nonparametric system identification by kernel methods a new nonparametric estimate for nonlinear discrete time dynamic systems is considered the new algorithm is weakly consistent under a specific condition on the transition probability operator of a stationary markov process the estimate is applicable when a parametric state model of the system is difficult to choose

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

subspace learning from image gradient orientations we introduce the notion of subspace learning from image gradient orientations for appearance based object recognition as image data are typically noisy and noise is substantially different from gaussian traditional subspace learning from pixel intensities very often fails to estimate reliably the low dimensional subspace of a given data population we show that replacing pixel intensities with gradient orientations and the l2 norm with a cosine based distance measure offers to some extend a remedy to this problem within this framework which we coin image gradient orientations igo subspace learning we first formulate and study the properties of principal component analysis of image gradient orientations igo pca we then show its connection to previously proposed robust pca techniques both theoretically and experimentally finally we derive a number of other popular subspace learning techniques namely linear discriminant analysis lda locally linear embedding lle and laplacian eigenmaps le experimental results show that our algorithms significantly outperform popular methods such as gabor features and local binary patterns and achieve state of the art performance for difficult problems such as illumination and occlusion robust face recognition in addition to this the proposed igo methods require the eigendecomposition of simple covariance matrices and are as computationally efficient as their corresponding l2 norm intensity based counterparts matlab code for the methods presented in this paper can be found at http ibug doc ic ac uk resources

pseudopolar based estimation of large translations rotations and scalings in images one of the major challenges related to image registration is the estimation of large motions without prior knowledge this work presents a fourier based approach that estimates large translations scalings and rotations the algorithm uses the pseudopolar pp fourier transform to achieve substantial improved approximations of the polar and log polar fourier transforms of an image thus rotations and scalings are reduced to translations which are estimated using phase correlation by utilizing the pp grid we increase the performance accuracy speed and robustness of the registration algorithms scales up to 4 and arbitrary rotation angles can be robustly recovered compared to a maximum scaling of 2 recovered by state of the art algorithms the algorithm only utilizes one dimensional fast fourier transform computations whose overall complexity is significantly lower than prior works experimental results demonstrate the applicability of the proposed algorithms

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

variable to fixed length codes for markov sources petry s efficient and optimal variable to fixed length source code for discrete memoryless sources was described by schalkwijk by extending this coding technique we are able to give an algorithm for markov sources that is easy to implement we can bound the loss of efficiency as a function of the code complexity and the mismatch between the source and the code rates arbitrarily close to the source entropy are shown to be achievable in this sense the codes introduced are optimal

generalized tunstall codes for sources with memory tunstall codes are variable to fixed length codes that maximize the expected number of source letters per dictionary string for discrete memoryless sources we analyze a generalization of tunstall coding to sources with memory and demonstrate that as the dictionary size increases the number of code letters per source symbol comes arbitrarily close to the minimum among all variable to fixed length codes of the same size we also find the asymptotic relationship between the dictionary size and the average length of a dictionary entry

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

an adaptable multilayer fractional fourier transform approach for image registration a novel adaptable accurate way for calculating polar fft and log polar fft is developed in this paper named multilayer fractional fourier transform mlfft mlfft is a necessary addition to the pseudo polar fft for the following reasons it has lower interpolation errors in both polar and log polar fourier transforms it reaches better accuracy with the nearly same computing complexity as the pseudo polar fft it provides a mechanism to increase the accuracy by increasing the user defined computing level this paper demonstrates both mlfft itself and its advantages theoretically and experimentally by emphasizing applications of mlfft in image registration with rotation and scaling our experiments suggest two major advantages of mlfft 1 scaling up to 5 and arbitrary rotation angles or scales up to 10 without rotation can be recovered by mlfft while currently the result recovered by the state of the art algorithms is the maximum scaling of 4 2 no iteration is needed to obtain large rotation and scaling values of images by mlfft hence it is more efficient than the pseudopolar based fft methods for image registration

shape similarity matching for query by example this paper describes a unified approach for two dimensional 2 d shape matching and similarity ranking of objects by means of a modal representation in particular we propose a new shape similarity metric in the eigenshape space for object image retrieval from a visual database via query by example this differs from prior work which performed point correspondence determination and similarity ranking of shapes in separate steps the proposed method employs selected boundary and or contour points of an object as a coarse to fine shape representation and does not require extraction of connected boundaries or silhouettes it is rotation translation and scale invariant and can handle mild deformations of objects e g due to partial occlusions or pose variations results comparing the unified method with an earlier two step approach using b spline based modal matching and hausdorff distance ranking are presented on retail and museum catalog style still image databases

