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

transformations in regression a robust analysis we consider two approaches to robust estimation for the box cox power transformation model one approach maximizes weighted modified likelihoods a second approach bounds a measure of gross error sensitivity among our primary concerns is the performance of these estimators on actual data in examples that we study there seem to be only minor differences between these two robust estimators but they behave rather differently than the maximum likelihood estimator or estimators that bound only the influence of the residuals these examples show that model selection determination of the transformation parameter and outlier identification are fundamentally interconnected

algebras with separating almost cyclic coherent auslander reiten components we prove that the class of artin algebras whose auslander reiten quiver admits a separating family of almost cyclic coherent components coincides with the class of generalized multicoil enlargements of concealed canonical algebras moreover the module category homological properties and the representation type of artin algebras with separating families of almost cyclic coherent auslander reiten components are described

a new statistic for influence in linear regression since the seminal article by cook the usual way to measure the influence of an observation in a statistical model is to delete the observation from the sample and compute a convenient norm of the change in the parameters or in the vector of forecasts in this article we define a new way to measure the influence of an observation based on how this observation is being influenced by the rest of the data more precisely the new statistic we propose is defined as the squared norm of the vector of changes of the forecast of one observation when each of the sample points are deleted one by one we prove that this new statistic has asymptotically a normal distribution and is able to detect a group of high leverage similar outliers that will be undetected by cook s statistic we show in several examples that the proposed statistic is useful for detecting heterogeneity in regression models in large high dimensional datasets

simultaneous camera pose and correspondence estimation with motion coherence traditionally the camera pose recovery problem has been formulated as one of estimating the optimal camera pose given a set of point correspondences this critically depends on the accuracy of the point correspondences and would have problems in dealing with ambiguous features such as edge contours and high visual clutter joint estimation of camera pose and correspondence attempts to improve performance by explicitly acknowledging the chicken and egg nature of the pose and correspondence problem however such joint approaches for the two view problem are still few and even then they face problems when scenes contain largely edge cues with few corners due to the fact that epipolar geometry only provides a soft point to line constraint viewed from the perspective of point set registration the point matching process can be regarded as the registration of points while preserving their relative positions i e preserving scene coherence by demanding that the point set should be transformed coherently across views this framework leverages on higher level perceptual information such as the shape of the contour while thus potentially allowing registration of non unique edge points the registration framework in its traditional form is subject to substantial point localization error and is thus not suitable for estimating camera pose in this paper we introduce an algorithm which jointly estimates camera pose and correspondence within a point set registration framework based on motion coherence with the camera pose helping to localize the edge registration while the ambiguous edge information helps to guide camera pose computation the algorithm can compute camera pose over large displacements and by utilizing the non unique edge points can recover camera pose from what were previously regarded as feature impoverished sfm scenes our algorithm is also sufficiently flexible to incorporate high dimensional feature descriptors and works well on traditional sfm scenes with adequate numbers of unique corners

a robust hybrid method for nonrigid image registration a nonrigid registration method is proposed to automatically align two images by registering two sets of sparse features extracted from the images motivated by the paradigm of robust point matching rpm algorithms 1 2 which were originally proposed for shape registration we develop robust hybrid image matching rhim algorithm by alternatively optimizing feature correspondence and spatial transformation for image registration our rhim algorithm is built to be robust to feature extraction errors a novel dynamic outlier rejection approach is described for removing outliers and a local refinement technique is applied to correct non exactly matched correspondences arising from image noise and deformations experimental results demonstrate the robustness and accuracy of our method

module categories with infinite radical cube zero abstract let a be an artin algebra and let mod a denote the category of finitely generated right a modules we denote by rad mod a the ideal in mod a generated by all non invertible morphisms between indecomposable modules in mod a the infinite radical rad mod a of mod a is the intersection of all powers rad i mod a i 1 of rad mod a it is known that a is representation finite if and only if rad mod a 2 0 in this paper we study the representation infinite algebras a such that rad mod a 3 0 examples of such algebras include all representation infinite tilted algebras of euclidean type

