soliton dynamics in computational anatomy computational anatomy ca has introduced the idea of anatomical structures being transformed by geodesic deformations on groups of diffeomorphisms among these geometric structures landmarks and image outlines in ca are shown to be singular solutions of a partial differential equation that is called the geodesic epdiff equation a recently discovered momentum map for singular solutions of epdiff yields their canonical hamiltonian formulation which in turn provides a complete parameterization of the landmarks by their canonical positions and momenta the momentum map provides an isomorphism between landmarks and outlines for images and singular soliton solutions of the epdiff equation this isomorphism suggests a new dynamical paradigm for ca as well as new data representation

empirical bayes hierarchical models for regularizing maximum likelihood estimation in the matrix gaussian procrustes problem procrustes analysis involves finding the optimal superposition of two or more forms via rotations translations and scalings procrustes problems arise in a wide range of scientific disciplines especially when the geometrical shapes of objects are compared contrasted and analyzed classically the optimal transformations are found by minimizing the sum of the squared distances between corresponding points in the forms despite its widespread use the ordinary unweighted least squares ls criterion can give erroneous solutions when the errors have heterogeneous variances heteroscedasticity or the errors are correlated both common occurrences with real data in contrast maximum likelihood ml estimation can provide accurate and consistent statistical estimates in the presence of both heteroscedasticity and correlation here we provide a complete solution to the nonisotropic ml procrustes problem assuming a matrix gaussian distribution with factored covariances our analysis generalizes simplifies and extends results from previous discussions of the ml procrustes problem an iterative algorithm is presented for the simultaneous numerical determination of the ml solutions

combining registration and fitting for functional models a registration method can be defined as a process of aligning features of a sample of curves by monotone transformations of their domain the aligned curves exhibit only amplitude variation and the domain transformations called warping functions capture the phase variation in the original curves in this article we precisely define a new type of registration process in which the warping functions optimize the fit of a principal components decomposition to the aligned curves the principal components are effectively the features that this process aligns we discuss the relationship of registration to closure of a function space under convex operations and define consistency for registration methods we define an explicit decomposition of functional variation into amplitude and phase partitions and develop an algorithm for combining registration with principal components analysis and apply it to simulated and real data

pivotal bootstrap methods for k sample problems in directional statistics and shape analysis we propose a novel bootstrap hypothesis testing approach for the problem of testing a null hypothesis of a common mean direction mean polar axis or mean shape across several populations of real unit vectors the directional case or complex unit vectors the two dimensional shape case multisample testing problems of this type arise frequently in directional statistics and shape analysis as in other areas of statistics but to date there has been relatively little discussion of nonparametric bootstrap approaches to this problem the bootstrap approach described here is based on a statistic that can be expressed as the smallest eigenvalue of a certain positive definite matrix we prove that this statistic has a limiting chi squared distribution under the null hypothesis of equality of means across populations although we focus mainly on the version of the statistic in which neither isotropy within populations nor constant dispersion structure across populations is assumed we explain how to modify th

a posteriori error estimation for unilateral contact with matching and non matching meshes in this paper we consider the unilateral contact problem between elastic bodies we propose an error estimator based on the concept of error in the constitutive relation in order to evaluate the finite element approximation involving matching and non matching meshes on the contact zone the determination of the a posteriori error estimate is linked to the building of kinematically admissible stress fields and statically admissible stress fields we then propose a finite element method for approximating the unilateral contact problem taking into account matching and non matching meshes on the contact zone then we describe the construction of admissible fields lastly we present optimized computations by using both the error estimates and a convenient mesh adaptivity procedure 2000 elsevier science s a all rights reserved

