skeleton search category specific object recognition and segmentation using a skeletal shape model we describe a top down object detection and segmentation approach that uses a skeleton based shape model and that works directly on real images the approach is based on three components first we propose a fragment based generative model for shape that is based on the shock graph and has minimal dependency among its shape fragments the model is capable of generating a wide variation of shapes as instances of a given object category second we develop a progressive selection mechanism to search among the generated shapes for the category instances that are present in the image the search begins with a large pool of candidates identified by a dynamic programming dp algorithm and progressively reduces it in size by applying series of criteria namely local minimum criterion extent of shape overlap and thresholding of the objective function to select the final object candidates third we propose the partitioned chamfer matching pcm measure to capture the support of image edges for a hypothesized shape this measure overcomes the shortcomings of the oriented chamfer matching and is robust against spurious edges missing edges and accidental alignment between the image edges and the shape boundary contour we have evaluated our approach on the ethz dataset and found it to perform well in both object detection and object segmentation tasks

a shape reconstructability measure of object part importance with applications to object detection and localization we propose a computational model which computes the importance of 2 d object shape parts and we apply it to detect and localize objects with and without occlusions the importance of a shape part a localized contour fragment is considered from the perspective of its contribution to the perception and recognition of the global shape of the object accordingly the part importance measure is defined based on the ability to estimate recall the global shapes of objects from the local part namely the part s shape reconstructability more precisely the shape reconstructability of a part is determined by two factors part variation and part uniqueness i part variation measures the precision of the global shape reconstruction i e the consistency of the reconstructed global shape with the true object shape and ii part uniqueness quantifies the ambiguity of matching the part to the object i e taking into account that the part could be matched to the object at several different locations taking both these factors into consideration an information theoretic formulation is proposed to measure part importance by the conditional entropy of the reconstruction of the object shape from the part experimental results demonstrate the benefit with the proposed part importance in object detection including the improvement of detection rate localization accuracy and detection efficiency by comparing with other state of the art object detectors in a challenging but common scenario object detection with occlusions we show a considerable improvement using the proposed importance measure with the detection rate increased over 10 10 on a subset of the challenging pascal dataset the interpolated average precision as used in the pascal voc challenge is improved by 4 8 moreover we perform a psychological experiment which provides evidence suggesting that humans use a similar measure for part importance when perceiving and recognizing shapes

a hamiltonian jacobi algorithm the nonsymmetric jacobi iteration is adapted to the special structure of hamiltonian matrices this hamiltonian jacobi algorithm uses symplectic unitary similarity transformations to solve algebraic riccati equations through the hamiltonian schur form it preserves hamiltonian structure without using a condensed form although it converges too slowly for use on conventional serial computers it may be attractive for some highly parallel architectures

parts of visual form computational aspects underlying recognition is an organization of objects and their parts into classes and hierarchies a representation of parts for recognition requires that they be invariant to rigid transformations robust in the presence of occlusions stable with changes in viewing geometry and be arranged in a hierarchy these constraints are captured in a general framework using notions of a part line and a partitioning scheme a proposed general principle of form from function motivates a particular partitioning scheme involving two types of parts neck based and limb based neck based parts arise from narrowings in shape or the local minima in distance between two points on the boundary while limb based parts arise from a pair of negative curvature minima which have co circular tangents in this paper we present computational support for the limb based and neck based parts by showing that they are invariant robust stable and yield a hierarchy of parts examples illustrate that the resulting decompositions are robust in the presence of occlusion and clutter for a range of man made and natural objects and lead to natural and intuitive parts which can be used for recognition

tangent bundle elastica and computer vision visual curve completion an early visual process that completes the occluded parts between observed boundary fragments a k a inducers is a major problem in perceptual organization and a critical step toward higher level visual tasks in both biological and machine vision most computational contributions to solving this problem suggest desired perceptual properties that the completed contour should satisfy in the image plane and then seek the mathematical curves that provide them alternatively few studies including by the authors have suggested to frame the problem not in the image plane but rather in the unit tangent bundler 2 s 1 the space that abstracts the primary visual cortex where curve completion allegedly occurs combining both schools here we propose and develop a biologically plausible theory of elastica in the tangent bundle that provides not only perceptually superior completion results but also a rigorous computational prediction that inducer curvatures greatly affects the shape of the completed curve as indeed indicated by human perception