detecting shocks outliers and breaks in time series abstract a single outlier in a regression model can be detected by the effect of its deletion on the residual sum of squares an equivalent procedure is the simple intervention in which an extra parameter is added for the mean of the observation in question similarly for unobserved components or structural time series models the effect of elaborations of the model on inferences can be investigated by the use of interventions involving a single parameter such as trend or level changes because such time series models contain more than one variance the effect of the intervention is measured by the change in individual variances we examine the effect on the estimated parameters of moving various kinds of intervention along the series the horrendous computational problems involved are overcome by the use of score statistics combined with recent developments in filtering and smoothing interpretation of the resulting time series plots of diagnostics is aided by simulation envelopes our procedures illustrated with four example permit keen insights into the fragility of inferences to specific shocks such as outliers and level breaks although the emphasis is mostly on parameter estimation forecast are also considered possible extensions include seasonal adjustment and detrending of series

on algebras of generalized standard semiregular type abstract we study the structure of artin algebras whose auslander reiten quiver consists of generalized standard semiregular components

diagnostics in linear discriminant analysis abstract some new diagnostic measures in discriminant analysis are proposed they can be expressed in terms of the two fundamental influence statistics in discriminant analysis d i 2 and i a theorem on the asymptotic distributions of the fundamental statistics is derived based on the theorem the proposed measures can be shown to be asymptotically distributed as functions of independent chi squared and standard normal random variables critical values and expected quantiles of the measures can then be constructed hence influential observations are detected using q q plots and significance tests two measures have analogous forms in regression the theorem is also useful for getting the asymptotic distributions of existing measures that are functions of d i 2 and i a comparison of the diagnostics in linear discriminant analysis linear regression and linear logistic regression discriminant analysis is made although discriminant coefficients can be determined under a regression model regress

using simulated envelopes in the evaluation of normal probability plots of regression residuals we investigate properties of a diagnostic envelope method for evaluating normal probability plots of regression residuals that was proposed by atkinson 1981 implemented by bmdp hardwick 1987 and extended to logistic regression by landwehr pregibon and shoemaker 1984 the envelope s stability properties and joint residual vector inclusion levels undocumented so far in the literature are explored here with several examples alternative resistant techniques for creating envelopes are considered interpretations that can be derived from these plots are discussed a resistant version of the envelopes shows good stability and good sensitivity to outlying residuals both full normal and half normal probability plots with this envelope method provide useful information to the analyst

probabilistic motion estimation based on temporal coherence we develop a theory for the temporal integration of visual motion motivated by psychophysical experiments the theory proposes that input data are temporally grouped and used to predict and estimate the motion flows in the image sequence this temporal grouping can be considered a generalization of the data association techniques that engineers use to study motion sequences our temporal grouping theory is expressed in terms of the bayesian generalization of standard kalman filtering to implement the theory we derive a parallel network that shares some properties of cortical networks computer simulations of this network demonstrate that our theory qualitatively accounts for psychophysical experiments on motion occlusion and motion outliers in deriving our theory we assumed spatial factorizability of the probability distributions and made the approximation of updating the marginal distributions of velocity at each point this allowed us to perform local computations and simplified our implementation we argue that these approximations are suitable for the stimuli we are considering for which spatial coherence effects are negligible

scaling theorems for zero crossings we characterize some properties of the zero crossings of the laplacian of signals in particular images filtered with linear filters as a function of the scale of the filter extending recent work by witkin 16 we prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the gaussian this result can be generalized to apply to level crossings of any linear differential operator it applies in particular to ridges and ravines in the image intensity in the case of the second derivative along the gradient there is no filter that avoids creation of zero crossings unless the filtering is performed after the derivative is applied

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

information theoretic shape matching in this paper we describe two related algorithms that provide both rigid and non rigid point set registration with different computational complexity and accuracy the first algorithm utilizes a nonlinear similarity measure known as correntropy the measure combines second and high order moments in its decision statistic showing improvements especially in the presence of impulsive noise the algorithm assumes that the correspondence between the point sets is known which is determined with the surprise metric the second algorithm mitigates the need to establish a correspondence by representing the point sets as probability density functions pdf the registration problem is then treated as a distribution alignment the method utilizes the cauchy schwarz divergence to measure the similarity distance between the point sets and recover the spatial transformation function needed to register them both algorithms utilize information theoretic descriptors however correntropy works at the realizations level whereas cauchy schwarz divergence works at the pdf level this allows correntropy to be less computationally expensive and for correct correspondence more accurate the two algorithms are robust against noise and outliers and perform well under varying levels of distortion they outperform several well known and state of the art methods for point set registration