asymptotics of greedy algorithms for variable to fixed length coding of markov sources in this paper alphabet extension for markov sources is studied such that each extension tree is grown by splitting the node with the maximum value for a weight as a generalization of the leaf probability in tunstall s 1967 algorithm we show that the optimal asymptotic rate of convergence of the per symbol code length to the entropy does not depend on an a priori selected proportional allocation of the sizes of the extension trees at the states we show this without imposing restrictive conditions on the weight by which the trees are extended further we prove the asymptotic optimality of an algorithm that allocates an increasing total number of leaves among the states finally we give exact formulas for all the relevant quantities of the trees grown

nonparametric kernel algorithm for recovery of functions from noisy measurements with applications this note presents a kernel algorithm for recovery of a regression function from noisy data conditions are provided that assure pointwise convergence in the mean square and almost sure senses an application to a class of linear system identification problems is discussed

recursive identification for nonlinear arx systems based on stochastic approximation algorithm the nonparametric identification for nonlinear autoregressive systems with exogenous inputs narx described by yk 1 f yk yk 1 n0 uk uk 1 n0 ek 1 is considered first a condition on f is introduced to guarantee ergodicity and stationarity of yk then the kernel function based stochastic approximation algorithm with expanding truncations saawet is proposed to recursively estimate the value of f at any given y 1 y n0 u 1 u n0 r2n0 it is shown that the estimate converges to the true value with probability one in establishing the strong consistency of the estimate the properties of the markov chain associated with the narx system play an important role numerical examples are given which show that the simulation results are consistent with the theoretical analysis the intention of the paper is not only to present a concrete solution to the problem under consideration but also to profile a new analysis method for nonlinear systems the proposed method consisting in combining the markov chain properties with stochastic approximation algorithms may be of future potential although a restrictive condition has to be imposed on f that is the growth rate of f x should not be faster than linear with coefficient less than 1 as x tends to infinity

radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems this paper presents a means to approximate the dynamic and static equations of stochastic nonlinear systems and to estimate state variables based on radial basis function neural network rbfnn after a nonparametric approximate model of the system is constructed from a priori experiments or simulations a suboptimal filter is designed based on the upper bound error in approximating the original unknown plant with nonlinear state and output equations the procedures for both training and state estimation are described along with discussions on approximation error nonlinear systems with linear output equations are considered as a special case of the general formulation finally applications of the proposed rbfnn to the state estimation of highly nonlinear systems are presented to demonstrate the performance and effectiveness of the method

on the construction of explicit khodak s code and its analysis variable to variable vv codes are very attractive yet not well understood data compression schemes in 1972 khodak claimed to provide upper and lower bounds for the achievable redundancy rate however he did not offer explicit construction of such codes in this paper we first present a constructive and transparent proof of khodak s result showing that for memoryless sources there exists a code with the average redundancy bounded by d 5 3 where d is the average delay e g the average length of a dictionary entry we also describe an algorithm that constructs a vv length code with a small redundancy rate for large d then we discuss several generalizations we prove that the worst case redundancy does not exceed d 4 3 furthermore we provide similar upper bound for markov sources of order 1 finally we consider bounds that are valid for almost all memoryless and markov sources for which the set of exceptional source parameters has zero measure in particular for all memoryless sources outside this exceptional class we prove there exists a vv code with the average redundancy rate bounded by d 1 m 3 epsiv and the worst case redundancy rate bounded by d 1 m 3 epsiv where m is the cardinality of the alphabet we complete our analysis with a lower bound showing that for all vv codes the average and the worst case redundancy rates are at least d 2m 1 epsiv for almost all memoryless sources in the sense that the set of exceptional source parameters has zero measure we prove these results using techniques of diophantine approximations

robust hausdorff distance matching algorithms using pyramidal structures abstract this paper proposes two hausdorff distance hd matching algorithms in which robust hd measures are implemented in pyramidal structures by computer simulations the matching performance of the conventional hd measures and the proposed robust hd matching algorithms using pyramidal structures is compared with real images which are degraded by noise and occlusions

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

image registration using log polar mappings for recovery of large scale similarity and projective transformations this paper describes a novel technique to recover large similarity transformations rotation scale translation and moderate perspective deformations among image pairs we introduce a hybrid algorithm that features log polar mappings and nonlinear least squares optimization the use of log polar techniques in the spatial domain is introduced as a preprocessing module to recover large scale changes e g at least four fold and arbitrary rotations although log polar techniques are used in the fourier mellin transform to accommodate rotation and scale in the frequency domain its use in registering images subjected to very large scale changes has not yet been exploited in the spatial domain in this paper we demonstrate the superior performance of the log polar transform in featureless image registration in the spatial domain we achieve subpixel accuracy through the use of nonlinear least squares optimization the registration process yields the eight parameters of the perspective transformation that best aligns the two input images extensive testing was performed on uncalibrated real images and an array of 10 000 image pairs with known transformations derived from the corel stock photo library of royalty free photographic images

