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

a model based approach to junction detection using radial energy a novel junction detector is presented that fits the neighborhood around a point to a junction model the junction model segments the neighborhood into wedges by determining a set of radial edges the radial edges are invariant to affine transforms creating an affine invariant junction detector the radial edges are evaluated based upon the pixels along the edge the angle between the pixel gradient and the vector to the potential junction point forms the initial basis for the measurement an initial set of radial edges is selected based upon identifying local maximums within a given arc distance an energy function is applied to the resulting radial segmentation and a greedy optimization routine is used to construct the minimal set of radial edges to identify the final junctions a second energy function is used that combines the components of the first energy function with the resulting change in standard deviation by separation into radial segments the junctions with the most energy in their local neighborhoods are selected as potential junctions the neighborhoods about the potential junctions are analyzed to determine if they represent a single line or multiple non parallel lines if the neighborhood represents multiple non parallel lines the point is classified as a junction point the junction detector is tested on several images including both synthetic and real images highlights of radially segmented junction points are displayed for the real images

a moment based unified approach to image feature detection in this paper a novel model based approach is proposed for generating a set of image feature maps or primal sketches for each type of feature a piecewise smooth parametric model is developed to characterize the local intensity function in an image projections of the intensity profile onto a set of orthogonal zernike moment generating polynomials are used to estimate model parameters and in turn generate the desired feature map a small set of moment based detectors is identified that can extract various kinds of primal sketches from intensity as well as range images one main advantage of using parametric model based techniques is that it is possible to extract complete information i e model parameters about the underlying image feature which is desirable in many high level vision tasks experimental results are included to demonstrate the effectiveness of proposed feature detectors

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

asymptotic equivalence of density estimation and gaussian white noise signal recovery in gaussian white noise with variance tending to zero has served for some time as a representative model for nonparametric curve estimation having all the essential traits in a pure form the equivalence has mostly been stated informally but an approximation in the sense of le cam s deficiency distance would make it precise the models are then asymptotically equivalent for all purposes of statistical decision with bounded loss in nonparametrics a first result of this kind has recently been established for gaussian regression we consider the analogous problem for the experiment given by n i i d observations having density f on the unit interval our basic result concerns the parameter space of densities which are in a holder ball with exponent 1 2 and which are uniformly bounded away from zero we show that an i i d sample of size n with density f is globally asymptotically equivalent to a white noise experiment with drift f l 2 and variance 1 4n l this represents a nonparametric analog of le cam s heteroscedastic gaussian approximation in the finite dimensional case the proof utilizes empirical process techniques related to the hungarian construction white noise models on f and log f are also considered allowing for various automatic asymptotic risk bounds in the i i d model from white noise

edge detection with embedded confidence computing the weighted average of the pixel values in a window is a basic module in many computer vision operators the process is reformulated in a linear vector space and the role of the different subspaces is emphasized within this framework wellknown artifacts of the gradient based edge detectors such as large spurious responses can be explained quantitatively it is also shown that template matching with a template derived from the input data is meaningful since it provides an independent measure of confidence in the presence of the employed edge model the widely used three step edge detection procedure gradient estimation non maxima suppression hysteresis thresholding is generalized to include the information provided by the confidence measure the additional amount of computation is minimal and experiments with several standard test images show the ability of the new procedure to detect weak edges

using angular dispersion of gradient direction for detecting edge ribbons edges in a scene generally project to smooth continuous curves nearly everywhere in the image which results in low angular deviation of the intensity gradients in small neighborhoods straddling edges angular deviation is shown to be a measure of snr a theoretical analysis of angular deviation arising due to independent and identically distributed n 0 sigma sup 2 random noise is presented angular deviation thresholds for neighborhood sizes from 3 3 to 11 11 pixels are determined both from this analysis and numerical examples the proposed gradient angular dispersion detection algorithm detects edge elements by comparing the measured angular deviation with values computed for the minimum acceptable snr low values of deviation violate the no edge hypothesis the algorithm is shown to make good use of the limited dynamic range of the imaging system the sensitivity and selectivity of the strategy are both shown to be high

