quasi invariant parameterisations and matching of curves in images in this paper we investigate quasi invariance on a smooth manifold and show that there exist quasi invariant parameterisations which are not exactly invariant but approximately invariant under group transformations and do not require high order derivatives the affine quasi invariant parameterisation is investigated in more detail and exploited for defining general affine semi local invariants from second order derivatives only the new invariants are implemented and used for matching curve segments under general affine motions and extracting symmetry axes of objects with 3d bilateral symmetry

view variation of point set and line segment features the variation with respect to view of 2d features defined for projections of 3d point sets and line segments is studied it is established that general case view invariants do not exist for any number of points given true perspective weak perspective or orthographic projection models feature variation under the weak perspective approximation is then addressed though there are no general case weak perspective invariants there are special case invariants of practical importance those cited in the literature are derived from linear dependence relations and the invariance of this type of relation to linear transformation the variation with respect to view is studied for an important set of 2d line segment features the relative orientation size and position of one line segment with respect to another the analysis includes an evaluation criterion for feature utility in terms of view variation this relationship is a function of both the feature and the particular configuration of 3d line segments the use of this information in objection recognition is demonstrated for difficult discrimination tasks

new estimation and model selection procedures for semiparametric modeling in longitudinal data analysis semiparametric regression models are very useful for longitudinal data analysis the complexity of semiparametric models and the structure of longitudinal data pose new challenges to parametric inferences and model selection that frequently arise from longitudinal data analysis in this article two new approaches are proposed for estimating the regression coefficients in a semiparametric model the asymptotic normality of the resulting estimators is established an innovative class of variable selection procedures is proposed to select significant variables in the semiparametric models the proposed procedures are distinguished from others in that they simultaneously select significant variables and estimate unknown parameters rates of convergence of the resulting estimators are established with a proper choice of regularization parameters and penalty functions the proposed variable selection procedures are shown to perform as well as an oracle estimator a robust standard error formula is derived usi

invariant properties of straight homogeneous generalized cylinders and their contours a fundamental group in computer vision is the recovery of three dimensional shape from image data while this problem is in general underconstrained the authors show that it can be simplified in the case where the objects being viewed are generalized cylinders they consider the class of straight homogeneous generalized cylinders shgcs without any further assumption on the viewing direction or the precise shape of these objects they present a rigorous mathematical study of the geometry of shgcs and characterize their gaussian curvature and occluding contours and use these results to prove several new invariant properties of the contours of shgcs these properties are in turn used in two implemented algorithms for recovering shgc descriptions from image contours several examples of segmentation of real images are given other applications are also discussed

3d object modeling and recognition using local affine invariant image descriptors and multi view spatial constraints this article introduces a novel representation for three dimensional 3d objects in terms of local affine invariant descriptors of their images and the spatial relationships between the corresponding surface patches geometric constraints associated with different views of the same patches under affine projection are combined with a normalized representation of their appearance to guide matching and reconstruction allowing the acquisition of true 3d affine and euclidean models from multiple unregistered images as well as their recognition in photographs taken from arbitrary viewpoints the proposed approach does not require a separate segmentation stage and it is applicable to highly cluttered scenes modeling and recognition results are presented

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

vision based pose estimation from points with unknown correspondences pose estimation from points with unknown correspondences currently is still a difficult problem in the field of computer vision to solve this problem the softsi algorithm is proposed which can simultaneously obtain pose and correspondences the softsi algorithm is based on the combination of the proposed pnp algorithm the si algorithm and two singular value decomposition svd based shape description theorems other main contributions of this paper are 1 two svd based shape description theorems are proposed 2 by analyzing the calculation process of the si algorithm the method to avoid pose ambiguity is proposed and 3 an acceleration method to quickly eliminate bad initial values for the softsi algorithm is proposed the simulation results show that the si algorithm is accurate while the softsi algorithm is fast robust to noise and has large convergence radius

an approximate analytical solution of time fractional telegraph equation abstract in this article the powerful easy to use and effective approximate analytical mathematical tool like homotopy analysis method ham is used to solve the telegraph equation with fractional time derivative 1

part based 3d descriptions of complex objects from a single image volumetric 3d part based descriptions of complex objects in a scene can be highly beneficial for many tasks such as generic object recognition navigation and manipulation however it has been difficult to derive such descriptions from image data there has been some progress in getting such descriptions from range data or from perfect contours but analysis of a real intensity image presents many difficulties the object and part boundaries do not completely correspond to image boundaries the detected boundaries are often fragmented and many boundaries due to surface markings shadows and noise are present in addition inference of 3d from a 2d image is difficult the paper describes a method to compute the desired descriptions from a single image by exploiting projective properties of a class of generalized cylinders and of possible joints between them experimental results on some examples are given

line drawing interpretation bilateral symmetry results previously derived by the author are used to investigate the implication of bilateral symmetry in line drawings it is shown that the line drawing of an orthographically protected surface of revolution exhibits bilateral symmetry about the projection of its axis of revolution irrespective of the viewing direction barring one exception a bilaterally symmetric line drawing is necessarily the orthographic projection of a local surface of revolution whenever its symmetry axis continues to be the projection of a fixed line in space under perturbation of viewpoint the axis of revolution is the invariant preimage of the symmetry axis various line drawing causes are detailed which facilitate the deduction of invariant preimages of symmetry axes and consequently of local surfaces of revolution