bias due to missing exposure data using complete case analysis in the proportional hazards regression model we studied bias due to missing exposure data in the proportional hazards regression model when using complete case analysis cca eleven missing data scenarios were considered one with missing completely at random mcar four missing at random mar and six non ignorable missingness scenarios with a variety of hazard ratios censoring fractions missingness fractions and sample sizes when missingness was mcar or dependent only on the exposure there was negligible bias 2 3 per cent that was similar to the difference between the estimate in the full data set with no missing data and the true parameter in contrast substantial bias occurred when missingness was dependent on outcome or both outcome and exposure for models with hazard ratio of 3 5 a sample size of 400 20 per cent censoring and 40 per cent missing data the relative bias for the hazard ratio ranged between 7 per cent and 64 per cent we observed important differences in the direction and magnitude of biases under the various missing data mechanisms for example in scenarios where missingness was associated with longer or shorter follow up the biases were notably different although both mechanisms are mar the hazard ratio was underestimated with larger bias when missingness was associated with longer follow up and overestimated with smaller bias when associated with shorter follow up if it is known that missingness is associated with a less frequently observed outcome or with both the outcome and exposure cca may result in an invalid inference and other methods for handling missing data should be considered

structure preserving parallel algorithms for solving the bethe salpeter eigenvalue problem abstract the bethe salpeter eigenvalue problem is a dense structured eigenvalue problem arising from discretized bethe salpeter equation in the context of computing exciton energies and states a computational challenge is that at least half of the eigenvalues and the associated eigenvectors are desired in practice we establish the equivalence between bethe salpeter eigenvalue problems and real hamiltonian eigenvalue problems based on theoretical analysis structure preserving algorithms for a class of bethe salpeter eigenvalue problems are proposed we also show that for this class of problems all eigenvalues obtained from the tamm dancoff approximation are overestimated in order to solve large scale problems of practical interest we discuss parallel implementations of our algorithms targeting distributed memory systems several numerical examples are presented to demonstrate the efficiency and accuracy of our algorithms

the perceptual organization of texture flow a contextual inference approach locally parallel dense patterns sometimes called texture flows define a perceptually coherent structure of particular significance to perceptual organization we argue that with applications ranging from image segmentation and edge classification to shading analysis and shape interpretation texture flows deserve attention equal to edge segment grouping and curve completion this paper develops the notion of texture flow from a geometrical point of view to argue that local measurements of such structures must incorporate two curvatures we show how basic theoretical considerations lead to a unique model for the local behavior of the flow and to a notion of texture flow good continuation this in turn translates to a specification of consistency constraints between nearby flow measurements which we use for the computation of globally piecewise coherent structure through the contextual framework of relaxation labeling we demonstrate the results on synthetic and natural images

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

completion energies and scale the detection of smooth curves in images and their completion over gaps are two important problems in perceptual grouping we examine the notion of completion energy of curve elements showing and exploiting its intrinsic dependence on length and width scales we introduce a fast method for computing the most likely completion between two elements by developing novel analytic approximations and a fast numerical procedure for computing the curve of least energy we then use our newly developed energies to find the most likely completions in images through a generalized summation of induction fields this is done through multiscale procedures i e separate processing at different scales with some interscale interactions such procedures allow the summation of all induction fields to be done in a total of only o n log n operations where n is the number of pixels in the image more important such procedures yield a more realistic dependence of the induction field on the length and width scales the field of a long element is very different from the sum of the fields of its composing short segments

proportional hazards regression with missing covariates abstract nonparametric maximum likelihood npml is used to estimate regression parameters in a proportional hazards regression model with missing covariates the npml estimator is shown to be consistent and asymptotically normally distributed under some conditions em type algorithms are applied to solve the maximization problem variance estimates of the regression parameters are obtained by a profile likelihood approach that uses em aided numerical differentiation simulation results indicate that the npml estimates of the regression parameters are more efficient than the approximate partial likelihood estimates and estimates from complete case analysis when missing covariates are missing completely at random and that the proposed method corrects for bias when the missing covariates are missing at random

likelihood based methods for missing covariates in the cox proportional hazards model problems associated with missing covariate data are well known but often ignored we present a method for estimating the parameters in the cox proportional hazards model when the missing data are missing at random mar and censoring is noninformative due to the computational burden of this method we introduce an approximation that allows us to use a weighted expectation maximization em algorithm to estimate the parameters more easily when the missing covariates are continuous rather than categorical we implement a monte carlo version of the em algorithm along with the gibbs sampler to obtain parameter estimates we also give the asymptotic distribution of these estimates the primary advantage of this method over complete case analysis is that it produces more efficient parameter estimates and corrects for bias in the mar setting to motivate the methodology we present an analysis of a phase iii melanoma clinical trial conducted by the eastern cooperative oncology group

stochastic completion fields a neural model of illusory contour shape and salience we describe an algorithm and representation level theory of illusory contour shape and salience unlike previous theories our model is derived from a single assumption that the prior probability distribution of boundary completion shape can be modeled by a random walk in a lattice whose points are positions and orientations in the image plane i e the space that one can reasonably assume is represented by neurons of the mammalian visual cortex our model does not employ numerical relaxation or other explicit minimization but instead relies on the fact that the probability that a particle following a random walk will pass through a given position and orientation on a path joining two boundary fragments can be computed directly as the product of two vector field convolutions we show that for the random walk we define the maximum likelihood paths are curves of least energy that is on average random walks follow paths commonly assumed to model the shape of illusory contours a computer model is demonstrated on numerous illusory contour stimuli from the literature