variational analysis of the natural decay rates and eigenmodes of cavity enclosed diffusive fields a variational approach to the analysis of the natural decay rates and eigenmodes of cavity enclosed diffusive fields in general anisotropic and heterogeneous materials is presented in the bulk material diffusivity and volume relaxivity are accounted for the interaction of the cavity s medium with the embedding material is modeled via a surface relaxivity on the boundary surface the pertaining eigenmodes are proven to be orthogonal and to form a complete expansion of an initially excited diffusive field in view of the variational approach a finite element type of computation presents itself as the natural tool for numerics the resulting implementation on a simplicial mesh allows for the modeling of cavities of arbitrary shape to investigate the feasibility of using the approach in the inverse problem of reconstructing the shape and size of cavities from measured values of the natural decay rates of the eigenmodes we carry out a number of numerical experiments on the forward problem they demonstrate the method to be simple and robust both in 2d and 3d complex geometries for a benchmark problem with a known analytic solution error estimates are presented applications are found in for example nuclear magnetic resonance imaging of subsurface rock pore geometry biological cell structure and the analysis of neurological defects in medical diagnostics

data driven version of neyman s smooth test of fit abstract neyman s smooth test for testing uniformity is a recognized goodness of fit procedure as stated by lariccia the test can be viewed as a compromise between omnibus test procedures with generally low power in all directions and procedures whose power is focused in the direction of a specific alternative the basic idea behind this test is to embed the null density into say a k dimensional exponential family and then to construct an asymptotically optimal test for the parametric testing problem the resulting procedure is neyman s test with k components the most difficult problem related with using this test is the choice of k recommendations in statistical literature are sometimes confusing some authors advocate a small number of components whereas others show that in some situations a larger number of components is profitable all existing suggestions concerning how to select k exploit in fact some preliminary knowledge about a possible alternative in this article a new data driven met

susan a new approach to low level image processing this paper describes a new approach to low level image processing in particular edge and corner detection and structure preserving noise reduction non linear filtering is used to define which parts of the image are closely related to each individual pixel each pixel has associated with it a local image region which is of similar brightness to that pixel the new feature detectors are based on the minimization of this local image region and the noise reduction method uses this region as the smoothing neighbourhood the resulting methods are accurate noise resistant and fast details of the new feature detectors and of the new noise reduction method are described along with test results

consistency and monte carlo simulation of a data driven version of smooth goodness of fit tests the data driven method of selecting the number of components in neyman s smooth test for uniformity introduced by ledwina is extended the resulting tests consist of a combination of schwarz s bayesian information criterion bic procedure and smooth tests the upper bound of the dimension of the exponential families in applying schwarz s rule is allowed to grow with the number of observations to infinity simulation results show that the data driven version of neyman s test performs very well for a wide range of alternatives and is competitive with other recently introduced data driven procedures it is shown that the data driven smooth tests are consistent against essentially all alternatives in proving consistency new results on schwarz s selection rule are derived which may be of independent interest

a computational approach for corner and vertex detection corners and vertexes are strong and useful features in computer vision for scene analysis stereo matching and motion analysis here we deal with the development of a computational approach to these important features we consider first a corner model and study analytically its behavior once it has been smoothed using the well known gaussian filter this allows us to clarify the behavior of some well knowncornerness measure based approaches used to detect these points of interest most of these classical approaches appear to detect points that do not correspond to the exact position of the corner a new scale space based approach that combines useful properties from the laplacian and beaudet s measure beaudet 1978 is then proposed in order to correct and detect exactly the corner position an extension of this approach is then developed to solve the problem of trihedral vertex characterization and detection in particular it is shown that a trihedral vertex has two elliptic maxima on extremal contrast surfaces if the contrast is sufficient and this allows us to classify trihedral vertexes in 2 classes vertex and vertex as corner the corner detection approach developed is applied to accurately detect trihedral vertexes using an additional test in order to make a distinction between trihedral vertexes and corners many experiments have been carried out using noisy synthetic data and real images containing corners and vertexes most of the promising results obtained are used to illustrate the experimental section of this paper

on achievable accuracy in edge localization edge localization occurs when an edge detector determines the location of an edge in an image the authors use statistical parameter estimation techniques to derive bounds on achievable accuracy in edge localization these bounds known as the cramer rao bounds reveal the effect on localization of factors such as signal to noise ratio snr extent of edge observed scale of smoothing filter and a priori uncertainty about edge intensity by using continuous values for both image coordinates and intensity the authors focus on the effect of these factors prior to sampling and quantization they also analyze the canny algorithm and show that for high snr its mean squared error is only a factor of two higher than the lower limit established by the cramer rao bound although this is very good the authors show that for high snr the maximum likelihood estimator which is also derived virtually achieves the lower bound