local polynomial regression analysis of clustered data this paper proposes a classical weighted least squares type of local polynomial smoothing for the analysis of clustered data with the key idea of using generalised inverses of correlation matrices the estimator has a simple closed form expression simplicity is achieved also for nonparametric generalised linear models with arbitrary link function via a transformation our approach can be characterised by local observations with local variances which yields intuitively correct results in the sense that correct incorrect specification of within cluster correlation has respective positive negative effects the approach is a natural extension of classical local polynomial smoothing consequently existing theory can be largely carried over and important issues such as bandwidth selection can be tackled in the classical fashion moreover the approach can handle various types of covariate such as cluster level subject level or partially cluster level numerical studies support the theoretical results the method is illustrated with a real example on luteinising hormone levels in cows

efficient estimation of the nonparametric mean and covariance functions for longitudinal and sparse functional data abstractwe consider the estimation of mean and covariance functions for longitudinal and sparse functional data by using the full quasi likelihood coupling a modification of the local kernel smooth

minimal representations of 3d models in terms of image parameters under calibrated and uncalibrated perspective indexing is a well known paradigm for object recognition in indexing each 3d model is represented as the set of values assumed by a given vector of image parameters in correspondence to all the possible images of the 3d model an open problem posed by jacobs 1992 concerned the minimum dimensionality of such sets under perspective this paper proves that under calibrated or uncalibrated perspective the minimum dimensionality of the set representing any 3d modeled point set is two two dimensional representations are found also for 3d curved objects

model based recognition of 3d objects from single images in this work we treat major problems of object recognition which have received relatively little attention lately among them are the loss of depth information in the projection from a 3d object to a single 2d image and the complexity of finding feature correspondences between images we use geometric invariants to reduce the complexity of these problems there are no geometric invariants of a projection from 3d to 2d however given certain modeling assumptions about the 3d object such invariants can be found the modeling assumptions can be either a particular model or a generic assumption about a class of models here we use such assumptions for single view recognition we find algebraic relations between the invariants of a 3d model and those of its 2d image under general projective projection these relations can be described geometrically as invariant models in a 3d invariant space illuminated by invariant light rays and projected onto an invariant version of the given image we apply the method to real images

improving generalised estimating equations using quadratic inference functions summary generalised estimating equations enable one to estimate regression parameters consistently in longitudinal data analysis even when the correlation structure is misspecified however under such misspecification the estimator of the regression parameter can be inefficient in this paper we introduce a method of quadratic inference functions that does not involve direct estimation of the correlation parameter and that remains optimal even if the working correlation structure is misspecified the idea is to represent the inverse of the working correlation matrix by the linear combination of basis matrices a representation that is valid for the working correlations most commonly used both asymptotic theory and simulation show that under misspecified working assumptions these estimators are more efficient than estimators from generalised estimating equations this approach also provides a chi squared inference function for testing nested models and a chi squared regression misspecification test furthermore the test statistic follows a chi squared distribution asymptotically whether or not the working correlation structure is correctly specified

groups of adjacent contour segments for object detection we present a family of scale invariant local shape features formed by chains of k connected roughly straight contour segments kas and their use for object class detection kas are able to cleanly encode pure fragments of an object boundary without including nearby clutter moreover they offer an attractive compromise between information content and repeatability and encompass a wide variety of local shape structures we also define a translation and scale invariant descriptor encoding the geometric configuration of the segments within a kas making kas easy to reuse in other frameworks for example as a replacement or addition to interest points ips software for detecting and describing kas is released at http lear inrialpes fr software we demonstrate the high performance of kas within a simple but powerful sliding window object detection scheme through extensive evaluations involving eight diverse object classes and more than 1 400 images we 1 study the evolution of performance as the degree of feature complexity k varies and determine the best degree 2 show that kas substantially outperform ips for detecting shape based classes and 3 compare our object detector to the recent state of the art system by dalal and triggs 2005

modal hermite spectral collocation method for solving multi dimensional hyperbolic telegraph equations abstract the present research is contemplated proposing a numerical solution of multi dimensional hyperbolic telegraph equations with appropriate initial time and boundary space conditions the truncated hermite series with unknown coefficients are used for approximating the solution in both of the spatial and temporal variables the basic idea for discretizing the considered one dimensional 1d two dimensional 2d and three dimensional 3d telegraph equations is based on the collocation method together with the hermite operational matrices of derivatives the resulted systems of linear algebraic equations are solved by some efficient methods such as lu factorization the solution of the algebraic system contains the coefficients of the truncated hermite series numerical experiments are provided to illustrate the accuracy and efficiency of the presented numerical scheme comparisons of numerical results associated to the proposed method with some of the existing numerical methods confirm that the method is accurate and fast experimentally