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

trace inference curvature consistency and curve detection an approach is described for curve inference that is based on curvature information the inference procedure is divided into two stages a trace inference stage which is the subject of the present work and a curve synthesis stage it is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time and that tangent and curvature information are sufficient these make it possible to specify powerful constraints between estimated tangents to a curve in terms of a neighborhood relationship called cocircularity and between curvature estimates in terms of a curvature consistency relation because all curve information is quantized special care must be taken to obtain accurate estimates of trace points tangents and curvatures this issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint the procedure is applied to two types of images artificial images designed to evaluate curvature and noise sensitivity and natural images

orthogonal moment operators for subpixel edge detection abstract a new approach to detect step edges with subpixel accuracy is presented the proposed approach is based on a set of orthogonal complex moments of the image known as zernike moments an ideal two dimensional 2d step edge is modeled in terms of four parameters the background gray level the step size the distance of the edge from the center of the mask and the orientation of the edge discrete zernike moments are used to obtain a total of three complex masks to compute all the edge parameters for subpixel detection for pixel level edge detection only two masks one real and one complex are required the theoretical analysis of the influence of noise on the location and the orientation of an edge is presented this analysis reveals that the accuracy of the proposed approach is virtually unaffected by the additive noise the technique is effective in detecting both the pixel level and subpixel level edges experimental results are presented to demonstrate the efficacy of the proposed technique

renewal theory in the analysis of tries and strings we give a survey of a number of simple applications of renewal theory to problems on random strings and tries insertion depth size insertion mode and imbalance of tries variations for b tries and patricia tries khodak and tunstall codes

a note on approximation of uniform distributions from variable to fixed length codes in this correspondence we prove that the probability distribution induced on the leaves of a tunstall parse tree for a given source is a unique lower bound in the partially ordered set of the probability distributions induced by all possible parse trees with a same number of leaves and ordered according to the majorization partial order we apply this result to the problem of optimally approximating a uniform distribution with flips of a biased coin

a master theorem for discrete divide and conquer recurrences divide and conquer recurrences are one of the most studied equations in computer science yet discrete versions of these recurrences namely for some known sequence an and given bj bj pj and j j present some challenges the discrete nature of this recurrence represented by the floor and ceiling functions introduces certain oscillations not captured by the traditional master theorem for example due to akra and bazzi 1998 who primary studied the continuous version of the recurrence we apply powerful techniques such as dirichlet series mellin perron formula and extended tauberian theorems of wiener ikehara to provide a complete and precise solution to this basic computer science recurrence we illustrate applicability of our results on several examples including a popular and fast arithmetic coding algorithm due to boncelet for which we estimate its average redundancy and prove the central limit theorem for the phrase length to the best of our knowledge discrete divide and conquer recurrences were not studied in this generality and such detail in particular this allows us to compare the redundancy of boncelet s algorithm to the asymptotically optimal tunstall scheme

extracting straight lines this paper presents a new approach to the extraction of straight lines in intensity images pixels are grouped into line support regions of similar gradient orientation and then the structure of the associated intensity surface is used to determine the location and properties of the edge the resulting regions and extracted edge parameters form a low level representation of the intensity variations in the image that can be used for a variety of purposes the algorithm appears to be more effective than previous techniques for two key reasons 1 the gradient orientation rather than gradient magnitude is used as the initial organizing criterion prior to the extraction of straight lines and 2 the global context of the intensity variations associated with a straight line is determined prior to any local decisions about participating edge elements

nonparametric identification of hammerstein systems a discrete time nonlinear hammerstein system is identified and the correlation and frequency domain methods for identification of its linear subsystem are presented the main results concern the estimation of the nonlinear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data it is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable pointwise as well as global consistencies are established for lipschitz characteristics the rate of the convergence in probability is o n sup 1 3

universal variable to fixed length source codes a universal variable to fixed length algorithm for binary memoryless sources which converges to the entropy of the source at the optimal rate is known we study the problem of universal variable to fixed length coding for the class of markov sources with finite alphabets we give an upper bound on the performance of the code for large dictionary sizes and show that the code is optimal in the sense that no codes exist that have better asymptotic performance the optimal redundancy is shown to be h log log m log m where h is the entropy rate of the source and m is the code size this result is analogous to rissanen s 1984 result for fixed to variable length codes we investigate the performance of a variable to fixed coding method which does not need to store the dictionaries either at the coder or the decoder we also consider the performance of both these source codes on individual sequences for individual sequences we bound the performance in terms of the best code length achievable by a class of coders all the codes that we consider are prefix free and complete

proprietes de convergence presque complete du predicteur a noyau let z n be a mixing process which is valued in mathbb e subset mathbb r q g be a real measurable function defined on mathbb e s and k be two positive integers we suppose the existence of a function r satisfying r e g z n s z n k 1 z n n n k and estimate the function r from a sequence z i i 1 n by r n with r n u frac sum limits i k n s g z i s k u z i k 1 cdots z i h n 1 sum limits i k n s k u z i k 1 cdots z i h n 1 forall u in mathbb e k where k is a kernel of kq and h n h n 0 we give various conditions on both the sequences h n and the sequence n which is associated with z n for the two following properties uniform complete convergence to r for the functional estimator r n and complete convergence to 0 for the real random variable r n z n k 1 z n r zn k 1 z n this last result concerns the predictor r n z n k 1 z n of g z n s from z i i 1 n when the process z n is stationary and markovian of order k