unmasking outliers and leverage points a confirmation abstract identification of multiple outliers and leverage points is difficult because of the masking effect recently rousseeuw and van zomeren suggested using high breakdown robust estimation methods the least median of squares and minimum volume ellipsoid for unmasking these observations these methods tend to declare too many observations as extreme however a stepwise analysis is proposed here for confirmation of outliers and leverage points detected using the robust methods diagnostic measures are constructed for observations added back to the reduced sample they are shown graphically the complementary use of robust and diagnostic methods gives satisfactory results in analyzing two data sets one data set consists often bad and four good leverage points four or 10 using a different cutoff extreme observations of the other data set of size 28 are identified using the robust methods but the stepwise analysis confirms only one the limitations of atkinson s confirmatory approach are discusse

diagnostic tests for transformations the evidence for transformation of the response in a regression model may sometimes depend crucially on one or a few observations expressions are derived for estimating the effect of deletion of observations on both the score test and the estimate of the transformation parameter the estimates are presented as index plots which are as easy to calculate as the wellknown added variable plots of constructed variables one advantage of the new procedure is that the importance of individual observations is not masked by the presence of leverage a second is that the plots refer directly to score statistics and parameter estimates both quantities of prime inferential importance examples are given for the power transformation and for the shifted power transformation with unknown origin

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 simultaneous approximations by radial basis function neural networks it is shown in this paper by a constructive method that any multivariate function and all its existing derivatives can be simultaneously approximated by a radial basis function rbf neural network where the assumptions on the rbfs are relatively mild by considering the translations of rbfs it is proved that an o m 1 2 order of simultaneous approximations to a certain class of functions can be achieved by using a translation network with just m neurons

robust point matching via vector field consensus in this paper we propose an efficient algorithm called vector field consensus for establishing robust point correspondences between two sets of points our algorithm starts by creating a set of putative correspondences which can contain a very large number of false correspondences or outliers in addition to a limited number of true correspondences inliers next we solve for correspondence by interpolating a vector field between the two point sets which involves estimating a consensus of inlier points whose matching follows a nonparametric geometrical constraint we formulate this a maximum a posteriori map estimation of a bayesian model with hidden latent variables indicating whether matches in the putative set are outliers or inliers we impose nonparametric geometrical constraints on the correspondence as a prior distribution using tikhonov regularizers in a reproducing kernel hilbert space map estimation is performed by the em algorithm which by also estimating the variance of the prior model initialized to a large value is able to obtain good estimates very quickly e g avoiding many of the local minima inherent in this formulation we illustrate this method on data sets in 2d and 3d and demonstrate that it is robust to a very large number of outliers even up to 90 we also show that in the special case where there is an underlying parametric geometrical model e g the epipolar line constraint that we obtain better results than standard alternatives like ransac if a large number of outliers are present this suggests a two stage strategy where we use our nonparametric model to reduce the size of the putative set and then apply a parametric variant of our approach to estimate the geometric parameters our algorithm is computationally efficient and we provide code for others to use it in addition our approach is general and can be applied to other problems such as learning with a badly corrupted training data set

concealed canonical algebras and separating tubular families we characterise those concealed canonical algebras which arise as endomorphism rings of tilting modules all of whose indecomposable summands have strictly positive rank as those artin algebras whose module categories have a separating exact subcategory that is a separating tubular family of standard tubes this paper develops further the technique of shift automorphisms which arises from the tubular structure it is related to the characterisation of hereditary noetherian categories with a tilting object as the categories of coherent sheaves on a weighted projective line

left ventricular motion reconstruction based on elastic vector splines in medical imaging it is common to reconstruct dense motion estimates from sparse measurements of that motion using some form of elastic spline thin plate spline snakes and other deformable models etc usually the elastic spline uses only bending energy second order smoothness constraint or stretching energy first order smoothness constraint or a combination of the two these elastic splines belong to a family of elastic vector splines called the laplacian splines this spline family is derived from an energy minimization functional which is composed of multiple order smoothness constraints these splines can be explicitly tuned to vary the smoothness of the solution according to the deformation in the modeled material tissue in this context it is natural to question which members of the family will reconstruct the motion more accurately the authors compare different members of this spline family to assess how well these splines reconstruct human cardiac motion they find that the commonly used splines containing first order and or second order smoothness terms only are not the most accurate for modeling human cardiac motion