shape changes in the plane for landmark data this paper deals with the statistical analysis of matched pairs of shapes of configurations of landmarks in the plane we provide inference procedures on the complex projective plane for a basic measure of shape change in the plane on observing that shapes of configurations of k 1 landmarks in the plane may be represented as points on cp k 1 and that complex rotations are the only maps on cs k 1 which preserve the usual hermitian inner product specifically if u 1 u n are fixed points on cp k 1 represented as cs k 1 u 1 and v 1 v n are random points on cp k 1 such that the distribution of v j depends only on v j au j 2 for some unknown complex rotation matrix a then this paper provides asymptotic inference procedures for a it is demonstrated that shape changes of a kind not detectable as location shifts by standard euclidean analysis can be found by this frequency domain method a numerical example is given

intrinsic inference on the mean geodesic of planar shapes and tree discrimination by leaf growth for planar landmark based shapes taking into account the non euclidean geometry of the shape space a statistical test for a common mean first geodesic principal component gpc is devised which rests on one of two asymptotic scenarios for both scenarios strong consistency and central limit theorems are established along with an algorithm for the computation of a ziezold mean geodesic in application this allows to verify the geodesic hypothesis for leaf growth of canadian black poplars and to discriminate genetically different trees by observations of leaf shape growth over brief time intervals with a test based on procrustes tangent space coordinates not involving the shape space s curvature neither can be achieved

shape curves and geodesic modelling a family of shape curves is introduced that is useful for modelling the changes in shape in a series of geometrical objects the relationship between the preshape sphere and the shape space is used to define a general family of curves based on horizontal geodesics on the preshape sphere methods for fitting geodesics and more general curves in the non euclidean shape space of point sets are discussed based on minimizing sums of squares of procrustes distances likelihood based inference is considered we illustrate the ideas by carrying out statistical analysis of two dimensional landmarks on rats skulls at various times in their development and three dimensional landmarks on lumbar vertebrae from three primate species

a linear time combinatorial algorithm to find the orthogonal hull of an object on the digital plane a combinatorial algorithm to compute the orthogonal hull of a digital object imposed on a background grid is presented in this paper the resolution and complexity of the orthogonal hull can be controlled by varying the grid size which may be used for a multiresolution analysis of a given object existing algorithms on finding the convex hull are based on divide and conquer strategy sweepline approach etc whereas the proposed algorithm is combinatorial in nature whose time complexity is linear on the object perimeter instead of the object area for a larger grid size the perimeter of an object decreases in length in terms of grid units and hence the runtime of the algorithm reduces significantly the algorithm uses only comparison and addition in the integer domain thereby making it amenable to usage in real world applications where speed is a prime factor experimental results including the cpu time demonstrate the elegance and efficacy of the proposed algorithm

a new convexity measure for polygons convexity estimators are commonly used in the analysis of shape in this paper we define and evaluate a new convexity measure for planar regions bounded by polygons the new convexity measure can be understood as a boundary based measure and in accordance with this it is more sensitive to measured boundary defects than the so called area based convexity measures when compared with the convexity measure defined as the ratio between the euclidean perimeter of the convex hull of the measured shape and the euclidean perimeter of the measured shape then the new convexity measure also shows some advantages particularly for shapes with holes the new convexity measure has the following desirable properties 1 the estimated convexity is always a number from 0 1 2 the estimated convexity is i if and only if the measured shape is convex 3 there are shapes whose estimated convexity is arbitrarily close to 0 4 the new convexity measure is invariant under similarity transformations and 5 there is a simple and fast procedure for computing the new convexity measure

new approach for automation of finite element analysis in this paper we propose a new approach for an optimization of finite element analysis in elasticity from a mechanical problem and a criterion of optimization the procedure provides an approximate solution satisfying the prescribed criterion an error measure based on the constitutive relation and an efficient adaptive technique which automatically takes into account steep gradient areas are used with such a procedure even a nonspecialist can carry out accurate finite element analysis in particular the user does not identify a priori the regions that must be refined several criteria of optimization have been developed and some examples show the efficiency of the method