shape quantization and recognition with randomized trees we explore a new approach to shape recognition based on a virtually infinite family of binary features queries of the image data designed to accommodate prior information about shape invariance and regularity each query corresponds to a spatial arrangement of several local topographic codes or tags which are in themselves too primitive and common to be informative about shape all the discriminating power derives from relative angles and distances among the tags the important attributes of the queries are a natural partial ordering corresponding to increasing structure and complexity semi invariance meaning that most shapes of a given class will answer the same way to two queries that are successive in the ordering and stability since the queries are not based on distinguished points and substructures no classifier based on the full feature set can be evaluated and it is impossible to determine a priori which arrangements are informative our approach is to select informative features and build tree classifiers at the same time by inductive learning in effect each tree provides an approximation to the full posterior where the features chosen depend on the branch that is traversed due to the number and nature of the queries standard decision tree construction based on a fixed length feature vector is not feasible instead we entertain only a small random sample of queries at each node constrain their complexity to increase with tree depth and grow multiple trees the terminal nodes are labeled by estimates of the corresponding posterior distribution over shape classes an image is classified by sending it down every tree and aggregating the resulting distributions the method is applied to classifying handwritten digits and synthetic linear and nonlinear deformations of three hundred l at e x symbols stateof the art error rates are achieved on the national institute of standards and technology database of digits the principal goal of the experiments on l at e x symbols is to analyze invariance generalization error and related issues and a comparison with artificial neural networks methods is presented in this context

probabilistic 3d object recognition a probabilistic 3d object recognition algorithm is presented in order to guide the recognition process the probability that match hypotheses between image features and model features are correct is computed a model is developed which uses the probabilistic peaking effect of measured angles and ratios of lengths by tracing iso angle and iso ratio curves on the viewing sphere the model also accounts for various types of uncertainty in the input such as incomplete and inexact edge detection for each match hypothesis the pose of the object and the pose uncertainty which is due to the uncertainty in vertex position are recovered this is used to find sets of hypotheses which reinforce each other by matching features of the same object with compatible uncertainty regions a probabilistic expression is used to rank these hypothesis sets the hypothesis sets with the highest rank are output the algorithm has been fully implemented and tested on real images

space and time bounds on indexing 3d models from 2d images model based visual recognition systems often match groups of image features to groups of model features to form initial hypotheses which are then verified in order to accelerate recognition considerably the model groups can be arranged in an index space hashed offline such that feasible matches are found by indexing into this space for the case of 2d images and 3d models consisting of point features bounds on the space required for indexing and on the speedup that such indexing can achieve are demonstrated it is proved that even in the absence of image error each model must be represented by a 2d surface in the index space this places an unexpected lower bound on the space required to implement indexing and proves that no quantity is invariant for all projections of a model into the image theoretical bounds on the speedup achieved by indexing in the presence of image error are also determined and an implementation of indexing for measuring this speedup empirically is presented it is found that indexing can produce only a minimal speedup on its own however when accompanied by a grouping operation indexing can provide significant speedups that grow exponentially with the number of features in the groups

when is it possible to identify 3d objects from single images using class constraints one approach to recognizing objects seen from arbitrary viewpoint is by extracting invariant properties of the objects from single images such properties are found in images of 3d objects only when the objects are constrained to belong to certain classes e g bilaterally symmetric objects existing studies that follow this approach propose how to compute invariant representations for a handful of classes of objects a fundamental question regarding the invariance approach is whether it can be applied to a wide range of classes to answer this question it is essential to study the set of classes for which invariance exists this paper introduces a new method for determining the existence of invariant functions for classes of objects together with the set of images from which these invariants can be computed we develop algebraic tests that determine whether the objects in a given class can be identified from single images these tests apply to classes of objects undergoing affine projection in addition these tests allow us to determine the set of views of the objects which are degenerate we apply these tests to several classes of objects and determine which of them is identifiable and which of their views are degenerate

new local estimation procedure for a non parametric regression function for longitudinal data this paper develops a new estimation of nonparametric regression functions for clustered or longitudinal data we propose to use cholesky decomposition and profile least squares techniques to estimate the correlation structure and regression function simultaneously we further prove that the proposed estimator is as asymptotically efficient as if the covariance matrix were known a monte carlo simulation study is conducted to examine the finite sample performance of the proposed procedure and to compare the proposed procedure with the existing ones based on our empirical studies the newly proposed procedure works better than the naive local linear regression with working independence error structure and the efficiency gain can be achieved in moderate sized samples our numerical comparison also shows that the newly proposed procedure outperforms some existing ones a real data set application is also provided to illustrate the proposed estimation procedure

an unconditionally stable fourth order method for telegraph equation based on hermite interpolation there have been many approaches to solve telegraph equations numerically in literature however very few are two level difference schemes in solving telegraph equations with dirichlet boundary conditions in this paper based on cubic hermite interpolation a two level method is presented for the numerical solutions of one dimensional telegraph equations the accuracy of the present scheme is of order o k 4 h 4 it is proved that the scheme is unconditionally stable numerical results are given to illustrate the efficiency of our method

