on the gaussian approximation of convolutions under multidimensional analogues of s n bernstein s inequality conditions on etudie le taux d approximation de distribution de sommes de vecteurs aleatoires independants par des distributions gaussiennes correspondantes

on critical point detection of digital shapes in this paper we present a nonlinear algorithm for critical point detection cpd of 2d digital shapes the algorithm eliminates the problems arising from curvature approximation and gaussian filtering in the existing algorithms based on the definition of critical level we establish a set of criteria for the design of an effective cpd algorithm for the first time by quantifying the critical level to the modified area confined by three consecutive pseudocritical points a simple but very effective algorithm is developed the comparison of our experimental results with those of many other cpd algorithms shows that the proposed algorithm is superior in that it provides a sequence of figures at every detail level and each has a smaller integral error than the others with the same number of critical points the experimental results on shapes with various complexities also show the algorithm is reliable and robust with regard to noise

a curve bend function based method to characterize contour shapes in this paper a new curve bend function cbf based method is presented to extract main features of a contour it utilizes two quantities one called a curve bend angle cba and the other known as a type coefficient of curve segment defined on a contour the cba measures the bending degree at each point on the contour while the type coefficient characterizes the properties convexity and concavity of simple curve segments the cbf combines the advantages of the two quantities and provides an overall description of a contour a local maximum or minimum of the cbf corresponds to a critical point of the contour and the peak value is the cosine of the cba hence the problem of locating critical points of a contour is reduced to the problem of finding peak points of the cbf the sign of a peak value indicates the related cba being an inner or outer angle our experimental results and comparisons between the cbf method and rosenfeld johnston s method show that our method is effective and accurate in generating the description of a contour

gaussian approximation of local empirical processes indexed by functions an extended notion of a local empirical process indexed by functions is introduced which includes kernel density and regression function estimators and the conditional empirical process as special cases under suitable regularity conditions a central limit theorem and a strong approximation by a sequence of gaussian processes are established for such processes a compact law of the iterated logarithm lil is then inferred from the corresponding lil for the approximating sequence of gaussian processes a number of statistical applications of our results are indicated

the bm l _ mathbf 1 norm density estimator process the notion of an l1 norm density estimator process indexed by a class of kernels is introduced then a functional central limit theorem and a glivenko cantelli theorem are established for this process while assembling the necessary machinery to prove these results a body of poissonization techniques and restricted chaining methods is developed which is useful for studying weak convergence of general processes indexed by a class of functions none of the theorems imposes any condition at all on the underlying lebesgue density f also somewhat unexpectedly the distribution of the limiting gaussian process does not depend on f

functional laws of the iterated logarithm for local empirical processes indexed by sets we introduce the notion of a multivariate local and tail empirical process indexed by sets and establish a number of functional laws of the iterated logarithm for such processes this leads to a unified methodology to study the almost sure behavior of various statistics which are local functionals of the empirical distribution such statistics include density estimators and the bahadur kiefer representation

asymptotic equivalence for nonparametric generalized linear models we establish that a non gaussian nonparametric regression model is asymptotically equivalent to a regression model with gaussian noise the approximation is in the sense of le cam s deficiency distance the models are then asymptotically equivalent for all purposes of statistical decision with bounded loss our result concerns a sequence of independent but not identically distributed observations with each distribution in the same real indexed exponential family the canonical parameter is a value f ti of a regression function f at a grid point ti nonparametric glm when f is in a holder ball with exponent we establish global asymptotic equivalence to observations of a signal f t in gaussian white noise where is related to a variance stabilizing transformation in the exponential family the result is a regression analog of the recently established gaussian approximation for the i i d model the proof is based on a functional version of the hungarian construction for the partial sum process

