a new approach to analyticity of dirichlet neumann operators this paper outlines the theoretical background of a new approach towards an accurate and well conditioned perturbative calculation of dirichlet neumann operators dnos on domains that are perturbations of simple geometries previous work on the analyticity of dnos has produced formulae that as we have found are very ill conditioned we show how a simple change of variables can lead to recursions that satisfy analyticity estimates without relying on subtle cancellation properties at the heart of previous formulae

shape retrieval using triangle area representation and dynamic space warping in this paper we present a shape retrieval method using triangle area representation for nonrigid shapes with closed contours the representation utilizes the areas of the triangles formed by the boundary points to measure the convexity concavity of each point at different scales or triangle side lengths this representation is effective in capturing both local and global characteristics of a shape invariant to translation rotation and scaling and robust against noise and moderate amounts of occlusion in the matching stage a dynamic space warping dsw algorithm is employed to search efficiently for the optimal least cost correspondence between the points of two shapes then a distance is derived based on the optimal correspondence the performance of our method is demonstrated using four standard tests on two well known shape databases the results show the superiority of our method over other recent methods in the literature

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

invariant image recognition by zernike moments the problem of rotation scale and translation invariant recognition of images is discussed a set of rotation invariant features are introduced they are the magnitudes of a set of orthogonal complex moments of the image known as zernike moments scale and translation invariance are obtained by first normalizing the image with respect to these parameters using its regular geometrical moments a systematic reconstruction based method for deciding the highest order zernike moments required in a classification problem is developed the quality of the reconstructed image is examined through its comparison to the original one the orthogonality property of the zernike moments which simplifies the process of image reconstruction make the suggest feature selection approach practical features of each order can also be weighted according to their contribution to the reconstruction process the superiority of zernike moment features over regular moments and moment invariants was experimentally verified

improved data visualisation through multiple dissimilarity modelling popular dimension reduction and visualisation algorithms rely on the assumption that input dissimilarities are typically euclidean for instance metric multidimensional scaling t distributed stochastic neighbour embedding and the gaussian process latent variable model it is well known that this assumption does not hold for most datasets and often high dimensional data sits upon a manifold of unknown global geometry we present a method for improving the manifold charting process coupled with elastic mds such that we no longer assume that the manifold is euclidean or of any particular structure we draw on the benefits of different dissimilarity measures allowing for the relative responsibilities under a linear combination to drive the visualisation process

robust shape similarity retrieval based on contour segmentation polygonal multiresolution and elastic matching in this paper we are going to present a novel shape similarity retrieval algorithm that can be used to match and recognize 2d objects the match process uses a new multi resolution polygonal shape descriptor that is invariant to scale rotation and translation the shape descriptor equally segments the contour of any shape regardless of its complexity and captures three features around its center including the distance and slope relative to the center all parameters are normalized relative to the max values the novel shape matching algorithm uses the shape descriptor and applies it by linearly scanning a stored set of shapes and measuring the similarity using elastic comparisons of shape segments similarity measurement is achieved by the sum of differences distance measure the multi resolution segmentation provides flexibility for applications that have different time and space requirements while maintaining high accuracy results and the elastic matching adds an advantage when matching partially occluded shapes we applied our algorithms on many test databases including the mpeg 7 shape core experiment and achieved the highest result reported with a score of 84 33 for the mpeg 7 part b similarity test

curvilinear component analysis a self organizing neural network for nonlinear mapping of data sets we present a new strategy called curvilinear component analysis cca for dimensionality reduction and representation of multidimensional data sets the principle of cca is a self organized neural network performing two tasks vector quantization vq of the submanifold in the data set input space and nonlinear projection p of these quantizing vectors toward an output space providing a revealing unfolding of the submanifold after learning the network has the ability to continuously map any new point from one space into another forward mapping of new points in the input space or backward mapping of an arbitrary position in the output space

improved data visualisation through nonlinear dissimilarity modelling inherent to state of the art dimension reduction algorithms is the assumption that global distances between observations are euclidean despite the potential for altogether non euclidean data manifolds we demonstrate that a non euclidean manifold chart can be approximated by implementing a universal approximator over a dictionary of dissimilarity measures building on recent developments in the field this approach is transferable across domains such that observations can be vectors distributions graphs and time series for instance our novel dissimilarity learning method is illustrated with four standard visualisation datasets showing the benefits over the linear dissimilarity learning approach