wavelet galerkin solutions for one dimensional partial differential equations in this paper we describe how wavelets may be used to solve partial differential equations these problems are currently solved by techniques such as finite differences finite elements and multi grid the wavelet method however offers several advantages over traditional methods wavelets have the ability to represent functions at different levels of resolution thereby providing a logical means of developing a hierarchy of solutions furthermore compactly supported wavelets such as those due to daubechies1 are localized in space which means that the solution can be refined in regions of high gradient e g stress concentrations without having to regenerate the mesh for the entire problem in order to demonstrate the wavelet technique we consider the one dimensional counterpart of helmholtz s equation by comparison with a simple finite difference solution to this problem with periodic boundary conditions we show how a wavelet technique may be efficiently developed dirichlet boundary conditions are then imposed using the capacitance matrix method described by proskurowski and widlund2 and others the convergence rates of the wavelet solutions are examined and they are found to compare extremely favourably to the finite difference solutions preliminary investigations also indicate that the wavelet technique is a strong contender to the finite element method at least for problems with simple geometries

marginal nonparametric kernel regression accounting for within subject correlation there has been substantial recent interest in non and semiparametric methods for longitudinal or clustered data with dependence within clusters it has been shown rather inexplicably that when standard kernel smoothing methods are used in a natural way higher efficiency is obtained by assuming independence than by using the true correlation structure it is shown here that this result is a natural consequence of how standard kernel methods incorporate the within subject correlation in the asymptotic setting considered where the cluster sizes are fixed and the cluster number increases in this paper an alternative kernel smoothing method is proposed unlike the standard methods the smallest variance of the new estimator is achieved when the true correlation is assumed asymptotically the variance of the proposed method is uniformly smaller than that of the most efficient working independence approach a small simulation study shows that significant improvement is obtained for finite samples

invariants of six points and projective reconstruction from three uncalibrated images there are three projective invariants of a set of six points in general position in space it is well known that these invariants cannot be recovered from one image however an invariant relationship does exist between space invariants and image invariants this invariant relationship is first derived for a single image then this invariant relationship is used to derive the space invariants when multiple images are available this paper establishes that the minimum number of images for computing these invariants is three and the computation of invariants of six points from three images can have as many as three solutions algorithms are presented for computing these invariants in closed form the accuracy and stability with respect to image noise selection of the triplets of images and distance between viewing positions are studied both through real and simulated images applications of these invariants are also presented both the results of faugeras 1992 and hartley et al 1992 for projective reconstruction and sturm s method 1869 for epipolar geometry determination from two uncalibrated images with at least seven points are extended to the case of three uncalibrated images with only six points

geometric invariants and object recognition we discuss the role of the general invariance concept in object recognition and review the classical and recent literature on projective invariance invariants help solve major problems of object recognition for instance different images of the same object often differ from each other because of the different viewpoint from which they were obtained to match the two images common methods thus need to find the correct viewpoint a difficult problem that can involve search in a high dimensional space of all possible points of view and or finding point correspondences geometric invariants are shape descriptors computed from the geometry of the shape that remain unchanged under geometric transformations such as changing the viewpoint thus they can be matched without search deformations of objects are another important class of geometric changes for which invariance is useful

analytic and approximate solutions for nagumo telegraph reaction diffusion equation it is known now that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion in several branches of sciences we generalized nagumo equation to the telegraph reaction diffusion equation and present its analytic approximate solution a by using picard iteration method also using the linear piecewise approximation traveling wave solution are presented the results corresponding to the standard nagumo reaction diffusion equation are regained

high order variable mesh off step discretization for the solution of 1 d non linear hyperbolic equation abstract in this paper we propose a new high order three level implicit method based on off step discretization on a non uniform mesh for the solution of 1 d non linear hyperbolic partial differential equation of the form u tt u xx g x t u u x u t subject to appropriate initial and dirichlet boundary conditions we use only three evaluations of the function g and three grid points at each time level in a compact cell our method is directly applicable to the wave equation in polar coordinates and we do not require any special technique to handle singular coefficients of the differential equation the method is convergent for uniform mesh numerical results are provided to justify the usefulness of the proposed method

analysis of longitudinal data with semiparametric estimation of covariance function improving efficiency for regression coefficients and predicting trajectories of individuals are two important aspects in the analysis of longitudinal data both involve estimation of the covariance function yet challenges arise in estimating the covariance function of longitudinal data collected at irregular time points a class of semiparametric models for the covariance function by that imposes a parametric correlation structure while allowing a nonparametric variance function is proposed a kernel estimator for estimating the nonparametric variance function is developed two methods for estimating parameters in the correlation structure a quasi likelihood approach and a minimum generalized variance method are proposed a semiparametric varying coefficient partially linear model for longitudinal data is introduced and an estimation procedure for model coefficients using a profile weighted least squares approach is proposed sampling properties of the proposed estimation procedures are studied and asy

finding the limbs and cusps of generalized cylinders this paper addresses the problem of finding analytically the limbs and cusps of generalized cylinders orthographic projections of generalized cylinders whose axis is straight and whose axis is an arbitrary 3d curve are considered in turn in both cases the general equations of the limbs and cusps are given they are solved for three classes of generalized cylinders solids of revolution straight homogeneous generalized cylinders whose scaling sweeping rule is a polynomial of degree less than or equal to 5 and generalized cylinders whose axis is an arbitrary 3d curve but the cross section is circular and constant examples of limbs and cusps found for each class are given applications and extensions to perspective projection and completely general straight generalized cylinders are discussed