large sample theory of intrinsic and extrinsic sample means on manifolds ii this article develops nonparametric inference procedures for estimation and testing problems for means on manifolds a central limit theorem for frechet sample means is derived leading to an asymptotic distribution theory of intrinsic sample means on riemannian manifolds central limit theorems are also obtained for extrinsic sample means w r t an arbitrary embedding of a differentiable manifold in a euclidean space bootstrap methods particularly suitable for these problems are presented applications are given to distributions on the sphere s d directional spaces real projective space rp n 1 axial spaces complex projective space cp k 2 planar shape spaces w r t veronese whitney embeddings and a three dimensional shape space 4 3

learning to match deriving optimal template matching algorithms from probabilistic image models finding correspondences between images by template matching is a common problem in image understanding although a variety of solutions have been proposed most of them rely on the arbitrary choice of a template and a matching function often different cost functions lead to different results and the choice of a good cost for a specific application remains an art statistical models on the other hand allow us to derive optimal learning and matching algorithms from modeling assumptions using likelihood maximization principles the key contribution of this paper is the development of a statistical framework for learning what function to optimize from training examples we present a family of statistical models for grayscale images which allow us to derive optimal template matching algorithms the intensity at each pixel is described by a random variable whose distribution is encoded by a deformable template firstly we assume the intensity distribution to be gaussian and derive an intensity matching algorithm which is a generalization of the classical sum of squared differences then we introduce a hidden segmentation variable in the probabilistic model and derive a segmentation matching algorithm that can handle photometric variations both models are exemplified on the automatic detection of anatomical landmarks in brain magnetic resonance images

a simple error estimator and adaptive procedure for practical engineerng analysis a new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes the estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors it can thus be combined with a full adaptive process of refinement or more simply provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials when combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable estimates other than the energy norm have successfully been applied giving for instance a predetermined accuracy of stresses

parametric regression on the grassmannian we address the problem of fitting parametric curves on the grassmann manifold for the purpose of intrinsic parametric regression we start from the energy minimization formulation of linear least squares in euclidean space and generalize this concept to general nonflat riemannian manifolds following an optimal control point of view we then specialize this idea to the grassmann manifold and demonstrate that it yields a simple extensible and easy to implement solution to the parametric regression problem in fact it allows us to extend the basic geodesic model to 1 a time warped variant and 2 cubic splines we demonstrate the utility of the proposed solution on different vision problems such as shape regression as a function of age traffic speed estimation and crowd counting from surveillance video clips most notably these problems can be conveniently solved within the same framework without any specifically tailored steps along the processing pipeline

modeling network traffic using generalized cauchy process abstract processes with long range dependence lrd have gained wide applications in many fields of science and technologies ranging from hydrology to network traffic two key properties of such processes are lrd that is characterized by the hurst parameter h and self similarity ss that is measured by the fractal dimension d however in the popular traffic model using fractional gaussian noise fgn these two parameters are linearly related this may be regarded as a limitation of fgn in traffic modeling from the point of view of either accurately fitting real traffic or appropriately explaining the particular multi fractal phenomena of traffic in this paper we discuss recent results in traffic modeling from a view of the generalized cauchy gc process the gc process is indexed by two parameters d and h the parameter d in the gc model is independent of h hence it provides a more flexible way to describe the multi fractal phenomena of traffic in addition to accurately modeling traffic for both short term lags and long term ones

toward a conformal field theory for schramm loewner evolutions we discuss the partition function point of view for chordal schramm loewner evolutions and their relationship with correlation functions in conformal field theory both are closely related to crossing probabilities and interfaces in critical models in two dimensional statistical mechanics we gather and supplement previous results with different perspectives point out remaining difficulties and suggest directions for future studies

statistical analysis of shape through triangulation of landmarks a study of sexual dimorphism in hominids two objects with homologous landmarks are said to be of the same shape if the configuration of landmarks of one object can be exactly matched with that of the other by translation rotation reflection and scaling in an earlier paper the authors proposed statistical analysis of shape by considering logarithmic differences of all possible euclidean distances between landmarks tests of significance for differences in the shape of objects and methods of discrimination between populations were developed with such data in the present paper the corresponding statistical methodology is developed by triangulation of the landmarks and by considering the angles as natural measurements of shape this method is applied to the study of sexual dimorphism in hominids