optimal order multigrid methods for solving exterior boundary value problems the coupling of boundary elements and finite elements combines the advantage of boundary elements for treating domains extended to infinity and that of finite elements in treating the nonhomogeneity of equations and the complexity of domains in the case of the laplacian by taking a circle or a sphere as the artificial coupling boundary it is shown that the corresponding boundary integral equation can be solved without any cost and the coupled system is reduced to a simple finite element system two multigrid methods are proposed to solve this finite element linear system both methods are of optimal order and can be used to solve such finite element equations as efficiently as to solve those arising from interior boundary value problems numerical experiments are included to show the efficiency and advantages of the methods an apparent significance of the methods is that the boundary elements appear neither in the discretization nor in the coding

weak solvability of interior transmission problems via mixed finite elements and dirichlet to neumann mappings we study the weak solvability of an interior linear nonlinear transmission problem arising in steady heat transfer and potential theory for the variational formulation we use a dirichlet to neumann mapping on the interface which is obtained from the application of the boundary integral method to the linear domain and we utilize a mixed finite element method in the nonlinear region existence and uniqueness of solution for the continuous formulation are provided and general approximation results for a fully discrete galerkin method are derived in particular a compatibility condition between the mesh sizes involved is deduced in order to conclude the solvability and stability of this galerkin scheme

accurate calculation of zernike moments zernike moments zms are very effective global image descriptors which are used in many digital image processing applications the digitization process compromises the accuracy of the moments and therefore several of its properties are affected there are two major discretization errors namely the geometric error and numerical integration error in this paper we propose two new algorithms which eliminate these errors the first algorithm performs the exact computation of geometric moments gms over a unit disk and then uses gms to zms relationship to compute the latter this algorithm is computationally more expensive and it becomes numerically instable for higher order moments therefore we develop a second algorithm based on gaussian quadrature numerical integration the second algorithm reduces both the errors simultaneously and its accuracy increases as the degree of gaussian quadrature numerical integration increases the proposed algorithms are observed to provide very accurate zms which result in improved image reconstruction reduction in reconstruction error and improvement in rotation and scale invariance exhaustive experiments are provided to support improved accuracy of zms and time complexity analysis is performed for the existing and the proposed methods

elastic shape texture matching for human face recognition in this paper a novel elastic shape texture matching method namely estm for human face recognition is proposed in our approach both the shape and the texture information are used to compare two faces without establishing any precise pixel wise correspondence the edge map is used to represent the shape of an image while the texture information is characterized by both the gabor representations and the gradient direction of each pixel combining these features a shape texture hausdorff distance is devised to compute the similarity of two face images the elastic matching is robust to small local distortions of the feature points such as those caused by facial expression variations in addition the use of the edge map gabor representations and the direction of the image gradient can all alleviate the effect of illumination to a certain extent with different databases experimental results show that our algorithm can always achieve a better performance than other face recognition algorithms under different conditions except when an image is under poor and uneven illumination experiments based on the yale database ar database orl database and yaleb database show that our proposed method can achieve recognition rates of 88 7 97 7 78 3 and 89 5 respectively

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

numerical differentiation for use in integrating unified constitutive equations the nonss method for numerically integrating time dependent constitutive equations requires evaluation of the partial derivatives of the constitutive equations a numerical method for evaluating these partial derivatives has been developed thus avoiding the cumbersome task of analytically re deriving the partial derivatives when improvements to the constitutive model are evaluated this method is based upon the adaptive finite difference algorithm published by stepleman and winarsky modifications of their algorithm are described that allow its efficient use within an extended version of nonss called nonss nd using the matmod constitutive equations the capabilities of nonss nd are demonstrated by comparing the results of a wide variety of deformation simulations with those of nonss for which the derivatives are computed from analytical solutions the numerical differentiation within nonss nd is shown to be sufficiently accurate for use in integrating time dependent constitutive equations but results in a 30 100 per cent increase in computation time multi element structural calculations are therefore found to be uneconomical but nonss nd is well suited for testing alternative constitutive models owing to its accuracy and its general applicability to highly non linear systems of differential equations