b spline contour representation and symmetry detection the detection of edges is only one of many steps in the understanding of images further processing necessarily involves grouping operations between contours we present a representation of edge contours by approximating b splines and show that such a representation facilitates the extraction of symmetries between contours our representation is rich compact stable and does not critically depend on feature extraction we turn our attention to the detection of three types of symmetries skew symmetries and parallel symmetries which have proven to be of great importance in inferring shape from contour and smooth local symmetries which have been used for planar shape description we show that our representation facilitates the computation of these symmetries

matching 3 d models to 2 d images we consider the problem of analytically characterizing the set of all 2 d images that a group of 3 d features may produce and demonstrate that this is a useful thing to do our results apply for simple point features and point features with associated orientation vectors when we model projection as a 3 d to 2 d affine transformation we show how to represent the set of images that a group of 3 d points produces with two lines 1 d subspaces one in each of two orthogonal high dimensional spaces where a single image group corresponds to one point in each space the images of groups of oriented point features can be represented by a 2 d hyperbolic surface in a single high dimensional space the problem of matching an image to models is essentially reduced to the problem of matching a point to simple geometric structures moreover we show that these are the simplest and lowest dimensional representations possible for these cases we demonstrate the value of this way of approaching matching by applying our results to a variety of vision problems in particular we use this result to build a space efficient indexing system that performs 3 d to 2 d matching by table lookup this system is analytically built and accessed accounts for the effects of sensing error and is tested on real images we also derive new results concerning the existence of invariants and non accidental properties in this domain finally we show that oriented points present unexpected difficulties indexing requires fundamentally more space with oriented than with simple points we must use more images in a motion sequence to determine the affine structure of oriented points and the linear combinations result does not hold for oriented points

analysis of a continuous galerkin method with mesh modification for two dimensional telegraph equation abstract in this paper we investigate the convergence of a space time continuous galerkin stcg method for two dimensional 2 d telegraph equation the variable time steps and spatial mesh structures are allowed which are necessary for adaptive computations on unstructured mesh we demonstrate existence and uniqueness of the numerical solution and give a priori estimate in l l 2 norm without space time mesh restrictions the analysis method presented here develops and improves the existing theories so that it can be used to study the more general time dependent partial differential equations pdes some numerical experiments are provided and compared with the standard finite element fe method to confirm the high efficiency and the high accuracy for the proposed scheme

a computational model of view degeneracy we quantify the observation by kender and freudenstein 1987 that degenerate views occupy a significant fraction of the viewing sphere surrounding an object for a perspective camera geometry we introduce a computational model that can be used to estimate the probability that a view degeneracy will occur in a random view of a polyhedral object for a typical recognition system parameterization view degeneracies typically occur with probabilities of 20 percent and depending on the parameterization as high as 50 percent we discuss the impact of view degeneracy on the problem of object recognition and for a particular recognition framework relate the cost of object disambiguation to the probability of view degeneracy to reduce this cost we incorporate our model of view degeneracy in an active focal length control paradigm that balances the probability of view degeneracy with the camera field of view in order to validate both our view degeneracy model as well as our active focal length control model a set of experiments are reported using a real recognition system operating on real images

object recognition by combining paraperspective images this paper provides a study on object recognition under paraperspective projection discussed is the problem of determining whether or not a given image was obtained from a 3 d object to be recognized first it is clarified that paraperspective projection is the first order approximation of perspective projection then it is shown that if we represent an object as a set of its feature points and the object undergoes a rigid transformation or an affine transformation any paraperspective image can be expressed as a linear combination of several appropriate paraperspective images we need at least three images for rigid transformations whereas we need at least two images for affine transformations particularly in the case of a rigid transformation the coefficients of the combination have to satisfy two conditions orthogonality and norm equality a simple algorithm to solve the above problem based on these properties is presented a linear single shot algorithm some experimental results with synthetic images and real images are also given

the medial scaffold of 3d unorganized point clouds we introduce the notion of the medial scaffold a hierarchical organization of the medial axis of a 3d shape in the form of a graph constructed from special medial curves connecting special medial points a key advantage of the scaffold is that it captures the qualitative aspects of shape in a hierarchical and tightly condensed representation we propose an efficient and exact method for computing the medial scaffold based on a notion of propagation along the scaffold itself starting from initial sources of the flow and constructing the scaffold during the propagation we examine this method specifically in the context of an unorganized cloud of points in 3d e g as obtained from laser range finders which typically involve hundreds of thousands of points but the ideas are generalizable to data arising from geometrically described surface patches the computational bottleneck in the propagation based scheme is in finding the initial sources of the flow we thus present several ideas to avoid the unnecessary consideration of pairs of points which cannot possibly form a medial point source such as the visibility of a point from another given a third point and the interaction of clusters of points an application of using the medial scaffold for the representation of point samplings of real life objects is also illustrated

nonparametric function estimation for clustered data when the predictor is measured without with error abstract we consider local polynomial kernel regression with a single covariate for clustered data using estimating equations we assume that at most m observations are available on each cluster in the case of random regressors with no measurement error in the predictor we show that it is generally the best strategy to ignore entirely the correlation structure within each cluster and instead pretend that all observations are independent in the further special case of longitudinal data on individuals with fixed common observation times we show that equivalent to the pooled data approach is the strategy of fitting separate nonparametric regressions at each observation time and constructing an optimal weighted average we also consider what happens when the predictor is measured with error using the simex approach to correct for measurement error we construct an asymptotic theory for both the pooled and the weighted average estimators surprisingly for the same amount of smoothing the weighted a

