a new super kp system and a characterization of the jacobians of arbitrary algebraic super curves a set of super commuting vector fields is defined on the super grassmannians a characterization of the jacobian varieties of super curves super schottky problem is established in the following manner every finite dimensional integral manifold of these vector fields has a canonical structure of the jacobian variety of an algebraic super curve and conversely the jacobian variety of an arbitrary algebraic super curve is obtained in this way the vector fields restricted on the super grassmannian of index 0 0 give a completely integrable system of partial super differential equations which gives a new supersymmetric generalization of the kp system thus every finite dimensional solution of this new system gives rise to a jacobian variety of an algebraic super curve the correspondence between this super grassmannian and the group of monic super pseudo differential operators of order zero the super sato correspondence is also established table of

morphological decomposition of 2 d binary shapes into modestly overlapped octagonal and disk components one problem with several leading morphological shape representation algorithms is the heavy overlapping among the representative disks of the same size a shape component formed by grouping connected disk centers may use many heavily overlapping disks to represent a simple shape part sometimes these representative disks form complicated structures a generalized skeleton transform was recently introduced which allows a shape to be represented as a collection of modestly overlapped octagonal shape parts however the generalized skeleton transform needs to be applied many times furthermore an octagonal component is not easily matched up with another octagonal component in this paper we describe a octagon fitting algorithm which identifies a special maximal octagon for each image point in a given shape this transform leads to the development of two new shape decomposition algorithms these algorithms are more efficient to implement the octagon fitting algorithm only needs to be applied once the components generated are better characterized mathematically the disk components used in the second decomposition algorithm are more primitive than octagons and easily matched up with other disk components from another shape the experiments show that the new decomposition algorithms produce as efficient representations as the old algorithm for both exact and approximate cases a simple shape matching algorithm using disk components is also demonstrated

shape description and matching using integral invariants on eccentricity transformed images matching occluded and noisy shapes is a problem frequently encountered in medical image analysis and more generally in computer vision to keep track of changes inside the breast for example it is important for a computer aided detection system to establish correspondences between regions of interest shape transformations computed both with integral invariants ii and with geodesic distance yield signatures that are invariant to isometric deformations such as bending and articulations integral invariants describe the boundaries of planar shapes however they provide no information about where a particular feature lies on the boundary with regard to the overall shape structure conversely eccentricity transforms ecc can match shapes by signatures of geodesic distance histograms based on information from inside the shape but they ignore the boundary information we describe a method that combines the boundary signature of a shape obtained from ii and structural information from the ecc to yield results that improve on them separately

accurate computation of zernike moments in polar coordinates an algorithm for high precision numerical computation of zernike moments is presented the algorithm based on the introduced polar pixel tiling scheme does not exhibit the geometric error and numerical integration error which are inherent in conventional methods based on cartesian coordinates this yields a dramatic improvement of the zernike moments accuracy in terms of their reconstruction and invariance properties the introduced image tiling requires an interpolation algorithm which turns out to be of the second order importance compared to the discretization error various comparisons are made between the accuracy of the proposed method and that of commonly used techniques the results reveal the great advantage of our approach

a hybrid probabilistic framework for content based image retrieval with feature weighting in this paper we propose a probabilistic framework for efficient retrieval and indexing of image collections this framework uncovers the hierarchical structure underlying the collection from image features based on a hybrid model that combines both generative and discriminative learning we adopt the generalized dirichlet mixture and maximum likelihood for the generative learning in order to estimate accurately the statistical model of the data then the resulting model is refined by a new discriminative likelihood that enhances the power of relevant features consequently this new model is suitable for modeling high dimensional data described by both semantic and low level visual features the semantic features are defined according to a known ontology while visual features represent the visual appearance such as color shape and texture for validation purposes we propose a new visual feature which has nice invariance properties to image transformations experiments on the microsoft s collection msrcid show clearly the merits of our approach in both retrieval and indexing

2 d shape classification using hidden markov model the authors present a planar shape recognition approach based on the hidden markov model and autoregressive parameters this approach segments closed shapes to make classifications at a finer level the algorithm can tolerate a lot of shape contour perturbation and a moderate amount of occlusion an orientation scheme is described to make the overall classification insensitive to shape orientation excellent recognition results have been reported a distinct advantage of the approach is that the classifier does not have to be trained again when a new class of shapes is added

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

color texture description with novel local binary patterns for effective image retrieval abstract we propose a novel local color texture descriptor called local binary pattern for color images lbpc the proposed descriptor uses a plane to threshold color pixels in the neighborhood of a local window into two categories to boost the discriminative power of the proposed lbpc operator local binary patterns of the hue component in the hsi color space called the local binary pattern of the hue lbph is derived further lbpc lbph are fused to derive lbpc lbph which when combined with the color histogram ch of the hue component results in an effective image retrieval method lbpc lbph ch the uniform patterns of the two proposed descriptors ulbpc and ulbph are combined to yield another low dimension local color descriptor ulbpc ulbph ch which provides a good tradeoff between retrieval accuracy and speed detailed experiments conducted on wang holidays corel 5k and corel 10k datasets demonstrate that the proposed low dimension descriptors lbpc lbph ch and ulbpc ulbph ch outperform the state of the art color texture descriptors in terms of retrieval accuracy and speed

