter we investigate the asymptotic behavior ofa weighted sample mean and covariance where the weights are determined by the mahalanobis distances with respect to initial robust estimators we derive an explicit expansion for the weighted estimators from this expansion it can be seen that reweighting does not improve the rate ofconvergence ofthe initial estimators we also show that ifone uses smooth s estimators to determine the weights the weighted estimators are asymptotically normal finally we will compare the efficiency and local robustness of the reweighted s estimators with two other improvements of s estimators estimators and constrained m estimators

coupled principal component analysis a framework for a class of coupled principal component learning rules is presented in coupled rules eigenvectors and eigenvalues of a covariance matrix are simultaneously estimated in coupled equations coupled rules can mitigate the stability speed problem affecting noncoupled learning rules since the convergence speed in all eigendirections of the jacobian becomes widely independent of the eigenvalues of the covariance matrix a number of coupled learning rule systems for principal component analysis two of them new is derived by applying newton s method to an information criterion the relations to other systems of this class the adaptive learning algorithm ala the robust recursive least squares algorithm rrlsa and a rule with explicit renormalization of the weight vector length are established

mir an approach to robust clustering application to range image segmentation this paper describes an unsupervised region merging technique based on a novel robust statistical test the merging decision is derived from the mutual inlier ratio mir of adjacent regions this ratio is computed using robust regression techniques and a novel method to estimate the robust scale of the gaussian distribution a discrimination value to recognize identical gaussian distributions with the mir is derived theoretically as a function of the sizes of the compared sets the presented method to test distributions is compared with the established kolmogorov smirnov test and implemented into a segmentation algorithm for planar range images the iterative region growing technique is evaluated using an established framework for range image segmentation comparison involving 60 real range images the evaluation incorporates a comparison with four state of the art algorithms and gives an experimental demonstration of the need for robust methods capable of handling noisy data in real applications

robust parameter estimation in computer vision estimation techniques in computer vision applications must estimate accurate model parameters despite small scale noise in the data occasional large scale measurement errors outliers and measurements from multiple populations in the same data set increasingly robust estimation techniques some borrowed from the statistics literature and others described in the computer vision literature have been used in solving these parameter estimation problems ideally these techniques should effectively ignore the outliers and measurements from other populations treating them as outliers when estimating the parameters of a single population two frequently used techniques are least median of squares lms p j rousseeuw j amer statist assoc 79 1984 pp 871 880 and m estimators robust statistics the approach based on influence functions f r hampel et al john wiley 1986 robust statistics p j huber john wiley 1981 lms handles large fractions of outliers up to the theoretical limit of 50 for estimators invariant to affine changes to the data but has low statistical efficiency m estimators have higher statistical efficiency but tolerate much lower percentages of outliers unless properly initialized while robust estimators have been used in a variety of computer vision applications three are considered here in analysis of range images images containing depth or x y z measurements at each pixel instead of intensity measurements robust estimators have been used successfully to estimate surface model parameters in small image regions in stereo and motion analysis they have been used to estimate parameters of what is called the fundamental matrix which characterizes the relative imaging geometry of two cameras imaging the same scene recently robust estimators have been applied to estimating a quadratic image to image transformation model necessary to create a composite mosaic image from a series of images of the human retina in each case a straightforward application of standard robust estimators is insufficient and carefully developed extensions are used to solve the problem

computer intensive methods in statistical regression this is a survey of modern developments in statistical regression written for the mathematically educated nonstatistician it begins with a review of the traditional theory of least squares curve fitting modern developments in regression theory have developed in response to the practical limitations of the least squares approach recent progress has been made feasible by the electronic computer which frees statisticians from the confines of mathematical tractability topics discussed include robust regression bootstrap measures of variability local smoothing and cross validation projection pursuit mallows c p criterion stein estimation generalized regression for poisson data and regression methods for censored data all of the methods are illustrated with real life examples

face recognition a convolutional neural network approach we present a hybrid neural network for human face recognition which compares favourably with other methods the system combines local image sampling a self organizing map som neural network and a convolutional neural network the som provides a quantization of the image samples into a topological space where inputs that are nearby in the original space are also nearby in the output space thereby providing dimensionality reduction and invariance to minor changes in the image sample and the convolutional neural network provides partial invariance to translation rotation scale and deformation the convolutional network extracts successively larger features in a hierarchical set of layers we present results using the karhunen loeve transform in place of the som and a multilayer perceptron mlp in place of the convolutional network for comparison we use a database of 400 images of 40 individuals which contains quite a high degree of variability in expression pose and facial details we analyze the computational complexity and discuss how new classes could be added to the trained recognizer

