a note on the unification of the akaike information criterion to measure the distance between a robust function evaluated under the true regression model and under a fitted model we propose generalized kullback leibler information using this generalization we have developed three robust model selection criteria aicr aiccr and aiccr that allow the selection of candidate models that not only fit the majority of the data but also take into account non normally distributed errors the aicr and aiccr criteria can unify most existing akaike information criteria three examples of such unification are given simulation studies are presented to illustrate the relative performance of each criterion

tracking while zooming using affine transfer and multifocal tensors this paper presents algorithms for tracking unknown objects in the presence of zoom since prior models are unavailable point and line matches in affine views are used to characterize the structure and to transfer a fixation point into new images in a sequence because any affine projection matrix is permitted the intrinsic camera parameters such as focal length may change freely also since the techniques do not require long feature tracks a further desirable property is insensitivity to partial occlusion caused for instance by part of the object falling off the image plane while zooming in if only point matches are available a previous method based on factorization is applied when also incorporating lines the affine trifocal and quadrifocal tensors are used for tracking in monocular and stereo systems respectively methods for computing the tensors minimizing algebraic error are developed in comparison with their projective counterparts the affine tensors offer significant advantages in terms of computation time and convenience of parameterization and the relations between the different tensors are shown to be much simpler successful tracking is demonstrated on several real image sequences

algebraic varieties with quasi projective universal cover we prove that the universal cover of a normal projective variety x is quasi projective if and only if a finite etale cover of x is a fiber bundle over an abelian variety with simply connected fiber

multiple view geometry of general algebraic curves we introduce a number of new results in the context of multi view geometry from general algebraic curves we start with the recovery of camera geometry from matching curves we first show how one can compute without any knowledge on the camera the homography induced by a single planar curve then we continue with the derivation of the extended kruppa s equations which are responsible for describing the epipolar constraint of two projections of a general algebraic curve as part of the derivation of those constraints we address the issue of dimension analysis and as a result establish the minimal number of algebraic curves required for a solution of the epipolar geometry as a function of their degree and genus we then establish new results on the reconstruction of general algebraic curves from multiple views we address three different representations of curves i the regular point representation in which we show that the reconstruction from two views of a curve of degree d admits two solutions one of degree d and the other of degree d d 1 moreover using this representation we address the problem of homography recovery for planar curves ii dual space representation tangents for which we derive a lower bound for the number of views necessary for reconstruction as a function of the curve degree and genus and iii a new representation to computer vision based on the set of lines meeting the curve which does not require any curve fitting in image space for which we also derive lower bounds for the number of views necessary for reconstruction as a function of curve degree alone

using least squares and tobit in second stage dea efficiency analyses the paper examines second stage dea efficiency analyses within the context of a censoring data generating process dgp and a fractional data dgp when efficiency scores are treated as descriptive measures of the relative performance of units in the sample it is argued that the efficiency scores are not generated by a censoring process but are fractional data tobit estimation in this situation is inappropriate in contrast ordinary least squares is a consistent estimator and if white s white h 1980 a heteroskedastic consistent covariance matrix and a direct test for heteroskedasticity econometrica 48 817 838 heteroskedastic consistent standard errors are calculated large sample tests can be performed which are robust to heteroskedasticity and the distribution of the disturbances for a more refined analysis papke and wooldridge s papke l e wooldridge j m 1996 econometric methods for fractional response variables with an application to 401 k plan participation rates journal of applied econometrics 11 6 619 632 method has some advantages but is more complex and requires special programming

robust linear model selection based on least angle regression in this article we consider the problem of building a linear prediction model when the number of candidate predictors is large and the data possibly contain anomalies that are difficult to visualize and clean we want to predict the nonoutlying cases therefore we need a method that is simultaneously robust and scalable we consider the stepwise least angle regression lars algorithm which is computationally very efficient but sensitive to outliers we introduce two different approaches to robustify lars the plug in approach replaces the classical correlations in lars by robust correlation estimates the cleaning approach first transforms the data set by shrinking the outliers toward the bulk of the data which we call multivariate winsorization and then applies lars to the transformed data we show that the plug in approach is time efficient and scalable and that the bootstrap can be used to stabilize its results we recommend using bootstrapped robustified lars to sequence a number of candidate pred