shape matching using a binary search tree structure of weak classifiers in this paper a novel algorithm for shape matching based on the hausdorff distance and a binary search tree data structure is proposed the shapes are stored in a binary search tree that can be traversed according to a hausdorff like similarity measure that allows us to make routing decisions at any given internal node each node functions as a classifier that can be trained using supervised learning these node classifiers are very similar to perceptrons and can be trained by formulating a probabilistic criterion for the expected performance of the classifier then maximizing that criterion methods for node insertion and deletion are also available so that a tree can be dynamically updated while offline training is time consuming all online training and both online and offline testing operations can be performed in o logn time experimental results on pedestrian detection indicate the efficiency of the proposed method in shape matching

stochastic models for closed boundary analysis representation and reconstruction the analysis of closed boundaries of arbitrary shapes on a plane is discussed specifically the problems of representation and reconstruction are considered a one to one correspondence between the given closed boundary and a univariate or multivariate sequence of real numbers is set up univariate or multivariate circular autoregressive models are suggested for the representation of the sequence of numbers derived from the closed boundary the stochastic model representing the closed boundary is invariant to transformations like sealing translation choice of starting point and rotation over angles that are multiples of 2 pi n where n is the number of observations methods for estimating the unknown parameters of the model are given and a decision rule for choosing the appropriate number of coefficients is included constraints on the estimates are derived so that the estimates are invariant to the transformations of the boundaries the stochastic model enables the reconstruction of a dosed boundary using fft algorithms results of simulations are included and the application to contour coding is discussed

new forms of shape invariants from elliptic fourier descriptors abstract new forms of shape invariants are derived using matrix trace operators for pattern recognition these invariants form a non redundant set have more straightforward and understandable geometric meanings and require fewer computations they are independent of the shape rotation and translation these invariants are interpreted geometrically and compared to those defined by grandlund possible utilizations for pattern recognition are discussed

shape error concealment based on a shape preserving boundary approximation in object based video representation video scenes are composed of several arbitrarily shaped video objects vos defined by their texture shape and motion in error prone communications packet loss results in missing information at the decoder the impact of transmission errors is minimized through error concealment in this paper we propose a spatial error concealment technique for recovering lost shape data we consider a geometric shape representation consisting of the object boundary which can be extracted from the plane missing macroblocks result in a broken boundary a b spline curve is constructed to replace a missing boundary segment based on a t spline representation of the received boundary we use t splines because they produce shape preserving approximations and do not change the characteristics of the original boundary the representation ensures a good estimation of the first derivatives at the points touching the missing segment applying smoothing conditions we manage to construct a new spline that joins smoothly with the received boundary leading to successful concealment results experimental results on object shapes with different concealment difficulty demonstrate the performance of the proposed method comparisons with prior proposed methods are also presented

a supersymmetric extension of the kadomtsev petviashvili hierarchy an extension of the kadomtsev petviashvili hierarchy by odd variables is given conservation laws and formal integrability are proved

dynamic time warping under pointwise shape context similarity measures are of fundamental importance in time series data mining dynamic time warping dtw is a quite popular measure because it handles time distortions well however dtw has an inherent shortcoming in that dtw can lead to pathological alignments between time series where a single point maps onto a large subsection of another time series to overcome this problem we propose a novel variant of dtw named sc dtw sc dtw employs shape context a rich local shape descriptor to replace the raw observed values considered by conventional dtw the main novelties of sc dtw are 1 it deeply explores both the numerical nature and shape nature of time series and 2 neighborhood information for each point is taken into account sc dtw can generate a more feature to feature alignment between time series and thus serves as a robust similarity measure we test the performance of sc dtw on ucr time series datasets using the one nearest neighbor 1nn classifier compared with other well established methods sc dtw provides better accuracy on 24 of 34 datasets

a zernike moment phase based descriptor for local image representation and matching a local image descriptor robust to the common photometric transformations blur illumination noise and jpeg compression and geometric transformations rotation scaling translation and viewpoint is crucial to many image understanding and computer vision applications in this paper the representation and matching power of region descriptors are to be evaluated a common set of elliptical interest regions is used to evaluate the performance the elliptical regions are further normalized to be circular with a fixed size the normalized circular regions will become affine invariant up to a rotational ambiguity here a new distinctive image descriptor to represent the normalized region is proposed which primarily comprises the zernike moment zm phase information an accurate and robust estimation of the rotation angle between a pair of normalized regions is then described and used to measure the similarity between two matching regions the discriminative power of the new zm phase descriptor is compared with five major existing region descriptors sift gloh pca sift complex moments and steerable filters based on the precision recall criterion the experimental results involving more than 15 million region pairs indicate the proposed zm phase descriptor has generally speaking the best performance under the common photometric and geometric transformations both quantitative and qualitative analyses on the descriptor performances are given to account for the performance discrepancy first the key factor for its striking performance is due to the fact that the zm phase has accurate estimation accuracy of the rotation angle between two matching regions second the feature dimensionality and feature orthogonality also affect the descriptor performance third the zm phase is more robust under the nonuniform image intensity fluctuation finally a time complexity analysis is provided