a generalized information criterion for generalized minor component extraction generalized minor component analysis gmca is an essential technique in data classification and signal processing in this paper we propose an information criterion for gmca and derive a fast gmca algorithm for extracting the first generalized minor component gmc by using quasi newton method to this information criterion in order to extract multiple gmcs through the weighed matrix method this information criterion is extended into a weighted one which has a unique global maximum attained if and only if its state matrices converge to the gmcs of the matrix pencil composed of the autocorrelation matrices of two stochastic processes a gradient algorithm is also derived based on this weighted information criterion theoretical analysis shows that the gradient algorithm has self stabilizing property and does not need the normalization operation required in other algorithms the global convergence analysis of the proposed algorithm is accomplished through the lyapunov method numerical simulations and real application are carried out to further demonstrate the accuracy and speed advantages of the proposed algorithms

convergence adaptive refinement and scaling in 1d peridynamics we introduce here adaptive refinement algorithms for the non local method peridynamics which was proposed in j mech phys solids 2000 48 175 209 as a reformulation of classical elasticity for discontinuities and long range forces we use scaling of the micromodulus and horizon and discuss the particular features of adaptivity in peridynamics for which multiscale modeling and grid refinement are closely connected we discuss three types of numerical convergence for peridynamics and obtain uniform convergence to the classical solutions of static and dynamic elasticity problems in 1d in the limit of the horizon going to zero continuous micromoduli lead to optimal rates of convergence independent of the grid used while discontinuous micromoduli produce optimal rates of convergence only for uniform grids examples for static and dynamic elasticity problems in 1d are shown the relative error for the static and dynamic solutions obtained using adaptive refinement are significantly lower than those obtained using uniform refinement for the same number of nodes copyright 2008 john wiley sons ltd

outlier robust corner preserving methods for reconstructing noisy images the ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother unfortunately they usually seem to be at odds with each other one can only improve one property at the cost of the other by combining m smoothing and least squares trimming the tm smoother is introduced as a means to unify corner preserving properties and outlier robustness to identify edge and corner preserving properties a new theory based on differential geometry is developed further robustness concepts are transferred to image processing in two examples the tm smoother outperforms other corner preserving smoothers a software package containing both the tm and the m smoother can be downloaded from the internet

a generalized ordinary finite deformation constitutive correspondence model for peridynamics abstract a finite deformation constitutive framework for peridynamics that uses generalized kirchhoff stress measures as intermediate quantities in computing the peridynamic material point interactions is proposed it is shown to be a generalization of a previous finite deformation constitutive correspondence theory and has additional useful properties the new model is shown to be an ordinary material model and therefore conserves angular momentum without additional restrictions additionally it does not suffer from well known surface effects present in some peridynamic material models has improved material stability properties and allows for inclusion of elasto plastic behavior in a straightforward manner

the cross search algorithm for motion estimation image coding a fast block matching algorithm for motion estimation is presented it is based on a logarithmic step where in each search step only four locations are tested for a motion displacement of w pels frame this technique requires 5 4 log sub 2 w computations to locate the best match using sequences of cif standard pictures the interframe motion compensated prediction error with this technique is compared to the other fast methods the computational complexity of this algorithm is also compared against those methods

parametric classification of bingham distributions based on grassmann manifolds in this paper we present a novel bayesian classification framework of the matrix variate bingham distributions with the inclusion of its normalizing constant and develop a consistent general parametric modeling framework based on the grassmann manifolds to calculate the normalizing constants of the bingham model this paper extends the method of saddle point approximation spa to a new setting furthermore it employs the standard theory of maximum likelihood estimation mle to evaluate the involved parameters in the used probability density functions the validity and performance of the proposed approach are tested on 14 real world visual classification databases we have compared the classification performance of our proposed approach with the baselines from the previous related approaches the comparison shows that on most of the databases the performance of our approach is superior