structure from motion using line correspondences a theory is presented for the computation of three dimensional motion and structure from dynamic imagery using only line correspondences the traditional approach of corresponding microfeatures interesting points highlights corners high curvature points etc is reviewed and its shortcomings are discussed then a theory is presented that describes a closed form solution to the motion and structure determination problem from line correspondences in three views the theory is compared with previous ones that are based on nonlinear equations and iterative methods

global generation of pluricanonical and adjoint linear series on smooth projective threefolds the purpose of this paper is to show how the cohomological techniques developed by kawamata reid shokurov and others lead to some effective and practical results of reider type on freeness of linear series on smooth complex projective threefolds in recent years there has been a great deal of interest in the geometric properties of pluricanonical and adjoint linear systems on surfaces and higherdimensional varieties among other things one wants to understand as explicitly as possible when the systems in question are base point free or very ample modem work in this area goes back to kodaira kod and bombieri bmb who studied pluricanonical maps of surfaces of general type more recently many of their results have emerged as special cases of a celebrated theorem of reider rdr reider uses vector bundle techniques to show that if b is a nef line bundle on a surface x such that b2 5 then kx b is globally generated unless there exist certain special curves c c x such that b c 1 he also obtains analogous criteria for kx b to be very ample a cohomological approach to these theorems based on miyaoka s vanishing theorem for zariski decompositions was given by sakai sak2

seshadri constants and periods of polarized abelian varieties the purpose of this paper is to study the seshadri constants of abelian varieties consider a polarized abelian variety a l of dimension g over the field of complex numbers one can associate to a l a real number e a l its seshadri constant which in effect measures how much of the positivity of l can be concentrated at any given point of a the number e a l can be defined as the rate of growth in k of the number of jets that one can specify in the linear series oa kl alternatively one considers the blow up f x blx x x of x at a point x with exceptional divisor e x over x and defines e a l def sup e r f l ee is nef

large discrete sets in stein manifolds we construct infinite discrete subsets of stein manifolds with remarkable properties these generalize results of rosay and rudin on discrete subsets of mathbb c n

evidence based modelling of strategic fit an introduction to rcarbs this paper presents an important development of a novel non parametric object classification technique namely carbs classification and ranking belief simplex to enable regression type analyses termed rcarbs it is as with carbs an evidence based technique with its mathematical operations based on the dempster shafer theory of evidence its exposition is demonstrated here by modelling the strategic fit of a set of public organizations in addition to the consideration of the predictive fit of a series of models graphical exploration of the contribution of individual variables in the derived models is also undertaken when using rcarbs comparison analyses including through fivefold cross validation are carried out using multiple regression and neural networks models the findings highlight that rcarbs achieves parity of test set predictive fit with regression and better fit than neural networks the rcarbs technique can also enable researchers to explore non linear relationships contributions between variables in greater detail than either regression or neural networks models

variable selection for 1d regression models variable selection the search for j relevant predictor variables from a group of p candidates is a standard problem in regression analysis the class of 1d regression models is a broad class that includes generalized linear models we show that existing variable selection algorithms originally meant for multiple linear regression and based on ordinary least squares and mallows s cp can also be used for 1d models graphical aids for variable selection are also provided

robust model selection criteria for robust liu estimator in linear regression analysis outliers often have large influence in the model variable selection process the aim of this study is to select the subsets of independent variables which explain dependent variables in the presence of multicollinearity outliers and possible departures from the normality assumption of the error distribution in robust regression analysis in this study to overcome this combined problem of multicollinearity and outliers we suggest to use robust selection criterion with liu and liu type m lm estimators

