on the isometric composition operators on the bloch space in cn abstract let be a holomorphic self map of a bounded homogeneous domain d in c n in this work we show that the composition operator c f f is bounded on the bloch space b of the domain and provide estimates on its operator norm we also give a sufficient condition for to induce an isometry on b this condition allows us to construct non trivial examples of isometric composition operators in the case when d has the unit disk as a factor we then obtain some necessary conditions for c to be an isometry on b when d is a cartan classical domain finally we give the complete description of the spectrum of the isometric composition operators in the case of the unit disk and for a wide class of symbols on the polydisk

model choice and influential cases for survival studies summary deletion diagnostics are developed for identifying observations that influence the estimates of regression parameters and the mixture parameter in the families of relative risk functions for failure time data the diagnostic for the regression parameters is a generalization of cain and lange s 1984 biometrics40 493 499 measure of individual influence the generalizations of martingale residuals schoenfeld s partial residuals 1982 biometrika69 239 241 and score residuals by therneau grambsch and fleming 1990 biometrika77 147 160 are also obtained the influence of some observations on regression parameters can be drastically modified as the mixture parameter changes even for a very small change in addition adding or deleting some observations might result in choosing different models the diagnostics are applied to a family proposed by guerrero and johnson 1982 biometrika69 309 314 one illustrative example is presented

l_ 1 norm low rank matrix decomposition by neural networks and mollifiers the l 1 norm cost function of the low rank approximation of the matrix with missing entries is not smooth and also cannot be transformed into a standard linear or quadratic programming problem and thus the optimization of this cost function is still not well solved to tackle this problem first a mollifier is used to smooth the cost function high closeness of the smoothed function to the original one can be obtained by tuning the parameters contained in the mollifier next a recurrent neural network is proposed to optimize the mollified function which will converge to a local minimum in addition to boost the speed of the system the mollifying process is implemented by a filtering procedure the influence of two mollifier parameters is theoretically analyzed and experimentally confirmed showing that one of the parameters is critical to computational efficiency and accuracy while the other not a large number of experiments on synthetic data show that the proposed method is competitive to the state of the art methods in particular the experiments on large matrices and a real application in the structure from motion indicate that the memory requirement of the proposed algorithm is mild making it suitable for real applications that often involve large scale matrix decomposition

a paraperspective factorization method for shape and motion recovery the factorization method first developed by tomasi and kanade 1992 recovers both the shape of an object and its motion from a sequence of images using many images and tracking many feature points to obtain highly redundant feature position information the method robustly processes the feature trajectory information using singular value decomposition svd taking advantage of the linear algebraic properties of orthographic projection however an orthographic formulation limits the range of motions the method can accommodate paraperspective projection first introduced by ohta et al 1981 is a projection model that closely approximates perspective projection by modeling several effects not modeled under orthographic projection while retaining linear algebraic properties our paraperspective factorization method can be applied to a much wider range of motion scenarios including image sequences containing motion toward the camera and aerial image sequences of terrain taken from a low altitude airplane

toward dynamic image mosaic generation with robustness to parallax mosaicing is largely dependent on the quality of registration among the constituent input images parallax and object motion present challenges to image registration leading to artifacts in the result to reduce the impact of these artifacts traditional image mosaicing approaches often impose planar scene constraints or rely on purely rotational camera motion or dense sampling however these requirements are often impractical or fail to address the needs of all applications instead taking advantage of depth cues and a smooth transition criterion we achieve significantly improved mosaicing results for static scenes coping effectively with nontrivial parallax in the input we extend this approach to the synthesis of dynamic video mosaics incorporating foreground background segmentation and a consistent motion perception criterion although further additions are required to cope with unconstrained object motion our algorithm can synthesize a perceptually convincing output conveying the same appearance of motion as seen in the input sequences