a quasi newton adaptive algorithm for generalized symmetric eigenvalue problem we first recast the generalized symmetric eigenvalue problem where the underlying matrix pencil consists of symmetric positive definite matrices into an unconstrained minimization problem by constructing an appropriate cost function we then extend it to the case of multiple eigen vectors using an inflation technique based on this asymptotic formulation we derive a quasi newton based adaptive algorithm for estimating the required generalized eigen vectors in the data case the resulting algorithm is modular and parallel and it is globally convergent with probability one we also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices in the pencil on the resulting eigenstructure simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank one updating algorithm of karasalo 1986 further the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems

convergence analysis of a deterministic discrete time system of oja s pca learning algorithm the convergence of oja s principal component analysis pca learning algorithms is a difficult topic for direct study and analysis traditionally the convergence of these algorithms is indirectly analyzed via certain deterministic continuous time dct systems such a method will require the learning rate to converge to zero which is not a reasonable requirement to impose in many practical applications recently deterministic discrete time ddt systems have been proposed instead to indirectly interpret the dynamics of the learning algorithms unlike dct systems ddt systems allow learning rates to be constant which can be a nonzero this paper will provide some important results relating to the convergence of a ddt system of oja s pca learning algorithm it has the following contributions 1 a number of invariant sets are obtained based on which we can show that any trajectory starting from a point in the invariant set will remain in the set forever thus the nondivergence of the trajectories is guaranteed 2 the convergence of the ddt system is analyzed rigorously it is proven in the paper that almost all trajectories of the system starting from points in an invariant set will converge exponentially to the unit eigenvector associated with the largest eigenvalue of the correlation matrix in addition exponential convergence rate are obtained providing useful guidelines for the selection of fast convergence learning rate 3 since the trajectories may diverge the careful choice of initial vectors is an important issue this paper suggests to use the domain of unit hyper sphere as initial vectors to guarantee convergence 4 simulation results will be furnished to illustrate the theoretical results achieved

a novel unified and self stabilizing algorithm for generalized eigenpairs extraction generalized eigendecomposition problem has been widely employed in many signal processing applications in this paper we propose a unified and self stabilizing algorithm which is able to extract the first principal and minor generalized eigenvectors of a matrix pencil of two vector sequences adaptively furthermore we extend the proposed algorithm to extract multiple generalized eigenvectors the performance analysis shows that only the desired equilibrium point of the proposed algorithm is stable and all others are unstable repellers or saddle points convergence analysis based on the deterministic discrete time approach shows that for a step size within a certain range the norm of the principal minor state vector converges to a fixed value that relates to the corresponding principal minor generalized eigenvalue thus the proposed algorithm is a generalized eigenpairs eigenvectors and eigenvalues extraction algorithm finally the simulation experiments are carried to further demonstrate the efficiency of the proposed algorithm

linearized state based peridynamics for 2 d problems summary in this work the authors formulate a 2 d linearized ordinary state based peridynamic model of elastic deformations and compute the stiffness matrix for 2 d plane stress strain conditions this model is then verified by testing the recovery of elastic properties for given poisson s ratios in the range 0 1 0 45 the convergence behavior of peridynamic solutions in terms of the size of the nonlocal region by comparison with the classical local mechanics model is also discussed the degree to which the peridynamic surface effect influences the recovery of elastic properties is examined and stress strain recovery values are found to have a definite influence on the results the technique used here can provide the basis for applying 2 d peridynamic models to the study of fatigue failure and quasi static fracture problems copyright 2016 john wiley sons ltd

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

empirically derived estimates of the complexity of labeling line drawings of polyhedral scenes abstract several results have been obtained in the past about the complexity of understanding line drawings of polyhedral scenes kirousis and papadimitriou 1988 have shown that the problem of labeling line drawings of trihedral scenes is np complete the human brain however seems to grasp at a glance the 3d structure associated with a line drawing a possible explanation of this discrepancy offered by kirousis and papadimitriou themselves is that the worst case complexity does not reflect the real difficulty of labeling line drawings which might be far less in the average or in typical cases however no statistical analysis has ever been carried out to test this conjecture the core of this paper is an algorithm for the generation of random instances of polyhedral scenes random instances of line drawings are then obtained as perspective projections of these scenes and can be used as an input to standard labeling algorithms so as to derive experimental estimates of the complexity of these algorithms the results indicate that the median case complexity is linear in the number of junctions this substantiates the conjecture that typical instances of line drawings are easy to label and may help explain the ease by which the brain is able to solve the problem