the 3d line motion matrix and alignment of line reconstructions we study the problem of aligning two 3d line reconstructions in projective affine metric or euclidean space we introduce the 6 6 3d line motion matrix that acts on plucker coordinates we characterize its algebraic properties and its relation to the usual 4 4 point motion matrix and propose various methods for estimating 3d motion from line correspondences based on cost functions defined in images or 3d space we assess the quality of the different estimation methods using simulated data and real images

projective reconstruction and invariants from multiple images this correspondence investigates projective reconstruction of geometric configurations seen in two or more perspective views and the computation of projective invariants of these configurations from their images a basic tool in this investigation is the fundamental matrix that describes the epipolar correspondence between image pairs it is proven that once the epipolar geometry is known the configurations of many geometric structures for instance sets of points or lines are determined up to a collineation of projective 3 space spl pscrsup 3 by their projection in two independent images this theorem is the key to a method for the computation of invariants of the geometry invariants of six points in spl pscrsup 3 and of four lines in spl pscrsup 3 are defined and discussed an example with real images shows that they are effective in distinguishing different geometrical configurations since the fundamental matrix is a basic tool in the computation of these invariants new methods of computing the fundamental matrix from seven point correspondences in two images or six point correspondences in three images are given

sequential updating of projective and affine structure from motion a structure from motion algorithm is described which recovers structure and camera position modulo a projective ambiguity camera calibration is not required and camera parameters such as focal length can be altered freely during motion the structure is updated sequentially over an image sequence in contrast to schemes which employ a batch process a specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described together with a method to periodically update the affine coordinate frame to prevent drift over time we describe the constraint used to obtain this specialisation structure is recovered from image corners detected and matched automatically and reliably in real image sequences results are shown for reference objects and indoor environments and accuracy of recovered structure is fully evaluated and compared for a number of reconstruction schemes a specific application of the work is demonstrated affine structure is used to compute free space maps enabling navigation through unstructured environments and avoidance of obstacles the path planning involves only affine constructions

motion and structure from line correspondences closed form solution uniqueness and optimization this work discusses estimating motion and structure parameters from line correspondences of a rigid scene the authors present a closed form solution to motion and structure parameters from line correspondences through three monocular perspective views the algorithm makes use of redundancy in the data to improve the accuracy of the solutions the uniqueness of the solution is established and necessary and sufficient conditions for degenerate spatial line configurations are given optimization has been employed to further improve the accuracy of the estimates in the presence of noise simulations have shown that the errors of the optimized estimates are close to the theoretical lower error bound

lines and points in three views and the trifocal tensor this paper discusses the basic role of the trifocal tensor in scene reconstruction from three views this 3 times 3 times 3 tensor plays a role in the analysis of scenes from three views analogous to the role played by the fundamental matrix in the two view case in particular the trifocal tensor may be computed by a linear algorithm from a set of 13 line correspondences in three views it is further shown in this paper that the trifocal tensor is essentially identical to a set of coefficients introduced by shashua to effect point transfer in the three view case this observation means that the 13 line algorithm may be extended to allow for the computation of the trifocal tensor given any mixture of sufficiently many line and point correspondences from the trifocal tensor the camera matrices of the images may be computed and the scene may be reconstructed for unrelated uncalibrated cameras this reconstruction will be unique up to projectivity thus projective reconstruction of a set of lines and points may be carried out linearly from three views

a numerical criterion for very ample line bundles let x be a projective algebraic manifold of dimension n and let l be an ample line bundle over x we give a numerical criterion ensuring that the adjoint bundle kx l is very ample the sufficient conditions are expressed in terms of lower bounds for the intersection numbers l y over subvarieties y of x in the case of surfaces our criterion gives universal bounds and is only slightly weaker than i reider s criterion when dimx 3 and codimy 2 the lower bounds for l y involve a numerical constant which depends on the geometry of x by means of an iteration process it is finally shown that 2kx ml is very ample form 12n our approach is mostly analytic and based on a combination of hormander s l estimates for the operator lelong number theory and the aubin calabi yau theorem