a test of non identifying restrictions and confidence regions for partially identified parameters abstract we propose an easily implementable test of the validity of a set of theoretical restrictions on the relationship between economic variables which do not necessarily identify the data generating process the restrictions can be derived from any model of interactions allowing censoring and multiple equilibria when the restrictions are parameterized the test can be inverted to yield confidence regions for partially identified parameters thereby complementing other proposals primarily chernozhukov et al chernozhukov v hong h tamer e 2007 estimation and confidence regions for parameter sets in econometric models econometrica 75 1243 1285

a robust method for scale independent detection of curvature based criticalities and intersections in line drawings a novel two phase iterative method is proposed to identify curvature based criticalities and intersections in line drawings the method is based on evaluating a field obtained from the image via diffusion using adaptively changing ellipse shaped analysis windows the deviation of the average field strength values within the analysis windows from that of an external reference field is used as a metric to evaluate the criticality of a region the external reference field is computed from an image of a straight line the experimental results depict that the method is effective in detecting curvature based criticalities and intersections even for noisy and disconnected drawings as well as drawings drawn with a variety of brush characteristics such as glass ocean ripple scatter stamp strokes effects our method can be employed as a part of a design grammar interpreter highlightsthe method detects curvature based criticalities and intersections efficiently the method is effective for the noisy and disconnected line drawings the method is effective for line drawings with a variety of brush characteristics the method is utilized to represent shapes in a design grammar interpreter features in varying scales can be detected in digital drawings

functional limit laws for the increments of kaplan meier product limit processes and applications we prove functional limit laws for the increment functions of empirical processes based upon randomly right censored data the increment sizes we consider are classified into different classes covering the whole possible spectrum we apply these results to obtain a description of the strong limiting behavior of a series of estimators of local functionals of lifetime distributions in particular we treat the case of kernel density and hazard rate estimators

new polygonal approximation schemes for object shape representation abstract object shape representation is an important issue in pattern recognition and computer vision applications a set of new polygonal approximation schemes namely the internal maximum area polygonal approximation imapa the external minimum area polygonal approximation emapa and the minimum area deviation polygonal approximation madpa are proposed for object shape representation the area deviation between the initial object shape and its approximation polygon is defined as the cost function instead of outputting a unique approximation polygon each proposed scheme outputs a sequence of approximation polygons with different numbers of line segments and different area deviations for various application situations for a given area deviation bound and an initial object shape each proposed scheme can give a corresponding optimal approximation polygon with a minimum number of line segments a performance comparison among the proposed schemes is included the proposed schemes are compared with two other existing schemes some experimental results show the feasibility of the proposed approaches

scale based detection of corners of planar curves a technique for detecting and localizing corners of planar curves is proposed the technique is based on gaussian scale space which consists of the maxima of absolute curvature of the boundary function presented at all scales the scale space of isolated simple and double corners is first analyzed to investigate the behavior of scale space due to smoothing and interactions between two adjacent corners the analysis shows that the resulting scale space contains line patterns that either persist terminate or merge with a neighboring line next the scale space is transformed into a tree that provides simple but concise representation of corners at multiple scales finally a multiple scale corner detection scheme is developed using a coarse to fine tree parsing technique the parsing scheme is based on a stability criterion that states that the presence of a corner must concur with a curvature maximum observable at a majority of scales experiments were performed to show that the scale space corner detector is reliable for objects with multiple size features and noisy boundaries and compares favorably with other corner detectors tested

gaussian approximation of suprema of empirical processes we develop a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of gaussian processes without taking the route of approximating empirical processes themselves in the sup norm we prove an abstract approximation theorem that is applicable to a wide variety of problems primarily in statistics especially the bound in the main approximation theorem is non asymptotic and the theorem does not require uniform boundedness of the class of functions the proof of the approximation theorem builds on a new coupling inequality for maxima of sums of random vectors the proof of which depends on an effective use of stein s method for normal approximation and some new empirical processes techniques we study applications of this approximation theorem to local empirical processes and series estimation in nonparametric regression where the classes of functions change with the sample size and are not donsker type importantly our new technique is able to prove the gaussian approximation for the supremum type statistics under considerably weak regularity conditions especially concerning the bandwidth and the number of series functions in those examples