parametric reconstruction of generalized cylinders from limb edges the three dimensional 3 d reconstruction of generalized cylinders gcs is an important research field in computer vision one of the main difficulties is that some contour features in images cannot be reconstructed by traditional stereovision because they do not correspond to reflectance discontinuities of surface in space in this paper we present a novel parametric approach for the 3 d reconstruction of circular generalized cylinders cgcs only from the limb edges of cgcs in two images instead of exploiting the invariant and quasiinvariant properties of some specific subclasses of gcs in projections our reconstruction is achieved by some general assumptions on gcs and can therefore be applied to a broader subclass of gcs in order to improve robustness we perform the extraction and labeling of the limb edge interactively and estimate the epipolar geometry between two images by an optimal algorithm then for different types of gcs three kinds of symmetries parallel symmetry skew symmetry and local smooth symmetry are employed to compute the symmetry of limb edges the surface points corresponding to limb edges in images are reconstructed by integrating the recovered epipolar geometry and the properties induced from the assumptions that we make on the gcs finally a homography based method is exploited to further refine the 3 d description of the gc with a coplanar curved axis

introduction to wavelets in engineering the aim of this paper is to provide an introduction to the subject of wavelet analysis for engineering applications the paper selects from the recent mathematical literature on wavelets the results necessary to develop wavelet based numerical algorithms in particular we provide extensive details of the derivation of mallat s transform and daubechies wavelet coefficients since these are fundamental to gaining an insight into the properties of wavelets the potential benefits of using wavelets are highlighted by presenting results of our research in one and two dimensional data analysis and in wavelet solutions of partial differential equations

volumetric descriptions from a single intensity image since the early days of computer vision research shape from contour has been one of the most challenging problems many researchers in the field have attempted to understand this problem and proposed different approaches to solve it shape from contour still remains one of the hardest problems in the field the problem has two major difficulties first 2d properties of contours of viewed objects are generally not sufficient by themselves to uniquely determine 3d shape as one dimension is lost in the projection second real images produce imperfect contours that make their interpretation particularly difficult the first problem has received some attention in the research community but in the context of perfect contours the second one however has received very little in this work we propose a promising methodology to address this last problem for a large class of objects generalized cylinders it is based on exploiting mathematical invariant properties of the contours of generalized cylinders in a perceptual grouping approach we show that using these properties greatly helps addressing the figure ground problem in a more rigorous way than previous intuitive perceptual grouping methods our approach exploits the interplay between local and global features by handling different levels of the feature hierarchy we have developed and implemented a method that handles shgcs in complex seenes with markings and occlusion we demonstrate the application of our method of shape description and scene segmentation on complex real images we also demonstrate the usage of the obtained descriptions for recovery of complete 3 d object centered descriptions of viewed objects from a single intensity image

recognition without correspondence using multidimensionalreceptive field histograms the appearance of an object is composed of local structure this local structure can be described and characterized by a vector of local features measured by local operators such as gaussian derivatives or gabor filters this article presents a technique where appearances of objects are represented by the joint statistics of such local neighborhood operators as such this represents a new class of appearance based techniques for computer vision based on joint statistics the paper develops techniques for the identification of multiple objects at arbitrary positions and orientations in a cluttered scene experiments show that these techniques can identify over 100 objects in the presence of major occlusions most remarkably the techniques have low complexity and therefore run in real time

a numerical algorithm for the solution of telegraph equations abstract in this paper we present a new competitive numerical scheme to solve nonlinear telegraph equations the method is based on rothe s approximation in time discretization and on the wavelet galerkin in the spatial discretization the approximate solutions converge in the space c 0 t l 2 l 2 0 t w 0 1 2 to the variational solution a full error analysis is performed and a numerical experiment is given to illustrate the good convergence behavior of the approximate solution

the probabilistic peaking effect of viewed angles and distances with application to 3 d object recognition two novel probabilistic models for viewed angles and distances are derived using an observability sphere method the method which is based on the assumption that the prior probability density is isotropic for all viewing orientations can be used for the computation of observation probabilities for object s aspects features and probability densities of their quantitative attributes using the sphere it is discovered that the probability densities of viewed angles distances and even projected curvature have sharp peaks at their original values from this peaking effect it is concluded that in most cases the values of angles and distances are being altered only slightly by the imaging process and they can still serve as a strong cue for model based recognition the probabilistic models for 3 d object recognition from monocular images are used to form the angular elements that are needed the objects are represented by their linear features and specific points primitives using the joint density model of angles and distances the probabilities of initial matching hypotheses and mutual information coefficients are estimated these results are then used for object recognition by optimal matching search and stochastic labeling schemes various synthetic and real objects are recognized by this approach