adaptive hypothesis testing using wavelets let a function f be observed with a noise we wish to test the null hypothesis that the function is identically zero against a composite nonparametric alternative functions from the alternative set are separated away from zero in an integral e g l 2 norm and also possess some smoothness properties the minimax rate of testing for this problem was evaluated in earlier papers by ingster and by lepski and spokoiny under different kinds of smoothness assumptions it was shown that both the optimal rate of testing and the structure of optimal in rate tests depend on smoothness parameters which are usually unknown in practical applications in this paper the problem of adaptive assumption free testing is considered it is shown that adaptive testing without loss of efficiency is impossible an extra log log factor is inessential but unavoidable payment for the adaptation a simple adaptive test based on wavelet technique is constructed which is nearly minimax for a wide range of besov classes

multiscale testing of qualitative hypotheses suppose that one observes a process y on the unit interval where dy t n1 2f t dt dw t with an unknown function parameter f given scale parameter n 1 sample size and standard brownian motion w we propose two classes of tests of qualitative nonparametric hypotheses about f such as monotonicity or concavity these tests are asymptotically optimal and adaptive in a certain sense they are constructed via a new class of multiscale statistics and an extension of levy s modulus of continuity of brownian motion

local asymptotics for linear rank statistics with estimated score functions on etudie des versions modifiees de statistiques de rang lineaires s n avec une fonction de score pour le probleme de test de l aleatoire a deux echantillons

optimal calibration for multiple testing against local inhomogeneity in higher dimension based on two independent samples x 1 x m and x m 1 x n drawn from multivariate distributions with unknown lebesgue densities p and q respectively we propose an exact multiple test in order to identify simultaneously regions of significant deviations between p and q the construction is built from randomized nearest neighbor statistics it does not require any preliminary information about the multivariate densities such as compact support strict positivity or smoothness and shape properties the properly adjusted multiple testing procedure is shown to be sharp optimal for typical arrangements of the observation values which appear with probability close to one the proof relies on a new coupling bernstein type exponential inequality reflecting the non subgaussian tail behavior of a combinatorial process for power investigation of the proposed method a reparametrized minimax set up is introduced reducing the composite hypothesis p q to a simple one with the multivariate mixed density m n p 1 m n q as infinite dimensional nuisance parameter within this framework the test is shown to be spatially and sharply asymptotically adaptive with respect to uniform loss on isotropic holder classes the exact minimax risk asymptotics are obtained in terms of solutions of the optimal recovery

efficient and adaptive nonparametric test for the two sample problem the notion of efficient test for a euclidean parameter in a semiparametric model was introduced by stein proc third berkeley symp math statist probab 1 1956 187 195 such tests are locally most powerful for a wide class of infinite dimensional nuisance parameters the first formal application of this notion to a suitably parametrized two sample problem was provided by hajek ann math statist 33 1962 1124 1147 however this and subsequent solutions appear to be not well suited for practical applications this article aims to show that an adaptive two sample test introduced recently by janic wroblewska and ledwina scand j statist 27 2000 281 297 is locally most powerful under a more realistic setting

asymptotically exact nonparametric hypothesis testing in sup norm and at a fixed point for the signal in gaussian white noise model we consider the problem of testing the hypothesis h 0 f 0 the signal f is zero against the nonparametric alternative h 1 f where is a set of functions on r 1 of the form f f f c here is a holder or sobolev class of functions f is either the sup norm of f or the value of f at a fixed point c 0 is a constant is the minimax rate of testing and 0 is the asymptotic parameter of the model we find exact separation constants c 0 such that a test with the given summarized asymptotic errors of first and second type is possible for c c and is not possible for c c we propose asymptotically minimax test statistics

precision edge contrast and orientation estimation the contrast and orientation estimation accuracy of several edge operators that have been proposed in the literature is examined both for the noiseless case and in the presence of additive gaussian noise the test image is an ideal step edge that has been sampled with a square aperture grid the effects of subpixel translations and rotations of the edge on the performance of the operators are studied it is shown that the effect of subpixel translations of an edge can generate more error than moderate noise levels methods with improved results are presented for sobel angle estimates and the nevatia babu operator and theoretical noise performance evaluations are also provided an edge operator based on two dimensional spatial moments is presented all methods are compared according to worst case and rms error in an ideal noiseless situation and rms error under various noise levels