robust adaptive beamforming for general rank signal models the performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment sources or sensor array this is especially true when the desired signal components are present in the beamformer training data snapshots because in this case the adaptive array performance is very sensitive to array and model imperfections the similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly but the training sample size is small we propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary type mismatches of the desired signal array response our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank one point source and higher rank scattered source fluctuating wavefront desired signal models the proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst case performance optimization simple closed form solutions to the considered robust adaptive beamforming problems are derived our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms while at the same time offer a significantly improved robustness and faster convergence rates

computation and analysis of image motion a synopsis of current problems and methods the goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis and of the methods proposed exposing the underlying models and supporting assumptions a sufficient number of pointers to the literature will be given concentrating mostly on recent contributions emphasis will be on the detection measurement and segmentation of image motion tracking and deformable motion issues will be also addressed finally a number of related questions which could require more investigations will be presented

robust estimation for range image segmentation and reconstruction this correspondence presents a segmentation and fitting method using a new robust estimation technique we present a robust estimation method with high breakdown point which can tolerate more than 80 of outliers the method randomly samples appropriate range image points in the current processing region and solves equations determined by these points for parameters of selected primitive type from k samples we choose one set of sample points that determines a best fit equation for the largest homogeneous surface patch in the region this choice is made by measuring a residual consensus resc using a compressed histogram method which is effective at various noise levels after we get the best fit surface parameters the surface patch can be segmented from the region and the process is repeated until no pixel left the method segments the range image into planar and quadratic surfaces the resc method is a substantial improvement over the least median squares method by using histogram approach to inferring residual consensus a genetic algorithm is also incorporated to accelerate the random search

robust regression using repeated medians abstract the repeated median algorithm is a robustified u statistic in which nested medians replace the single mean unlike many generalizations of the univariate median repeated median estimates maintain the high 50 breakdown value and can resist the effects of outliers even when they comprise nearly half of the data because they are calculated directly not iteratively repeated median procedures can be used as starting values for iterative robust estimation methods for bivariate linear regression with symmetric errors repeated median estimates are unbiased and fisher consistent and their efficiency under gaussian sampling can be comparable to the efficiency of the univariate median author

the effect of median filtering on edge estimation and detection in this paper we consider the effect of median prefiltering on the subsequent estimation and detection of edges in digital images where possible a quantitative statistical comparison is made for a number of filters defined with two dimensional geometries in some cases one dimensional analyses are required to illustrate certain points noise images prefiltered by median filters defined with a variety of windowing geometries are used to support the analysis and it is found that median prefiltering improves the performance of both thresholding and zero crossing based edge detectors

nonmetric calibration of camera lens distortion differential methods and robust estimation this paper addresses the problem of calibrating camera lens distortion which can be significant in medium to wide angle lenses our approach is based on the analysis of distorted images of straight lines we derive new distortion measures that can be optimized using nonlinear search techniques to find the best distortion parameters that straighten these lines unlike the other existing approaches we also provide fast closed form solutions to the distortion coefficients we prove that including both the distortion center and the decentering coefficients in the nonlinear optimization step may lead to instability of the estimation algorithm our approach provides a way to get around this and at the same time it reduces the search space of the calibration problem without sacrificing the accuracy and produces more stable and noise robust results in addition while almost all existing nonmetric distortion calibration methods needs user involvement in one form or another we present a robust approach to distortion calibration based on the least median of squares estimator our approach is thus able to proceed in a fully automatic manner while being less sensitive to erroneous input data such as image curves that are mistakenly considered projections of three dimensional linear segments experiments to evaluate the performance of this approach on synthetic and real data are reported

connectivity based multiple circle fitting this paper proposes a connectivity based method for circle fitting the use of pixel connectivity effectively avoids false circle detection improves the robustness against noise and significantly reduces the computational load the desired circular models are extracted by searching for meaningful circular arcs the algorithm does not require a good initial guess and is effective for extracting an a priori unknown number of circles even when the number of outliers exceeds 50 the experimental results demonstrate that the proposed method performs well in detecting multiple intersecting or occluded circles