rank 1 weighted factorization for 3d structure recovery algorithms and performance analysis the paper describes the rank 1 weighted factorization solution to the structure from motion problem this method recovers the 3d structure from the factorization of a data matrix that is rank 1 rather than rank 3 this matrix collects the estimates of the 2d motions of a set of feature points of the rigid object these estimates are weighted by the inverse of the estimates error standard deviation so that the 2d motion estimates for sharper features which are usually well estimated are given more weight while the noisier motion estimates for smoother features are weighted less we analyze the performance of the rank 1 weighted factorization algorithm to determine what are the most suitable 3d shapes or the best 3d motions to recover the 3d structure of a rigid object from the 2d motions of the features our approach is developed for the orthographic camera model it avoids expensive singular value decompositions by using the power method and is suitable to handle dense sets of feature points and long video sequences experimental studies with synthetic and real data illustrate the good performance of our approach

a multibody factorization method for independently moving objects the structure from motion problem has been extensively studied in the field of computer vision yet the bulk of the existing work assumes that the scene contains only a single moving object the more realistic case where an unknown number of objects move in the scene has received little attention especially for its theoretical treatment in this paper we present a new method for separating and recovering the motion and shape of multiple independently moving objects in a sequence of images the method does not require prior knowledge of the number of objects nor is dependent on any grouping of features into an object at the image level for this purpose we introduce a mathematical construct of object shapes called the shape interaction matrix which is invariant to both the object motions and the selection of coordinate systems this invariant structure is computable solely from the observed trajectories of image features without grouping them into individual objects once the matrix is computed it allows for segmenting features into objects by the process of transforming it into a canonical form as well as recovering the shape and motion of each object the theory works under a broad set of projection models scaled orthography paraperspective and affine but they must be linear so it excludes projective cameras

singular value decomposition eigenfaces and 3d reconstructions singular value decomposition svd is one of the most important and useful factoriza tions in linear algebra we describe how svd is applied to problems involving image processing in particular how svd aids the calculation of so called eigenfaces which pro vide an efficient representation of facial images in face recognition although the eigenface technique was developed for ordinary grayscale images the technique is not limited to these images imagine an image where the different shades of gray convey the physical three dimensional structure of a face although the eigenface technique can again be applied the problem is finding the three dimensional image in the first place we therefore also show how svd can be used to reconstruct three dimensional objects from a two dimensional video stream

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

epipolar plane image analysis an approach to determining structure from motion we present a technique for building a three dimensional description of a static scene from a dense sequence of images these images are taken in such rapid succession that they form a solid block of data in which the temporal continuity from image to image is approximately equal to the spatial continuity in an individual image the technique utilizes knowledge of the camera motion to form and analyze slices of this solid these slices directly encode not only the three dimensional positions of objects but also such spatiotemporal events as the occlusion of one object by another for straight line camera motions these slices have a simple linear structure that makes them easier to analyze the analysis computes the three dimensional positions of object features marks occlusion boundaries on the objects and builds a three dimensional map of free space in our article we first describe the application of this technique to a simple camera motion and then show how projective duality is used to extend the analysis to a wider class of camera motions and object types that include curved and moving objects

an analysis of linear subspace approaches for computer vision and pattern recognition linear subspace analysis lsa has become rather ubiquitous in a wide range of problems arising in pattern recognition and computer vision the essence of these approaches is that certain structures are intrinsically or approximately low dimensional for example the factorization approach to the problem of structure from motion sfm and principal component analysis pca based approach to face recognition in lsa the singular value decomposition svd is usually the basic mathematical tool however analysis of the performance in the presence of noise has been lacking we present such an analysis here first the denoising capacity of the svd is analysed specifically given a rank r matrix corrupted by noise how much noise remains in the rank r projected version of that corrupted matrix second we study the learning capacity of the lsa based recognition system in a noise corrupted environment specifically lsa systems that attempt to capture a data class as belonging to a rank r column space will be affected by noise in both the training samples measurement noise will mean the learning samples will not produce the true subspace and the test sample which will also have measurement noise on top of the ideal clean sample belonging to the true subspace these results should help one to predict aspects of performance and to design more optimal systems in computer vision particularly in tasks such as sfm and face recognition our analysis agrees with certain observed phenomenon and these observations together with our simulations verify the correctness of our theory

