spectral and scattering theory for gauss bonnet operators on perturbed topological crystals abstract in this paper we investigate the spectral and the scattering theory of gauss bonnet operators acting on perturbed periodic combinatorial graphs two types of perturbation are considered either a multiplication operator by a short range or a long range potential or a short range type modification of the graph for short range perturbations existence and completeness of local wave operators are proved in addition similar results are provided for the laplacian acting on edges

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

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

albanese maps and off diagonal long time asymptotics for the heat kernel we discuss long time asymptotic behaviors of the heat kernel on a non compact riemannian manifold which admits a discontinuous free action of an abelian isometry group with a compact quotient a local central limit theorem and the asymptotic power series expansion for the heat kernel as the time parameter goes to infinity are established by employing perturbation arguments on eigenvalues and eigenfunctions of twisted laplacians our ideas and techniques are motivated partly by analogy with floque bloch theory on periodic schrodinger operators for the asymptotic expansion we make careful use of the classical laplace method in the course of a discussion we observe that the notion of albanese maps associated with the abelian group action is closely related to the asymptotics a similar idea is available for asymptotics of the transition probability of a random walk on a lattice graph the results obtained in the present paper refine our previous ones 4 in the asymptotics the euclidean distance associated with the standard realization of the lattice graph which we call the albanese distance plays a crucial role

a holonomic systems approach to special functions identities abstract we observe that many special functions are solutions of so called holonomic systems bernstein s deep theory of holonomic systems is then invoked to show that any identity involving sums and integrals of products of these special functions can be verified in a finite number of steps this is partially substantiated by an algorithm that proves terminating hypergeometric series identities and that is given both in english and in maple

homology wiener integrals and integrated densities of states we investigate large time asymptotics of certain wiener integrals over the space of closed paths with a fixed homology class in a closed manifold the basic strategy is to employ a trace formula and perturbation theory for the first eigenvalues of schrodinger operators we also establish a remarkable property of the integrated density of states associated with the homology universal covering map

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

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

large deviation and the tangent cone at infinity of a crystal lattice we discuss a large deviation property of a periodic random walk on a crystal lattice in view of geometry and relate it to a rational convex polyhedron in the first homology group of a finite graph which as we shall observe has remarkable combinatorial features and shows up also in the gromov hausdorff limit of a crystal lattice

spectral and asymptotic properties of grover walks on crystal lattices abstract we propose a twisted szegedy walk for estimating the limit behavior of a discrete time quantum walk on a crystal lattice an infinite abelian covering graph whose notion was introduced by 14 first we show that the spectrum of the twisted szegedy walk on the quotient graph can be expressed by mapping the spectrum of a twisted random walk onto the unit circle secondly we show that the spatial fourier transform of the twisted szegedy walk on a finite graph with appropriate parameters becomes the grover walk on its infinite abelian covering graph finally as an application we show that if the betti number of the quotient graph is strictly greater than one then localization is ensured with some appropriated initial state we also compute the limit density function for the grover walk on z d with flip flop shift which implies the coexistence of linear spreading and localization we partially obtain the abstractive shape of the limit density function the support is within the d dimensional sphere of radius 1 d and 2 d singular points reside on the sphere s surface

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

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

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

invariants for laplacians on periodic graphs we consider a laplacian on periodic discrete graphs its spectrum consists of a finite number of bands in a class of periodic 1 forms i e functions defined on edges of the periodic graph we introduce a subclass of minimal forms with a minimal number mathcal i of edges in their supports on the period we obtain a specific decomposition of the laplacian into a direct integral in terms of minimal forms where fiber laplacians matrices have the minimal number 2 mathcal i of coefficients depending on the quasimomentum and show that the number mathcal i is an invariant of the periodic graph using this decomposition we estimate the position of each band the lebesgue measure of the laplacian spectrum and the effective masses at the bottom of the spectrum in terms of the invariant mathcal i and the minimal forms in addition we consider an inverse problem we determine necessary and sufficient conditions for matrices depending on the quasimomentum on a finite graph to be fiber laplacians moreover similar results for schrodinger operators with periodic potentials are obtained