trace inference curvature consistency and curve detection an approach is described for curve inference that is based on curvature information the inference procedure is divided into two stages a trace inference stage which is the subject of the present work and a curve synthesis stage it is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time and that tangent and curvature information are sufficient these make it possible to specify powerful constraints between estimated tangents to a curve in terms of a neighborhood relationship called cocircularity and between curvature estimates in terms of a curvature consistency relation because all curve information is quantized special care must be taken to obtain accurate estimates of trace points tangents and curvatures this issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint the procedure is applied to two types of images artificial images designed to evaluate curvature and noise sensitivity and natural images

a sort jacobi algorithm for semisimple lie algebras the classical jacobi algorithm is extended to an unified lie algebraic approach the conventional jacobi algorithm minimize the distance to diagonality they reduce the off norm i e the sum of squares of off diagonal entries sorting the diagonal elements after each step would accelerate the convergence but there are difficulties to apply this sorting to the off norm that has to minimize using the gradient flow of a trace function it r w brockett dynamical systems that sort lists diagonalize matrices and solve linear programming problems linear algebra appl 146 79 91 1991 zbl 0719 90045 as a more appropriate distance measure matrices can be diagonalized and the eigenvalues can be simultaneously sorted in this paper the sort jacobi algorithm is extended to a large class of structured matrices besides the semisimple lie algebra cases such as e g the symmetric hermitian and skew symmetric eigenvalue problem and the real and complex singular value decomposition par the local quadratic convergence of the sort jacobi method is proved for the regular case but not for the case in which the eigenvalues or singular values occur in clusters for these more complicated irregular problem a future publication is announced par the results are illustrated considering the lie algebra of derivations of the complex octonions

a case cohort design for epidemiologic cohort studies and disease prevention trials summary suppose that a cohort of individuals is to be followed in order to relate failure rates to preceding covariate histories a design is proposed which involves covariate data only for cases experiencing failure and for members of a randomly selected subcohort odds ratio and relative risk estimation procedures are presented for such a case cohort design a small simulation study compares case cohort relative risk estimation procedures to full cohort and synthetic case control analyses relevance to epidemiologic cohort studies and disease prevention trials is discussed

the design and use of steerable filters the authors present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters allowing one to adaptively steer a filter to any orientation and to determine analytically the filter output as a function of orientation steerable filters may be designed in quadrature pairs to allow adaptive control over phase as well as orientation the authors show how to design and steer the filters and present examples of their use in the analysis of orientation and phase angularly adaptive filtering edge detection and shape from shading one can also build a self similar steerable pyramid representation the same concepts can be generalized to the design of 3 d steerable filters

the elastic ratio introducing curvature into ratio based globally optimal image segmentation in this paper we present the first globally optimal ratio based image segmentation method allowing to impose curvature regularity of the region boundary the proposed method is fully unsupervised and compares favorably to other such approaches to identify the optimal foreground region in the image the algorithm minimizes the ratio of flux over a weighted sum of length and curvature regularity of the region boundary the key concept is to find cycles in a product graph where each node corresponds to a pair of image locations furthermore our results allow to draw conclusions about certain global optima of a reformulated snakes functional which is independent of parameterization the proposed algorithm allows to find parameter sets where the modified snakes functional has a meaningful solution and simultaneously provides the corresponding global solution

regression with missing x s a review abstract the literature of regression analysis with missing values of the independent variables is reviewed six classes of procedures are distinguished complete case analysis available case methods least squares on imputed data maximum likelihood bayesian methods and multiple imputation methods are compared and illustrated when missing data are confined to one independent variable and extensions to more general patterns are indicated attention is paid to the performance of methods when the missing data are not missing completely at random least squares methods that fill in missing x s using only data on the x s are contrasted with likelihood based methods that use data on the x s and y the latter approach is preferred and provides methods for elaboration of the basic normal linear regression model it is suggested that more widely distributed software is needed that advances beyond complete case analysis available case analysis and naive imputation methods bayesian simulation methods and mu

visual extrapolation of contour geometry computing the shapes of object boundaries from fragmentary image contours poses a formidable problem for the visual system we investigated the extrapolation of contour shape by human vision measurements of extrapolation position and orientation were taken at six distances from the point of occlusion thereby yielding a detailed representation of the extrapolated contours analyses of these measurements revealed that i extrapolation curvature increases linearly with the curvature of the inducing contour although there is individual bias in the slope ii the precision with which an extrapolated contour is represented is roughly constant in angular terms with increasing distance from the point of occlusion iii there is a substantial cost of curvature in that the overall precision of an extrapolated contour decreases systematically with curvature iv the shapes of visually extrapolated contours are characterized by a nonlinear decrease in curvature asymptoting to zero and v this decaying pattern of curvature is explained by a bayesian model in which with increasing distance from the point of occlusion the prior tendency to minimize curvature gradually dominates the likelihood tendency to minimize variation in curvature