review of shape representation and description techniques more and more images have been generated in digital form around the world there is a growing interest in 1nding images in large collections or from remote databases in order to 1nd an image the image has to be described or represented by certain features shape is an important visual feature of an image searching for images using shape features has attracted much attention there are many shape representation anddescription techniques in the literature in this paper we classify and review these important techniques we examine implementation procedures for each technique and discuss its advantages and disadvantages some recent research results are also included and discussed in this paper finally we identify some promising techniques for image retrieval according to standard principles

a generalized morphological skeleton transform using both internal and external skeleton points the morphological skeleton transform mst is a leading morphological shape representation scheme in the mst a given shape is represented as the union of all the maximal disks contained in the shape the concept of external skeleton points and external maximal disks has been used for shape description and characterization purposes in this paper we develop a generalized morphological skeleton transform that combines the concepts of internal and external maximal disks into a unified framework in this framework a shape is described in terms of disk components that need to be added as well as disk components that need to be removed the procedures and formulae describing the extraction of the disk components and the reconstruction of the original shape from these components are developed the correctness of the procedures and formulae is established this new framework seems to provide a more powerful and more natural way of modeling the approximation and reconstruction of binary shapes using primitive shape components

ecds an effective shape signature using electrical charge distribution on the shape abstract motivated by the fact that electrical charge distributions are almost the same for similar shapes but not vice versa when shapes reach their electrical equilibrium condition we propose a novel shape signature based on the electrical charge distribution on the shape ecds compared to other shape signatures ecds has the following interesting properties 1 ecds is a local measure but computed in a global manner thus it is more robust to noise and shape variations 2 ecds is articulation insensitive and therefore exhibits better performance by the introduction of generalized coulomb potentials this allows it to better match shapes whose parts can move independently such as scissors 3 the sum of ecds remains constant during the process of reaching electrical equilibrium which does favor some applications numerous experiments have been done on several public shape databases mpeg 7 database articulated shape data set kimia silhouettes and eth 80 data set demonstrating that ecds has the above properties and compares well with other shape descriptors in many kinds of shape retrieval and recognition tasks

efficient planar affine canonicalization abstract this paper presents a fast and accurate affine canonicalization method for planar shapes this method improves on previous ones based on iterative optimization that produce multiple canonical versions canonicalization provides a common reference frame for shape comparison without the loss of discrimination ability often caused by invariant features it also gives for free the alignment transformation between any pair of shapes the proposed method is based on the properties of the joint angular distribution of marginal skewness and kurtosis the so called sk signature which can be efficiently computed in closed form from the raw image moments the experiments demonstrate that the method is robust to the non affine distortions caused by natural perspective image conditions thus it can be used as an automatic preprocessing step to add affine invariance in statistical pattern recognition applications

pattern recognition with moment invariants a comparative study and new results abstract moment invariants have been proposed as pattern sensitive features in classification and recognition applications in this paper the authors present a comprehensive study of the effectiveness of different moment invariants in pattern recognition applications by considering two sets of data handwritten numerals and aircrafts the authors also present a detailed study of zernike and pseudo zernike moment invariants including a new procedure for deriving the moment invariants in addition the authors introduce a new normalization scheme that reduces the large dynamic range of these invariants as well as implicit redundancies in these invariants based on a comprehensive study with both handwritten numerals and aircraft data the authors show that the new method of deriving zernike moment invariants along with the new normalization scheme yield the best overall performance even when the data are degraded by additive noise

an experimental comparison of autoregressive and fourier based descriptors in 2d shape classification an experimental comparison of shape classification methods based on autoregressive modeling and fourier descriptors of closed contours is carried out the performance is evaluated using two independent sets of data images of letters and airplanes silhouette contours are extracted from non occluded 2d objects rotated scaled and translated in 3d space several versions of both types of methods are implemented and tested systematically the comparison clearly shows better performance of fourier based methods especially for images containing noise

an approach to the parameterization of structure for fast categorization a decomposition is described which parameterizes the geometry and appearance of contours and regions of gray scale images with the goal of fast categorization to express the contour geometry a contour is transformed into a local global space from which parameters are derived classifying its global geometry arc inflexion or alternating and describing its local aspects degree of curvature edginess symmetry regions are parameterized based on their symmetric axes which are evolved with a wave propagation process enabling to generate the distance map for fragmented contour images the methodology is evaluated on three image sets the caltech 101 set and two sets drawn from the corel collection the performance nearly reaches the one of other categorization systems for unsupervised learning