the dual bootstrap iterative closest point algorithm with application to retinal image registration motivated by the problem of retinal image registration this paper introduces and analyzes a new registration algorithm called dual bootstrap iterative closest point dual bootstrap icp the approach is to start from one or more initial low order estimates that are only accurate in small image regions called bootstrap regions in each bootstrap region the algorithm iteratively 1 refines the transformation estimate using constraints only from within the bootstrap region 2 expands the bootstrap region and 3 tests to see if a higher order transformation model can be used stopping when the region expands to cover the overlap between images steps 1 and 3 the bootstrap steps are governed by the covariance matrix of the estimated transformation estimation refinement step 2 uses a novel robust version of the icp algorithm in registering retinal image pairs dual bootstrap icp is initialized by automatically matching individual vascular landmarks and it aligns images based on detected blood vessel centerlines the resulting quadratic transformations are accurate to less than a pixel on tests involving approximately 6000 image pairs it successfully registered 99 5 of the pairs containing at least one common landmark and 100 of the pairs containing at least one common landmark and at least 35 image overlap

spatially eigen weighted hausdorff distances for human face recognition abstract hausdorff distance is an efficient measure of the similarity of two point sets in this paper we propose a new spatially weighted hausdorff distance measure for human face recognition the weighting function used in the hausdorff distance measure is based on an eigenface which has a large value at locations of importance facial features and can reflect the face structure more effectively two modified hausdorff distances namely spatially eigen weighted hausdorff distance sewhd and spatially eigen weighted doubly hausdorff distance sew2hd are proposed which incorporate the information about the location of important facial features such as eyes mouth and face contour so that distances at those regions will be emphasized experimental results based on a combination of the orl mit and yale face databases show that sew2hd can achieve recognition rates of 83 90 and 92 for the first one the first three and the first five likely matched faces respectively while the corresponding recognition rates of sewhd are 80 83 and 88 respectively

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

guaranteed stable sliding dft algorithm with minimal computational requirements the discrete fourier transform dft is the most widely used technique for determining the frequency spectra of digital signals however in the sliding transform scenario where the transform window is shifted one sample at a time and the transform process is repeated the use of dft becomes difficult due to its heavy computational burden this paper proposes an optimal sliding dft osdft algorithm that achieves both the lowest computational requirement and the highest computational accuracy among existing sliding dft algorithms the proposed osdft algorithm directly computes the dft bins of the shifted window by simply adding or subtracting the bins of a previous window and an updating vector we show that the updating vector can be efficiently computed with a low complexity in the sliding transform scenario our simulations demonstrate that the proposed algorithm outperforms the existing sliding dft algorithms in terms of computational accuracy and processing time

line based recognition using a multidimensional hausdorff distance a line feature based approach for model based recognition using a four dimensional hausdorff distance is proposed this approach reduces the problem of finding the rotation scaling and translation transformations between a model and an image to the problem of finding a single translation minimizing the hausdorff distance between two sets of points in a four dimensional space the implementation of the proposed algorithm can be naturally extended to higher dimensional spaces to efficiently find correspondences between n dimensional patterns the method performance and sensitivity to segmentation problems are quantitatively characterized using an experimental protocol with simulated data it is shown that the algorithm performs well is robust to occlusion and outliers and that it degrades nicely as the segmentation problems increase experiments with real images are also presented

identification of iir nonlinear systems without prior structural information in this paper we propose a kernel method for identification of infinite impulse response iir nonlinear systems without prior structural information the main result of the paper is to establish the conditions for asymptotic convergence in terms of the input to output exponential stability the performance of the method is tested on real world applications and computer simulations the results obtained show the efficacy of the method

relations between redundancy patterns of the shannon code and wave diffraction patterns of partially disordered media the average redundancy of the shannon code rn as a function of the block length n is known to exhibit two very different types of behavior depending on the rationality or irrationality of certain parameters of the source it either converges to 1 2 as n grows without bound or it may have a nonvanishing oscillatory quasi periodic pattern around the value 1 2 for all large n in this paper we make an attempt to shed some insight into this erratic behavior of rn by drawing an analogy with the realm of physics of wave propagation in particular the elementary theory of scattering and diffraction it turns out that there are two types of behavior of wave diffraction patterns formed by crystals which are correspondingly analogous to the two types of patterns of rn when the crystal is perfect the diffraction intensity spectrum exhibits very sharp peaks a k a bragg peaks at wavelengths of full constructive interference these wavelengths correspond to the frequencies of the harmonic waves of the oscillatory mode of rn on the other hand when the crystal is imperfect and there is a considerable degree of disorder in its structure the bragg peaks disappear and the behavior of this mode is analogous to the one where rn is convergent