analysis of multi type recurrent events in longitudinal studies application to a skin cancer prevention trial we consider the statistical modeling and analysis of replicated multi type point process data with covariates such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types the underlying processes are modeled as nonhomogeneous mixed poisson processes with random subject and fixed covariate effects the method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients score tests and likelihood ratio statistics are used for covariate selection a graphical test of goodness of fit of the selected model is based on generalized residuals measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed an application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer

a sequential factorization method for recovering shape and motion from image streams we present a sequential factorization method for recovering the three dimensional shape of an object and the motion of the camera from a sequence of images using tracked features the factorization method originally proposed by tomasi and kanade 1992 produces robust and accurate results incorporating the singular value decomposition however it is still difficult to apply the method to real time applications since it is based on a batch type operation and the cost of the singular value decomposition is large we develop the factorization method into a sequential method by regarding the feature positions as a vector time series the new method produces estimates of shape and motion at each frame the singular value decomposition is replaced with an updating computation of only three dominant eigenvectors which can be performed in o p sup 2 time while the complete singular value decomposition requires o fp sup 2 operations for an f spl times p matrix also the method is able to handle infinite sequences since it does not store any increasingly large matrices experiments using synthetic and real images illustrate that the method has nearly the same accuracy and robustness as the original method

comparison of case deletion diagnostic methods for cox regression case deletion diagnostics are a routine component of regression analysis since they identify unusual observations that substantially affect parameter estimates the exact approach is to compute the change in each regression parameter by dropping that individual and refitting the model repeating a cox regression for the removal of each individual is very time consuming and therefore not done in practice the two methods commonly used to approximate the exact case deletion change for cox regression are the empirical influence function approach and the covariate vector augmentation approach this paper reports the results of a simulation study on how well these methods estimate the exact change in a parameter estimate when deleting a known outlier or a known non outlier additionally we investigate how well these methods correctly identify outliers and non outliers the covariate augmentation approach clearly outperformed the influence function approach in these simulations

approximate case influence for the proportional hazards regression model with censored data a method is presented for approximating the influence of individual cases upon regression coefficient estimates obtained from the cox proportional hazards model observations can thus be identified which may greatly influence statistical inferences regarding the effects of prognostic factors upon survival time an example from a cancer clinical trial is given

quasi perspective projection model theory and application to structure and motion factorization from uncalibrated image sequences this paper addresses the problem of factorization based 3d reconstruction from uncalibrated image sequences previous studies on structure and motion factorization are either based on simplified affine assumption or general perspective projection the affine approximation is widely adopted due to its simplicity whereas the extension to perspective model suffers from recovering projective depths to fill the gap between simplicity of affine and accuracy of perspective model we propose a quasi perspective projection model for structure and motion recovery of rigid and nonrigid objects based on factorization framework the novelty and contribution of this paper are as follows firstly under the assumption that the camera is far away from the object with small lateral rotations we prove that the imaging process can be modeled by quasi perspective projection which is more accurate than affine model from both geometrical error analysis and experimental studies secondly we apply the model to establish a framework of rigid and nonrigid factorization under quasi perspective assumption finally we propose an extended cholesky decomposition to recover the rotation part of the euclidean upgrading matrix we also prove that the last column of the upgrading matrix corresponds to a global scale and translation of the camera thus may be set freely the proposed method is validated and evaluated extensively on synthetic and real image sequences and improved results over existing schemes are observed

uniqueness and estimation of three dimensional motion parameters of rigid objects with curved surfaces two main results are established in this paper first we show that seven point correspondences are sufficient to uniquely determine from two perspective views the three dimensional motion parameters within a scale factor for the translations of a rigid object with curved surfaces the seven points should not be traversed by two planes with one plane containing the origin nor by a cone containing the origin second a set of essential parameters are introduced which uniquely determine the motion parameters up to a scale factor for the translations and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points the actual motion parameters can subsequently be determined by computing the singular value decomposition svd of a 3 3 matrix containing the essential parameters