supervised principal component analysis visualization classification and regression on subspaces and submanifolds we propose supervised principal component analysis supervised pca a generalization of pca that is uniquely effective for regression and classification problems with high dimensional input data it works by estimating a sequence of principal components that have maximal dependence on the response variable the proposed supervised pca is solvable in closed form and has a dual formulation that significantly reduces the computational complexity of problems in which the number of predictors greatly exceeds the number of observations such as dna microarray experiments furthermore we show how the algorithm can be kernelized which makes it applicable to non linear dimensionality reduction tasks experimental results on various visualization classification and regression problems show significant improvement over other supervised approaches both in accuracy and computational efficiency

hessian eigenmaps locally linear embedding techniques for high dimensional data we describe a method for recovering the underlying parametrization of scattered data m i lying on a manifold m embedded in high dimensional euclidean space the method hessian based locally linear embedding derives from a conceptual framework of local isometry in which the manifold m viewed as a riemannian submanifold of the ambient euclidean space r n is locally isometric to an open connected subset of euclidean space r d because does not have to be convex this framework is able to handle a significantly wider class of situations than the original isomap algorithm the theoretical framework revolves around a quadratic form h f m h f m f dm defined on functions f m r here hf denotes the hessian of f and h f averages the frobenius norm of the hessian over m to define the hessian we use orthogonal coordinates on the tangent planes of m the key observation is that if m truly is locally isometric to an open connected subset of r d then h f has a d 1 dimensional null space consisting of the constant functions and a d dimensional space of functions spanned by the original isometric coordinates hence the isometric coordinates can be recovered up to a linear isometry our method may be viewed as a modification of locally linear embedding and our theoretical framework as a modification of the laplacian eigenmaps framework where we substitute a quadratic form based on the hessian in place of one based on the laplacian

coupling of finite and boundary element methods for an elastoplastic interface problem a class of transmission problems is considered in which a nonlinear variational problem in one domain is coupled with a linear elliptic problem in a second domain a typical example is a problem from three dimensional elasticity theory where an elastoplastic material is embedded into a linear elastic material the nonlinear problem is given in variational form with a strictly convex functional the linear elliptic problem is described by boundary integral equations on the coupling boundary the typical saddle point structure of such problems is analyzed galerkin approximations are studied which consist of a finite element approximation in the first domain coupled with a boundary element method on the coupling boundary the convergence of the galerkin approximation is based on the saddle point structure which is shown to hold for the exact as well as the discretized problems

generalized correlation for shape alignment ordered set valued functions are introduced in this study to represent arbitrary shapes in a simple manner the arithmetic of ordered set valued functions is meaningless hence a novel concept namely generalized correlation is proposed to handle shape alignment problems generalized correlation is an extension of correlation from single valued functions to ordered set valued functions it is especially designed for shape alignment but not for a general mathematical definition moreover efficient algorithms are proposed to compute generalized correlation in 2d and 3d cases experiments indicate that the proposed alignment methods converge rapidly and globally furthermore generalized correlation is used handle registration problems to demonstrate its potential in computer vision tasks

synchronized submanifold embedding for person independent pose estimation and beyond precise 3 d head pose estimation plays a significant role in developing human computer interfaces and practical face recognition systems this task is challenging due to the particular appearance variations caused by pose changes for a certain subject in this paper the pose data space is considered as a union of submanifolds which characterize different subjects instead of a single continuous manifold as conventionally regarded a novel manifold embedding algorithm dually supervised by both identity and pose information called snchronized submanifold embedding sse is proposed for person independent precise 3 d pose estimation which means that the testing subject may not appear in the model training stage first the submanifold of a certain subject is approximated as a set of simplexes constructed using neighboring samples then these simplexized submanifolds from different subjects are embedded by synchronizing the locally propagated poses within the simplexes and at the same time maximizing the intrasubmanifold variances finally the pose of a new datum is estimated as the propagated pose of the nearest point within the simplex constructed by its nearest neighbors in the dimensionality reduced feature space the experiments on the 3 d pose estimation database chil data for clear07 evaluation and the extended application for age estimation on fg net aging database demonstrate the superiority of sse over conventional regression algorithms as well as unsupervised manifold learning algorithms

a visual shape descriptor using sectors and shape context of contour lines this paper describes a visual shape descriptor based on the sectors and shape context of contour lines to represent the image local features used for image matching the proposed descriptor consists of two component feature vectors first the local region is separated into sectors and their gradient magnitude and orientation values are extracted a feature vector is then constructed from these values second local shape features are obtained using the shape context of contour lines another feature vector is then constructed from these contour lines the proposed approach calculates the local shape feature without needing to consider the edges this can overcome the difficulty associated with textured images and images with ill defined edges the combination of two component feature vectors makes the proposed descriptor more robust to image scale changes illumination variations and noise the proposed visual shape descriptor outperformed other descriptors in terms of the matching accuracy 14 525 better than sift 21 better than pca sift 11 86 better than gloh and 25 66 better than the shape context