shape classification using line segment statistics in this study we use straight line segment statistics for shape analysis for each contour point we consider a continuous portion with length equal to a pre defined percentage of the contour size then we compute the length of the straight line segment between its extreme points for the set of straight line segments we compute statistical moments average and stardard deviation contour shape description is an important field in computer vision this is due to the fact that shape is an important low level image feature in light of this many approaches have been proposed in order to analyze it therefore this paper introduces a very simple yet efficient shape descriptor based on straight line segment statistics for each contour point we consider a continuous portion of the contour with length equal to a pre defined percentage of the contour size then we compute the length of the straight line segment between its extreme points for the set of straight line segments we compute statistical moments average and standard deviation lastly we perform this calculation for different lengths of contour portions the proposed shape descriptor is a powerful tool for shape discrimination it is robust it can characterize a huge set of different classes of shapes and is tolerant to variations in the shapes scale and orientation classification results of the proposed method overcome traditional methods found in literature proving that it is an efficient tool for shape analysis

invariant description and retrieval of planar shapes using radon composite features this paper proposes a novel feature based invariant descriptor termed radon composite features rcfs for planar shapes instead of analyzing shapes directly in the spatial domain some shape features are extracted from the radon transform plane using statistical and spectral analysis the proposed method overcomes the drawbacks of existing shape representation techniques since it accomplishes the invariances to common geometrical transformations without any normalization process which usually causes inaccuracies a novel hierarchical strategy with rcfs can achieve low complexity and coarse to fine retrieval and perform accurately when retrieving shapes while remaining robust against variations experiments demonstrate that rcf provides a higher degree of discrimination as compared with several state of the art approaches

dynamical systems that sort lists diagonalize matrices and solve linear programming problems abstract we establish a number of properties associated with the dynamical system h h h n where h and n are symmetric n by n matrices and a b ab ba the most important of these come from the fact that this equation is equivalent to a certain gradient flow on the space of orthogonal matrices we are especially interested in the role of this equation as an analog computer for example we show how to map the data associated with a linear programming problem into h 0 and n in such a way as to have h h h n evolve to a solution of the linear programming problem this result can be applied to find systems which solve a variety of genetic combinatorial optimization problems and it even provides an algorithm for diagonalizing symmetric matrices

complete integrability of the kadomtsev petviashvili equation abstract the total hierarchy of the kadomtsev petviashvili kp equation is transformed to the system of linear partial differential equations with constant coefficients the complete integrability of the kp equation is proved by using this linear system the existence and uniqueness theorem of the cauchy problem of the kp hierarchy is obtained

matching invariant to translations rotations and scale changes abstract an optimization approach to invariant matching is proposed in this approach an object or a pattern is invariantly represented by an object centred description called an attributed relational structure ars embedding invariant properties and relations between the primitives of the pattern such as line segments and points noise effect is taken into account such that a scene can consist of noisy sub parts of a model the matching is then to find the optimal mapping between the arss of the scene and the model a gain functional is formulated to measure the goodness of fit and is to be maximized by using the relaxation labelling method experiments are shown to illustrate the matching algorithm and to demonstrate that the approach is truly invariant to arbitrary translations rotations and scale changes under noise

multiscale distance matrix for fast plant leaf recognition in this brief we propose a novel contour based shape descriptor called the multiscale distance matrix to capture the shape geometry while being invariant to translation rotation scaling and bilateral symmetry the descriptor is further combined with a dimensionality reduction to improve its discriminative power the proposed method avoids the time consuming pointwise matching encountered in most of the previously used shape recognition algorithms it is therefore fast and suitable for real time applications we applied the proposed method to the task of plan leaf recognition with experiments on two data sets the swedish leaf data set and the icl leaf data set the experimental results clearly demonstrate the effectiveness and efficiency of the proposed descriptor

perceptually relevant and piecewise linear matching of silhouettes in this paper a novel alignment method for silhouettes is proposed this method is based on the establishment of correspondences between landmarks on their boundaries and in turn on the establishment of correspondences of the boundary pieces in between these landmarks the method yields more correct correspondences than conventional methods that scale the arc length descriptions of silhouettes to align them the selection of landmarks is investigated as to the robustness of their localization and their perceptual relevance matching of silhouettes is then achieved by quantifying the dissimilarity of a pair of silhouette boundaries based on a novel dissimilarity metric the matching procedure is evaluated based on retrieval experiments and it is concluded that the precision of the results is higher than that obtained by conventional pointwise comparison methods

on hidden markov models and cyclic strings for shape recognition abstract shape descriptions and the corresponding matching techniques must be robust to noise and invariant to transformations for their use in recognition tasks most transformations are relatively easy to handle when contours are represented by strings however starting point invariance is difficult to achieve one interesting possibility is the use of cyclic strings which are strings that have no starting and final points we propose new methodologies to use hidden markov models to classify contours represented by cyclic strings experimental results show that our proposals outperform other methods in the literature

algebraic aspects of brockett type equations abstract it is well known that soliton equations can be written in lax form where the bracket of two linear differential n kdv or pseudo differential kp operators appears in this work we introduce a new hierarchy each equation of which is defined by a double bracket of two pseudo differential operators these double bracket equations arose originally in the study by brockett of the steepest descent equations corresponding to certain least squares matching and sorting problems we deal with some algebraic properties of these equations in particular we show that as in the classical case they are related to the presence of an infinite sequence of first integrals