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

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

robust fft based scale invariant image registration with image gradients we present a robust fft based approach to scale invariant image registration our method relies on fft based correlation twice once in the log polar fourier domain to estimate the scaling and rotation and once in the spatial domain to recover the residual translation previous methods based on the same principles are not robust to equip our scheme with robustness and accuracy we introduce modifications which tailor the method to the nature of images first we derive efficient log polar fourier representations by replacing image functions with complex gray level edge maps we show that this representation both captures the structure of salient image features and circumvents problems related to the low pass nature of images interpolation errors border effects and aliasing second to recover the unknown parameters we introduce the normalized gradient correlation we show that using image gradients to perform correlation the errors induced by outliers are mapped to a uniform distribution for which our normalized gradient correlation features robust performance exhaustive experimentation with real images showed that unlike any other fourier based correlation techniques the proposed method was able to estimate translations arbitrary rotations and scale factors up to 6

markov additive processes i eigenvalue properties and limit theorems on etudie d un point de vue general les proprietes d existence et de regularite des valeurs propres et des fonctions propres de l operateur de feynman kac

asymptotic average redundancy of huffman and other block codes we study asymptotically the redundancy of huffman and other codes it has been known from the inception of the huffman 1952 code that in the worst case its redundancy defined as the excess of the code length over the optimal ideal code length is not more than one however to the best of our knowledge no precise asymptotic results have been reported in literature thus far we consider here a memoryless binary source generating a sequence of length n distributed as binomial n p with p being the probability of emitting 0 based on the results of stubley 1994 we prove that for p 1 2 1 m 1 2 sup 1 m 2 sup m o spl rho sup n spl alpha n m rational where spl alpha log sub 2 1 p p and spl beta log sub 2 1 p spl rho x x is the fractional part of x the appearance of the fractal like function explains the erratic behavior of the huffman redundancy and its resistance to succumb to a precise analysis as a side result we prove that the average redundancy of the shannon block code is as n spl rarr spl infin r sub n sup s 1 2 o 1 spl alpha irrational 1 2 1 m 1 2 o spl rho sup n spl alpha n m rational where spl rho 1 finally we derive the redundancy of the golomb 1966 code for the geometric distribution which can be viewed as a special case of the huffman and shannon codes golomb s code redundancy has only oscillating behavior i e there is not convergent mode these findings are obtained by analytic methods such as theory of distribution of sequences modulo 1 and fourier series

a nonparametric algorithm for identification of linear dynamic siso systems of unknown order a new nonparametric algorithm is presented for estimation of the weighting function of linear dynamic single input single output systems the behavior of the mean squared error of the proposed estimate is examined finally the optimal parameter is found for the best speed of uniform mean squared consistency

on system identification by nonparametric function fitting a new nonparametric algorithm for function fitting is proposed and its application to a broad class of system identification problems is discussed

a probabilistic approach to some asymptotics in noiseless communication renewal theory is a powerful tool in the analysis of source codes we use renewal theory to obtain some asymptotic properties of finite state noiseless channels we discuss the relationship between these results and earlier uses of renewal theory to analyze the lempel ziv 1977 1978 codes and the tunstall 1967 code as a new application of our results we provide the asymptotic performance of two of the perl garey and even 1975 prefix condition codes

nonlinear processing and analysis of angular signals physical quantities referring to angles like vector direction color hue etc exhibit an inherently periodic nature due to this periodicity digital filters and edge operators proposed for data on the line cannot be applied on such data we introduce filters for angular signals circular mean circular median circular a trimmed mean circular modified trimmed mean particular emphasis is given to the circular median filter for which some interesting properties are derived we also use estimators of circular dispersion to introduce edge detectors for angular signals three variations for the extension of quasirange to circular data are proposed and expressions for their output pdf are derived these circular quasiranges have good and user controlled properties as edge detectors in noisy angular signals the performance of the proposed edge operators is evaluated on angular edges using certain quantitative criteria finally a series of experiments featuring one dimensional 1 d angular signals and hue images is used to illustrate the operation of the new filters and edge detectors

radial projection an efficient update rule for relaxation labeling relaxation labeling uses contextual information for finding consistent labelings of graphs although relaxation labeling is parallel and iterative the complexity of updating with standard rules is too costly for practical implementation a description is given of a computationally more efficient updating rule that utilizes radial projection instead of normal projection to avoid the complexities incurred by previous update rules when boundaries to the labeling space are encountered this reduction in complexity is achieved by first restricting support vectors to the positive quadrant and then using radial projection onto the constraint instead of normal projection crucial order information is conserved through smooth convergence towards the optimum and a rate of convergence proportional to the magnitudes of the support functions

