some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

optimal correspondence of string subsequences the definition of optimal correspondent subsequence ocs which extends the finite alphabet editing error minimization matching to infinite alphabet penalty minimization matching is given the authors prove that the string distance derived from ocs is a metric an algorithm to compute the string to string ocs is given the computational complexity of ocs is analyzed ocs is more efficient than relaxation and elastic matching for 1d problems an algorithm combining syntactic information in template matching is given to show the ease of integrating regular grammar into the ocs technique since in different applications different penalty functions may be required two of them are discussed one pointwise and the other piecewise the pointwise application consists of a stereo epipolar line matching problem solved by using string to string ocs the feasibility of applying ocs to upc bar code recognition is investigated showing the elegance of string to regular expression ocs compared to the relaxation and elastic matching techniques

common structure of techniques for choosing smoothing parameters in regression problems on tente de relier deux methodes de choix du parametre de lissage l une basee sur la mesure du risque et l autre sur le degre d ajustement de la regression aux donnees

local affinity in heterogeneous growing networks abstract in this paper we present a study of the influence of local affinity in heterogeneous preferential attachment pa networks heterogeneous pa models are a generalization of the barabasi albert model to heterogeneous networks where the affinity between nodes biases the attachment probability of links threshold models are a class of heterogeneous pa models where the affinity between nodes is inversely related to the distance between their states we propose a generalization of threshold models where network nodes have individual affinity functions which are then combined to yield the affinity of each potential interaction we analyze the influence of the affinity functions in the topological properties averaged over a network ensemble the network topology is evaluated through the distributions of connectivity degrees clustering coefficients and geodesic distances we show that the relaxation of the criterion of a single global affinity still leads to a reasonable power law scaling in the connectivity and clustering distributions under a wide spectrum of assumptions we also show that the richer behavior of the model often exhibits a better agreement with the empirical observations on real networks

assessing influence on regression coefficients in generalized linear models summary suggested diagnostics for influence on the estimated regression coefficients in a generalized linear model have generally approximated the effect of deleting a single case we apply the local influence method of cook 1986 to assess the effect of small perturbations of the data including the vector of responses case weights explanatory variables and the components of one case the resulting diagnostics allow one to check for different kinds of influence and may give insight into its workings two examples illustrate some of the diagnostics

encoding of a priori information in active contour models the theory of active contours models the problem of contour recovery as an energy minimization process the computational solutions based on dynamic programming require that the energy associated with a contour candidate can be decomposed into an integral of local energy contributions in this paper we propose a grammatical framework that can model different local energy models and a set of allowable transitions between these models the grammatical encodings are utilized to represent a priori knowledge about the shape of the object and the associated signatures in the underlying images the variability encountered in numerical experiments is addressed with the energy minimization procedure which is embedded in the grammatical framework we propose an algorithmic solution that combines a nondeterministic version of the knuth morris pratt algorithm for string matching with a time delayed discrete dynamic programming algorithm for energy minimization the numerical experiments address practical problems encountered in contour recovery such as noise robustness and occlusion

modal matching for correspondence and recognition modal matching is a new method for establishing correspondences and computing canonical descriptions the method is based on the idea of describing objects in terms of generalized symmetries as defined by each object s eigenmodes the resulting modal description is used for object recognition and categorization where shape similarities are expressed as the amounts of modal deformation energy needed to align the two objects in general modes provide a global to local ordering of shape deformation and thus allow for selecting which types of deformations are used in object alignment and comparison in contrast to previous techniques which required correspondence to be computed with an initial or prototype shape modal matching utilizes a new type of finite element formulation that allows for an object s eigenmodes to be computed directly from available image information this improved formulation provides greater generality and accuracy and is applicable to data of any dimensionality correspondence results with 2d contour and point feature data are shown and recognition experiments with 2d images of hand tools and airplanes are described

influence diagnostics for the cross validated smoothing parameter in spline smoothing abstract this article addresses the problem of influence in estimating the smoothing parameter when fitting a univariate smoothing spline diagnostics are presented that can identify observations that locally influence the choice of smoothing parameter by generalized cross validation either through their case weights or observed responses generalized cross validation and the diagnostic methods are given a frequency interpretation and illustrated with examples

shape based tracking of left ventricular wall motion an approach for tracking and quantifying the nonrigid nonuniform motion of the left ventricular lv endocardial wall from two dimensional 2 d cardiac image sequences on a point by point basis over the entire cardiac cycle is presented given a set of boundaries motion computation involves first matching local segments on one contour to segments on the next contour in the sequence using a shape based strategy results from the match process are incorporated with a smoothness term into an optimization functional the global minimum of this functional is found resulting in a smooth flow field that is consistent with the match data the computation is performed for all pairs of frames in the temporal sequence and equally sampled points on one contour are tracked throughout the sequence resulting in a composite flow field over the entire sequence two perspectives on characterizing the optimization functional are presented which result in a tradeoff resolved by the confidence in the initial boundary segmentation experimental results for contours derived from diagnostic image sequences of three different imaging modalities are presented a comparison of trajectory estimates with trajectories of gold standard markers implanted in the lv wall are presented for validation the results of this comparison confirm that although cardiac motion is a three dimensional 3 d problem two dimensional 2 d analysis provides a rich testing ground for algorithm development

game theoretic integration for image segmentation robust segmentation of structures from an image is essential for a variety of image analysis problems however the conventional methods of region based segmentation and gradient based boundary finding are often frustrated by poor image quality here we propose a method to integrate the two approaches using game theory in an effort to form a unified approach that is robust to noise and poor initialization this combines the perceptual notions of complete boundary information using edge data and shape priors with gray level homogeneity using two computational modules the novelty of the method is that this is a bidirectional framework whereby both computational modules improve their results through mutual information sharing a number of experiments were performed both on synthetic datasets and datasets of real images to evaluate the new approach and it is shown that the integrated method typically performs better than conventional gradient based boundary finding