super brockett equations a graded gradient integrable system rather recently equations of lax type defined by a double commutator the so called brockett equations have received considerable attention in this paper we prove that a supersymmetric version of a brockett hierarchy is an infinite dimensional integrable gradient system as far as we know this is the only graded system of this type existing in the literature

description and discrimination of planar shapes using shape matrices a shape descriptor has been developed which can describe a shape independent of its translation rotation and scaling the description is in the form of a matrix and it is obtained by a polar quantization of a shape the quantization process takes into consideration not only a shape s outer geometry but its inner geometry as well the descriptor is information preserving and if the quantization parameters are selected properly it is possible to reconstruct an original shape from its description in this technique shape discrimination is possible by a simple exclusive or operation on shape descriptions

molecular evolution under fitness fluctuations molecular evolution is a stochastic process governed by fitness mutations and reproductive fluctuations in a population here we study evolution where fitness itself is stochastic with random switches in the direction of selection at individual genomic loci as the correlation time of these fluctuations becomes larger than the diffusion time of mutations within the population fitness changes from an annealed to a quenched random variable we show that the rate of evolution has its maximum in the crossover regime where both time scales are comparable adaptive evolution emerges in the quenched fitness regime evidence for such fitness fluctuations has recently been found in genomic data the joint statistical theory of reproductive and fitness fluctuations establishes a conceptual connection between evolutionary genetics and statistical physics of disordered systems

a bayesian exemplar based approach to hierarchical shape matching this paper presents a novel probabilistic approach to hierarchical exemplar based shape matching no feature correspondence is needed among exemplars just a suitable pairwise similarity measure the approach uses a template tree to efficiently represent and match the variety of shape exemplars the tree is generated offline by a bottom up clustering approach using stochastic optimization online matching involves a simultaneous coarse to fine approach over the template tree and over the transformation parameters the main contribution of this paper is a bayesian model to estimate the a posteriori probability of the object class after a certain match at a node of the tree this model takes into account object scale and saliency and allows for a principled setting of the matching thresholds such that unpromising paths in the tree traversal process are eliminated early on the proposed approach was tested in a variety of application domains here results are presented on one of the more challenging domains real time pedestrian detection from a moving vehicle a significant speed up is obtained when comparing the proposed probabilistic matching approach with a manually tuned nonprobabilistic variant both utilizing the same template tree structure

wesd weighted spectral distance for measuring shape dissimilarity this paper presents a new distance for measuring shape dissimilarity between objects recent publications introduced the use of eigenvalues of the laplace operator as compact shape descriptors here we revisit the eigenvalues to define a proper distance called weighted spectral distance wesd for quantifying shape dissimilarity the definition of wesd is derived through analyzing the heat trace this analysis provides the proposed distance with an intuitive meaning and mathematically links it to the intrinsic geometry of objects we analyze the resulting distance definition present and prove its important theoretical properties some of these properties include 1 wesd is defined over the entire sequence of eigenvalues yet it is guaranteed to converge 2 it is a pseudometric 3 it is accurately approximated with a finite number of eigenvalues and 4 it can be mapped to the 0 1 interval last experiments conducted on synthetic and real objects are presented these experiments highlight the practical benefits of wesd for applications in vision and medical image analysis

structure integral transform versus radon transform a 2d mathematical tool for invariant shape recognition in this paper we present a novel mathematical tool structure integral transform sit for invariant shape description and recognition different from the radon transform rt which integrates the shape image function over a 1d line in the image plane the proposed sit builds upon two orthogonal integrals over a 2d k cross dissecting structure spanning across all rotation angles by which the shape regions are bisected in each integral the proposed sit brings the following advantages over the rt 1 it has the extra function of describing the interior structural relationship within the shape which provides a more powerful discriminative ability for shape recognition 2 the shape regions are dissected by the k cross in a coarse to fine hierarchical order that can characterize the shape in a better spatial organization scanning from the center to the periphery and 3 it is easier to build a completely invariant shape descriptor the experimental results of applying sit to shape recognition demonstrate its superior performance over the well known radon transform and the well known shape contexts and the polar harmonic transforms

a bivariate autoregressive technique for analysis and classification of planar shapes a bivariate autoregressive model is introduced for the analysis and classification of closed planar shapes the boundary coordinate sequence of a digitized binary image is sampled to produce a polygonal approximation to an object s shape this circular sample sequence is then represented by a vector autoregressive difference equation which models the individual cartesian coordinate sequences as well as coordinate interdependencies several classification features which are functions or transformations of the estimated coefficient matrices and the associated residual error covariance matrices are developed these features are shown to be invariant to object transformations such as translation rotation and scaling laboratory experiments involving object sets representative of industrial shapes are presented superior classification results are demonstrated

classification of partial 2 d shapes using fourier descriptors we present a method for the classification of 2 d partial shapes using fourier descriptors we formulate the problem as one of estimating the fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments the method used for obtaining the estimates of the fourier descriptors minimizes a sum of two terms the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2 area of the unknown shape experiments with synthetic and real boundaries show that estimates closer to the true values of fourier descriptors of complete boundaries are obtained also classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20 30 percent of the data is missing