adaptive control for systems with bounded disturbances the authors present an identification algorithm that can be used to design globally stable indirect adaptive controllers for minimum and nonminimum phase systems subject to bounded disturbances the parameter estimation scheme is a least squares algorithm with dead zone the dead zone is such that the estimates converge and make it possible to define projected estimates having the same convergence properties as the original estimates in the minimum phase case the projection facility can be used to ensure that the leading coefficient projected estimate is greater than or equal to the true leading coefficient in absolute value the projection procedure can also be used to avoid pole zero cancellations in an adaptive pole placement algorithm

tunstall code khodak variations and random walks a variable to fixed length encoder partitions the source string into variable length phrases that belong to a given and fixed dictionary tunstall and independently khodak designed variable to fixed length codes for memoryless sources that are optimal under certain constraints in this paper we study the tunstall and khodak codes using variety of techniques ranging from stopping times for sums of independent random variables to tauberian theorems and mellin transform after proposing an algebraic characterization of the tunstall and khodak codes we present new results on the variance and a central limit theorem for dictionary phrase lengths this analysis also provides a new argument for obtaining asymptotic results about the mean dictionary phrase length and average redundancy rates

improving classifier performance through repeated sampling abstract in traditional pattern recognition the classification decision is based on a single observation of the input in this paper we show that by relaxing this assumption the performance of the classifier can be improved substantially we present a detailed analysis of one particular method for achieving this taking a consensus vote on the classifier s output for repeated samples of the input we prove that this approach always yields a net improvement in recognition accuracy for common distributions of interest upper and lower bounds on the improvement are also discussed under certain conditions it is even possible to beat the bayes error bound associated with the classifier we conclude by presenting results from three sets of experiments examining the effectiveness of the idea

a new adaptive framework for unbiased orientation estimation in textured images this paper focuses on directional texture analysis we propose a new approach for orientation estimation this approach hinges on two classes of convolution masks i e the gradient and the valleyness operators we provide a framework for their optimization regarding bias reduction and noise robustness as the gradient and the valleyness operators are complementary we propose a combination named gv joe this combination consists in using the gradient on inflexion pixels the valleyness on crests and valleys and a linear mixture of both elsewhere we implement an adaptive selection of the size of our operators in order to take into account the variations of the texture scale in the image we apply our approach both on synthetic and natural textures these experiments show that when used separately both classes of operators are more accurate than classical derivative approaches in noisy cases the gv joe implementation improves the robustness of our operators without affecting their accuracy moreover compared to well known orientation estimators it gives the best estimates in the most difficult cases i e for high frequency textures and low snr

reinforcement of linear structure using parametrized relaxation labeling the problem of reinforcing local evidence of linear structure while suppressing unwanted information in noisy images is considered using a modified form of relaxation labeling the methodology is based on parametrizing a continuous set of orientation labels via a single vector and using a sigmoidal thresholding function to bias neighborhood influence and ensure convergence to a meaningful stable state label strength and label no label decisions are incorporated into a single functional optimal points of the functional represent the cases where as many pixels objects as possible have achieved the desirable linear structure reinforced and noise suppressed labelings three different linear structure reinforcement tasks are considered within the general framework edge reinforcement edge reinforcement with thinning and bar line segment reinforcement results from several image data sets are presented this approach can directly handle continuous feature information from low level image analysis operators and the computational complexity of labeling is reduced

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

nonlinear adaptive tracking using kernel estimators estimation and test for linearity we present some statistical results on nonlinear adaptive control using kernel estimators we are concerned with a nonlinear autoregressive model of the form x n 1 f x n u n xi n 1 hskip 0 4cm n in mathbb n controlled using a nonparametric estimator of the unknown function f and derived from a tracking control policy we prove an almost sure convergence result for the noise density estimator a pointwise central limit theorem for f and a test for linearity of the driving function f

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

efficient online subspace learning with an indefinite kernel for visual tracking and recognition we propose an exact framework for online learning with a family of indefinite not positive kernels as we study the case of nonpositive kernels we first show how to extend kernel principal component analysis kpca from a reproducing kernel hilbert space to krein space we then formulate an incremental kpca in krein space that does not require the calculation of preimages and therefore is both efficient and exact our approach has been motivated by the application of visual tracking for which we wish to employ a robust gradient based kernel we use the proposed nonlinear appearance model learned online via kpca in krein space for visual tracking in many popular and difficult tracking scenarios we also show applications of our kernel framework for the problem of face recognition

average redundancy of the shannon code for markov sources it is known that for memoryless sources the average and maximal redundancy of fixed to variable length codes such as the shannon and huffman codes exhibit two modes of behavior for long blocks it either converges to a limit or it has an oscillatory pattern depending on the irrationality or rationality respectively of certain parameters that depend on the source in this paper we extend these findings concerning the shannon code to the case of a markov source we provide a precise characterization of the convergent versus oscillatory behavior of the shannon code redundancy for a class of irreducible periodic and aperiodic markov sources these findings are obtained by analytic methods such as fourier fejer series analysis and spectral analysis of matrices