assessing goodness of fit of parametric regression models for lifetime data graphical methods graphical methods are often used to check goodness of fit of models to data it is common to plot residuals against a reference distribution so that when the model fits the data the configuration should be close to a straight line since the resemblance to a straight line is often unclear it has been suggested to add simulated envelopes within which the configuration is expected to lie the implementation of this method for survival data analysis is not straightforward in this paper we point out the difficulties which arise in constructing envelopes on residual plots for randomly censored data methods are suggested to deal with the problems and evaluated they are illustrated by simulated data and on a follow up study of myeloma

diagnostics for heteroscedasticity in regression summary for the usual regression model without replication we provide a diagnostic test for heteroscedasticity based on the score statistic a graphical procedure to complement the score test is also presented some key u ords influence linear model residual score test diagnostic methods in linear regression are used to examine the appropriateness of assumptions underlying the modelling process and to locate unusual characteristics of the data that may influence conclusions the recent literature on diagnostics is dominated by studies of methods for the detection of influential observations cook weisberg 1982 provide a review diagnostics for the relevance of specific assumptions however have not received the same degree of attention even though these may be of equal importance our purpose here is to provide appropriate diagnostic techniques to aid in an assessment of the validity of the usual assumption of homoscedasticity when little or no replication is present available methods for studying this assumption include both graphical and nongraphical procedures the usual graphical procedure consists of plotting the ordinary least squares residuals against fitted values or an explanatory variable a megaphone shaped pattern is taken as evidence that the variance depends on the quantity plotted on tlle abscissa weisberg 1980 chapter 6 in 3 we suggest several ways in which this

robust l_ 2 e estimation of transformation for non rigid registration we introduce a new transformation estimation algorithm using the l 2 e estimator and apply it to non rigid registration for building robust sparse and dense correspondences in the sparse point case our method iteratively recovers the point correspondence and estimates the transformation between two point sets feature descriptors such as shape context are used to establish rough correspondence we then estimate the transformation using our robust algorithm this enables us to deal with the noise and outliers which arise in the correspondence step the transformation is specified in a functional space more specifically a reproducing kernel hilbert space in the dense point case for nonrigid image registration our approach consists of matching both sparsely and densely sampled sift features and it has particular advantages in handling significant scale changes and rotations the experimental results show that our approach greatly outperforms state of the art methods particularly when the data contains severe outliers

diagnostics for smoothing splines summary diagnostic measures appropriate for use with smoothing splines are derived and their properties are investigated the proposed measures focus on detection of observations which substantially influence the fit and provide additional information over that obtained from examination of residuals alone a numerical example illustrates the technique

the mean field theory in em procedures for blind markov random field image restoration a markov random field mrf model based em expectation maximization procedure for simultaneously estimating the degradation model and restoring the image is described the mrf is a coupled one which provides continuity inside regions of smooth gray tones and discontinuity at region boundaries constraints for the restoration problem which is in general ill posed the computational difficulty associated with the em procedure for mrfs is resolved by using the mean field theory from statistical mechanics an orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates experimental results on synthetic and real world images show that this approach provides good blur estimates and restored images the restored images are comparable to those obtained by a wiener filter in mean square error but are most visually pleasing

unmasking multivariate outliers and leverage points abstract detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers that is how the outliers get masked to avoid the masking effect we propose to compute distances based on very robust estimates of location and covariance these robust distances are better suited to expose the outliers in the case of regression data the classical least squares approach masks outliers in a similar way also here the outliers may be unmasked by using a highly robust regression method finally a new display is proposed in which the robust regression residuals are plotted versus the robust distances this plot classifies the data into regular observations vertical outliers good leverage points and bad leverage points several examples are discussed

gaussian field consensus a robust nonparametric matching method for outlier rejection abstract in this paper we propose a robust method called gaussian field consensus gfc for outlier rejection from given putative point set matching correspondences finding correct correspondences inliers is a key component in many computer vision and pattern recognition tasks and the goal of outlier mismatch rejection is to fit the transformation function that maps one feature point set to another our gfc starts by inputting a putative correspondence set which is contaminated by many outliers and the main task of our gfc is to identify the underlying true correspondences from outliers then we formulate this challenging problem by gaussian field nonparametric matching model which bases on the exponential distance loss and kernel method in a reproducing kernel hilbert space next we introduce a local linear constraint based on the regularization theory to preserve the topological structure of the feature points moreover the sparse approximation is used to reduce the search space in this way we can handle a large number of points easily finally we test the gfc method on several real image datasets in the presence of outliers where the experimental results show that our proposed method outperforms current state of the art methods in most test scenarios