local orientation analysis in images by means of the hermite transform we introduce new theoretical results on how the local differential structure in images can be described processed and coded efficiently by means of the hermite transform it is shown that the hermite transform can take many alternative forms all of which have their specific advantages the various forms of the hermite transform correspond to different ways of coding the local orientation in the image and we describe a systematic theory based on well known principles from vector spaces for deriving such alternative forms one specific case called the sampled hermite transform is shown to be especially interesting for adaptive image processing and coding an application in the field of adaptive noise reduction is included by way of illustration

statistical estimation and optimal recovery new formulas are given for the minimax linear risk in estimating a linear functional of an unknown object from indirect data contaminated with random gaussian noise the formulas cover a variety of loss functions and do not require the symmetry of the convex a priori class it is shown that affine minimax rules are within a few percent of minimax even among nonlinear rules for a variety of loss functions it is also shown that difficulty of estimation is measured by the modulus of continuity of the functional to be estimated the method of proof exposes a correspondence between minimax affine estimates in the statistical estimation problem and optimal algorithms in the theory of optimal recovery

on the edge location error for local maximum and zero crossing edge detectors examines the localization criterion for edge detection and determine the probability density function describing the edge location error canny 1986 defines the measure of localization as the reciprocal of the root mean square edge location error and formulates an expression of this measure for local maximum detectors however tagare and defigueiredo 1990 point out that an incorrect assumption is made in the calculation the same procedure is used by sarkar and boyer 1991 for their localization measure for zero crossing detectors we modify the analysis and obtain a closed form solution of the probability density function of the edge location error examination of the density function indicates the variance of the edge location error does not exist and hence cannot be used directly as a measure of localization

robust and efficient image alignment based on relative gradient matching in this paper we present a robust image alignment algorithm based on matching of relative gradient maps this algorithm consists of two stages namely a learning based approximate pattern search and an iterative energy minimization procedure for matching relative image gradient the first stage finds some candidate poses of the pattern from the image through a fast nearest neighbor search of the best match of the relative gradient features computed from training database of feature vectors which are obtained from the synthesis of the geometrically transformed template image with the transformation parameters uniformly sampled from a given transformation parameter space subsequently the candidate poses are further verified and refined by matching the relative gradient images through an iterative energy minimization procedure this approach based on the matching of relative gradients is robust against nonuniform illumination variations experimental results on both simulated and real images are shown to demonstrate superior efficiency and robustness of the proposed algorithm over the conventional normalized correlation method

test of significance based on wavelet thresholding and neyman s truncation abstract traditional nonparametric tests such as the kolmogorov smirnov test and the cramer von mises test are based on the empirical distribution functions although these tests possess root n consistency they effectively use only information contained in the low frequencies this leads to low power in detecting fine features such as sharp and short aberrants as well as global features such as high frequency alternations the drawback can be repaired via smoothing based test statistics in this article we propose two such kind of test statistics based on the wavelet thresholding and the neyman truncation we provide extensive evidence to demonstrate that the proposed tests have higher power in detecting sharp peaks and high frequency alternations while maintaining the same capability in detecting smooth alternative densities as the traditional tests similar conclusions can be made for two sample nonparametric tests of distribution functions in that case the traditional linear rank tests such as th

finding edges in noisy scenes edge detection in the presence of noise is a well known problem this paper examines an applications motivated approach for solving the problem using novel techniques and presents a method developed by the authors that performs well on a large class of targets roc curves are used to compare this method with other well known edge detection operators with favorable results a theoretical argument is presented that favors lmmse filtering over median filtering in extremely noisy scenes simulated results of the research are presented

adaptive goodness of fit tests based on signed ranks within the nonparametric regression model with unknown regression function l and independent symmetric errors a new multiscale signed rank statistic is introduced and a conditional multiple test of the simple hypothesis l 0 against a nonparametric alternative is proposed this test is distribution free and exact for finite samples even in the heteroscedastic case it adapts in a certain sense to the unknown smoothness of the regression function under the alternative and it is uniformly consistent against alternatives whose sup norm tends to zero at the fastest possible rate the test is shown to be asymptotically optimal in two senses it is rate optimal adaptive against holder classes furthermore its relative asymptotic efficiency with respect to an asymptotically minimax optimal test under sup norm loss is close to 1 in case of homoscedastic gaussian errors within a broad range of holder classes simultaneously