vibration mode shape recognition using image processing abstract currently the most widely used method for comparing mode shapes from finite elements and experimental measurements is the modal assurance criterion mac which can be interpreted as the cosine of the angle between the numerical and measured eigenvectors however the eigenvectors only contain the displacement of discrete coordinates so that the mac index carries no explicit information on shape features new techniques based upon the well developed philosophies of image processing ip and pattern recognition pr are considered in this paper the zernike moment descriptor zmd fourier descriptor fd and wavelet descriptor wd are the most popular shape descriptors due to their outstanding properties in ip and pr these include 1 for the zmd rotational invariance expression and computing efficiency ease of reconstruction and robustness to noise 2 for the fd separation of the global shape and shape details by low and high frequency components respectively invariance under geometric transformation 3 for the wd multi scale representation and local feature detection once a shape descriptor has been adopted the comparison of mode shapes is transformed to a comparison of multidimensional shape feature vectors deterministic and statistical methods are presented the deterministic problem of measuring the degree of similarity between two mode shapes possibly one from a vibration test and the other from a finite element model may be carried out using pearson s correlation similar shape feature vectors may be arranged in clusters separated by euclidian distances in the feature space in the statistical analysis we are typically concerned with the classification of a test mode shape according to clusters of shape feature vectors obtained from a randomised finite element model the dimension of the statistical problem may often be reduced by principal component analysis then in addition to the euclidian distance the mahalanobis distance defining the separation of the test point from the cluster in terms of its standard deviation becomes an important measure bayesian decision theory may be applied to formally minimise the risk of misclassification of the test shape feature vector in this paper the zmd is applied to the problem of mode shape recognition for a circular plate results show that the zmd has considerable advantages over the traditional mac index when identifying the cyclically symmetric mode shapes that occur in axisymmetric structures at identical frequencies mode shape recognition of rectangular plates is carried out by the fd also the wd is applied to the problem of recognising the mode shapes in the thin and thick regions of a plate with different thicknesses it shows the benefit of using the wd to identify mode shapes having both local and global components the comparison and classification of mode shapes using ip and pr provides a toolkit to complement the conventional mac approach the selection of a particular shape descriptor and classification method will depend upon the problem in hand and the experience of the analyst

on image analysis by moments research has been performed investigating the use of moments for pattern recognition in recent years the basic problem of the influence of discretization and noise on moment accuracy as object descriptors has been barely investigated in this paper the detailed error analysis involved in the moment method is discussed several new techniques to increase the accuracy and efficiency of moment descriptor are proposed we utilize these results for the problem of image reconstruction from the orthogonal legendre moments computed from discrete and noisy data the automatic selection of an optimal number of moments is also discussed

least squares matching problems abstract a large class of matching problems can be thought of in the following way one is given a group g which acts on a riemannian manifold and one is given two points x 1 and x 2 in the manifold the problem is to find g g such that d g x 1 x 2 is as small as possible if the group has finite cardinality this is a combinatorial optimization problem whereas if g is a lie group one can use the calculus to obtain necessary conditions our main results establish circumstances under which one can relax the combinatorial problem to an appropriate lie group problem and then solve it by the method of steepest descent an interesting class of applications involves embedding the permutation group on n letters in the orthogonal group o n with the latter acting on r n n 1 2 via a symmetricized tensor product the convergence properties of the descent equation which arises in this way are analyzed in some detail

a robust approach for object matching and classification using partial dominant orientation descriptor this paper introduces a novel approach to measure the correspondence between objects and exploit it for object and image classification tasks using the proposed partial dominant orientation descriptor pdod in particular the object is represented by a set of stable and informative key locations sampled using difference of gaussian the proposed pdod at each extracted key location takes into account the position and partially computes the dominant orientation of other key locations relative to it thus offering a global distinctive and discriminative characterization this allows us to learn features that are largely invariant to common image transformations including changes in object colors and textures the correspondence in between two objects is performed by finding for each key location in one object the key location in the other object that has the most similar descriptor object classification proceeds by assigning the most relevant category that has maximally similar stored prototype objects to the query object using k nearest neighbors algorithm with adaptive object distance for efficiency we further investigate pdod for image classification by developing powerful image representations based on the popular bag of words model the extensive experiments demonstrate that the proposed approach greatly improves the matching and classification results while achieving the state of the art performances on several challenging benchmark datasets the obtained results suggest also broader applicability to other classification modalities we propose a novel descriptor for complex object matching and classification the proposed descriptor combines both local and global properties of interest points the proposed descriptor is highly distinctive and insensitive to common image transformations adaptive object distance is proposed to measure the similarity between objects we compare our approach with many existing methods and we achieve the state of the art performances on several benchmarks