compact differences of composition operators abstract a characterization of compact difference is given for composition operators acting on the standard weighted bergman spaces and necessary conditions are given on a larger scale of weighted dirichlet spaces conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts the additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component

maximum weighted partial likelihood estimators for the cox model new estimators for cox regression that maximize a weighted version of the partial likelihood are considered their asymptotic properties on the model are sketched estimators with bounded influence curves are identified and shown to have good asymptotic relative efficiency the results of a small simulation study are included the estimators are applied to a well known data set the possible influence of an outlying observation on the cox estimator can be of any magnitude individuals who survive longest have a high potential of being influential in analogy with weighted linear rank tests we introduce estimators of the regression coefficients that maximize a weighted partial likelihood for instance by using weights proportional to the number at risk one obtains a wilcoxon type estimator this estimator has bounded influence provided the covariate space is compact and in a wide variety of situations its asymptotic relative efficiency is at least as good as that of the wilcoxon test asymptotic prop

influence functions for iteratively defined statistics summary hampel s influence function and its finite sample counterparts are the basis for a number of diagnostic statistics these diagnostics can be expensive to compute in the natural way when the estimation calculations are iterative as they frequently are when maximum likelihood or robust methods are used we show how the influence function can be calculated in these situations by implicit differentiation of the fixed point equation satisfied by the limit of the iterative procesb we consider in particular the cases of newton s method and iteratively reweighted least squares where interesting analytic results are available as an application we consider the generalization of pregibon s 1981 logistic regression diagnostics to cover generalized linear models with noncanonical link functions such as probit regression

depth estimation of face images using the nonlinear least squares model in this paper we propose an efficient algorithm to reconstruct the 3d structure of a human face from one or more of its 2d images with different poses in our algorithm the nonlinear least squares model is first employed to estimate the depth values of facial feature points and the pose of the 2d face image concerned by means of the similarity transform furthermore different optimization schemes are presented with regard to the accuracy levels and the training time required our algorithm also embeds the symmetrical property of the human face into the optimization procedure in order to alleviate the sensitivities arising from changes in pose in addition the regularization term based on linear correlation is added in the objective function to improve the estimation accuracy of the 3d structure further a model integration method is proposed to improve the depth estimation accuracy when multiple nonfrontal view face images are available experimental results on the 2d and 3d databases demonstrate the feasibility and efficiency of the proposed methods

nonparametric estimates of standard error the jackknife the bootstrap and other methods summary we discuss several nonparametric methods for attaching a standard error to a point estimate the jackknife the bootstrap half sampling subsampling balanced repeated replications the infinitesimal jackknife influence function techniques and the delta method the last three methods are shown to be identical all the methods derive from the same basic idea which is also the idea underlying the common parametric methods extended numerical comparisons are made for the special case of the correlation coefficient

compact composition operators on the bloch space necessary and sufficient conditions are given for a composition operator cof f o q to be compact on the bloch space w and on the little bloch space o weakly compact composition operators on o are shown to be compact if q e o is a conformal mapping of the unit disk d into itself whose image q d approaches the unit circle t only in a finite number of nontangential cusps then co is compact on 7o on the other hand if there is a point of t n q d at which q d does not have a cusp then co is not compact

difference of composition operators between different hardy spaces abstract some estimates for the norm and essential norm of the difference of two composition operators between different hardy spaces are given in this paper

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

on residual plots for relative risk regression summary martingale based residuals proposed for proportional hazards regression by barlow prentice 1988 are considered plots of such residuals against time are shown to exhibit systematic patterns which are not a priori predictable even when the model is appropriate for the plots to be fully useful therefore account needs to be taken of the expected pattern under the model a simple amendment is suggested

a diagnostic for cox regression and general conditional likelihoods abstract diagnostics for changes in the maximum likelihood estimate of due to deletion of single observations in linear and logistic regression models are equivalent to diagnostics obtained from fitting augmented regression models for the cox proportional hazards model and in conditional models for arbitrarily matched or stratified data diagnostics derived from augmented regression models are again useful and easy to compute these diagnostics are applicable to different formulations for the multiplicative covariable effects over time or over strata an exact or approximate treatment of tied failure times or multiple case matching and time dependent covariates