contour inferences for image understanding we present a new approach to the algorithmic study of planar curves with applications to estimations of contours in images we construct spaces of curves satisfying constraints suited to specific problems exploit their geometric structure to quantify properties of contours and solve optimization and inference problems applications include new algorithms for computing planar elasticae with enhanced performance and speed and geometric algorithms for the estimation of contours of partially occluded objects in images

the elastic ratio introducing curvature into ratio based image segmentation we present the first ratio based image segmentation method that allows imposing curvature regularity of the region boundary our approach is a generalization of the ratio framework pioneered by jermyn and ishikawa so as to allow penalty functions that take into account the local curvature of the curve the key idea is to cast the segmentation problem as one of finding cyclic paths of minimal ratio in a graph where each graph node represents a line segment among ratios whose discrete counterparts can be globally minimized with our approach we focus in particular on the elastic ratio 0l c i c s c s ds vl c 0l c c s qds that depends given an image i on the oriented boundary c of the segmented region candidate minimizing this ratio amounts to finding a curve neither small nor too curvy through which the brightness flux is maximal we prove the existence of minimizers for this criterion among continuous curves with mild regularity assumptions we also prove that the discrete minimizers provided by our graph based algorithm converge as the resolution increases to continuous minimizers in contrast to most existing segmentation methods with computable and meaningful i e nondegenerate global optima the proposed approach is fully unsupervised in the sense that it does not require any kind of user input such as seed nodes numerical experiments demonstrate that curvature regularity allows substantial improvement of the quality of segmentations furthermore our results allow drawing conclusions about global optima of a parameterization independent version of the snakes functional the proposed algorithm allows determining parameter values where the functional has a meaningful solution and simultaneously provides the corresponding global solution

a symplectic qr like algorithm for the solution of the real algebraic riccati equation a method is presented to solve the real algebraic riccati equation xnx xa a t x k 0 where k k t and n n t the solution for the corresponding eigenvalue problem mx lambda x where m is a hamiltonian matrix is computed by an algorithm similar to the qr algorithm special symplectic matrices are used for the transformation of m such that the hamiltonian form is preserved during the computations

perceptual grouping by selection of a logically minimal model this paper presents a logic based approach to grouping and perceptual organization called minimal model theory and presents efficient methods for computing interpretations in this framework grouping interpretations are first defined as logical structures built out of atomic qualitative scene descriptors regularities that are derived from considerations of non accidentalness these interpretations can then be partially ordered by their degree of regularity or constraint measured numerically by their logical depth the genericity constraint the principle that interpretations should minimize coincidences in the observed configuration dictates that the preferred interpretation will be the minimum in this partial order i e the interpretation with maximum depth this maximum depth interpretation also called the minimal model or minimal interpretation is in a sense the simplest algebraically minimal interpretation available of the image configuration as a side effect the most salient or most structured part of the scene can be identified as the maximum depth subtree of the minimal model an efficient o n2 method for computing the minimal interpretation is presented along with examples computational experiments show that the algorithm performs well under a wide range of parameter settings

a comparison of measures for detecting natural shapes in cluttered backgrounds we propose a new measure of perceptual saliency and quantitatively compare its ability to detect natural shapes in cluttered backgrounds to five previously proposed measures as defined in the new measure the saliency of an edge is the fraction of closed random walks which contain that edge the transition probability matrix defining the random walk between edges is based on a distribution of natural shapes modeled by a stochastic motion each of the saliency measures in our comparison is a function of a set of affinity values assigned to pairs of edges although the authors of each measure define the affinity between a pair of edges somewhat differently all incorporate the gestalt principles of good continuation and proximity in some form in order to make the comparison meaningful we use a single definition of affinity and focus instead on the performance of the different functions for combining affinity values the primary performance criterion is accuracy we compute false positive rates in classifying edges as signal or noise for a large set of test figures in almost every case the new measure significantly outperforms previous measures

euler spiral for shape completion in this paper we address the curve completion problem e g the geometric continuation of boundaries of objects which are temporarily interrupted by occlusion also known as the gap completion or shape completion problem this problem is a significant element of perceptual grouping of edge elements and has been approached by using cubic splines or biarcs which minimize total curvature squared elastica as motivated by a physical analogy our approach is motivated by railroad design methods of the early 1900 s which connect two rail segments by transition curves and by the work of knuth on mathematical typography we propose that in using an energy minimizing solution completion curves should not penalize curvature as in elastica but curvature variation the minimization of total curvature variation leads to an euler spiral solution a curve whose curvature varies linearly with arclength the construction of this curve from a pair of points and tangents at these points is reduced to a nonlinear system of equations involving fresnel integrals whose solution relies on optimization from a suitable initial condition constrained to satisfy given boundary conditions since the choice of an appropriate initial curve is critical in this optimization we analytically derive an optimal solution in the class of biarc curves which is then used as the initial curve the resulting interpolations yield intuitive interpolation across gaps and occlusions and are extensible in contrast to scale invariant elastica in addition euler spiral segments can be used in other applications of curve completions e g modeling boundary segments between curvature extrema or skeletal branch geometry