point set registration coherent point drift point set registration is a key component in many computer vision tasks the goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other multiple factors including an unknown nonrigid spatial transformation large dimensionality of point set noise and outliers make the point set registration a challenging problem we introduce a probabilistic method called the coherent point drift cpd algorithm for both rigid and nonrigid point set registration we consider the alignment of two point sets as a probability density estimation problem we fit the gaussian mixture model gmm centroids representing the first point set to the data the second point set by maximizing the likelihood we force the gmm centroids to move coherently as a group to preserve the topological structure of the point sets in the rigid case we impose the coherence constraint by reparameterization of gmm centroid locations with rigid parameters and derive a closed form solution of the maximization step of the em algorithm in arbitrary dimensions in the nonrigid case we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation we also introduce a fast algorithm that reduces the method computation complexity to linear we test the cpd algorithm for both rigid and nonrigid transformations in the presence of noise outliers and missing points where cpd shows accurate results and outperforms current state of the art methods

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

a generalized extreme studentized residual multiple outlier detection procedure in linear regression this article is concerned with procedures for detecting multiple y outhers in linear regression a generalized extreme studentized residual gesr procedure which controls type i error rate is developed an approximate formula to calculate the percentiles is given for large samples and more accurate percentiles for n 25 are tabulated the performance of this procedure is compared with others by monte carlo techniques and found to be superior the procedure however fails in detecting y outliers that are on high leverage cases for this a two phase procedure is suggested in phase 1 a set of suspect observations is identified by gesr and one of the diagnostics applied sequentially in phase 2 a backward testing is conducted using the gesr procedure to see which of the suspect cases are outlicrs several examples are analyzed

two graphical displays for outlying and influential observations in regression summary the paper describes two procedures for detecting observations with outlying values either in the response variable or in the explanatory variables in multiple regression these procedures are presented as half normal plots with envelopes derived from simulation in order to avoid overinterpretation of the data analysis of a well known data set leads to the use of a data transformation a simple test for which is commended and to some comments on the relationship with robust regression the widespread availability of sophisticated computer software has made the fitting of multiple regression equations painless but the very ease of these procedures may cause insufficient care to be given to checking and scrutiny of the data transcription punching and data manipulation errors may lead to bad values both of the observations y and of the independent or explanatory variables x it is the purpose of the present paper to describe and exemplify two plots which provide checks against such bad values it is argued that these plots and a test for transformations should accompany any thorough regression analysis bad values of the response or outliers have long been detected by a variety of plots of residuals bad values of the explanatory variables are less easily detected even when they lead to an extreme point in the design space since the fitted equation will pass close to such an influential observation the residual may not be especially large even after allowance has been made for the small variance of the fitted value at such a point to detect such behaviour a quantity is needed which exhibits the dependence of the fitted model on each point or group of points discussions of such quantities are given by hoaglin welsch 1978 and more recently by belsley kuh welsch 1980 2 1 by cook weisberg 1980 and by pregibon 1981 the quantity used here is a modification of a statistic proposed by cook 1977 which is derived in 2 two half normal plots are presented in 3 as an aid to interpretation envelopes to the plots are generated by simulation examples of the plots are given in 4 both for simulated data and for the stack loss data given by brownlee 1965 p 454 transformations of this data set are discussed in 5 the paper concludes with some comments on the relationship with robust

a mathematical analysis of the motion coherence theory in motion perception there are a number of important phenomena involving coherence examples include motion capture and motion cooperativity we propose a theoretical model called the motion coherence theory that gives a possible explanation for these effects 1 2 in this framework the aperture problem can also be thought of as a problem of coherence and given a similar explanation we propose the concept of a velocity field defined everywhere in the image even where there is no explicit motion information available theough a cost function the model imposes smoothness on the velocity field in a more general way than in previous theories in this paper we provide a detailed theoretical analysis of the motion coherence theory we discuss its relations with previous theories and show that some of them are approximations to it a second paper 3 provides extensions for temporal coherence and comparisons to psychophysical phenomena the theory applies to both short range and long range motion it places them in the same computational framework and provides a way to define interactions between the two processes