generalized composition operators on zygmund spaces and bloch type spaces the boundedness and compactness of the generalized composition operator on zygmund spaces and bloch type spaces are investigated in this paper

on a new integral type operator from the bloch space to bloch type spaces on the unit ball abstract we introduce the following integral type operator on the space h b of all holomorphic functions on the unit ball b c n p g f z 0 1 f t z g t z d t t z b where g h b g 0 0 and is a holomorphic self map of b the boundedness and compactness of the operator from the bloch space b or the little bloch space b 0 to the bloch type space b or the little bloch type space b 0 are characterized in the main results we calculate the essential norm of the operators p g b or b 0 b or b 0 in an elegant way

recovering the missing components in a large noisy low rank matrix application to sfm in computer vision it is common to require operations on matrices with missing data for example because of occlusion or tracking failures in the structure from motion sfm problem such a problem can be tackled allowing the recovery of the missing values if the matrix should be of low rank when noise free the filling in of missing values is known as imputation imputation can also be applied in the various subspace techniques for face and shape classification online recommender systems and a wide variety of other applications however iterative imputation can lead to the recovery of data that is seriously in error in this paper we provide a method to recover the most reliable imputation in terms of deciding when the inclusion of extra rows or columns containing significant numbers of missing entries is likely to lead to poor recovery of the missing parts although the proposed approach can be equally applied to a wide range of imputation methods this paper addresses only the sfm problem the performance of the proposed method is compared with jacobs and shum s methods for sfm

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

on an integral type operator from iterated logarithmic bloch spaces into bloch type spaces let h b denote the space of all holomorphic functions on the open unit ball b of c n let f f 1 f n be a holomorphic self map of b and email protected h b such that g 0 0 in this paper we study the boundedness and compactness of the following integral type operator recently introduced by xiangling zhu and the second authori f gf z email protected 0 1rf f tz g tz dtt email protected b from the iterated logarithmic bloch spaces into the bloch type spaces for the case when f z z we also obtain a sufficient and necessary condition for the boundedness of this operator from the iterated logarithmic bloch space into the little bloch type space

two view motion segmentation with model selection and outlier removal by ransac enhanced dirichlet process mixture models we propose a novel motion segmentation algorithm based on mixture of dirichlet process mdp models in contrast to previous approaches we consider motion segmentation and its model selection regarding to the number of motion models as an inseparable problem our algorithm can simultaneously infer the number of motion models estimate the cluster memberships of correspondences and identify the outliers the main idea is to use mdp models to fully exploit the geometric consistencies before making premature decisions about the number of motion models to handle outliers we incorporate ransac into the inference process of mdp models in the experiments we compare the proposed algorithm with naive ransac gpca and schindler s method on both synthetic data and real image data the experimental results show that we can handle more motions and have satisfactory performance in the presence of various levels of noise and outlier

visual perception of three dimensional motion as an observer moves and explores the environment the visual stimulation in his eye is constantly changing somehow he is able to perceive the spatial layout of the scene and to discern his movement through space computational vision researchers have been trying to solve this problem for a number of years with only limited success it is a difficult problem to solve because the relationship between the optical flow field the 3d motion parameters and depth is nonlinear we have come to understand that this nonlinear equation describing the optical flow field can be split by an exact algebraic manipulation to yield an equation that relates the image velocities to the translational component of the 3d motion alone thus the depth and the rotational velocity need not be known or estimated prior to solving for the translational velocity the algorithm applies to the general case of arbitrary motion with respect to an arbitrary scene it is simple to compute and it is plausible biologically

differences of generalized composition operators on the bloch space abstract the boundedness and compactness of the differences of two generalized composition operators on the bloch space in the unit disk are investigated in this paper