projective reconstruction from line correspondences in multiple uncalibrated images a new approach is proposed for reconstructing 3d lines and cameras from 2d corresponding lines across multiple uncalibrated views there is no requirement that the 2d corresponding lines on different images represent the same segment of a 3d line which may not appear on all images a 3d line is reconstructed by minimizing a geometric cost function that measures the distance of the reprojected end points of the 3d segment from the measured 2d lines on different images an algorithmic procedure is provided with guaranteed convergence to a solution where the geometric cost function achieves a local minimum

invariants of six points and projective reconstruction from three uncalibrated images there are three projective invariants of a set of six points in general position in space it is well known that these invariants cannot be recovered from one image however an invariant relationship does exist between space invariants and image invariants this invariant relationship is first derived for a single image then this invariant relationship is used to derive the space invariants when multiple images are available this paper establishes that the minimum number of images for computing these invariants is three and the computation of invariants of six points from three images can have as many as three solutions algorithms are presented for computing these invariants in closed form the accuracy and stability with respect to image noise selection of the triplets of images and distance between viewing positions are studied both through real and simulated images applications of these invariants are also presented both the results of faugeras 1992 and hartley et al 1992 for projective reconstruction and sturm s method 1869 for epipolar geometry determination from two uncalibrated images with at least seven points are extended to the case of three uncalibrated images with only six points

a robust version of mallows s c p abstract we present a robust version of mallows s c p for regression models it is defined by rc p w p 2 u p v p where w p i 2 i r 2 i is a weighted residual sum of squares computed from a robust fit of model p 2 is a robust and consistent estimator of 2 in the full model and u p and v p are constants depending on the weight function and the number of parameters in model p good subset models are those with rc p close to v p or smaller than v p when the weights are identically 1 w p becomes the residual sum of squares of a least squares fit and rc p reduces to mallows s c p the robust model selection procedure based on rc p allows us to choose the models that fit the majority of the data by taking into account the presence of outliers and possible departures from the normality assumption on the error distribution together with the classical c p the robust version suggests several models from which we can choose

controlling variable selection by the addition of pseudovariables we propose a new approach to variable selection designed to control the false selection rate fsr defined as the proportion of uninformative variables included in selected models the method works by adding a known number of pseudovariables to the real dataset running a variable selection procedure and monitoring the proportion of pseudovariables falsely selected information obtained from bootstrap like replications of this process is used to estimate the proportion of falsely selected real variables and to tune the selection procedure to control the fsr

robust inference for generalized linear models by starting from a natural class of robust estimators for generalized linear models based on the notion of quasi likelihood we define robust deviances that can be used for stepwise model selection as in the classical framework we derive the asymptotic distribution of tests based on robust deviances and we investigate the stability of their asymptotic level under contamination the binomial and poisson models are treated in detail two applications to real data and a sensitivity analysis show that the inference obtained by means of the new techniques is more reliable than that obtained by classical estimation and testing procedures

equations of 1 d polarized abelian surfaces in this paper we study the equations of projectively embedded abelian surfaces with a polarization of type 1 d classical results say that given an ample line bundle l on an abelian surface a the line bundle l n is very ample for n 3 and furthermore in case n is even and n 4 the generators of the homogeneous ideal ia of the embedding of a via l n are all quadratic a possible choice for a set of generators of ia are the riemann theta relations on the other hand much less is known about embeddings via line bundles l of type 1 d that is line bundles l which are not powers of another line bundle on a it is well known that if d 5 and a is a general abelian surface then l is very ample while l can never be very ample for d 5 however even if d 5 l may not be very ample for special abelian surfaces we will restrict our attention in what follows only to the general abelian surface and wish to know what form the equations take for such a projectively embedded abelian surface a few special cases are well documented in the literature d 4 in which case the general surface is a singular octic in p3 cf blvs and d 5 in which case the abelian surface is described as the zero set of a section of the horrocks mumford bundle hm whereas its homogeneous ideal is generated by 3 heisenberg invariant quintics and 15 sextics cf ma also recent work by manolache and schreyer ms and by ranestad ra provides a description of the equations and syzygies in the case d 7