line segment hausdorff distance on face matching abstract a novel concept of line segment hausdorff distance is proposed in this paper researchers apply hausdorff distance to measure the similarity of two point sets it is extended here to match two sets of line segments the new approach has the advantage to incorporate structural and spatial information to compute the similarity the added information can conceptually provide more and better distinctive capability for recognition this would strengthen and enhance the matching process of similar objects such as faces the proposed technique has been applied online segments generated from the edge maps of faces with encouraging result that supports the concept experimentally the results also implicate that line segments could provide sufficient information for face recognition this might imply a new way for face coding and recognition

comparing face images using the modified hausdorff distance abstract we introduce a novel methodology applicable to face matching and fast screening of large facial databases the proposed shape comparison method operates on edge maps and derives holistic similarity measures yet it does not require solving the point correspondence problem while the use of edge images is important to introduce robustness to changes in illumination the lack of point to point matching delivers speed and tolerance to local non rigid distortions in particular we propose a face similarity measure derived as a variant of the hausdorff distance by introducing the notion of a neighborhood function n and associated penalties p experimental results on a large set of face images demonstrate that our approach produces excellent recognition results even when less than 3 of the original grey scale face image information is stored in the face database gallery these results implicate that the process of face recognition may start at a much earlier stage of visual processing than it was earlier suggested we argue that edge like retinal images of faces are initially screened at a glance without the involvement of high level cognitive functions thus delivering high speed and reducing computational complexity

hammerstein system identification by non parametric regression estimation a discrete time multiple input non linear hammerstein system is identified the dynamical subsystem is recovered using the standard correlation method the main results concern estimation of the non linear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a non parametric kernel estimate of the regression function calculated from the dependent data it is shown that the algorithm converges to the characteristic of the subsystem in the pointwise as well as the global sense for sufficiently smooth characteristics the rate of convergence is o n 1 2 d in probability where d is the dimension of the input variable

intravital leukocyte detection using the gradient inverse coefficient of variation the problem of identifying and counting rolling leukocytes within intravital microscopy is of both theoretical and practical interest currently methods exist for tracking rolling leukocytes in vivo but these methods rely on manual detection of the cells in this paper we propose a technique for accurately detecting rolling leukocytes based on bayesian classification the classification depends on a feature score the gradient inverse coefficient of variation gicov which serves to discriminate rolling leukocytes from a cluttered environment the leukocyte detection process consists of three sequential steps the first step utilizes an ellipse matching algorithm to coarsely identify the leukocytes by finding the ellipses with a locally maximal gicov in the second step starting from each of the ellipses found in the first step a b spline snake is evolved to refine the leukocytes boundaries by maximizing the associated gicov score the third and final step retains only the extracted contours that have a gicov score above the analytically determined threshold experimental results using 327 rolling leukocytes were compared to those of human experts and currently used methods the proposed gicov method achieves 78 6 leukocyte detection accuracy with 13 1 false alarm rate

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

an fft based technique for translation rotation and scale invariant image registration this correspondence discusses an extension of the well known phase correlation technique to cover translation rotation and scaling fourier scaling properties and fourier rotational properties are used to find scale and rotational movement the phase correlation technique determines the translational movement this method shows excellent robustness against random noise

recursive estimation in diffusion model this paper is concerned with the nonlinear identification of dynamical systems disturbed by white noise an important problem in control engineering a nonparametric identification procedure for such systems which are usually described by a diffusion model is given in banon 1977 1978 where weak consistency of estimators has been obtained and simulation study has been carried out successfully in this paper we prove a stronger result concerning asymptotic properties of the estimators of the drift term namely strong consistency and also related results

nonparametric fitting of multivariate functions a nonparametric algorithm based on the multiple fejer s sum for fitting of multivariate functions is proposed the mean square error convergence and the speed of convergence are investigated

texture synthesis using the structure tensor this paper proposes a two stage texture synthesis algorithm at the first stage a structure tensor map carrying information about the local orientation is synthesized from the exemplar s data and used at the second stage to constrain the synthesis of the texture keeping in mind that the algorithm should be able to reproduce as faithfully as possible the visual aspect statistics and morphology of the input sample the method is tested on various textures and compared objectively with existing methods highlighting its strength in successfully synthesizing the output texture in many situations where traditional algorithms fail to reproduce the exemplar s patterns the promising results pave the way towards the synthesis of accurately large and multi scale patterns as it is the case for carbon material samples showing laminar structures for example

a method to detect and characterize ellipses using the hough transform we describe a new technique for detecting and characterizing ellipsoidal shapes automatically from any type of image this technique is a single pass algorithm which can extract any group of ellipse parameters or characteristics which can be computed from those parameters without having to detect all five parameters for each ellipsoidal shape moreover the method can explicitly incorporate any a priori knowledge the user may have concerning ellipse parameters the method is based on techniques from projective geometry and on the hough transform this technique can significantly reduce interpretation and computation time by automatically extracting only those features or geometric parameters of interest from images and making exact use of a priori information