a symplectic acceleration method for the solution of the algebraic riccati equation on a parallel computer abstract we give a cubic acceleration method for improving the current symplectic jacobi like algorithm for computing the hamiltonian schur decomposition of a hamiltonian matrix and finding the positive semidefinite solution of the riccati equation the acceleration method can speed up the rate of convergence at the end of the symplectic jacobi like process when the norm of the current strictly j lower triangle has become sufficiently small it has high parallelism and takes o n computational time when implemented on a mesh connected n n array processor system a quantitative analysis of convergence and numerical comparisons of one jacobi sweep versus one correction step are presented

fitting cox s proportional hazards models from survey data summary the proportional hazards model makes a number of assumptions which may not always be completely satisfied however fitting such models can have both descriptive and analytical value we discuss the implications of the survey design for large scale studies we propose a weighted estimator and derive a design based estimator for the variance of the estimated parameters the derivation requires using methods not previously used in the context of analysis of survey data we conduct a small simulation study comparing the proposed method with others in the literature

a bayesian multiple hypothesis approach to edge grouping and contour segmentation a contour segmentation algorithm is presented that takes an edge map and extracts continuous curves of arbitrary smoothness correctly handling curve intersections and capable of extrapolating over significant measurement gaps the algorithm incorporates noise models of the edge detection process and limited scene statistics it is based on an explicit contour model and employs a statistical distance measure to quantify the likelihood of each segmentation hypothesis a bayesian multiple hypothesis tree organizes possible segementations making it possible to postpone grouping decisions until a sufficient amount of information is available we have demonstrated its performance on real and synthetic images

a schur decomposition for hamiltonian matrices abstract a schur type decomposition for hamiltonian matrices is given that relies on unitary symplectic similarity transformations these transformations preserve the hamiltonian structure and are numerically stable making them ideal for analysis and computation using this decomposition and a special singular value decomposition for unitary symplectic matrices a canonical reduction of the algebraic riccati equation is obtained which sheds light on the sensitivity of the nonnegative definite solution after presenting some real decompositions for real hamiltonian matrices we look into the possibility of an orthogonal symplectic version of the qr algorithm suitable for hamiltonian matrices a finite step initial reduction to a hessenberg type canonical form is presented however no extension of the francis implicit shift technique was found and reasons for the difficulty are given

steerable wedge filters for local orientation analysis steerable filters have been used to analyze local orientation patterns in imagery such filters are typically based on directional derivatives whose symmetry produces orientation responses that are periodic with period spl pi independent of image structure we present a more general set of steerable filters that alleviate this problem

stereo processing by semiglobal matching and mutual information this paper describes the semiglobal matching sgm stereo method it uses a pixelwise mutual information ml based matching cost for compensating radiometric differences of input images pixelwise matching is supported by a smoothness constraint that is usually expressed as a global cost function sgm performs a fast approximation by pathwise optimizations from all directions the discussion also addresses occlusion detection subpixel refinement and multibaseline matching additionally postprocessing steps for removing outliers recovering from specific problems of structured environments and the interpolation of gaps are presented finally strategies for processing almost arbitrarily large images and fusion of disparity images using orthographic projection are proposed a comparison on standard stereo images shows that sgm is among the currently top ranked algorithms and is best if subpixel accuracy is considered the complexity is linear to the number of pixels and disparity range which results in a runtime of just 1 2 seconds on typical test images an in depth evaluation of the ml based matching cost demonstrates a tolerance against a wide range of radiometric transformations finally examples of reconstructions from huge aerial frame and pushbroom images demonstrate that the presented ideas are working well on practical problems

estimating equations with incomplete categorical covariates in the cox model incomplete covariate data is a common occurrence in many studies in which the outcome is survival time when a full likelihood is specified a useful technique for obtaining parameter estimates is the em algorithm we propose a set of estimating equations to estimate the parameters of cox s proportional hazards model when some covariate values are missing these estimating equations can be solved by an algorithm similar to the em algorithm because of the computational burden of finding a solution to these estimating equations we propose obtaining parameter estimates via monte carlo methods asymptotic variances of the parameter estimates are also derived we present a clinical trials example with three covariates two of which have some missing values

interpolation of two dimensional curves with euler spirals we propose an algorithm for the interpolation of two dimensional curves using euler spirals the method uses a lower order reconstruction to approximate solution derivatives at each sample point the computed tangents are then used to connect consecutive points with segments of euler spirals the resulting interpolation is g 1 in regions where the curve being interpolated is smooth the algorithm uses an adaptive stencil which allows it to construct an approximation free of oscillations near discontinuities in the function or its derivatives the approximation is based on geometrical shapes which makes it particularly suitable for two dimensional curves