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

least squares methods for the coupling of fem and bem in the present paper we propose least squares formulations for the numerical solution of exterior boundary value problems the partial differential equation is a first order system in a bounded subdomain and the unbounded subdomain is treated by means of boundary integral equations the first order system is derived from a strongly elliptic second order system the analysis of the present least squares formulations is reduced to the analysis of the galerkin method for the coupling of finite element and boundary element methods fem and bem of the second order problem the least squares approach requires no stability condition however it requires the computation of negative as well as of half integer sobolev norms the arising linear systems can be preconditioned to have condition numbers sim 1 the present methods benefit strongly from the use of biorthogonal wavelets on the coupling boundary and the computation of corresponding equivalent norms in sobolev spaces in particular the application of green s formula leads to an efficient discretization of least squares formulations

distance metric learning for large margin nearest neighbor classification the accuracy of k nearest neighbor knn classification depends significantly on the metric used to compute distances between different examples in this paper we show how to learn a mahalanobis distance metric for knn classification from labeled examples the mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes knn classification using euclidean distances in our approach the metric is trained with the goal that the k nearest neighbors always belong to the same class while examples from different classes are separated by a large margin as in support vector machines svms the margin criterion leads to a convex optimization based on the hinge loss unlike learning in svms however our approach requires no modification or extension for problems in multiway as opposed to binary classification in our framework the mahalanobis distance metric is obtained as the solution to a semidefinite program on several data sets of varying size and difficulty we find that metrics trained in this way lead to significant improvements in knn classification sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster we show how to learn and combine these local metrics in a globally integrated manner

robust symbolic representation for shape recognition and retrieval a new method for shape recognition and retrieval is proposed here the suggested algorithm is based on several steps the algorithm analyzes the contour of pairs of shapes their contours are recovered and represented by a pair of n points obtained by linear interpolation given two points p i and q j from the two shapes the cost of their matching is evaluated by using the shape context and by using dynamic programming the best matching between the point sets is obtained dynamic programming not only recovers the best matching but also identifies occlusions i e points in the two shapes which cannot be properly matched given the correspondence between the two point sets the two contours are aligned using procrustes analysis after alignment each contour is transformed into a string of symbols and a modified version of edit distance is used to compute the similarity between strings of symbols finally recognition and retrieval are obtained by a simple nearest neighbor procedure the algorithm has been tested on a large set of shape databases kimia mpeg 7 natural silhouette database gesture database marine database swedish leaf database diatom database eth 80 3d object database providing performances for both in recognition and in retrieval superior to most of previously proposed approaches

geometric and photometric invariant distinctive regions detection in this paper we present a number of enhancements to the kadir brady salient region detector which result in a significant improvement in performance the modifications we make include stabilising the difference between consecutive scales when calculating the inter scale saliency a new sampling strategy using overlap of pixels partial volume estimation and parzen windowing repeatability is used as the criterion for evaluating the performance of the algorithm we observe the repeatability for distinctive regions selected from an image and from the same image after applying a particular transformation the transformations we use include planar rotation pixel translation spatial scaling and intensity shifts and scaling experimental results show that the average repeatability rate is improved from 46 to approximately 78 when all the enhancements are applied we also compare our algorithm with other region detectors on a set of sequences of real images and our detector outperforms most of the state of the art detectors

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

shape classification by manifold learning in multiple observation spaces manifold learning is a non linear method with the aim of finding a constructive way to embed the data from a high dimensional space into a low dimensional one the improvement of shape classification is the major approach in this paper which is based on the continuity in feature space in accordance with the continuity in semantic one in this regard a non linear approach is employed to map the shape feature vectors to a new space while their semantics become similar with human opinion the euclidean distance between two feature vectors would be closed shapes are described by four contour based and region based techniques by the proposed method in other word they are described in four observation spaces furthermore a parameter space is learnt from multiple observation spaces based on fusion of dissimilarities in a supervised manner experimental results show the validity and efficiency of the proposed approach for shape classification over a variety of standard shape datasets