diagnostic plots in cox s regression model two diagnostic plots are presented for validating the fitting of a cox proportional hazards model the added variable plot is developed to assess the effect of adding a covariate to the model the constructed variable plot is applied to detect nonlinearity of a fitted covariate both plots are also useful for identifying influential observations on the issues of interest the methods are illustrated on examples of multiple myeloma and lung cancer data

residuals for relative risk regression summary several possible definitions of residuals are given for relative risk regression with time varying covariates each such residual has a representation as an estimator of a stochastic integral with respect to the martingale arising from a subject s failure time counting process previously proposed residuals for individual study subjects and for specific time points are shown to be special cases of this definition as are previously derived regression diagnostics an illustration and various generalizations are also given able methods are required to detect various departures from modelling assumptions suitably defined residuals may play an important role in such identification however the nonparametric aspect of the model the possibility that modelled regression variables may be varying with follow up time and most importantly the usual presence of right censorship implies that specialized residual definitions are required the class of residuals considered here is most easily formulated using counting process notation for the failure time data let ni t yi t and zi t represent respectively for the ith subject the values of counting censoring and covariate processes at follow up time t i 1 n while ni u yi u zi u 0c u t specifies the corresponding histories for the ith subject prior to time t thus in a typical univariate failure time application ni with right continuous sample paths will take value zero prior to the time of failure on the ith subject and value one thereafter while yi with left continuous sample paths will take value one at times at which the ith subject is at risk for an observed failure and value zero otherwise the counting process ni can be uniquely decomposed so that for all t i

joint cross range scaling and 3d geometry reconstruction of isar targets based on factorization method traditionally the factorization method is applied to reconstruct the 3d geometry of a target from its sequential inverse synthetic aperture radar images however this method requires performing cross range scaling to all the sub images and thus has a large computational burden to tackle this problem this paper proposes a novel method for joint cross range scaling and 3d geometry reconstruction of steadily moving targets in this method we model the equivalent rotational angular velocity rav by a linear polynomial with time and set its coefficients randomly to perform sub image cross range scaling then we generate the initial trajectory matrix of the scattering centers and solve the 3d geometry and projection vectors by the factorization method with relaxed constraints after that the coefficients of the polynomial are estimated from the projection vectors to obtain the rav finally the trajectory matrix is re scaled using the estimated rotational angle and accurate 3d geometry is reconstructed the two major steps i e the cross range scaling and the factorization are performed repeatedly to achieve precise 3d geometry reconstruction simulation results have proved the effectiveness and robustness of the proposed method

global measures of local influence for proportional hazards regression models cox proportional hazards regression models have been extended to multiple failure times and other situations by using a robust covariance matrix instead of the usual inverse of the information matrix we modify an existing measure of individual influence by substituting the robust covariance matrix for the inverse of the information matrix this provides a scalar measure of influence with known mean and bounded range on the interval 0 1 the measure is applicable to marginal multiple failure time models two examples are presented

learning intermediate level representations of form and motion from natural movies we present a model of intermediate level visual representation that is based on learning invariances from movies of the natural environment the model is composed of two stages of processing an early feature representation layer and a second layer in which invariances are explicitly represented invariances are learned as the result of factoring apart the temporally stable and dynamic components embedded in the early feature representation the structure contained in these components is made explicit in the activities of second layer units that capture invariances in both form and motion when trained on natural movies the first layer produces a factorization or separation of image content into a temporally persistent part representing local edge structure and a dynamic part representing local motion structure consistent with known response properties in early visual cortex area v1 this factorization linearizes statistical dependencies among the first layer units making them learnable by the second layer the second layer units are split into two populations according to the factorization in the first layer the form selective units receive their input from the temporally persistent part local edge structure and after training result in a diverse set of higher order shape features consisting of extended contours multiscale edges textures and texture boundaries the motion selective units receive their input from the dynamic part local motion structure and after training result in a representation of image translation over different spatial scales and directions in addition to more complex deformations these representations provide a rich description of dynamic natural images and testable hypotheses regarding intermediate level representation in visual cortex