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

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

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

difference equations isoperimetric inequality and transience of certain random walks the difference laplacian on a square lattice in rn has been stud ied by many authors in this paper an analogous difference operator is studied for an arbitrary graph it is shown that many properties of the laplacian in the continuous setting e g the maximum principle the harnack inequality and cheeger s bound for the lowest eigenvalue hold for this difference oper ator the difference laplacian governs the random walk on a graph just as the laplace operator governs the brownian motion as an application of the theory of the difference laplacian it is shown that the random walk on a class of graphs is transient the random walks we consider are defined as follows let k be a connected graph i e a one dimensional simplicial complex for a vertex x e k let m x denote the number of edges emanating from x the probability that a particle moves from x to another vertex y e k is l m x if x and y are connected by an edge and it is zero otherwise as observed by courant friedrichs and lewy cfl for the case of a square lattice in the plane this random walk is intimately related to the difference analog of the laplacian

random walks on periodic graphs this paper concerns random walks on periodic graphs embedded in the d dimensional euclidian space r d and obtains asymptotic expansions of the green functions of them up to the second order term which expressed fairly explicitly are easily computable for many examples the result is used to derive an asymptotic form of the hitting distribution of a hyperplane of codimension one which involves not only the first but also second order terms of the expansion of the green function we also give similar expansions of the transition probabilities of the walks

essential spectrum of the discrete laplacian on a perturbed periodic graph abstract we address the laplacian on a perturbed periodic graph which might not be a periodic graph we give a criterion for the essential spectrum of the laplacian on the perturbed graph to include that on the unperturbed graph this criterion is applicable to a wide class of graphs obtained by a non compact perturbation such as adding or removing infinitely many vertices and edges using this criterion we demonstrate how to determine the spectra of cone like graphs the upper half plane and graphs obtained from z 2 by randomly adding vertices

fast evaluation of holonomic functions abstract a holonomic function is an analytic function which satisfies a linear differential equation with polynomial coefficients in particular the elementary functions exp log sin etc and many special functions like erf si bessel functions etc are holonomic functions given a holonomic function f determined by the linear differential equation it satisfies and initial conditions in a non singular point z we show how to perform arbitrary precision evaluations of f at a non singular point z on the riemann surface of f while estimating the error moreover if the coefficients of the polynomials in the equation for f are algebraic numbers then our algorithm is asymptotically very fast if m n is the time needed to multiply two n digit numbers then we need a time o m n log 2 n log log n to compute n digits of f z

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

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

eigenbasis of the evolution operator of 2 tessellable quantum walks abstract staggered quantum walks on graphs are based on the concept of graph tessellation and generalize some well known discrete time quantum walk models in this work we address the class of 2 tessellable quantum walks with the goal of obtaining an eigenbasis of the evolution operator by interpreting the evolution operator as a quantum markov chain on an underlying multigraph we define the concept of quantum detailed balance which helps to obtain the eigenbasis a subset of the eigenvectors is obtained from the eigenvectors of the double discriminant matrix of the quantum markov chain to obtain the remaining eigenvectors we have to use the quantum detailed balance conditions if the quantum markov chain has a quantum detailed balance there is an eigenvector for each fundamental cycle of the underlying multigraph if the quantum markov chain does not have a quantum detailed balance we have to use two fundamental cycles linked by a path in order to find the remaining eigenvectors we exemplify the process of obtaining the eigenbasis of the evolution operator using the kagome lattice the line graph of the hexagonal lattice which has symmetry properties that help in the calculation process

long time asymptotics of non symmetric random walks on crystal lattices abstract in the present paper we study long time asymptotics of non symmetric random walks on crystal lattices from a view point of discrete geometric analysis due to kotani and sunada 11 25 we observe that the euclidean metric associated with the standard realization of the crystal lattice called the albanese metric naturally appears in the asymptotics in the former half of the present paper we establish two kinds of functional central limit theorems for random walks we first show that the brownian motion on the euclidean space with the albanese metric appears as the scaling limit of the usual central limit theorem for the random walk next we introduce a family of random walks which interpolates between the original non symmetric random walk and the symmetrized one we then capture the brownian motion with a constant drift of the asymptotic direction on the euclidean space with the albanese metric associated with the symmetrized random walk through another kind of central limit theorem for the family of random walks in the latter half of the present paper we give a spectral geometric proof of the asymptotic expansion of the n step transition probability for the non symmetric random walk this asymptotic expansion is a refinement of the local central limit theorem obtained by sunada 22 23 and is a generalization of the result in 11 for symmetric random walks on crystal lattices to non symmetric cases

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

asymptotic behavior of the transition probability of a random walk on an infinite graph ideas cultivated in spectral geometry are applied to obtain an asymptotic property of a reversible random walk on an infinite graph satisfying a certain periodic condition in the course of our argument we employ perturbation theory for the maximal eigenvalues of twisted transition operator as a result an asymptotic of the probabilityp n x y that a particle starting atxreachesyat timenasngoes to infinity is established

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

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

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

the spectrum of magnetic schrodinger operators on a graph with periodic structure abstract for discrete magnetic schrodinger operators on covering graphs of a finite graph we investigate two spectral properties 1 the relationship between the spectrum of the operator on the covering graph and that on a finite graph 2 the analyticity of the bottom of the spectrum with respect to magnetic flow also we compute the second derivative of the bottom of the spectrum and represent it in terms of geometry of a graph

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

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