reconstruction of general curves using factorization and bundle adjustment in this paper we extend the notion of affine shape introduced by sparr from finite point sets to curves the extension makes it possible to reconstruct 3d curves up to projective transformations from a number of their 2d projections we also extend the bundle adjustment technique from point features to curves the first step of the curve reconstruction algorithm is based on affine shape it is independent of choice of coordinates is robust does not rely on any preselected parameters and works for an arbitrary number of images in particular this means that except for a small set of curves e g a moving line a solution is given to the aperture problem of finding point correspondences between curves the second step takes advantage of any knowledge of measurement errors in the images this is possible by extending the bundle adjustment technique to curves finally experiments are performed on both synthetic and real data to show the performance and applicability of the algorithm

rank classification of linear line structures from images by trifocal tensor determinability the problem we address is given line correspondences over three views what is the condition of the line correspondences for the spatial relation of the three associated camera positions to be uniquely recoverable the observed set of lines in space is called critical if there are multiple projectively nonequivalent configurations of the camera positions that can picture the same image triplet of the lines we tackle the problem from the perspective of trifocal tensor a quantity that captures the relative pose of the cameras in relation to the captured views we show that the rank of a matrix that leads to the estimation of the tensor is reduced to 7 11 15 if the observed lines come from a line pencil a line bundle and a line field respectively which are line families belonging to linear line space and 12 19 23 if the lines come from a general linear ruled surface a general linear line congruence and a general linear line complex which are subclasses of linear line structures we show that the above line structures with the exception of linear line congruence and linear line complex ought to be critical line structures all of these structures are quite typical in reality and thus the findings are important to the validity and stability of practically all algorithms related to structure from motion and projective reconstruction using line correspondences

projective reconstruction from multiple views with minimization of 2d reprojection error the problem of projective reconstruction by minimization of the 2d reprojection error in multiple images is considered although bundle adjustment techniques can be used to minimize the 2d reprojection error these methods being based on nonlinear optimization algorithms require a good starting point quasi linear algorithms with better global convergence properties can be used to generate an initial solution before submitting it to bundle adjustment for refinement in this paper we propose a factorization based method to integrate the initial search as well as the bundle adjustment into a single algorithm consisting of a sequence of weighted least squares problems in which a control parameter is initially set to a relaxed state to allow the search of a good initial solution and subsequently tightened up to force the final solution to approach a minimum point of the 2d reprojection error the proposed algorithm is guaranteed to converge our method readily handles images with missing points

the evidential reasoning approach for multi attribute decision analysis under interval uncertainty abstract the evidential reasoning er approach is a method for multiple attribute decision analysis mada under uncertainties it improves the insightfulness and rationality of a decision making process by using a belief decision matrix bdm for problem modelling and the dempster shafer d s theory of evidence for attribute aggregation the d s theory provides scope and flexibility to deal with interval uncertainties or local ignorance in decision analysis which is not explored in the original er approach and will be investigated in this paper firstly interval uncertainty will be defined and modelled in the er framework then an extended er algorithm ier is derived which enables the er approach to deal with interval uncertainty in assessing alternatives on an attribute it is proved that the original er algorithm is a special case of the ier algorithm the latter is demonstrated using numerical examples

high breakdown inference for mixed linear models mixed linear models are used to analyze data in many settings these models have a multivariate normal formulation in most cases the maximum likelihood estimator mle or the residual mle reml is usually chosen to estimate the parameters however the latter are based on the strong assumption of exact multivariate normality welsh and richardson have shown that these estimators are not robust to small deviations from multivariate normality this means that in practice a small proportion of data even only one can drive the value of the estimates on their own because the model is multivariate we propose a high breakdown robust estimator for very general mixed linear models that include for example covariates this robust estimator belongs to the class of s estimators from which we can derive asymptotic properties for inference we also use it as a diagnostic tool to detect outlying subjects we discuss the advantages of this estimator compared with other robust estimators proposed previously and i