a uniform functional law of the logarithm for the local empirical process we prove a uniform functional law of the logarithm for the local empirical process to accomplish this we combine techniques from classical and abstract empirical process theory gaussian distributional approximation and probability on banach spaces the body of techniques we develop should prove useful to the study of the strong consistency of d variate kernel type nonparametric function estimators

uniform consistency of automatic and location adaptive delta sequence estimators the class of delta sequence estimators for a probability density includes the kernel histogram and orthogonal series types because each can be characterized as a collection of averages of some function that is indexed by a smoothing parameter there are two important extensions of this class the first allows a random smoothing parameter for example that specified by a cross validation method the second allows the smoothing parameter to be a function of location for example an estimator based on nearest neighbor distance in this paper a general method is presented which establishes uniform consistency for all of these estimators

curve segmentation under partial occlusion 2 d shape boundary segmentation is required as a fundamental and important stage in the recognition of partially occluded objects we introduce here a new segmentation method capable of extracting a controlled number of segments along a smooth boundary curve this new approach is invariant to similarity transformation and partial occlusion has only marginal influence on the segmentation of the visible part the basic concept is to transform the curve into another one which intersects itself points of intersection of the new curve are re transformed to the original curve and serve as endpoints of segments properties of the transform are discussed and conditions for existence of intersection points are given simulation results of gray level images are presented and advantages of our method over conventional approaches relying on singular points of the curvature are discussed

polygonal approximation of digital planar curves through break point suppression this paper presents a new algorithm that detects a set of dominant points on the boundary of an eight connected shape to obtain a polygonal approximation of the shape itself the set of dominant points is obtained from the original break points of the initial boundary where the integral square is zero for this goal most of the original break points are deleted by suppressing those whose perpendicular distance to an approximating straight line is lower than a variable threshold value the proposed algorithm iteratively deletes redundant break points until the required approximation which relies on a decrease in the length of the contour and the highest error is achieved a comparative experiment with another commonly used algorithm showed that the proposed method produced efficient and effective polygonal approximations for digital planar curves with features of several sizes

on the detection of dominant points on digital curves a parallel algorithm is presented for detecting dominant points on a digital closed curve the procedure requires no input parameter and remains reliable even when features of multiple sizes are present on the digital curve the procedure first determines the region of support for each point based on its local properties then computes measures of relative significance e g curvature of each point and finally detects dominant points by a process of nonmaximum suppression this procedure leads to the observation that the performance of dominant points detection depends not only on the accuracy of the measure of significance but also on the precise determination of the region of support this solves the fundamental problem of scale factor selection encountered in various dominant point detection algorithms the inherent nature of scale space filtering in the procedure is addressed and the performance of the procedure is compared to those of several other dominant point detection algorithms using a number of examples

central limit theorems for stochastic processes under random entropy conditions necessary and sufficient conditions are found for the weak convergence of the row sums of an infinitesimal row independent triangular array nj of stochastic processes indexed by a set s to a sample continuous gaussian process when the array satisfies a random entropy condition analogous to one used by gine and zinn 1984 for empirical processes this entropy condition is satisfied when s is a class of sets or functions with the vapnik ervonenkis property and each nj f fd nj is of the form njc for some reasonable random finite signed measure vnj as a result we obtain necessary and sufficient conditions for the weak convergence of possibly non i i d partial sum processes and new sufficient conditions for empirical processes indexed by vapnik ervonenkis classes special cases include prokhorov s 1956 central limit theorem for empirical processes and shorack s 1979 theorems on weighted empirical processes