on the smoothness of the partition function for multiple schramm loewner evolutions we consider the measure on multiple chordal schramm loewner evolution textit sle kappa curves we establish a derivative estimate and use it to give a direct proof that the partition function is c 2 if kappa 4

toward a universal h p adaptive finite element strategy part 1 constrained approximation and data structure abstract this is the first of a series of papers devoted to the development of an adaptive finite element method to solve various boundary value problems arising in solid and fluid mechanics the paper deals with the general concepts of h p finite element methods constrained approximation and data structure and related issues several numerical examples illustrate the main ideas of the method

error estimate procedure in the finite element method and applications statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models the error on constitutive law for these fields yields an expression of the finite element error moreover the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy

toward a universal h p adaptive finite element strategy part 2 a posteriori error estimation abstract in this second paper of the series on h p adaptive finite element methods we present five different techniques for a posteriori error estimation of h p methods for linear elliptic boundary value problems the techniques are referred to as the residual estimation method the duality method the subdomain residual method a method based on interpolation theory and a post processing method the present study examines the theory and behavior of such techniques applied specifically to h p adaptive finite element methods several numerical examples illustrate the efficiency of the methods

rapid elastic image registration for 3 d ultrasound a subvolume based algorithm for elastic ultrasound registration sure was developed and evaluated designed primarily to improve spatial resolution in three dimensional compound imaging the algorithm registers individual image volumes nonlinearly before combination into compound volumes sure works in one or two stages optionally using miami fuse spl copy software first to determine a global affine registration before iteratively dividing the volume into subvolumes and computing local rigid registrations in the second stage connectivity of the entire volume is ensured by global interpolation using thin plate splines after each iteration the performance of sure was quantified in 20 synthetically deformed in vivo ultrasound volumes and in two phantom scans one of which was distorted at acquisition by placing an aberrating layer in the sound path the aberrating layer was designed to induce beam aberrations reported for the female breast synthetic deformations of 1 5 2 5 mm were reduced by over 85 when sure was applied to register the distorted image volumes with the original ones registration times were below 5 min on a 500 mhz cpu for an average data set size of 13mb in the aberrated phantom scans sure reduced the average deformation between the two volumes from 1 01 to 0 30mm this was a statistically significant p 0 01 improvement over rigid and affine registration transformations which produced reductions to 0 59 and 0 50 mm respectively

invariance identifiability and morphometrics the form of an object is that characteristic that remains invariant under a group of transformations comprising translation rotation and possibly reflection group invariance thus naturally plays an important role in the statistical analysis of forms we examine the existing methods for the statistical analysis of form from the invariance perspective we begin with a review of the important basic ideas behind invariance and derive a maximal invariant under the group of transformations consisting of rotation reflection and translation and its distribution under the gaussian and elliptically symmetric perturbation models we first consider the single sample case and discuss the issue of identifiability of the parameters we show that method of moments estimators based on the distances between landmarks and maximum likelihood estimators mles based on the size and shape coordinates are invariant and estimate identifiable parameters however a number of commonly used methods do not we compare the stati

on the techniques for constructing admissible stress fields in model verification performances on engineering examples robust global goal oriented error estimation is used nowadays to control the approximate finite element solutions obtained from simulation in the context of computational mechanics the construction of admissible stress fields ie stress tensors which verify the equilibrium equations is required to set up strict and guaranteed error bounds using residual based error estimators and plays an important role in the quality of the error estimates this work focuses on the different procedures used in the calculation of admissible stress fields which is a crucial and technically complicated point the three main techniques that currently exist called the element equilibration technique eet the star patch equilibration technique spet and the element equilibration star patch technique eespt are investigated and compared with respect to three different criteria namely the quality of associated error estimators computational cost and easiness of practical implementation into commercial finite element codes the numerical results which are presented focus on industrial problems they highlight the main advantages and drawbacks of the different methods and show that the behavior of the three estimators which have the same convergence rate as the exact global error is consistent two and three dimensional experiments have been carried out in order to compare the performance and the computational cost of the three different approaches the analysis of the results reveals that the spet is more accurate than eet and eespt methods but the corresponding computational cost is higher overall the numerical tests prove the interest of the hybrid method eespt and show that it is a correct compromise between quality of the error estimate practical implementation and computational cost furthermore the influence of the cost function involved in the eet and the eespt is studied in order to optimize the estimators