rapid simulation of the time dependent diffusion coefficient in complex materials a finite difference approach is presented for the analysis of the time dependent diffusion coefficient for general heterogeneous materials that are either cavity enclosed or periodic in the bulk material diffusivity and volume relaxivity are accounted for the interaction of the diffusive medium with non diffusive inclusions is modeled via a surface relaxivity the time dependence is modeled using matrix exponentials that are shown to be efficiently evaluated using a krylov subspace approach for a 3d model grid composed of m voxels of diffusive material voxels containing non diffusive material are not stored in the kernel matrix the memory requirement is 15m and the computational time complexity for two large scale example models is shown to be of order m1 39 and m1 10 error estimate formulas are presented that can be used to guide the choice of domain grid resolution richardson extrapolation is shown to be effective in lowering simulation error we apply this approach to modeling the nuclear magnetic resonance response of several subsurface rock pore geometries they demonstrate the method to be simple and robust in both 2d and 3d complex geometries

evaluation of ridge seeking operators for multimodality medical image matching ridge like structures in digital images may be extracted by convolving the images with derivatives of gaussians the choice of the convolution operator and of the parameters involved defines a specific ridge image in this paper various ridge measures related to isophote curvature are constructed reviewed and evaluated with respect to their usability in ct mri matching of human brain scans construction is initially done using heuristics in two dimensional images and then established firmly in a mathematical framework attention is paid to the necessity of operator invariance scale of the operator extension to three dimensional images and relations to isophote and principal curvature it is shown that one of the ridge measures appears well suited for the purpose of matching despite the fact that the measure fails to detect ridges in a number of stylized scenes

on detecting edges an edge in an image corresponds to a discontinuity in the intensity surface of the underlying scene it can be approximated by a piecewise straight curve composed of edgels i e short linear edge elements each characterized by a direction and a position the approach to edgel detection here is to fit a series of one dimensional surfaces to each window kernel of the operator and accept the surface description which is adequate in the least squares sense and has the fewest parameters a one dimensional surface is one which is constant along some direction the tanh is an adequate basis for the stepedge and its combinations are adequate for the roofedge and the line edge the proposed method of step edgel detection is robust with respect to noise for step size noise 2 5 it has subpixel position localization position and an angular localization better than 10 further it is designed to be insensitive to smooth shading these results are demonstrated by some simple analysis statistical data and edgelimages also included is a comparison of performance on a real image with a typical operator difference of gaussians the results indicate that the proposed operator is superior with respect to detection localization and resolution

random walks and nmr measurements in porous media the paper studies the relationship between nmr measurements of the magnetization decay in porous media and random walk problems the behaviour of this decay can be related to the statistical properties of random walks which interact with the pore solid interface via perfectly reflecting boundary conditions an efficient numerical technique measures these statistics using a variable step size random walk simulation this technique is applied to three simple models for porous materials the results indicate that there is a regime of stretched exponential relaxation of the magnetization for a percolation model

spatial aggregation of local likelihood estimates with applications to classification this paper presents a new method for spatially adaptive local constant likelihood estimation which applies to a broad class of nonparametric models including the gaussian poisson and binary response models the main idea of the method is given a sequence of local likelihood estimates weak estimates to construct a new aggregated estimate whose pointwise risk is of order of the smallest risk among all weak estimates we also propose a new approach toward selecting the parameters of the procedure by providing the prescribed behavior of the resulting estimate in the simple parametric situation we establish a number of important theoretical results concerning the optimality of the aggregated estimate in particular our oracle result claims that its risk is up to some logarithmic multiplier equal to the smallest risk for the given family of estimates the performance of the procedure is illustrated by application to the classification problem a numerical study demonstrates its reasonable performance in simulated and real life examples

image field categorization and edge corner detection from gradient covariance edges corners and vertices in an image correspond to 1d one dimensional and 2d discontinuities in the intensity surface of the underlying scene ridges and peaks correspond to 1d and 2d extrema in it all of them can be characterized by the distribution of gradients particularly by the dimensionality of it the approach to image field categorization here is to construct a covariance matrix of the gradient vector in each small window and apply the canonical correlation analysis to it schwarz s inequality on the matrix determinant and the related differential equation is the key to this analysis we obtain two operators p sub eg and q sub eg to categorize the image field into a unidirectionally varying region univar an omidirectionally varying region omnivar and a nonvarying region we investigate the conditions under which their absolute maximum response i e p sub eg 1 and q sub eg 1 occurs in the small window and show that they are respectively the desired 1d and 2d discontinuities extrema and omnivar is in many cases a 1d pattern in polar coordinates this leads to an algorithm to obtain further classification and accurate localization of them into edges ridges peaks corners and vertices through detailed analysis in the informative varying axis of them we examined and compared the performance of the operators and the localization algorithm on various types of images and various noise levels the results indicate that the proposed method is superior with respect to stability localization and resolution