facial expression recognition on multiple manifolds manifold learning has been successfully applied to facial expression recognition by modeling different expressions as a smooth manifold embedded in a high dimensional space however the assumption of single manifold is still arguable and therefore does not necessarily guarantee the best classification accuracy in this paper a generalized framework for modeling and recognizing facial expressions on multiple manifolds is presented which assumes that different expressions may reside on different manifolds of possibly different dimensionalities the intrinsic features of each expression are firstly learned separately and the genetic algorithm ga is then employed to obtain the nearly optimal dimensionality of each expression manifold from the classification viewpoint classification is performed under a newly defined criterion that is based on the minimum reconstruction error on manifolds extensive experiments on both the cohn kanade and feedtum databases show the effectiveness of the proposed multiple manifold based approach

a primal mixed formulation for exterior transmission problems in bf r 2 we combine a primal mixed finite element approach with a dirichlet to neumann mapping arising from the boundary integral equation method to study the weak solvability and galerkin approximations of a class of linear exterior transmission problems in potential theory our results are mainly based on the babuska brezzi theory for variational problems with constraints we establish the uniqueness of solution for the continuous and discrete formulations and show that finite element subspac es of lagrange type satisfy the discrete compatibility conditions in addition we provide the error analysis including polygonal approximations of the domain and prove strong convergence of the galerkin solutions moreover under additional regularity assumptions on the solution of the continuous formulation we obtain the asymptotic rate of convergence o h

multi view face identification and pose estimation using b spline interpolation the available face views in the training set are mostly limited in this paper we present a view interpolation method using nonlinear b spline on face manifolds two models the inner outer ellipse model and the moment of inertia model are developed to estimate the pose orientation we use the limited view pose face images to form the pose eigen space then based on these nonlinear manifolds we form a b spline for each individual identification is to compute the shortest euclidean distance from a given test view to the nearest point within one of these b splines once the test view is classified as a familiar individual in the training set not only can the individual be identified but also the pose angle can be estimated experimental results show that b spline interpolation can achieve a recognition rate of 95

learning context sensitive shape similarity by graph transduction shape similarity and shape retrieval are very important topics in computer vision the recent progress in this domain has been mostly driven by designing smart shape descriptors for providing better similarity measure between pairs of shapes in this paper we provide a new perspective to this problem by considering the existing shapes as a group and study their similarity measures to the query shape in a graph structure our method is general and can be built on top of any existing shape similarity measure for a given similarity measure a new similarity is learned through graph transduction the new similarity is learned iteratively so that the neighbors of a given shape influence its final similarity to the query the basic idea here is related to pagerank ranking which forms a foundation of google web search the presented experimental results demonstrate that the proposed approach yields significant improvements over the state of art shape matching algorithms we obtained a retrieval rate of 91 61 percent on the mpeg 7 data set which is the highest ever reported in the literature moreover the learned similarity by the proposed method also achieves promising improvements on both shape classification and shape clustering

shape similarity measure based on correspondence of visual parts a cognitively motivated similarity measure is presented and its properties are analyzed with respect to retrieval of similar objects in image databases of silhouettes of 2d objects to reduce influence of digitization noise as well as segmentation errors the shapes are simplified by a novel process of digital curve evolution to compute our similarity measure we first establish the best possible correspondence of visual parts without explicitly computing the visual parts then the similarity between corresponding parts is computed and aggregated we applied our similarity measure to shape matching of object contours in various image databases and compared it to well known approaches in the literature the experimental results justify that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions

coupling of mixed finite elements and boundary elements for a hyperelastic interface problem we apply the coupling of mixed finite elements and boundary integral methods using two integral equations on the coupling boundary to study the weak solvability of a nonlinear elliptic problem arising in elastostatics our procedure is based on both the usual brezzi s theory for linear constrained variational problems and some fundamental tools from nonlinear functional analysis we derive existence and uniqueness of solution for the continuous variational formulations and provide general approximation results for the corresponding galerkin schemes although we consider bounded domains the same analysis applies for the case in which the boundary element region is unbounded

variational formulations of transmission problems via fem bem and dtn mappings the purpose of this work is to review some of the main results on the weak solvability and galerkin approximations of interior and exterior transmission problems arising in potential theory and elastostatics both linear and nonlinear model problems are included in our presentation we consider variational formulations based on the combination of mixed finite elements with either boundary integral equations or dirichlet to neumann dtn mappings we provide existence and uniqueness of solution for the continuous formulations and give general approximation estimates for the associated galerkin schemes some open questions are also mentioned