matrix factorizations for symplectic qr like methods abstract symplectic qr like methods use symplectic or unitary symplectic similarity transformations instead of the usual unitary similarity transformations in the qr process a fundamental problem for the development of such methods is the choice of a suitable type of decomposition a sr corresponding to the qr decomposition where s is symplectic or unitary symplectic decompositions of this type are studied with regard to their application in a qr like process

sketches with curvature the curve indicator random field and markov processes while complaints about typical edge operators are common proposals articulating a notion of the perfect edge map are comparatively rare hindering the improvement of contour enhancement techniques to address this situation we suggest that one objective of visual contour computation is the estimation of a clean sketch from a corrupted rendition the latter modeling noisy and low contrast edge or line operator responses to an image our formal model of this clean sketch is the curve indicator random field cirf whose role is to provide a basis for defining edge likelihood models by eliminating the parameter along each curve to create an image of curves for curves modeled with stationary markov processes this ideal edge prior is non gaussian and its moment generating functional has a form closely related to the feynman kac formula this sketch model leads to a nonlinear minimum mean squared error contour enhancement filter that requires the solution of two elliptic partial differential equations the framework is also independent of the order of the contour model allowing us to introduce a markov process model for contour curvature we analyze the distribution of such curves and show that its mode is the euler spiral a curve minimizing changes in curvature example computations using the contour enhancement filter with the curvature based contour model are provided highlighting how the filter is curvature selective even when curvature is absent in the input

hamilton and jacobi come full circle jacobi algorithms for structured hamiltonian eigenproblems we develop jacobi algorithms for solving the complete eigenproblem for hamiltonian and skew hamiltonian matrices that are also symmetric or skew symmetric based on the direct solution of 4 4 and in one case 8 8 subproblems these structure preserving algorithms produce symplectic orthogonal bases for the invariant subspaces associated with a matrix in any one of the four classes under consideration the key step in the construction of the algorithms is a quaternion characterization of the 4 4 symplectic orthogonal group and the subspaces of 4 4 hamiltonian skew hamiltonian symmetric and skew symmetric matrices in addition to preserving structure these algorithms are inherently parallelizable numerically stable and show asymptotic quadratic convergence

on using the cox proportional hazards model with missing covariates summary we propose two methods for handling missing covariates in using the cox proportional hazards model the maximum partial likelihood estimator based only on study subjects having complete covariates does not utilise all available information also it is biased when the probability of missingness depends on the failure or censoring time our suggestion is to impute the conditional expectation of the statistic involving missing covariates given the available information the proposed method provides a consistent regression parameter estimator when the probability of missingness depends on the failure or censoring time as well as on the observed covariates also the proposed estimator is more efficient than the estimator suggested previously by lin ying 1993 when data are missing completely at random

potentials valleys and dynamic global coverings we present a new approach to effect the transition between local and global representations it is based on the notion of a covering or a collection of objects whose union is equivalent to the full one the mathematics of computing global coverings are developed in the context of curve detection where an intermediate representation the tangent field provides a reliable local description of curve structure this local information is put together globally in the form of a potential distribution the elements of the covering are then short curves each of which evolves in parallel to seek the valleys of the potential distribution the initial curve positions are also derived from the tangent field and their evolution is governed by variational principles when stationary configurations are achieved the global dynamic covering is defined by the union of the local dynamic curves

stochastic differential equations and geometric flows in previous years curve evolution applied to a single contour or to the level sets of an image via partial differential equations has emerged as an important tool in image processing and computer vision curve evolution techniques have been utilized in problems such as image smoothing segmentation and shape analysis we give a local stochastic interpretation of the basic curve smoothing equation the so called geometric heat equation and show that this evolution amounts to a tangential diffusion movement of the particles along the contour moreover assuming that a priori information about the shapes of objects in an image is known we present modifications of the geometric heat equation designed to preserve certain features in these shapes while removing noise we also show how these new flows may be applied to smooth noisy curves without destroying their larger scale features in contrast to the original geometric heat flow which tends to circularize any closed curve

a two point g1 hermite interpolating family of spirals a one parameter family of spirals that can match planar two point g 1 hermite data is presented these spirals can be used as an alternative to the biarc which is also a one parameter family of curves that can match two point g 1 hermite data some suggestions on choosing the free parameter of the family of spirals is given it is shown that there is a unique g 1 hermite interpolating spiral that passes through a given point in an allowable region three examples of the use of these spirals are given curve completion with spirals design with spirals and approximation of the clothoid by spirals