projective reconstruction of ellipses from multiple images this paper presents a new approach for reconstructing 3d ellipses including circles from a sequence of 2d images taken by uncalibrated cameras our strategy is to estimate an ellipse in 3d space by reconstructing n 5 3d points called representative points on it where the representative points are reconstructed by minimizing the distances from their projections to the measured 2d ellipses on different images i e 2d reprojection error this minimization problem is transformed into a sequence of minimization sub problems that can be readily solved by an algorithm which is guaranteed to converge to a local minimum of the 2d reprojection error our method can reconstruct multiple 3d ellipses simultaneously from multiple images and it readily handles images with missing and or partially occluded ellipses the proposed method is evaluated using both synthetic and real data

a new notion of tameness abstract we generalize the notion of tame discrete sets introduced by rosay and rudin from complex euclidean space to arbitrary complex manifolds and establish their basic properties we show that complex linear algebraic groups different from the complex line or the punctured complex line contain tame discrete sets

cyclic coverings and higher order embeddings of algebraic varieties in the present paper we study higher order embeddings in the context of cyclic coverings analyzing the positivity of the line bundle downstairs and its relationship with the branch divisor we provide criteria for its pull back to define an embedding of given order we show that the obtained criteria are sharp finally we apply them to various sometimes seemingly unrelated problems in algebraic geometry

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

primitive higher order embeddings of abelian surfaces the aim of this note is to study higher order embeddings of abelian surfaces de nedby primitive line bundles in recent years several concepts of higher order embeddings have been studied in particular k spannedness k very ampleness and k jet ampleness see 7 for refer ences on this topic recall that a line bundle lon a smooth projective variety xis called k jet ample if for any choice of distinct points x

generalised information criteria in model selection summary the problem of evaluating the goodness of statistical models is investigated from an information theoretic point of view information criteria are proposed for evaluating models constructed by various estimation procedures when the specified family of probability distributions does not contain the distribution generating the data the proposed criteria are applied to the evaluation of models estimated by maximum likelihood robust penalised likelihood bayes procedures etc we also discuss the use of the bootstrap in model evaluation problems and present a variance reduction technique in the bootstrap simulation

on one step gm estimates and stability of inferences in linear regression abstract the folklore on one step estimation is that it inherits the breakdown point of the preliminary estimator and yet has the same large sample distribution as the fully iterated version as long as the preliminary estimate converges faster than n 1 4 where n is the sample size we investigate the extent to which this folklore is valid for one step gm estimators and their associated standard errors in linear regression we find that one step gm estimates based on newton raphson or scoring inherit the breakdown point of high breakdown point initial estimates such as least median of squares provided the usual weights that limit the influence of extreme points in the design space are based on location and scatter estimates with high breakdown points moreover these estimators have bounded influence functions and their standard errors can have high breakdown points the folklore concerning the large sample theory is correct assuming the regression errors are symmetrically distributed and homoscedastic

conic reconstruction and correspondence from two views conics are widely accepted as one of the most fundamental image features together with points and line segments the problem of space reconstruction and correspondence of two conics from two views is addressed in this paper it is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views given the relative orientation of the two views these two correspondence conditions are derived algebraically and one of them is shown to be fundamental in establishing the correspondences of conics a unified closed form solution is also developed for both projective reconstruction of conics in space from two uncalibrated camera views and metric reconstruction from two calibrated camera views experiments are conducted to demonstrate the discriminality of the correspondence conditions and the accuracy and stability of the reconstruction both for simulated and real images