detection of influential observation in linear regression a new measure based on confidence ellipsoids is developed for judging the contribution of each data point to the determination of the least squares estimate of the parameter vector in full rank linear regression models it is shown that the measure combines information from the studentized residuals and the variances of the residuals and predicted values two examples are presented

deformable contour method a constrained optimization approach in this paper a class of deformable contour methods using a constrained optimization approach of minimizing a contour energy function satisfying an interior homogeneity constraint is proposed the class is defined by any positive potential function describing the contour interior characterization an evolutionary strategy is used to derive the algorithm a similarity threshold tv can be used to determine the interior size and shape of the contour sensitivity and significance of tv and a spreadness measure are also discussed and shown experiments on noisy images and the convergence to a minimum energy gap contour are included the developed method has been applied to a variety of medical images from ct abdominal section mri image slices of brain brain tumor a pig heart ultrasound image sequence to visual blood cell images as the results show the algorithm can be adapted to a broad range of medical images containing objects with vague complex and or irregular shape boundary inhomogeneous and noisy interior and contour with small gaps

graph matching for object recognition and recovery abstract a robust skeleton based graph matching method for object recognition and recovery applications is presented the object model uses both a skeleton model and contour segment models for object recognition and recovery the presented skeleton based shape matching method uses a combination of both structural and statistical methods that are applied in a sequential manner which largely reduce the matching space when compared with previous works this also provides a good alternate means to alleviate difficulties encountered in segmentation problems experiments of object recovery using real biomedical image samples have shown satisfactory results

a flexible and fast method for automatic smoothing abstract the choice of smoothing parameter or bandwidth is crucial when applying nonparametric regression estimators such as kernel estimators the optimal choice depends on the data at hand a data driven bandwidth selection close to the optimal one would make these curve estimators objective more reliable and easier to use minimizing residual mean squared error criteria such as cross validation have been frequently proposed to estimate the optimal smoothing parameter empirical and theoretical evidence indicates that cross validation rules and related methods lead to rather variable estimated optimal bandwidths the method presented here builds on estimating the asymptotically optimal bandwidth from the data since estimators for the residual variance and for an asymptotic expression for the bias are plugged into the asymptotic formula such selection rules are called plug in estimators the functional that quantifies bias is approximated by the integrated squared second derivative of the regre

from stein s unbiased risk estimates to the method of generalized cross validation this paper concerns the method of generalized cross validation gcv a promising way of choosing between linear estimates based on stein estimates and the associated unbiased risk estimates stein 1981 a new approach to gcv is developed many consistency results are obtained for the cross validated steinized estimates in the contexts of nearest neighbor nonparametric regression model selection ridge regression and smoothing splines moreover the associated stein s unbiased risk estimate is shown to be uniformly consistent in assessing the true loss not the risk consistency properties are examined as well when the sampling error is unknown finally we propose a variant of gcv to handle the case that the dimension of the raw data is known to be greater than that of their expected values

simulating the grassfire transform using an active contour model a method for shape description of planar objects that integrates both region and boundary features is presented the method is an implementation of a 2d dynamic grassfire that relies on a distance surface on which elastic contours minimize an energy function the method is based on an active contour model numerous implementation aspects of the shape description method were optimized a euclidean metric was used for optimal accuracy and the active contour model permits bypassing some of the discretization limitations inherent in using a digital grid noise filtering was performed on the basis of both contour feature measures and region measures that is curvature extremum significance and ridge support respectively to obtain robust shape descriptors other improvements and variations of the algorithmic implementation are proposed

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

a framework for automatic landmark identification using a new method of nonrigid correspondence a framework for automatic landmark identification is presented based on an algorithm for corresponding the boundaries of two shapes the auto landmarking framework employs a binary tree of corresponded pairs of shapes to generate landmarks automatically on each of a set of example shapes the landmarks are used to train statistical shape models known as point distribution models the correspondence algorithm locates a matching pair of sparse polygonal approximations one for each of a pair of boundaries by minimizing a cost function using a greedy algorithm the cost function expresses the dissimilarity in both the shape and representation error with respect to the defining boundary of the sparse polygons results are presented for three classes of shape which exhibit various types of nonrigid deformation

recognize objects with three kinds of information in landmarks abstract object recognition is one of the most important tasks in computer vision domain and it has been extensively applied in many areas during the last three decades in this paper a method is proposed to recognize objects in shape spaces in which landmarks have three kinds of information i e landmarks position angle and feature vector by comparing angle and feature vector a landmark in an image can correspond with a few number of landmarks in another image then the pixel s positions of landmarks from two images are used to calculate the procrustean distance in a shape space if the value of the procrustean distance is smaller than a predefined threshold the two sets of landmarks will be considered to match each other applying the proposed method two dimensional objects including occluded objects can be recognized quickly

boundary finding with parametrically deformable models segmentation using boundary finding is enhanced both by considering the boundary as a whole and by using model based global shape information the authors apply flexible constraints in the form of a probabilistic deformable model to the problem of segmenting natural 2 d objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form the parametric model is based on the elliptic fourier decomposition of the boundary probability distributions on the parameters of the representation bias the model to a particular overall shape while allowing for deformations boundary finding is formulated as an optimization problem using a maximum a posteriori objective function results of the method applied to real and synthetic images are presented including an evaluation of the dependence of the method on prior information and image quality