an alternative approach to normalization and evaluation for gait patterns procrustes analysis applied to the cyclograms of sprinters and middle distance runners in order to compare gait patterns a common procedure is to normalize strides both in time and magnitude the stride duration is usually normalized to a time percentage before averaging curves as the timing of event occurrences may shift across strides the shape of the averaged curves is distorted and therefore the standard deviation is overvalued stride magnitude normalization is performed by means of dimensionless numbers however there is little agreement on which body size correction methods should be used the procrustes method describes curve shape and shape change in a mathematical and statistical framework independently of time and size factors the present study aims to explore how this technique may be used for time and magnitude stride normalization to reflect individual and group mean responses the procrustes method which combines quantitative and visual features is applied to the shape of the ankle and knee cyclograms superimposition of 25 cyclograms 10 for sprinters sp and 15 for middle distance runners mdr was supplemented by statistical procedures principal component analysis discriminant function to extract the main key events which vary according to the athletic specialities in comparison with the mdr poulaine shaped cyclogram the ovoid cyclogram of sp reveals the following gait indicators a short braking phase a rapid initial lower limb swing in the forward direction a fast upward movement of the knee and ankle and an active foot contact the procrustes approach could be used to describe other quasi periodic movements through relative motion plots e g cyclograms angle angle diagrams phase plane portraits

the emerging discipline of computational functional anatomy computational functional anatomy cfa is the study of functional and physiological response variables in anatomical coordinates for this we focus on two things i the construction of bijections via diffeomorphisms between the coordinatized manifolds of human anatomy and ii the transfer group action and parallel transport of functional information into anatomical atlases via these bijections we review advances in the unification of the bijective comparison of anatomical submanifolds via point sets including points curves and surface triangulations as well as dense imagery we examine the transfer via these bijections of functional response variables into anatomical coordinates via group action on scalars and matrices in dti as well as parallel transport of metric information across multiple templates which preserves the inner product

the statistical analysis of dynamic curves and sections abstract by a curve we shall understand a one dimensional smooth path lying in r 2 or r 3 which can be naturally parametrized by a real coordinate the coordinate could represent physical time or any other variable which can be interpreted dynamically in some cases the curve will arise as the linear section of a higher dimensional structure such as the planar section of a surface in r 3 in this paper we develop a model for the shape of planar curves based on their curvatures that is reasonably robust to the location of landmarks or knots used to approximate the contours of the curve the measurement for the shape difference between two curves that we propose is also based on the curvatures of the curves and directly inherits the simple euclidean property for averages

consistency of procrustes estimators lele has shown that the procrustes estimator of form is inconsistent and raised the question about the consistency of the procrustes estimator of shape in this paper the consistency of estimators of form and shape is studied under various assumptions in particular it is shown that the procrustes estimator of shape is consistent under the assumption of an isotropic error distribution and that consistency breaks down if the assumption of isotropy is relaxed the relevance of these results for practical shape analysis is discussed as a by product some new results are derived for the offset uniform distribution from directional data