a bounded influence high breakdown efficient regression estimator abstract we consider the multiple linear regression model y i x i e i i 1 2 n with random carriers and focus on the estimation of this article s main contribution is to present an estimator that is affine regression and scale equivariant has both a high breakdown point and a bounded influence function and has an asymptotic efficiency greater than 95 versus least squares under gaussian errors we give conditions under which the estimator a one step general m estimator that uses schweppe weights and is based on a high breakdown initial estimator satisfies these properties the major conditions necessary for the estimator are a it must be based on a n consistent initial estimator with a 50 breakdown point and b it must be based on a psi function that is odd bounded and strictly increasing the advantage of this estimator over previous approaches is that it does not downweight high leverage points without first considering how they fit the bulk of the data methods of computi

differential evolution algorithm with separated groups for multi dimensional optimization problems the classical differential evolution de algorithm one of population based evolutionary computation methods proved to be a successful approach for relatively simple problems but does not perform well for difficult multi dimensional non convex functions a number of significant modifications of de have been proposed in recent years including very few approaches referring to the idea of distributed evolutionary algorithms the present paper presents a new algorithm to improve optimization performance namely de with separated groups de sg which distributes population into small groups defines rules of exchange of information and individuals between the groups and uses two different strategies to keep balance between exploration and exploitation capabilities the performance of de sg is compared to that of eight algorithms belonging to the class of evolutionary strategies covariance matrix adaptation es particle swarm optimization comprehensive learning pso and efficient population utilization strategy pso differential evolution distributed de with explorative exploitative population families self adaptive de de with global and local neighbours and grouping differential evolution and multi algorithms amalgam the comparison is carried out for a set of 10 30 and 50 dimensional rotated test problems of varying difficulty including 10 and 30 dimensional composition functions from cec2005 although slow for simple functions the proposed de sg algorithm achieves a great success rate for more difficult 30 and 50 dimensional problems

algebraic functions for recognition in the general case a trilinear relationship between three perspective views is shown to exist the trilinearity result is shown to be of much practical use in visual recognition by alignment yielding a direct reprojection method that cuts through the computations of camera transformation scene structure and epipolar geometry moreover the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection the proof of the central result may be of further interest as it demonstrates certain regularities across homographics of the plane and introduces new view invariants experiments on simulated and real image data were conducted including a comparative analysis with epipolar intersection and the linear combination methods with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks

motion of points and lines in the uncalibrated case in the present paper we address the problem of computing structure and motion given a set point and or line correspondences in a monocular image sequence when the camera is not calibrated

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 novel technique of object ranking and classification under ignorance an application to the corporate failure risk problem this paper exposits a novel technique for the ranking and classification of objects to a particular state each object is described by measurements from a number of variables which may offer different levels of support for the individual objects to be associated with the two states a given hypothesis and not the hypothesis the dempster shafer theory of evidence is a central component of this technique this allows for a measure of concomitant ignorance which may encompass the precision of the individual measurements as well as the possible ambiguity of their influence in the subsequent classification of objects the level of ignorance present influences the utilisation of the technique as a tool for the ranking or classification of objects a simplex plot method of representing data allows a clear visual representation interpretation to the degree of interaction of the support from the variables to the ranking or classification of the objects to illustrate the proposed technique the application considered here is the elucidation of the risk of corporate failure of a number of companies subsequently each variable financial and non financial may offer support for the ranking and classification of companies to between the extreme states of being a failed or non failed company a comparison on the ranking and classification of companies is made with a traditional multivariate discriminant analysis

an improved method to construct basic probability assignment based on the confusion matrix for classification problem the determination of basic probability assignment bpa is a crucial issue in the application of dempster shafer evidence theory classification is a process of determining the class label that a sample belongs to in classification problem the construction of bpa based on the confusion matrix has been studied however the existing methods do not make full use of the available information provided by the confusion matrix in this paper an improved method to construct the bpa is proposed based on the confusion matrix the proposed method takes into account both the precision rate and the recall rate of each class an illustrative case regarding the prediction of transmembrane protein topology is given to demonstrate the effectiveness of the proposed method