deletion diagnostics for the generalised linear mixed model with independent random effects the generalised linear mixed model glmm is widely used for modelling environmental data however such data are prone to influential observations which can distort the estimated exposure response curve particularly in regions of high exposure deletion diagnostics for iterative estimation schemes commonly derive the deleted estimates based on a single iteration of the full system holding certain pivotal quantities such as the information matrix to be constant in this paper we present an approximate formula for the deleted estimates and cook s distance for the glmm which does not assume that the estimates of variance parameters are unaffected by deletion the procedure allows the user to calculate standardised dfbetas for mean as well as variance parameters in certain cases such as when using the glmm as a device for smoothing such residuals for the variance parameters are interesting in their own right in general the procedure leads to deleted estimates of mean parameters which are corrected for the effect of deletion on variance components as estimation of the two sets of parameters is interdependent the probabilistic behaviour of these residuals is investigated and a simulation based procedure suggested for their standardisation the method is used to identify influential individuals in an occupational cohort exposed to silica the results show that failure to conduct post model fitting diagnostics for variance components can lead to erroneous conclusions about the fitted curve and unstable confidence intervals

a diagnostic for cox regression with discrete failure time models summary changes in maximum likelihood parameter estimates due to deletion of individual observations are useful statistics both for regression diagnostics and for computing robust estimates of covariance for many likelihoods including those in the exponential family these delete one statistics can be approximated analytically from a one step newton raphson iteration on the full maximum likelihood solution but for general conditional likelihoods and the related cox partial likelihood the one step method does not reduce to an analytic solution for these likelihoods an alternative analytic approximation that relies on an appropriately augmented design matrix has been proposed in this paper we extend the augmentation approach to explicitly deal with discrete failure time models in these models an individual subject may contribute information at several time points thereby appearing in multiple risk sets before eventually experiencing a failure or being censored our extension also allows the covariates to be time dependent the new augmentation requires no additional computational resources while improving results

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

a diagnostic statistic for the score test abstract this article provides exact and approximate expressions for the change in the score test on deletion of observations deletions of individuals and of entire risk sets from matched case control and survival studies are discussed in detail a simple formula is derived which measures the contribution of individual strata to score tests based on combining several contingency tables the diagnostic is illustrated by application to the stanford heart transplant data

martingale based residuals for survival models summary graphical methods based on the analysis of residuals are considered for the setting of the highly used cox 1972 regression model and for the andersen gill 1982 generalization of that model we start with a class of martingale based residuals as proposed by barlow prentice 1988 these residuals and or their transforms are useful for investigating the functional form of a covariate the proportional hazards assumption the leverage of each subject upon the estimates of 13 and the lack of model fit to a given subject 1 1 model consider a set of n independent subjects such that the counting process ni ni t t o for the ith subject in the set indicates the number of observed events experienced over time t the sample paths of the ni are step functions with jumps of size 1 and with ni 0 0 we assume that the intensity function for ni t is given by yi t da t zi t yi t ep z t dao t 1 where yi t is a 0 1 process indicating whether the ith subject is a risk at time t 13 is a vector of regression coefficients zi t is a p dimensional vector of covariate processes and ao is the baseline cumulative hazard function several familar survival models fit into this framework the andersen gill 1982 generalization of the cox 1972 model arises when ao t is completely unspecified the further restriction that yi t 1 until the first event or censoring and is 0 thereafter yields the cox model the parametric form ao t t yields a poisson model or an exponential if restricted to a single event per subject and ao t tp a weibull model our attention will focus primarily on the andersen gill and cox models however the