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

surface bounded growth modeling applied to human mandibles from a set of longitudinal three dimensional scans of the same anatomical structure the authors have accurately modeled the temporal shape and size changes using a linear shape model on a total of 31 computed tomography scans of the mandible from six patients 14 851 semilandmarks are found automatically using shape features and a new algorithm called geometry constrained diffusion the semilandmarks are mapped into procrustes space principal component analysis extracts a one dimensional subspace which is used to construct a linear growth model the worst case mean modeling error in a cross validation study is 3 7 mm

segmentation registration and measurement of shape variation via image object shape a model of object shape by nets of medial and boundary primitives is justified as richly capturing multiple aspects of shape and yet requiring representation space and image analysis work proportional to the number of primitives metrics are described that compute an object representation s prior probability of local geometry by reflecting variabilities in the net s node and link parameter values and that compute a likelihood function measuring the degree of match of an image to that object representation a paradigm for image analysis of deforming such a model to optimize a posteriori probability is described and this paradigm is shown to be usable as a uniform approach for object definition object based registration between images of the same or different imaging modalities and measurement of shape variation of an abnormal anatomical object compared with a normal anatomical object examples of applications of these methods in radiotherapy surgery and psychiatry are given

automatic construction of correspondences for tubular surfaces statistical shape modeling is an established technique and is used for a variety of tasks in medical image processing such as image segmentation and analysis a challenging task in the construction of a shape model is establishing a good correspondence across the set of training shapes especially for shapes of cylindrical topology very little work has been done this paper describes an automatic method to obtain a correspondence for a set of cylindrical shapes the method starts from an initial correspondence which is provided by cylindrical parameterization the quality of the obtained correspondence measured in terms of the description length is then improved by deforming the parameterizations using cylindrical b spline deformations and by optimization of the spatial alignment of the shapes in order to allow efficient gradient guided optimization an analytic expression is provided for the gradient of this quality measure with respect to the parameters of the parameterization deformation and the spatial alignment a comparison is made between models obtained from the correspondences before and after the optimization the results show that in comparison with parameterization based correspondences this new method establishes correspondences that generate models with significantly increased performance in terms of reconstruction error generalization ability and specificity

validation of a posteriori error estimators by numerical approach abstract a numerical methodology which determines the quality or robustness of a posteriori error estimators is described the methodology accounts precisely for the factors which affect the quality of error estimators for finite element solutions of linear elliptic problems namely the local geometry of the grid and the structure of the solution the methodology can be employed to check the robustness of any estimator for the complex grids which are used in engineering computations

morphometric tools for landmark data geometry and biology 1 introduction 2 preliminaries 3 landmarks 4 distance measures 5 shape coordinates 6 principal axes of shape change for triangles 7 features of shape comparison 8 retrospect and prospect

graphical templates for model registration a new method of model registration is proposed using graphical templates a graph of landmarks is chosen in the template image all possible candidates for these landmarks are found in the data image using local operators a dynamic programming algorithm on decomposable subgraphs of the template graph finds the optimal match to a subset of the candidate points in polynomial time this combination of local operators to describe points of interest landmarks and a graph to describe their geometric orientation in the plane yields fast and precise matches of the model to the data with no initialization required

a posteriori error control of finite element approximations for coulomb s frictional contact this paper is concerned with the frictional unilateral contact problem governed by coulomb s law we define an a posteriori error estimator based on the concept of error in the constitutive relation to quantify the accuracy of a finite element approximation of the problem we propose and study different mixed finite element approaches and discuss their properties in order to compute the estimator the information given by the error estimates is then coupled with a mesh adaptivity technique which provides the user with the desired quality and minimizes the computation costs the numerical implementation of the error estimator as well as optimized computations are performed

generalized whittle matern random field as a model of correlated fluctuations this paper considers a generalization of the gaussian random field with covariance function of the whittle matern family such a random field can be obtained as the solution to the fractional stochastic differential equation with two fractional orders asymptotic properties of the covariance functions belonging to this generalized whittle matern family are studied which are used to deduce the sample path properties of the random field the whittle matern field has been widely used in modeling geostatistical data such as sea beam data wind speed field temperature and soil data in this paper we show that the generalized whittle matern field provides a more flexible model for wind speed data

criteria to achieve nearly optimal meshes in theh adaptive finite element method five adaptive modification strategies amss are studied as means to obtain nearly optimal meshes using an adaptive finite element modelling system based on the h version of the fem these strategies include the method traditionally seem in the literature as well as four additional methods the five strategies are tested over five numerical examples one of them producing convergence oscillations in one example the principal characteristic of our system is that it permits the user to control certain parameters of the adaptive process which contributes to an improvement in the results