semiparametric estimation in general repeated measures problems summary the paper considers a wide class of semiparametric problems with a parametric part for some covariate effects and repeated evaluations of a nonparametric function special cases in our approach include marginal models for longitudinal or clustered data conditional logistic regression for matched case control studies multivariate measurement error models generalized linear mixed models with a semiparametric component and many others we propose profile kernel and backfitting estimation methods for these problems derive their asymptotic distributions and show that in likelihood problems the methods are semiparametric efficient although generally not true it transpires that with our methods profiling and backfitting are asymptotically equivalent we also consider pseudolikelihood methods where some nuisance parameters are estimated from a different algorithm the methods proposed are evaluated by using simulation studies and applied to the kenya haemoglobin data

the computation of wavelet galerkin approximation on a bounded interval this paper describes exact evaluations of various finite integrals whose integrands involve products of daubechies compactly supported wavelets and their derivatives and or integrals these finite integrals play an essential role in the wavelet galerkin approximation of differential or integral equations on a bounded interval

maximum norm error estimates of efficient difference schemes for second order wave equations the three level explicit scheme is efficient for numerical approximation of the second order wave equations by employing a fourth order accurate scheme to approximate the solution at first time level it is shown that the discrete solution is conditionally convergent in the maximum norm with the convergence order of two since the asymptotic expansion of the difference solution consists of odd powers of the mesh parameters time step and spacings an unusual richardson extrapolation formula is needed in promoting the second order solution to fourth order accuracy extensions of our technique to the classical adi scheme also yield the maximum norm error estimate of the discrete solution and its extrapolation numerical experiments are presented to support our theoretical results

lattice boltzmann model for generalized nonlinear wave equations in this paper a lattice boltzmann model is developed to solve a class of the nonlinear wave equations through selecting equilibrium distribution function and an amending function properly the governing evolution equation can be recovered correctly according to our proposed scheme in which the chapman enskog expansion is employed we validate the algorithm on some problems where analytic solutions are available including the second order telegraph equation the nonlinear klein gordon equation and the damped driven sine gordon equation it is found that the numerical results agree well with the analytic solutions which indicates that the present algorithm is very effective and can be used to solve more general nonlinear problems

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

three dimensional descriptions based on the analysis of the invariant and quasi invariant properties of some curved axis generalized cylinders we address the recovery of object level 3d descriptions of some classes of curved axis generalized cylinders for this the first part of the paper analyzes the projective properties of two common generic shapes planar right constant generalized cylinders prcgcs and circular planar right generalized cylinders circular prgcs the properties we analyze include new geometric invariant and quasi invariant properties of the orthographic projection of the above shapes and a useful classification of their structural properties as functions of their pose the second part of the paper describes an implemented system which detects and recovers prcgcs and circular prgcs from an intensity image in the presence of noise surface markings shadows and partial occlusion the methods exploit the projective properties to hypothesize and verify relevant curved axis objects thus explicitly using the three dimensionality of the objects and of the desired descriptions this work extends past work on the recovery of volumetric shapes from an intensity image by addressing new primitives deriving new properties and by developing a system that recovers them from an intensity image we demonstrate our method on several real intensity images

a new fast algorithm based on half step discretization for one space dimensional quasilinear hyperbolic equations abstract in this article we describe a new compact three level implicit method of order four in time and space based on half step discretization for one space dimensional quasilinear hyperbolic equation u tt a x t u u xx f x t u u x u t defined in the semi infinite solution region where a 0 we require only nine grid points for the unknown variable u x t and two extra half step points each for x and t variables the proposed method is directly applicable to wave equation with singular coefficients which is main attraction of our work we do not require extra grid points for computation we describe the derivation of the method in detail the proposed method when applied to damped wave equation is shown to be unconditionally stable many benchmark problems are solved to confirm the fourth order convergence of the proposed method

a joint modelling approach for longitudinal studies in longitudinal studies it is of fundamental importance to understand the dynamics in the mean function variance function and correlations of the repeated or clustered measurements for modelling the covariance structure cholesky type decomposition based approaches have been demonstrated to be effective however parsimonious approaches for directly revealing the correlation structure between longitudinal measurements remain less well explored and existing joint modelling approaches may encounter difficulty in interpreting the covariation structure we propose a novel joint mean variance correlation modelling approach for longitudinal studies by applying hyperspherical co ordinates we obtain an unconstrained parameterization for the correlation matrix that automatically guarantees its positive definiteness and we develop a regression approach to model the correlation matrix of the longitudinal measurements by exploiting the parameterization the modelling framework proposed is parsimonious interpretable and flexible for analysing longitudinal data extensive data examples and simulations support the effectiveness of the approach proposed

interpreting line drawings of curved objects in this thesis we study the problem of interpreting line drawings of scenes composed or opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them it is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint that the line drawing is error free and that there are no lines due to shadows or specularities our definition implicitly excludes laminae wires and the apices of cones a major component of the interpretation of line drawings is line labelling by line labelling we mean a classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene and b further subclassification of each kind of discontinuity for a depth discontinuity we determine whether it is a limb a locus of points on the surface where the line of sight is tangent to the surface or an occluding edge a tangent plane discontinuity of the surface for an orientation discontinuity we determine whether it corresponds to a convex or concave edge this thesis presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described by analysing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing an algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing a local minimum complexity rule at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex is used in order to prune highly counter intuitive interpretations the labelling scheme was implemented and tested on a number of line drawings the labellings obtained are few and by and large in accordance with human interpretations