location of several outliers in multiple regression data using elemental sets the outlying tendency of any case in a multiple regression of p predictors may be estimated by drawing all subsets of size p from the remaining cases and fitting the model each such subset yields an elemental residual for the case in question and a suitable summary statistic of them can be used as an estimate of the case s outlying tendency we propose two such summary statistics an unweighted median which is of bounded influence and a weighted median which is more efficient but less robust the computational load of the procedure is reduced by using random samples in place of the full set of subsets of size p as a byproduct the method yields useful information on the influence or leverage of cases and the mutual masking of high leverage points

computation and analysis of image motion a synopsis of current problems and methods the goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis and of the methods proposed exposing the underlying models and supporting assumptions a sufficient number of pointers to the literature will be given concentrating mostly on recent contributions emphasis will be on the detection measurement and segmentation of image motion tracking and deformable motion issues will be also addressed finally a number of related questions which could require more investigations will be presented

3 d kalman filter for image motion estimation this paper presents a new three dimensional 3 d markov model for motion vector fields the three dimensions consist of the two space dimensions plus a scale dimension we use a compound signal model to handle motion discontinuity in this 3 d markov random field mrf for motion estimation we use an extended kalman filter as a pel recursive estimator since a single observation can be sensitive to local image characteristics especially when the model is not accurate we employ windowed multiple observations at each pixel to increase accuracy these multiple observations employ different weighting values for each observation since the uncertainty in each observation is different finally we compare this 3 d model with earlier proposed one dimensional 1 d coarse to fine scale and two dimensional 2d spatial compound models in terms of motion estimation performance on a synthetic and a real image sequence

motion compensated compression of dynamic voxelized point clouds dynamic point clouds are a potential new frontier in visual communication systems a few articles have addressed the compression of point clouds but very few references exist on exploring temporal redundancies this paper presents a novel motion compensated approach to encoding dynamic voxelized point clouds at low bit rates a simple coder breaks the voxelized point cloud at each frame into blocks of voxels each block is either encoded in intra frame mode or is replaced by a motion compensated version of a block in the previous frame the decision is optimized in a rate distortion sense in this way both the geometry and the color are encoded with distortion allowing for reduced bit rates in loop filtering is employed to minimize compression artifacts caused by distortion in the geometry information simulations reveal that this simple motion compensated coder can efficiently extend the compression range of dynamic voxelized point clouds to rates below what intra frame coding alone can accommodate trading rate for geometry accuracy

robust point sets matching by fusing feature and spatial information using nonuniform gaussian mixture models most of the traditional methods that handle the point sets matching between two images are based on local feature descriptors and the succedent mismatch eliminating strategies which usually suffers from the sparsity of the initial match set because some correct ambiguous associations are easily filtered out by the ratio test of sift matching due to their second ranking in feature similarity in this paper we propose a nonuniform gaussian mixture model ngmm for point sets matching between a pair of images which combines feature with position information of the local feature points extracted from the image pair to achieve point sets matching in a gmm framework the proposed point set matching using an ngmm is able to change the correspondence assignments throughout the matching process and has the potential to match up even ambiguous matches correctly the proposed ngmm framework can be either used to directly find matches between two point sets obtained from two images or applied to remove outliers in a match set when finding matches ngmm tries to learn a nonrigid transformation between the two point sets and provide a probability for every found match to measure the reliability of the match then a probability threshold can be used to get the final robust match set when removing outliers ngmm requires that the vector field formed by the correct matches to be coherent and the matches contradicting the coherent vector field will be regarded as mismatches to be removed a number of comparison and evaluation experiments reveal the good performance of the proposed ngmm framework in both finding matches and discarding mismatches

robust point set registration using gaussian mixture models in this paper we present a unified framework for the rigid and nonrigid point set registration problem in the presence of significant amounts of noise and outliers the key idea of this registration framework is to represent the input point sets using gaussian mixture models then the problem of point set registration is reformulated as the problem of aligning two gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized we show that the popular iterative closest point icp method and several existing point set registration methods in the field are closely related and can be reinterpreted meaningfully in our general framework our instantiation of this general framework is based on the the l2 distance between two gaussian mixtures which has the closed form expression and in turn leads to a computationally efficient registration algorithm the resulting registration algorithm exhibits inherent statistical robustness has an intuitive interpretation and is simple to implement we also provide theoretical and experimental comparisons with other robust methods for point set registration