rank constraints for homographies over two views revisiting the rank four constraint it is well known that one can collect the coefficients of five or more homographies between two views into a large rank deficient matrix in principle this implies that one can refine the accuracy of the estimates of the homography coefficients by exploiting the rank constraint however the standard rank projection approach is impractical for two different reasons it requires many homographies to even score a modest gain and secondly correlations between the errors in the coefficients will lead to poor estimates in this paper we study these problems and provide solutions to each firstly we show that the matrices of the homography coefficients can be recast into two parts each consistent with ranks of only one this immediately establishes the prospect of realistically that is with as few as only three or four homographies exploiting the redundancies of the homographies over two views we also tackle the remaining issue correlated coefficients we compare our approach with the gold standard that is non linear bundle adjustment initialized from the ground truth estimate the ideal initialization the results confirm our theory and show one can implement rank constrained projection and come close to the gold standard in effectiveness indeed our algorithm by itself or our algorithm further refined by a bundle adjustment stage may be a practical algorithm providing generally better results than the standard dlt direct linear transformation algorithm and even better than the bundle adjustment result with the dlt result as the starting point our unoptimized version has roughly the same cost as bundle adjustment and yet can generally produce close to the gold standard estimate as illustrated by comparison with bundle adjustment initialized from the ground truth independent of the merits or otherwise of our algorithm we have illuminated why the naive approach of direct rank projection is relatively doomed to failure moreover in revealing that there are further rank constraints not previously known we have added to the understanding of these issues and this may pave the way for further improvements

outlier correction from uncalibrated image sequence using the triangulation method we propose a robust algorithm for estimating the projective reconstruction from image features using the ransac based triangulation method in this method we select input points randomly separate the input points into inliers and outliers by computing their reprojection error and correct the outliers so that they can become inliers the reprojection error and correcting outliers are computed using the triangulation method after correcting the outliers we can reliably recover projective motion and structure using the projective factorization method experimental results showed that errors can be reduced significantly compared to the previous research as a result of robustly estimated projective reconstruction

topological structures of the sets of composition operators on the bloch spaces we study properties of the topological sets of composition operators on bloch and little bloch spaces in the operator topology

sequential karhunen loeve basis extraction and its application to images the karhunen loeve kl transform is an optimal method for approximating a set of vectors or images which was used in image processing and computer vision for several tasks such as face and object recognition its computational demands and its batch calculation nature have limited its application here we present a new sequential algorithm for calculating the kl basis which is faster in typical applications and is especially advantageous for image sequences the kl basis calculation is done with much lower delay and allows for dynamic updating of image databases systematic tests of the implemented algorithm show that these advantages are indeed obtained with the same accuracy available from batch kl algorithms

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

rigid body segmentation and shape description from dense optical flow under weak perspective we present an algorithm for identifying and tracking independently moving rigid objects from optical flow some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field while discontinuities do indicate a change in scene depth they do not in general signal a boundary between two separate objects the proposed method uses the fact that each independently moving object has a unique epipolar constraint associated with its motion thus motion discontinuities based on self occlusion can be distinguished from those due to separate objects the use of epipolar geometry allows for the determination of individual motion parameters for each object as well as the recovery of relative depth for each point on the object the algorithm assumes an affine camera where perspective effects are limited to changes in overall scale no camera calibration parameters are required a kalman filter based approach is used for tracking motion parameters with time

the generic bilinear calibration estimation problem we identify a very general recurring pattern in a number of well known problems in biological and machine vision many problems are of a peculiar double sided nature one attempts to estimate certain properties of the environment using a certain type of equipment and simultaneously one attempts to calibrate the same equipment on the structure of the environment at first sight this appears the kind of the chicken and the egg problem that might well prove to be insoluble however due to basic constraints that universally apply e g the world is only three dimensional a solution up to a certain class of ambiguity transformations often exists the more complicated the problem is the less important the remaining ambiguity will be at least in a relative sense many well known problems are special in that they can be cast in bilinear form sometimes after transformation or the introduction of dummy variables instances include photometric stereo photometric estimations e g of lightness local differential image operators a variety of photogrammetric problems etc it turns out that many of these problems and together these make up a large fraction of the generic problems in machine vision today can be cast in a simple universal framework this framework enables one to handle arbitrarily large that is not minimal consistent configurations noisy thus inconsistent date sets automatically the level at which prior information either of a deterministic or a statistical nature is used assumptions such as constant albedo rigidity uniform distributions etc is clearly separated as an additional typically nonlinear stage