an automatic procedure with a control of accuracy for finite element analysis in 2d elasticity abstract this paper gives a procedure for an automation of the entire finite element analysis for 2d or axisymmetric elastic structures with a control of accuracy the user describes the problem and the level of desired accuracy the procedure then provides an approximate solution for a minimal computation cost this procedure uses an error measure based on the constitutive relation 1 5 and an efficient adaptive technique 6 which automatically take account of the regions of stress concentration examples are presented for discretizations using 3 or 6 node triangular elements

statistical assessment of bilateral symmetry of shapes summary this paper formulates the problem of measuring bilateral symmetry of objects analytically for landmark data and develops various new testing procedures and exploratory data analyses the development is linked with the fundamental biological problem of measuring directional asymmetry and fluctuating asymmetry we distinguish two types of symmetry object symmetry and matching symmetry and provide tests under assumptions of isotropic landmark variability as well as non isotropy the tests require novel statistical and geometrical analyses of the procrustes shape manifold for describing components of symmetry and asymmetry within samples an extension of principal component analysis is introduced and illustrated by appropriate deformation techniques various real examples are used to illustrate the practical relevance of this work

cortical surface shape analysis based on spherical wavelets in vivo quantification of neuroanatomical shape variations is possible due to recent advances in medical imaging and has proven useful in the study of neuropathology and neurodevelopment in this paper we apply a spherical wavelet transformation to extract shape features of cortical surfaces reconstructed from magnetic resonance images mris of a set of subjects the spherical wavelet transformation can characterize the underlying functions in a local fashion in both space and frequency in contrast to spherical harmonics that have a global basis set we perform principal component analysis pca on these wavelet shape features to study patterns of shape variation within normal population from coarse to fine resolution in addition we study the development of cortical folding in newborns using the gompertz model in the wavelet domain which allows us to characterize the order of development of large scale and finer folding patterns independently given a limited amount of training data we use a regularization framework to estimate the parameters of the gompertz model to improve the prediction performance on new data we develop an efficient method to estimate this regularized gompertz model based on the broyden fletcher goldfarb shannon bfgs approximation promising results are presented using both pca and the folding development model in the wavelet domain the cortical folding development model provides quantitative anatomic information regarding macroscopic cortical folding development and may be of potential use as a biomarker for early diagnosis of neurologic deficits in newborns

morphometry of anatomical shape complexes with dense deformations and sparse parameters we propose a generic method for the statistical analysis of collections of anatomical shape complexes namely sets of surfaces that were previously segmented and labeled in a group of subjects the method estimates an anatomical model the template complex that is representative of the population under study its shape reflects anatomical invariants within the dataset in addition the method automatically places control points near the most variable parts of the template complex vectors attached to these points are parameters of deformations of the ambient 3d space these deformations warp the template to each subject s complex in a way that preserves the organization of the anatomical structures multivariate statistical analysis is applied to these deformation parameters to test for group differences results of the statistical analysis are then expressed in terms of deformation patterns of the template complex and can be visualized and interpreted the user needs only to specify the topology of the template complex and the number of control points the method then automatically estimates the shape of the template complex the optimal position of control points and deformation parameters the proposed approach is completely generic with respect to any type of application and well adapted to efficient use in clinical studies in that it does not require point correspondence across surfaces and is robust to mesh imperfections such as holes spikes inconsistent orientation or irregular meshing the approach is illustrated with a neuroimaging study of down syndrome ds the results demonstrate that the complex of deep brain structures shows a statistically significant shape difference between control and ds subjects the deformation based modelingis able to classify subjects with very high specificity and sensitivity thus showing important generalization capability even given a low sample size we show that the results remain significant even if the number of control points and hence the dimension of variables in the statistical model are drastically reduced the analysis may even suggest that parsimonious models have an increased statistical performance the method has been implemented in the software deformetrica which is publicly available at www deformetrica org