heteroscedastic regression in computer vision problems with bilinear constraint we present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise i e each data point having a different covariance matrix the algorithm is motivated by the recovery of bilinear forms one of the fundamental problems in computer vision which appears whenever the epipolar constraint is imposed or a conic is fit to noisy data points we employ the errors in variables eiv model and show why already at moderate noise levels most available methods fail to provide a satisfactory solution the improved behavior of the new algorithm is due to two factors taking into account the heteroscedastic nature of the errors arising from the linearization of the bilinear form and the use of generalized singular value decomposition gsvd in the computations the performance of the algorithm is compared with several methods proposed in the literature for ellipse fitting and estimation of the fundamental matrix it is shown that the algorithm achieves the accuracy of nonlinear optimization techniques at much less computational cost

least quantile regression via modern optimization we address the least quantile of squares lqs and in particular the least median of squares regression problem using modern optimization methods we propose a mixed integer optimization mio formulation of the lqs problem which allows us to find a provably global optimal solution for the lqs problem our mio framework has the appealing characteristic that if we terminate the algorithm early we obtain a solution with a guarantee on its sub optimality we also propose continuous optimization methods based on first order subdifferential methods sequential linear optimization and hybrid combinations of them to obtain near optimal solutions to the lqs problem the mio algorithm is found to benefit significantly from high quality solutions delivered by our continuous optimization based methods we further show that the mio approach leads to a an optimal solution for any dataset where the data points y i mathbf x i s are not necessarily in general position b a simple proof of the breakdown point of the lqs objective value that holds for any dataset and c an extension to situations where there are polyhedral constraints on the regression coefficient vector we report computational results with both synthetic and real world datasets showing that the mio algorithm with warm starts from the continuous optimization methods solve small n 100 and medium n 500 size problems to provable optimality in under two hours and outperform all publicly available methods for large scale n 10 000 lqs problems

dual horizon peridynamics a stable solution to varying horizons abstract in this paper we present a dual horizon peridynamics formulation which allows for simulations with dual horizon with minimal spurious wave reflection we prove the general dual property for dual horizon peridynamics based on which the balance of momentum and angular momentum in pd are naturally satisfied we also analyze the crack pattern of random point distribution and the multiple materials issue in peridynamics for selected benchmark problems we show that dh pd is less sensitive to the spatial than the original pd formulation

a robust competitive clustering algorithm with applications in computer vision this paper addresses three major issues associated with conventional partitional clustering namely sensitivity to initialization difficulty in determining the number of clusters and sensitivity to noise and outliers the proposed robust competitive agglomeration rca algorithm starts with a large number of clusters to reduce the sensitivity to initialization and determines the actual number of clusters by a process of competitive agglomeration noise immunity is achieved by incorporating concepts from robust statistics into the algorithm rca assigns two different sets of weights for each data point the first set of constrained weights represents degrees of sharing and is used to create a competitive environment and to generate a fuzzy partition of the data set the second set corresponds to robust weights and is used to obtain robust estimates of the cluster prototypes by choosing an appropriate distance measure in the objective function rca can be used to find an unknown number of clusters of various shapes in noisy data sets as well as to fit an unknown number of parametric models simultaneously several examples such as clustering mixture decomposition line plane fitting segmentation of range images and estimation of motion parameters of multiple objects are shown

rls based adaptive algorithms for generalized eigen decomposition the aim of this paper is to develop efficient online adaptive algorithms for the generalized eigen decomposition problem which arises in a variety of modern signal processing applications first we reinterpret the generalized eigen decomposition problem as an unconstrained minimization problem by constructing a novel cost function second by applying projection approximation method and recursive least square rls technique to the cost function a parallel adaptive algorithm for a basis for the r dimensional r 0 dominant generalized eigen subspace and a sequential algorithm based on deflation technique for the first r dominant generalized eigenvectors are derived these algorithms can be viewed as counterparts of the extended projection approximation subspace tracking past and pastd algorithms respectively furthermore we modify the parallel algorithm to explicitly estimate the first r generalized eigenvectors in parallel not the generalized eigen subspace more important the modified parallel algorithm can be used to extract multiple generalized eigenvectors of two nonstationary sequences while the proposed sequential algorithm lacks this ability because of slow convergence of minor generalized eigenvectors due to error propagation of the deflation technique third following convergence analysis methods for past and pastd we prove the asymptotic convergence properties of the proposed algorithms finally computer simulations are performed to investigate the accuracy and the speed advantages of the proposed algorithms