applications of vector fields to image processing we use rotational and curvature properties of vector fields to identify critical features of an image using vector analysis and dif ferential geometry we establish the properties needed and then use these properties in three ways first our results make it theoretically possible to identify extremal edges of an intensity function f x y of two variables by considering the gradient vector field v f there is also enough information in f to find regions of high curvature i e high curvature of the level paths of f for color images we use the vector field v i q in application the image is partitioned into a grid of squares on the boundary of each square v v is sampled and these unit vectors are used as the tangents of a curve the rotation number or topological degree and the average curvature f are computed for each square analysis of these numbers yields infor mation on edges and curvature experimental results from both simu lated and real data are described

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

local grayvalue invariants for image retrieval this paper addresses the problem of retrieving images from large image databases the method is based on local grayvalue invariants which are computed at automatically detected interest points a voting algorithm and semilocal constraints make retrieval possible indexing allows for efficient retrieval from a database of more than 1 000 images experimental results show correct retrieval in the case of partial visibility similarity transformations extraneous features and small perspective deformations

some defects in finite difference edge finders this work illustrates and explains various artifacts in the output of five finite difference edge finders those of j f canny 1983 1986 r a boie et al 1986 and r a boie and i j cox 1987 and three variations on that of d marr and e c hildreth 1980 reimplemented with a common output format and method of noise suppression these artifacts include gaps in boundaries spurious boundaries and deformation of region shape

sharp adaptive estimation of linear functionals we consider estimation of a linear functional t f where f is an unknown function observed in gaussian white noise we find asymptotically sharp adaptive estimators on various scales of smoothness classes in multidimensional situations the results allow evaluating explicitly the effect of dimension and treating general scales of classes furthermore we establish a connection between sharp adaptation and optimal recovery namely we propose a scheme that reduces the construction of sharp adaptive estimators on a scale of functional classes to a solution of the corresponding optimization problem

adaptive pseudo dilation for gestalt edge grouping and contour detection we consider the problem of detecting object contours in natural images in many cases local luminance changes turn out to be stronger in textured areas than on object contours therefore local edge features which only look at a small neighborhood of each pixel cannot be reliable indicators of the presence of a contour and some global analysis is needed we introduce a new morphological operator called adaptive pseudo dilation apd which uses context dependent structuring elements in order to identify long curvilinear structure in the edge map we show that grouping edge pixels as the connected components of the output of apd results in a good agreement with the gestalt law of good continuation the novelty of this operator is that dilation is limited to the voronoi cell of each edge pixel an efficient implementation of apd is presented the grouping algorithm is then embedded in a multithreshold contour detector at each threshold level small groups of edges are removed and contours are completed by means of a generalized reconstruction from markers the use of different thresholds makes the algorithm much less sensitive to the values of the input parameters both qualitative and quantitative comparison with existing approaches prove the superiority of the proposed contour detector in terms of larger amount of suppressed texture and more effective detection of low contrast contours

a general class of exponential inequalities for martingales and ratios in this paper we introduce a technique for obtaining exponential inequalities with particular emphasis placed on results involving ratios our main applications consist of approximations to the tail probability of the ratio of a martingale over its conditional variance or its quadratic variation for continuous martingales we provide examples that strictly extend several of the classical exponential inequalities for sums of independent random variables and martingales the spirit of this application is that when going from results for sums of independent random variables to martingales one should replace the variance by the conditional variance and the exponential of a function of the variance by the expectation of the exponential of the same function of the conditional variance the decoupling inequalities used to attain our goal are of independent interest they include a new exponential decoupling inequality with constraints and a sharp inequality for the probability of the intersection of a fixed number of dependent sets finally we also present an exponential inequality that does not require any integrability conditions involving the ratio of the sum of conditionally symmetric variables to its sum of squares

multiscale inference about a density we introduce a multiscale test statistic based on local order statistics and spacings that provides simultaneous confidence statements for the existence and location of local increases and decreases of a density or a failure rate the procedure provides guaranteed finite sample significance levels is easy to implement and possesses certain asymptotic optimality and adaptivity properties