partition functions loop measure and versions of sle we discuss the partition function view of the schramm loewner evolution after reviewing a number of known results in the framework of brownian loop measures and scaling rules for partition functions we give some speculation about multiply connected domains

the superconvergent patch recovery and a posteriori error estimates part 2 error estimates and adaptivity in this second part of the paper the issue of a posteriori error estimation is discussed in particular we derive a theorem showing the dependence of the effectivity index for the zienkiewicz zhu error estimator on the convergence rate of the recovered solution this shows that with superconvergent recovery the effectivity index tends asymptotically to unity the superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the zienkiewicz zhu error estimator to demonstrate accurate estimation of the exact error attainable numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient stress error estimation several examples of the performance of the error estimator in adaptive mesh refinement are also presented

disconnected skeleton shape at its absolute scale we present a new skeletal representation along with a matching framework to address the deformable shape recognition problem the disconnectedness arises as a result of excessive regularization that we use to describe a shape at an attainably coarse scale our motivation is to rely on stable properties the shape instead of inaccurately measured secondary details the new representation does not suffer from the common instability problems of the traditional connected skeletons and the matching process gives quite successful results on a diverse database of 2d shapes an important difference of our approach from the conventional use of skeleton is that we replace the local coordinate frame with a global euclidean frame supported by additional mechanisms to handle articulations and local boundary deformations as a result we can produce descriptions that are sensitive to any combination of changes in scale position orientation and articulation as well as invariant ones

an informational measure of association and dimension reduction for multiple sets and groups with applications in morphometric analysis in this article we propose a new general index that measures relationships between multiple sets of random vectors this index is based on kullback leibler kl information which measures linear or nonlinear dependence between multiple sets using joint and marginal densities of affine transformations of the random vectors estimates of the matrixes are obtained by maximizing the kl information and are shown to be consistent the motivation for introducing such an index comes from morphological integration studies a topic in biological science as a special case of this index we define an overall measure of association and two other measures for dimension reduction the use of these measures is illustrated through real data analysis in morphometric studies and extensive simulations and their performance is compared with that of approaches based on canonical correlation analysis extensions of the aforementioned measures to multiple groups are also discussed in contrast to canonical correlation analysi

morphometric analysis for early detection of changes in cellular structure in a toxicological experiment this paper presents a method for semi automatic analysis of morphometry in image cytometry studies we examine morphological changes in neuroblastoma cells caused by a toxin nuclei are automatically recognized from images using a constrained seeded region growing algorithm the shape of the nuclei is quantified by fitting ellipses to the identified regions features such as centroids elongation orientation and size are extracted from this fitting process under certain assumptions it is demonstrated that the log elongation measurement has an asymptotically normal distribution whose variance is dependent only on object size this allows weighted linear models to be fitted to elongation measurements hypothesis tests show that over time there is a significant elongation due to application of the toxin the other variables are not significant but there is a significant image effect the scientific implications of these findings are considered

the tps direct transport a new method for transporting deformations in the size and shape space modern shape analysis allows the fine comparison of shape changes occurring between different objects very often the classic machineries of generalized procrustes analysis and principal component analysis are used in order to contrast the shape change occurring among configurations represented by homologous landmarks however if size and shape data are structured in different groups thus constituting different morphological trajectories a data centering is needed if one wants to compare solely the deformation representing the trajectories to do that inter individual variation must be filtered out this maneuver is rarely applied in studies using simulated or real data a geometrical procedure named parallel transport that can be based on various connection types is necessary to perform such kind of data centering usually the levi civita connection is used for interpolation of curves in a riemannian space it can also be used to transport a deformation we demonstrate that this procedure does not preserve some important characters of the deformation even in the affine case we propose a novel procedure called tps direct transport which is able to perfectly transport deformation in the affine case and to better approximate non affine deformation in comparison to existing tools we recommend to center shape data using the methods described here when the differences in deformation rather than in shape are under study