shape based image retrieval using support vector machines fourier descriptors and self organizing maps image retrieval based on image content has become an important topic in the fields of image processing and computer vision in this paper we present a new method of shape based image retrieval using support vector machines svm fourier descriptors and self organizing maps a list of predicted classes for an input shape is obtained using the svm ranked according to their estimated likelihood the best match of the image to the top ranked class is then chosen by the minimum mean square error the nearest neighbors can be retrieved from the self organizing map of the class we employ three databases of 99 216 and 1045 shapes for our experiment and obtain prediction accuracy of 90 96 7 and 84 2 respectively our method outperforms some existing shape based methods in terms of speed and accuracy

learning and matching of dynamic shape manifolds for human action recognition in this paper we learn explicit representations for dynamic shape manifolds of moving humans for the task of action recognition we exploit locality preserving projections lpp for dimensionality reduction leading to a low dimensional embedding of human movements given a sequence of moving silhouettes associated to an action video by lpp we project them into a low dimensional space to characterize the spatiotemporal property of the action as well as to preserve much of the geometric structure to match the embedded action trajectories the median hausdorff distance or normalized spatiotemporal correlation is used for similarity measures action classification is then achieved in a nearest neighbor framework to evaluate the proposed method extensive experiments have been carried out on a recent dataset including ten actions performed by nine different subjects the experimental results show that the proposed method is able to not only recognize human actions effectively but also considerably tolerate some challenging conditions e g partial occlusion low quality videos changes in viewpoints scales and clothes within class variations caused by different subjects with different physical build styles of motion etc

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements

the uncoupling of boundary integral and finite element methods for nonlinear boundary value problems abstract in this paper the uncoupling of boundary integral and finite element methods is applied to study the weak solvability of certain nonlinear exterior boundary value problems as a model we consider a nonlinear second order elliptic equation in divergence form in a bounded inner region of the plane which becomes the laplace equation in the corresponding unbounded exterior region we provide sufficient conditions for the nonlinear coefficients from which existence uniqueness and approximation results are established in particular nonlinear equations yielding both monotone and nonmonotone operators are analyzed

edit distance based kernel functions for structural pattern classification a common approach in structural pattern classification is to define a dissimilarity measure on patterns and apply a distance based nearest neighbor classifier in this paper we introduce an alternative method for classification using kernel functions based on edit distance the proposed approach is applicable to both string and graph representations of patterns by means of the kernel functions introduced in this paper string and graph classification can be performed in an implicit vector space using powerful statistical algorithms the validity of the kernel method cannot be established for edit distance in general however by evaluating theoretical criteria we show that the kernel functions are nevertheless suitable for classification and experiments on various string and graph datasets clearly demonstrate that nearest neighbor classifiers can be outperformed by support vector machines using the proposed kernel functions

nonlinear dimensionality reduction using a temporal coherence principle temporal coherence principle is an attractive biologically inspired learning rule to extract slowly varying features from quickly varying input data in this paper we develop a new nonlinear neighborhood preserving nnp technique by utilizing the temporal coherence principle to find an optimal low dimensional representation from the original high dimensional data nnp is based on a nonlinear expansion of the original input data such as polynomials of a given degree it can be solved by the eigenvalue problem without using gradient descent and is guaranteed to find the global optimum nnp can be viewed as a nonlinear dimensionality reduction framework which takes into consideration both time series and data sets without an obvious temporal structure according to different situations we introduce three algorithms of nnp named nnp 1 nnp 2 and nnp 3 the objective function of nnp 1 is equal to slow feature analysis sfa and it works well for time series such as image sequences nnp 2 artificially constructs time series consisting of neighboring points for data sets without a clear temporal structure such as image data nnp 3 is proposed for classification tasks which can minimize the distances of neighboring points in the embedding space and ensure that the remaining points are as far apart as possible simultaneously furthermore the kernel extension of nnp is also discussed in this paper the proposed algorithms work very well on some image sequences and image data sets compared to other methods meanwhile we perform the classification task on the mnist handwritten digit database using the supervised nnp algorithms the experimental results demonstrate that nnp is an effective technique for nonlinear dimensionality reduction tasks