fast robust correlation a new fast statistically robust exhaustive translational image matching technique is presented fast robust correlation existing methods are either slow or non robust or rely on optimization fast robust correlation works by expressing a robust matching surface as a series of correlations speed is obtained by computing correlations in the frequency domain computational cost is analyzed and the method is shown to be fast speed is comparable to conventional correlation and for large images thousands of times faster than direct robust matching three experiments demonstrate the advantage of the technique over standard correlation

object matching algorithms using robust hausdorff distance measures a hausdorff distance hd is one of commonly used measures for object matching this work analyzes the conventional hd measures and proposes two robust hd measures based on m estimation and least trimmed square lts which are more efficient than the conventional hd measures by computer simulation the matching performance of the conventional and proposed hd measures is compared with synthetic and real images

improved one point quadrature algorithms for two dimensional peridynamic models based on analytical calculations the peridynamics theory is a reformulation of the classical theory of continuum mechanics based on long range interactions suitable for the description of material failure and damage integration plays a central role in this theory we study one point quadrature algorithms for the discretization of two dimensional integrals in peridynamics these algorithms are closely related to meshfree methods they assume an underlying reference lattice where each lattice point within a body is assigned a cell a main challenge in such algorithms is the accurate estimation of the area of the intersecting region between the neighborhood of a point and a neighbor cell we provide a classification of the different types of intersecting regions in square lattices and present analytical derivations for the exact calculation of their areas leading to improved integration accuracy to address convergence issues geometric centers of intersecting regions are taken as quadrature points replacing commonly used cell centers we present analytical derivations for the exact calculation of those geometric centers based on a decomposition of intersecting regions into subdomains of simple geometry by using exact values for the areas and geometric centers of intersecting regions we achieve an asymptotically monotonic convergence in numerical integration in contrast other algorithms from the literature exhibit a highly oscillatory behavior numerical results compare the proposed algorithms with others from the literature for different quantities of interest and demonstrate their improved accuracy and convergence error estimates for the quadrature algorithms are derived and extended and hybrid algorithms are discussed additional numerical studies using influence functions with a finite support and a controlled regularity suggest an alternative means to improve the convergence of discretization algorithms

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

threading fundamental matrices we present a new function that operates on fundamental matrices across a sequence of views the operation we call threading connects two consecutive fundamental matrices using the trifocal tensor as the connecting thread the threading operation guarantees that consecutive camera matrices are consistent with a unique 3d model without ever recovering a 3d model applications include recovery of camera ego motion from a sequence of views image stabilization across a sequence and multi view image based rendering

projection approximation subspace tracking subspace estimation plays an important role in a variety of modern signal processing applications we present a new approach for tracking the signal subspace recursively it is based on a novel interpretation of the signal subspace as the solution of a projection like unconstrained minimization problem we show that recursive least squares techniques can be applied to solve this problem by making an appropriate projection approximation the resulting algorithms have a computational complexity of o nr where n is the input vector dimension and r is the number of desired eigencomponents simulation results demonstrate that the tracking capability of these algorithms is similar to and in some cases more robust than the computationally expensive batch eigenvalue decomposition relations of the new algorithms to other subspace tracking methods and numerical issues are also discussed

hop diffusion monte carlo for epipolar geometry estimation between very wide baseline images we present a monte carlo approach for epipolar geometry estimation that efficiently searches for minimal sets of inlier correspondences in the presence of many outliers in the putative correspondence set a condition that is prevalent when we have wide baselines significant scale changes rotations in depth occlusion and repeated patterns the proposed monte carlo algorithm uses balanced local and global search blogs to find the best minimal set of correspondences the local search is a diffusion process using joint feature distributions that captures the dependencies among the correspondences and the global search is a hopping search process across the minimal set space controlled by photometric properties using a novel experimental protocol that involves computing errors for manually marked ground truth points and images with outlier rates as high as 90 percent we find that blogs is better than related approaches such as mapsac 1 napsac 2 and beem 3 blogs results are of similar quality as other approaches but blogs generate them in 10 times fewer iterations the time per iteration for blogs is also the lowest among the ones we studied