shape recognition with a neural classifier based on a fast polygon approximation technique abstract a method is presented for the fast recognition of two dimensional 2d binary shapes with complicated form like islands on a map or medical images the proposed method is based on a new polygon approximation technique which extracts suitable feature vectors with specified dimension which characterizes a given shape these feature vectors are used as inputs in an efficient neural based classifier for the fast recognition of the shape the proposed technique is characterized by high speed performance which is desired for real time applications

polygonal representation of digital planar curves through dominant point detection a nonparametric algorithm we describe a new algorithm that detects a set of feature points on the boundary of an 8 connected shape that constitute the vertices of a polygonal approximation of the shape itself the set of feature points nodes is a ranked subset of the original shape points whose connected left and right arm extents cover the entire shape nodes are ranked based on their strength in terms of their importance to other boundary points length of support region and distance from the centroid the polygon obtained by linking the detected nodes approximates the contour in an intuitive way the proposed algorithm does not require an input parameter and works well for shapes with features of multiple sizes

curvature and tangential deflection of discrete arcs a theory based on the commutator of scatter matrix pairs and its application to vertex detection in planar shape data this paper introduces a new theory for the tangential deflection and curvature of plane discrete curves our theory applies to discrete data in either rectangular boundary coordinate or chain coded formats its rationale is drawn from the statistical and geometric properties associated with the eigenvalue eigenvector structure of sample covariance matrices specifically we prove that the nonzero entry of the commutator of a piar of scatter matrices constructed from discrete arcs is related to the angle between their eigenspaces and further we show that this entry is in certain limiting cases also proportional to the analytical curvature of the plane curve from which the discrete data are drawn these results lend a sound theoretical basis to the notions of discrete curvature and tangential deflection and moreover they provide a means for computationally efficient implementation of algorithms which use these ideas in various image processing contexts as a concrete example we develop the commutator vertex detection cvd algorithm which identifies the location of vertices in shape data based on excessive cummulative tangential deflection and we compare its performance to several well established corner detectors that utilize the alternative strategy of finding approximate curvature extrema

learning visual models from shape contours using multiscale convex concave structure matching a novel approach is proposed for learning a visual model from real shape samples of the same class the approach can directly acquire a visual model by generalizing the multiscale convex concave structure of a class of shapes that is the approach is based on the concept that shape generalization is shape simplification wherein perceptually relevant features are retained the simplification does not mean the approximation of shapes but rather the extraction of the optimum scale convex concave structure common to shape samples of the class the common structure is obtained by applying the multiscale convex concave structure matching method to all shape pairs among given shape samples of the class and by integrating the matching results the matching method is applicable to heavily deformed shapes and is effectively implemented with dynamic programming techniques the approach can acquire a visual model from a few samples without any a priori knowledge of the class the obtained model is very useful for shape recognition results of applying the proposed method are presented

on almost sure convergence of conditional empirical distribution functions on etudie la convergence presque sure d une distribution empirique conditionnelle de type noyau a la fois en norme sup et en norme sup ponderee

cube root asymptotics we establish a new functional central limit theorem for empirical processes indexed by classes of functions in a neighborhood of a fixed parameter point an n 1 3 rescaling of the parameter is compensated for by an n 2 3 rescaling of the empirical measure resulting in a limiting gaussian process by means of a modified continuous mapping theorem for the location of the maximizing value we deduce limit theorems for several statistics defined by maximization or constrained minimization of a process derived from the empirical measure these statistics include the short rousseeuw s least median of squares estimator manski s maximum score estimator and the maximum likelihood estimator for a monotone density the limit theory depends on a simple new sufficient condition for a gaussian process to achieve its maximum almost surely at a unique point

a new algorithm for dominant points detection and polygonization of digital curves a new algorithm for detecting dominant points and polygonal approximation of digitized closed curves is presented it uses an optimal criterion for determining the region of support of each boundary point and a new mechanism for selecting the dominant points the algorithm does not require an input parameter and can handle shapes that contain features of multiple sizes efficiently in addition the approximating polygon preserves the symmetry of the shape