inverse perspective transform using zero curvature contour points application to the localization of some generalized cylinders from a single view the localization of some kinds of modeled generalized cylinders from a single brightness perspective image is addressed it is shown how the zero curvature points of their contours can be used to solve the inverse perspective problem three key theorems about the perspective projection of space curves and of the limbs of a straight homogeneous generalized cylinder whose scaling function has at least one zero curvature point are discussed in view of the localization of homogeneous generalized cylinders an algorithm previously developed by the authors which estimates the pose of a line triplet is adapted a new theoretical result about the inverse perspective projection of cones of revolution useful for the localization of objects of revolution is presented the corresponding algorithms have been implemented and results of experiments demonstrate the feasibility of the proposed localization methods

a formal classification of 3d medial axis points and their local geometry this paper proposes a novel hypergraph skeletal representation for 3d shape based on a formal derivation of the generic structure of its medial axis by classifying each skeletal point by its order of contact we show that genetically the medial axis consists of five types of points which are then organized into sheets curves and points 1 sheets manifolds with boundary which are the locus of bitangent spheres with regular tangency a sub 1 sup 2 a sub k sup n notation means n distinct k fold tangencies of the sphere of contact as explained in the text two types of curves 2 the intersection curve of three sheets and the locus of centers of tritangent spheres a sub 1 sup 3 and 3 the boundary of sheets which are the locus of centers of spheres whose radius equals the larger principal curvature i e higher order contact a sub 3 points and two types of points 4 centers of quad tangent spheres a sub 1 sup 4 and 5 centers of spheres with one regular tangency and one higher order tangency a sub 1 a sub 3 the geometry of the 3d medial axis thus consists of sheets a sub 1 sup 2 bounded by one type of curve a sub 3 on their free end which corresponds to ridges on the surface and attached to two other sheets at another type of curve a sub 1 sup 3 which support a generalized cylinder description the a sub 3 curves can only end in a sub 1 a sub 3 points where they must meet an a sub 1 sup 3 curve the a sub 1 sup 3 curves meet together in fours at an a sub 1 sup 4 point this formal result leads to a compact representation for 3d shape referred to as the medial axis hypergraph representation consisting of nodes a sub 1 sup 4 and a sub 1 a sub 3 points links between pairs of nodes a sub 1 sup 3 and a sub 3 curves and hyperlinks between groups of links a sub 1 sup 2 sheets the description of the local geometry at nodes by itself is sufficient to capture qualitative aspects of shapes in analogy to 2d we derive a pointwise reconstruction formula to reconstruct a surface from this medial axis hypergraph together with the radius function thus this information completely characterizes 3d shape and lays the theoretical foundation for its use in recognition morphing design and manipulation of shapes

interpreting line drawings as three dimensional surfaces understanding how line drawings convey tri dimensionality is of fundamental importance in explaining surface perception when photometry is either uninformative or too complex to model analytically we put forward here a computational model for interpreting line drawings as three dimensional surfaces based on constraints on local surface orientation along extremal and discontinuity boundaries specific techniques are described for two key processes recovering the three dimensional conformation of a space curve e g a surface boundary from its two dimensional projection in an image and interpolating smooth surfaces from orientation constraints along extremal boundaries the relevance of the model to a general theory of low level vision is discussed

perception of 3 d surfaces from 2 d contours inference of 3 d shape from 2 d contours in a single image is an important problem in machine vision the authors survey classes of techniques proposed in the past and provide a critical analysis they show that two kinds of symmetries in figures which are known as parallel and skew symmetries give significant information about surface shape for a variety of objects they derive the constraints imposed by these symmetries and show how to use them to infer 3 d shape they also discuss the zero gaussian curvature zgc surfaces in depth and show results on the recovery of surface orientation for various zgc surfaces

rigid motion and structure from several sets of parallel lines in a monocular image sequence abstract an image line is a very reliable feature in the feature based structure from motion sfm problem it has at least three advantages 1 it is not easily affected by occlusion 2 it can achieve subpixel accuracy 3 the correspondence problem is easier and less ambiguous although some generalized sfm algorithms using image line features have been recently developed they usually suffer from high error sensitivity and large matrix size besides in order to make their estimations more robust many line correspondences much more than the least requirement in theory are usually needed these shortages are not beneficial for practical use because many sets of parallel lines are frequently encountered in an artificial 3d environment and can be easily identified we try to utilize these identified parallel lines to simplify the generalized sfm problem and improve the performance of parameter estimation a fast and reliable algorithm is proposed in our paper both computer generated and real world images are tested and several satisfactory results have been obtained in addition its error sensitivity and data degeneracy will be discussed

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

the unique solution of projective invariants of six points from four uncalibrated images in this paper we show that four uncalibrated images are sufficient to uniquely determine the 3d projective invariants of a set of six points in general position in space an algorithm for computing the unique solution is proposed it computes by solving a set of linear equations for its two linear independent solutions and is simpler than other algorithms which compute the three possible solutions of 3d projective invariants by solving a set of nonlinear equations however a fourth image is needed to get the linear unique solution finally experimental results have shown the feasibility of this algorithm