radial symmetries based decomposition of cell clusters in binary and gray level images the segmentation of structures of complex cytological and histological images is a necessary intermediate step for image analysis that give rise to binary images in many cases these binary images can be rather far away from a subsequent object specific quantification because biological structures digitized by optoelectronic devices may situated close together so that they appear as one fused object in the projective image such fusions of objects may become complex so that large clusters of biological structures emerge to quantify individual objects of a cluster they must be separated the shape size and intensity variation of cells in complex organs like the brain may breed planar configurations that can be splitted only inadequate by common techniques e g watershed separation or basic morphological processing of images considering iteratively object contours suitable features of saliency can be accumulated that give rise to markers of singular objects such significant markers may drive a separation process more effective than common approaches the determination of markers by an iterative method should be scale translation and rotation invariant and robust with regard to noise due to the variability of biological specimen we realize a technique that splits cell clumps consisting of different cell sizes and shapes into meaningful parts the multiscale method applied here is based on the analysis of the contour shape and the object area by iterative voting using oriented kernels these cone shaped kernels vote iteratively for the local center of mass of the components of an aggregation the voting is performed along the gradient of the distance transformation of the binarized image of aggregates iterative voting is initialized by voting along the gradient direction where at each iteration the voting direction and shape of the kernel is refined resp the kernel topography is refined and reoriented iteratively it turned out that the kernel topography is unique because it votes for the most likely set of grid points where the gravity center of an individual cluster component may be located furthermore a new procedure is realized to use the local intensities of aggregations for kernel voting the last voted iteration provides gravitation centers resp centers of mass of the clumped cells these are extracted and used as markers to determine individual cell boundaries by a marker based watershed postprocessing the subject of this paper is to highlight the basic algorithm of iterative kernel voting and expanding it to process intensities within clusters as well as contour information the approach is applied to synthetic images that were modified systematically with regard to object topology natural aggregates of cells at the light microscopic level and cell clusters derived from high resolution flat bed scanning were splitted in addition to these examples images from a benchmark databases were investigated the splittings generated by the iterative voting approach were compared with expected splittings of test persons and with results of the watershed method especially the gray level based iterative voting method provides superior results for cell cluster separation in comparison to the watershed procedure

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

shape based invariant texture indexing this paper introduces a new texture analysis scheme which is invariant to local geometric and radiometric changes the proposed methodology relies on the topographic map of images obtained from the connected components of level sets this morphological tool providing a multi scale and contrast invariant representation of images is shown to be well suited to texture analysis we first make use of invariant moments to extract geometrical information from the topographic map this yields features that are invariant to local similarities or local affine transformations these features are invariant to any local contrast change we then relax this invariance by computing additional features that are invariant to local affine contrast changes and investigate the resulting analysis scheme by performing classification and retrieval experiments on three texture databases the obtained experimental results outperform the current state of the art in locally invariant texture analysis

fast and numerically stable methods for the computation of zernike moments zernike moments zms are used in many image processing applications due to their superior performance over other moments however they suffer from high computation cost and numerical instability at high order of moments in the past many recursive methods have been developed to improve their speed performance and considerable success has been achieved the analysis of numerical stability has also gained momentum as it affects the accuracy of moments and their invariance property there are three recursive methods which are normally used in zms calculation prata s kintner s and q recursive methods the earlier studies have found the q recursive method outperforming the two other methods in this paper we modify prata s method and present a recursive relation which is proved to be faster than the q recursive method numerical instability is observed at high orders of moments with the q recursive method suffering from the underflow problem while the modified prata s method suffering from finite precision error the modified kintner s method is the least susceptible to these errors keeping in view the better numerical stability we further make the modified kintner s method marginally faster than the q recursive method we recommend the modified prata s method for low orders 90 and kintner s fast method for high orders 90 of zms

surface fluid registration of conformal representation application to detect disease burden and genetic influence on hippocampus in this paper we develop a new automated surface registration system based on surface conformal parameterization by holomorphic 1 forms inverse consistent surface fluid registration and multivariate tensor based morphometry mtbm first we conformally map a surface onto a planar rectangle space with holomorphic 1 forms second we compute surface conformal representation by combining its local conformal factor and mean curvature and linearly scale the dynamic range of the conformal representation to form the feature image of the surface third we align the feature image with a chosen template image via the fluid image registration algorithm which has been extended into the curvilinear coordinates to adjust for the distortion introduced by surface parameterization the inverse consistent image registration algorithm is also incorporated in the system to jointly estimate the forward and inverse transformations between the study and template images this alignment induces a corresponding deformation on the surface we tested the system on alzheimer s disease neuroimaging initiative adni baseline dataset to study ad symptoms on hippocampus in our system by modeling a hippocampus as a 3d parametric surface we nonlinearly registered each surface with a selected template surface then we used mtbm to analyze the morphometry difference between diagnostic groups experimental results show that the new system has better performance than two publicly available subcortical surface registration tools first and spharm we also analyzed the genetic influence of the apolipoprotein e 4 allele apoe4 which is considered as the most prevalent risk factor for ad our work successfully detected statistically significant difference between apoe4 carriers and non carriers in both patients of mild cognitive impairment mci and healthy control subjects the results show evidence that the apoe genotype may be associated with accelerated brain atrophy so that our work provides a new mri analysis tool that may help presymptomatic ad research

efficiently locating objects using the hausdorff distance the hausdorff distance is a measure defined between two point sets here representing a model and an image the hausdorff distance is reliable even when the image contains multiple objects noise spurious features and occlusions in the past it has been used to search images for instances of a model that has been translated or translated and scaled by finding transformations that bring a large number of model features close to image features and vice versa in this paper we apply it to the task of locating an affine transformation of a model in an image this corresponds to determining the pose of a planar object that has undergone weak perspective projection we develop a rasterised approach to the search and a number of techniques that allow us to locate quickly all transformations of the model that satisfy two quality criteria we can also efficiently locate only the best transformation we discuss an implementation of this approach and present some examples of its use