a jacobi like method for solving algebraic riccati equations on parallel computers an algorithm to solve continuous time algebraic riccati equations through the hamiltonian schur form is developed it is an adaption for hamiltonian matrices of an asymmetric jacobi method of eberlein 1987 it uses unitary symplectic similarity transformations and preserves the hamiltonian structure of the matrix each iteration step needs only local information about the current matrix thus admitting efficient parallel implementations on certain parallel architectures convergence performance of the algorithm is compared with the hamiltonian jacobi algorithm of byers 1990 the numerical experiments suggest that the method presented here converges considerably faster for non hermitian hamiltonian matrices than byers hamiltonian jacobi algorithm besides that numerical experiments suggest that for the method presented here the number of iterations needed for convergence can be predicted by a simple function of the matrix size

inferring global perceptual contours from local features we address the problem of contour inference from partial data as obtained from state of the art edge detectors we argue that in order to obtain more pereeptually salient contours it is necessary to impose generic constraints such as continuity and co curvilinearity the implementation is in the form of a convolution with a mask which encodes both the orientation and the strength of the possible continuations we first show how the mask called the extension field is derived then how the contributions from different sites are collected to produce a saliency map we show that the scheme can handle a variety of input data from dot patterns to oriented edgels in a unified manner and demonstrate results on a variety of input stimuli we also present a similar approach to the problem of inferring contours formed by end points in both cases the scheme is non linear non iterative and unified in the sense that all types of input tokens are handled in the same manner

log linear analysis of censored survival data with partially observed covariates abstract log linear models provide a flexible means of extending life table techniques for the analysis of censored survival data with categorical covariates as discussed by holford 1980 and laird and olivier 1981 we extend this methodology to incorporate cases in which one or more of the categorical covariates are sometimes missing maximum likelihood estimates of the parameters are calculated using data from all cases this can result in large gains in efficiency over standard methods that require the exclusion of cases with incomplete data with this approach we assume that the hazard function conditional on the covariates is a stepwise function over disjoint intervals of time the model has two parts a log linear model describing the hazard parameters and a multinomial model describing the probabilities in the contingency table defined by the covariates the main interest is in the model for the hazard parameters we show how to calculate maximum likelihood estimates of parameters of the mo

general geometric good continuation from taylor to laplace via level sets good continuation is the gestalt observation that parts often group in particular ways to form coherent wholes perceptual integration of edges for example involves orientation good continuation a property which has been exploited computationally very extensively but more general local global relationships such as for shading or color have been elusive while taylor s theorem suggests certain modeling and smoothness criteria the consideration of level set geometry indicates a different approach using such first principles we derive for the first time a generalization of good continuation to all those visual structures that can be abstracted as scalar functions over the image plane based on second order differential constraints that reflect good continuation our analysis leads to a unique class of harmonic models and a cooperative algorithm for structure inference among the different applications of good continuation here we apply these results to the denoising of shading and intensity distributions and demonstrate how our approach eliminates spurious measurements while preserving both singularities and regular structure a property that facilitates higher level processes which depend so critically on both of these classes of visual structures

incomplete data in generalized linear models abstract this article examines incomplete data for the class of generalized linear models in which incompleteness is due to partially missing covariates on some observations under the assumption that the missing data are missing at random it is shown that the e step of the em algorithm for any generalized linear model can be expressed as a weighted complete data log likelihood when the unobserved covariates are assumed to come from a discrete distribution with finite range expressing the e step in this manner allows for a straightforward maximization in the m step thus leading to maximum likelihood estimates mle s for the parameters asymptotic variances of the mle s are also derived and results are illustrated with two examples

sledge sequential labeling of image edges for boundary detection our goal is to detect boundaries of objects or surfaces occurring in an arbitrary image we present a new approach that discovers boundaries by sequential labeling of a given set of image edges a visited edge is labeled as on or off a boundary based on the edge s photometric and geometric properties and evidence of its perceptual grouping with already identified boundaries we use both local gestalt cues e g proximity and good continuation and the global helmholtz principle of non accidental grouping a new formulation of the helmholtz principle is specified as the entropy of a layout of image edges for boundary discovery we formulate a new policy iteration algorithm called sledge training of sledge is iterative in each training image sledge labels a sequence of edges which induces loss with respect to the ground truth these sequences are then used as training examples for learning sledge in the next iteration such that the total loss is minimized for extracting image edges that are input to sledge we use our new low level detector it finds salient pixel sequences that separate distinct textures within the image on the benchmark berkeley segmentation datasets 300 and 500 our approach proves robust and effective we outperform the state of the art both in recall and precision for different input sets of image edges

a tangent bundle theory for visual curve completion visual curve completion is a fundamental perceptual mechanism that completes the missing parts e g due to occlusion between observed contour fragments previous research into the shape of completed curves has generally followed an axiomatic approach where desired perceptual geometrical properties are first defined as axioms followed by mathematical investigation into curves that satisfy them however determining psychophysically such desired properties is difficult and researchers still debate what they should be in the first place instead here we exploit the observation that curve completion is an early visual process to formalize the problem in the unit tangent bundle r2 s1 which abstracts the primary visual cortex v1 and facilitates exploration of basic principles from which perceptual properties are later derived rather than imposed exploring here the elementary principle of least action in v1 we show how the problem becomes one of finding minimum length admissible curves in r2 s1 we formalize the problem in variational terms we analyze it theoretically and we formulate practical algorithms for the reconstruction of these completed curves we then explore their induced visual properties vis a vis popular perceptual axioms and show how our theory predicts many perceptual properties reported in the corresponding perceptual literature finally we demonstrate a variety of curve completions and report comparisons to psychophysical data and other completion models