consistent gradient operators we propose optimal gradient operators based on a newly derived consistency criterion this criterion is based on an orthogonal decomposition of the difference between a continuous gradient and discrete gradients into the intrinsic smoothing effect and the self inconsistency involved in the operator we show that consistency assures the exactness of gradient direction of a locally 1d pattern in spite of its orientation spectral composition and sub pixel translation stressing that inconsistency reduction is of primary importance we derive an iterative algorithm which leads to accurate gradient operators of arbitrary size we compute the optimum 3 spl times 3 4 spl times 4 and 5 spl times 5 operators compare them with conventional operators and examine the performance for one synthetic and several real images the results indicate that the proposed operators are superior with respect to accuracy bandwidth and isotropy

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

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

fractional subpixel diffusion and fuzzy logic approach for ultrasound speckle reduction speckle is the dominant source of noise in ultrasound imaging and is a kind of multiplicative noise it is difficult to design a filter to remove speckle effectively in this paper a novel fuzzy subpixel fractional partial difference fsfpd for ultrasound speckle reduction is proposed euler lagrange equation acts as an increasing function of the fractional derivative s absolute value of the image intensity function the fractional order partial difference is computed in the frequency and fuzzy domain with subpixel precision we test the proposed method on both synthetic and real breast ultrasound bus images the comparisons of the experimental results show that the proposed method can preserve edges and structural details of ultrasound images well while removing speckle noise in addition the filtered images are assessed and evaluated by radiologists using double blind method the results demonstrate that the discrimination rate of breast cancers has been highly improved after employing the proposed method

gradient orientation pattern matching with the hamming distance abstract this paper presents a novel pattern matching technique that is robust to illumination changes and the occlusion problem the technique is based on the matching of gradient orientations in place of traditional image features such as intensities or gradients gradient orientations depend on the texture in an image they are known to be insensitive to changes of image intensities that are often caused by time varying illuminations or the auto gain control agc function of the camera moreover the proposed method employs a voting strategy in the process of matching gradient orientations the method works remarkably well even when a large part of the pattern is occluded with a foreign object consequently the proposed method is robust to both irregular lighting conditions and the occlusion problem

the influence of edge direction on the estimation of edge contrast and orientation abstract this paper concerns the influence of edge direction on the estimation of edge contrast and orientation we present an analytical study of general first order detectors we show that the gradient estimated using radial filters is not affected by edge orientation for non radial filters the gradient may be affected by edge orientation for instance we find that the estimated edge orientation using a non radial filter may be biased even if the image is noise free however there are non radial filters for which gradient is unaffected by edge orientation as in the case of radial filters the properties of these functions are given in this paper the results are illustrated by studying the detectors of canny deriche and shen castan we take into account discretization effects such as subpixel and tesselation of the image plane the quantitative results provide insights into the estimation of gradient by these commonly used detectors taken together the theoretical and experimental results give a clear indication of the effect of the rotation invariance property of an edge detector on its response thus providing a more precise meaning for this property in edge detection

hybrid image matching combining hausdorff distance with normalized gradient matching image matching has been a central problem in computer vision and image processing for decades most of the previous approaches to image matching can be categorized into the intensity based and edge based comparison hausdorff distance has been widely used for comparing point sets or edge maps since it does not require point correspondences in this paper we propose a new image similarity measure combining the hausdorff distance with a normalized gradient consistency score for image matching the normalized gradient consistency score is designed to compare the normalized image gradient fields between two images to alleviate the illumination variation problem in image matching by combining the edge based and intensity based information for image matching we are able to achieve robust image matching under different lighting conditions we show the superior robustness property of the proposed image matching technique through experiments on face recognition under different lighting conditions

an adaptive image euclidean distance the image euclidean distance imed considers the spatial relationship between the pixels of different images and can easily be embedded in existing image recognition algorithms that are based on euclidean distance imed uses the prior knowledge that pixels located near one another have little variance in gray scale values and defines a metric matrix according to the spatial distance between pixels in this paper we propose an adaptive image euclidean distance aimed which considers not only the prior spatial knowledge but also the prior gray level knowledge from images the most important advantage of the proposed aimed over imed is that aimed makes the metric matrix adaptive to the content of the concerned images two ways of using gray level information are proposed one is based on gray level distances and the other is based on cosine dissimilarity of gray levels experiments on two facial databases and a handwritten digital database show that aimed achieves the highest classification accuracy when it is embedded in nearest neighbor classifiers principal component analysis and support vector machines

a note on jackknifing kernel regression function estimators corresp estimation of the value of a regression function at a point of continuity using a kernel type estimator is considered and improvements by a jackknife technique are discussed it is seen that a so called generalized jackknife estimator asymptotically improves upon an ordinary kernel type estimator however for a fixed sample size the generalized jackknife method may inflate the mean square error