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

invariant pattern recognition using the rfm descriptor a pattern descriptor invariant to rotation scaling translation rst and robust to additive noise is proposed by using the radon fourier and mellin transforms the radon transform converts the rst transformations applied on a pattern image into transformations in the radial and angular coordinates of the pattern s radon image these beneficial properties of the radon transform make it an useful intermediate representation for the extraction of invariant features from pattern images for the purpose of indexing matching in this paper invariance to rst is obtained by applying the 1d fourier mellin and discrete fourier transforms on the radial and angular coordinates of the pattern s radon image respectively the implementation of the proposed descriptor is reasonably fast and correct based mainly on the fusion of the radon and fourier transforms and on a modification of the mellin transform theoretical arguments validate the robustness of the proposed descriptor to additive noise and empirical evidence on both occlusion deformation and noisy datasets shows its effectiveness

rectilinearity of 3d meshes in this paper we propose and evaluate a novel shape measure describing the extent to which a 3d polygon mesh is rectilinear the rectilinearity measure is based on the maximum ratio of the surface area to the sum of three orthogonal projected areas of the mesh it has the following desirable properties 1 the estimated rectilinearity is always a number from 0 1 2 the measure is invariant under scale rotation and translation 3 the 3d objects can be either open or closed meshes and we can also deal with degenerate meshes 4 the measure is insensitive to noise stable under small topology errors and robust against face deletion and mesh simplification moreover a genetic algorithm ga can be applied to compute the approximate rectilinearity efficiently we find that the calculation of rectilinearity can be used to normalize the pose of 3d meshes and in many cases it performs better than the principal component analysis pca based method by applying a simple selection criterion the combination of these two methods results in a new pose normalization algorithm which not only provides a higher successful alignment rate but also corresponds better with intuition finally we carry out several experiments showing that both the rectilinearity based pose normalization preprocessing and the combined signatures which consist of the rectilinearity measure and other shape descriptors can significantly improve the performance of 3d shape retrieval

complex autoregressive model for shape recognition a complex autoregressive model for invariant feature extraction to recognize arbitrary shapes on a plane is presented a fast algorithm to calculate complex autoregressive coefficients and complex parcor coefficients of the model is also shown the coefficients are invariant to rotation around the origin and to choice of the starting point in tracing a boundary it is possible to make them invariant to scale and translation experimental results that the complicated shapes like nonconvex boundaries can be recognized in high accuracy even in the low order model it is seen that the complex parcor coefficients tend to provide more accurate classification than the complex ar coefficients

fourier coding of image boundaries a transform coding scheme for closed image boundaries on a plane is described the given boundary is approximated by a series of straight line segments depending on the shape the boundary is represented by the x y coordinates of the endpoints of the line segments or by the magnitude of the successive radii vectors that are equispaced in angle around the given boundary due to the circularity present in the data the discrete fourier transform is used to exactly decorrelate the finite boundary data by fitting a gaussian circular autoregressive model to represent the boundary data estimates of the variances of the fourier coefficients are obtained using the variances of the fourier coefficients and the max quantizer the coding scheme is implemented the scheme is illustrated by an example

application of affine invariant fourier descriptors to recognition of 3 d objects the method of fourier descriptors is extended to produce a set of normalized coefficients which are invariant under any affine transformation translation rotation scaling and shearing the method is based on a parameterized boundary description which is transformed to the fourier domain and normalized there to eliminate dependencies on the affine transformation and on the starting point invariance to affine transforms allows considerable robustness when applied to images of objects which rotate in all three dimensions as is demonstrated by processing silhouettes of aircraft maneuvering in three space

perceptually motivated image features using contours dong et al examined the ability of 51 computational feature sets to estimate human perceptual texture similarity however none performed well for this task while it is well known that the human visual system is extremely adept at exploiting longer range aperiodic and periodic contour characteristics in images none of the investigated feature sets exploit higher order statistics hos over larger image regions 19 times 19 pixels we therefore hypothesise that long range hos in the form of contour data are useful for perceptual texture similarity estimation we present the results of a psychophysical experiment that shows that contour data are more important than local image patches or global second order data to human observers for this task inspired by this finding we propose a set of perceptually motivated image features pmif that encode the long range hos computed from spatial and angular distributions of contour segments we use two perceptual texture similarity estimation tasks to compare pmif against the 51 feature sets referred to above and four commonly used contour representations this new feature set is also examined in the context of two additional tasks sketch based image retrieval and natural scene recognition the results show that the proposed feature set performs better or at least comparably to all the other feature sets we attribute this promising performance to the fact that the proposed feature set exploits both short range and long range hos

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area