influence and a quadratic form in the andrews pregibon statistic a quadratic form found in the andrews pregibon ap statistic may be decomposed into two terms one of the terms has a simple geometric interpretation that relates naturally to the expression of influence found in cook s statistic the measure of influence derived from the quadratic form is easy to compute once the two factors of the ap statistic have been found this measure suggests a computing strategy for diagnostics and leads to an exact relation between the ap statistic and cook s statistic

diagnostic regression analysis and shifted power transformations diagnostic displays for outlying and influential observations are reviewed in some examples apparent outliers vanish after a power transformation of the data interpretation of the score statistic for transformations as regression on a constructed variable makes diagnostic methods available for detection of the influence of individual observations on the transformation methods for the power transformation are exemplified and extended to the power transformation after a shift in location for which there are two constructed variables the emphasis is on plots as diagnostic tools

a robust global and local mixture distance based non rigid point set registration we present a robust global and local mixture distance glmd based non rigid point set registration method which consists of an alternating two step process correspondence estimation and transformation updating we first define two distance features for measuring global and local structural differences between two point sets respectively the two distances are then combined to form a glmd based cost matrix which provides a flexible way to estimate correspondences by minimizing global or local structural differences using a linear assignment solution to improve the correspondence estimation and enhance the interaction between the two steps an annealing scheme is designed to gradually change the cost minimization from local to global and the thin plate spline transformation from rigid to non rigid during registration we test the performance of our method in contour registration sequence images and real images and compare with six state of the art methods where our method shows the best alignments in most scenarios highlightswe develop a multi feature based non rigid point set registration algorithm we define two distance based features a multi feature based cost matrix is designed for correspondence estimation we solve issues in the current iterative non rigid point set registration methods the performance of our method outperforms state of the art methods in this area

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

a characterization of cycle finite generalized double tilted algebras abstract we provide a new characterization of cycle finite generalized double tilted algebras by the existence of a faithful module which is the middle of at most finitely many short chains

learning with mixed hard soft pointwise constraints a learning paradigm is proposed and investigated in which the classical framework of learning from examples is enhanced by the introduction of hard pointwise constraints i e constraints imposed on a finite set of examples that cannot be violated such constraints arise e g when requiring coherent decisions of classifiers acting on different views of the same pattern the classical examples of supervised learning which can be violated at the cost of some penalization quantified by the choice of a suitable loss function play the role of soft pointwise constraints constrained variational calculus is exploited to derive a representer theorem that provides a description of the functional structure of the optimal solution to the proposed learning paradigm it is shown that such an optimal solution can be represented in terms of a set of support constraints which generalize the concept of support vectors and open the doors to a novel learning paradigm called support constraint machines the general theory is applied to derive the representation of the optimal solution to the problem of learning from hard linear pointwise constraints combined with soft pointwise constraints induced by supervised examples in some cases closed form optimal solutions are obtained

influence in principal components analysis summary in linear regression the theoretical influence function and the various sample versions of it have an established place as diagnostic tools these same functions are developed here to provide methods for the detection of influential observations in principal components analysis the perturbation theory of real symmetric matrices unifies this development some interesting points of contrast with the regression case are noted and explained theoretically

unmasking multivariate outliers and leverage points comment detecting outliers in a multivariate point cloud is not trivial especially when there are several outliers the classical identification method does not always find them because it is based on the sample mean and covariance matrix which are themselves affected by the outliers to avoid this masking effect we propose to compute distances based on very robust estimates of location and covariance in the case of regression data the outliers also may be unmasked by using a highly robust regression method a new display is proposed in which the robust regression residuals are plotted versus the robust distances

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

using recursive residuals calculated on adaptively ordered observations to identify outliers in linear regression a new procedure for identifying outliers or influential observations is proposed the procedure uses recursive residuals calculated on observations that have been ordered according to their studentized residuals values of cook s d or another regression diagnostic of the user s choice under the model these recursive residuals appropriately standardized have approximate student s t distributions thus convenient critical values are available for deciding which observations merit scrutiny and perhaps special treatment the power of the test procedure to identify one or more outliers is investigated through simulation and its dependence on the number and configuration of the outliers that is their placement with respect to the main body of the data explored the proposed procedure and two variations of it also based on these recursive residuals are compared with alternatives based on internally or externally studentized residuals the use of recursive residuals calculated on adaptively ordered observations increases power and helps to combat the masking of one outlier by another when multiple outliers are present in configurations that create masking