early jump out corner detectors the authors present two new corner detectors one works by using dissimilarity along the contour direction to detect curves in the image contour and the other estimates image curvature along the contour direction these operators are fast robust to noise and require no subjective thresholding

optimal and fast detection of spatial clusters with scan statistics we consider the detection of multivariate spatial clusters in the bernoulli model with n locations where the design distribution has weakly dependent marginals the locations are scanned with a rectangular window with sides parallel to the axes and with varying sizes and aspect ratios multivariate scan statistics pose a statistical problem due to the multiple testing over many scan windows as well as a computational problem because statistics have to be evaluated on many windows this paper introduces methodology that leads to both statistically optimal inference and computationally efficient algorithms the main difference to the traditional calibration of scan statistics is the concept of grouping scan windows according to their sizes and then applying different critical values to different groups it is shown that this calibration of the scan statistic results in optimal inference for spatial clusters on both small scales and on large scales as well as in the case where the cluster lives on one of the marginals methodology is introduced that allows for an efficient approximation of the set of all rectangles while still guaranteeing the statistical optimality results described above it is shown that the resulting scan statistic has a computational complexity that is almost linear in n

galton s test as a linear rank test with estimated scores and its local asymptotic efficiency based on rank estimators of b we consider an easy but rough and inconsistent rank estimator of b the resulting rank test turns out to be a generalization of galton s test a formula for local asymptotic power under arbitrary local alternatives is derived which allows for comparison of galton s test with every linear rank test for various types of alternatives the galton test is compared with the optimal linear rank test and with the wilcoxon test in order to get an impression of the validity of extrapolation to finite sample sizes we included a monte carlo study under the same types of fixed alternatives

asymptotic minimax risk for sup norm loss solution via optimal recovery we study the problem of estimating an unknown function on the unit interval or itsk th derivative with supremum norm loss when the function is observed in gaussian white noise and the unknown function is known only to obey lipschitz smoothness k 0 we discuss an optimization problem associated with the theory ofoptimal recovery although optimal recovery is concerned with deterministic noise chosen by a clever opponent the solution of this problem furnishes the kernel of the minimax linear estimate for gaussian white noise moreover this minimax linear estimator is asymptotically minimax among all estimates we sketch also applications to higher dimensions and to indirect measurement e g deconvolution problems

detection of composite edges the paper presents a new parametric model based approach to high precision composite edge detection using orthogonal zernike moment based operators it deals with two types of composite edges a generalized step and b pulse staircase edges a 2 d generalized step edge is modeled in terms of five parameters two gradients on two sides of the edge the distance from the center of the candidate pixel the orientation of the edge and the step size at the location of the edge a 2 d pulse staircase edge is modeled in terms of two steps located at two positions within the mask and the edge orientation a pulse edge is formed if the steps are of opposite polarities whereas a staircase edge results from two steps having the same polarity two complex and two real zernike moment based masks are designed to determine parameters of both the 2 d edge models for a given edge model estimated parameter values at a point are used to detect the presence or absence of that type of edge extensive noise analysis is performed to demonstrate the robustness of the proposed operators experimental results with intensity and range images are included to demonstrate the efficacy of the proposed edge detection technique as well as to compare its performance with the geometric moment based step edge detection technique and canny s 1986 edge detector

restoration of images corrupted by gaussian and uniform impulsive noise many approaches to image restoration are aimed at removing either gaussian or uniform impulsive noise this is because both types of degradation processes are distinct in nature and hence they are easier to manage when considered separately nevertheless it is possible to find them operating on the same image which produces a hard damage this happens when an image already contaminated by gaussian noise in the image acquisition procedure undergoes impulsive corruption during its digital transmission here we propose a principled method to remove both types of noise it is based on a bayesian classification of the input pixels which is combined with the kernel regression framework

extracting image orientation feature by using integration operator this paper presents an orientation operator to extract image local orientation features we show that a proper employment of image integration leads to an unbiased orientation estimate based on which an orientation operator is proposed the resulting discrete operator has flexibility in the scale selection as the scale change does not violate the bias minimization criteria an analytical formula is developed to compare orientation biases of various discrete operators the proposed operator shows lower bias than eight well known gradient operators experiments further demonstrate higher orientation accuracy of the proposed operator than these gradient operators