3d stochastic completion fields for mapping connectivity in diffusion mri the 2d stochastic completion field algorithm introduced by williams and jacobs 1 2 uses a directional random walk to model the prior probability of completion curves in the plane this construct has had a powerful impact in computer vision where it has been used to compute the shapes of likely completion curves between edge fragments in visual imagery motivated by these developments we extend the algorithm to 3d using a spherical harmonics basis to achieve a rotation invariant computational solution to the fokker planck equation describing the evolution of the probability density function underlying the model this provides a principled way to compute 3d completion patterns and to derive connectivity measures for orientation data in 3d as arises in 3d tracking motion capture and medical imaging we demonstrate the utility of the approach for the particular case of diffusion magnetic resonance imaging where we derive connectivity maps for synthetic data on a physical phantom and on an in vivo high angular resolution diffusion image of a human brain

salient closed boundary extraction with ratio contour we present ratio contour a novel graph based method for extracting salient closed boundaries from noisy images this method operates on a set of boundary fragments that are produced by edge detection boundary extraction identifies a subset of these fragments and connects them sequentially to form a closed boundary with the largest saliency we encode the gestalt laws of proximity and continuity in a novel boundary saliency measure based on the relative gap length and average curvature when connecting fragments to form a closed boundary this new measure attempts to remove a possible bias toward short boundaries we present a polynomial time algorithm for finding the most salient closed boundary we also present supplementary preprocessing steps that facilitate the application of ratio contour to real images we compare ratio contour to two closely related methods for extracting closed boundaries elder and zucker s method based on the shortest path algorithm and williams and thornber s method based on spectral analysis and a strongly connected components algorithm this comparison involves both theoretic analysis and experimental evaluation on both synthesized data and real images

tangent bundle curve completion with locally connected parallel networks we propose a theory for cortical representation and computation of visually completed curves that are generated by the visual system to fill in missing visual information e g due to occlusions recent computational theories and physiological evidence suggest that although such curves do not correspond to explicit image evidence along their length their construction emerges from corresponding activation patterns of orientation selective cells in the primary visual cortex previous theoretical work modeled these patterns as least energetic 3d curves in the mathematical continuous space which abstracts the mammalian striate cortex here we discuss the biological plausibility of this theory and present a neural architecture that implements it with locally connected parallel networks part of this contribution is also a first attempt to bridge the physiological literature on curve completion with the shape problem and a shape theory we present completion simulations of our model in natural and synthetic scenes and discuss various observations and predictions that emerge from this theory in the context of curve completion

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

indicator and stratification methods for missing explanatory variables in multiple linear regression abstract the statistical literature and folklore contain many methods for handling missing explanatory variable data in multiple linear regression one such approach is to incorporate into the regression model an indicator variable for whether an explanatory variable is observed another approach is to stratify the model based on the range of values for an explanatory variable with a separate stratum for those individuals in which the explanatory variable is missing for a least squares regression analysis using either of these two missing data approaches the exact biases of the estimators for the regression coefficients and the residual variance are derived and reported the complete case analysis in which individuals with any missing data are omitted is also investigated theoretically and is found to be free of bias in many situations though often wasteful of information a numerical evaluation of the bias of two missing indicator methods and the complete case analysis is reported the missing indi

g1 interpolation with a single cornu spiral segment cornu spiral segments are used in applications such as the geometric design of highways and railways robot path planning and shape completion for some applications e g shape completion in computer vision it is important to use a single visually pleasing curve segment to smoothly fill a gap even though the gap may not be filled in a curvature continuous manner an improved method for doing so using a cornu spiral segment is discussed the method is generally suitable for any application where it is required to smoothly fit a curve between two given points when the corresponding tangent directions but not the curvatures are also given or known

cox regression with incomplete covariate measurements abstract this article provides a general solution to the problem of missing covariate data under the cox regression model the estimating function for the vector of regression parameters is an approximation to the partial likelihood score function with full covariate measurements and reduces to the pseudolikelihood score function of self and prentice in the special setting of case cohort designs the resulting parameter estimator is consistent and asymptotically normal with a covariance matrix for which a simple and consistent estimator is provided extensive simulation studies show that the large sample approximations are adequate for practical use the proposed approach tends to be more efficient than the complete case analysis especially for large cohorts with infrequent failures for case cohort designs the new methodology offers a variance covariance estimator that is much easier to calculate than the existing ones and allows multiple subcohort augmentations to improve efficiency real data taken f