fast robust model selection in large datasets large datasets are increasingly common in many research fields in particular in the linear regression context it is often the case that a huge number of potential covariates are available to explain a response variable and the first step of a reasonable statistical analysis is to reduce the number of covariates this can be done in a forward selection procedure that includes selecting the variable to enter deciding to retain it or stop the selection and estimating the augmented model least squares plus t tests can be fast but the outcome of a forward selection might be suboptimal when there are outliers in this article we propose a complete algorithm for fast robust model selection including considerations for huge sample sizes because simply replacing the classical statistical criteria with robust ones is not computationally possible we develop simplified robust estimators selection criteria and testing procedures for linear regression the robust estimator is a one step weighted m estimato

weighted wilcoxon type smoothly clipped absolute deviation method summary shrinkage type variable selection procedures have recently seen increasing applications in biomedical research however their performance can be adversely influenced by outliers in either the response or the covariate space this article proposes a weighted wilcoxon type smoothly clipped absolute deviation ww scad method which deals with robust variable selection and robust estimation simultaneously the new procedure can be conveniently implemented with the statistical software r we establish that the ww scad correctly identifies the set of zero coefficients with probability approaching one and estimates the nonzero coefficients with the rate n 1 2 moreover with appropriately chosen weights the ww scad is robust with respect to outliers in both the x and y directions the important special case with constant weights yields an oracle type estimator with high efficiency in the presence of heavier tailed random errors the robustness of the ww scad is partly justified by its asymptotic performance under local shrinking contamination we propose a bayesian information criterion type tuning parameter selector for the ww scad the performance of the ww scad is demonstrated via simulations and by an application to a study that investigates the effects of personal characteristics and dietary factors on plasma beta carotene level

a theory of self calibration of a moving camera there is a close connection between the calibration of a single camera and the epipolar transformation obtained when the camera undergoes a displacement the epipolar transformation imposes two algebraic constraints on the camera calibration if two epipolar transformations arising from different camera displacements are available then the compatible camera calibrations are parameterized by an algebraic curve of genus four the curve can be represented either by a space curve of degree seven contained in the intersection of two cubic surfaces or by a curve of degree six in the dual of the image plane the curve in the dual plane has one singular point of order three and three singular points of order two if three epipolar transformations are available then two curves of degree six can be obtained in the dual plane such that one of the real intersections of the two yields the correct camera calibration the two curves have a common singular point of order three experimental results are given to demonstrate the feasibility of camera calibration based on the epipolar transformation the real intersections of the two dual curves are found by locating the zeros of a function defined on the interval 0 2 the intersection yielding the correct camera calibration is picked out by referring back to the three epipolar transformations

outlier robust model selection in linear regression we propose a new approach to the selection of regression models based on combining a robust penalized criterion and a robust conditional expected prediction loss function that is estimated using a stratified bootstrap both components of the procedure use robust criteria i e robust functions rather than squared error loss to reduce the effects of large residuals and poor bootstrap samples a key idea is to separate estimation from model selection by choosing estimators separately from the function using the stratified bootstrap further reduces the likelihood of obtaining poor bootstrap samples we show that the model selection procedure is consistent under some conditions and works well in our simulations in particular we find that simultaneous minimization of prediction error and conditional expected prediction loss is better than separate minimization of the prediction error or the conditional expected prediction loss

an application of the dempster shafer theory of evidence to the classification of knee function and detection of improvement due to total knee replacement surgery this paper utilises a novel method for the classification of subjects with osteoarthritic and normal knee function the classification method comprises a number of different components firstly the method exploits the dempster shafer theory of evidence allowing for a degree of ignorance in the subject s classification i e a level of uncertainty as to whether a gait variable indicates osteoarthritis or not secondly the inclusion of simplex plots allows both the classification of a subject and the contribution of each associated gait variable to that classification to be represented visually as a result the method is further able to highlight periodic changes in a subject s knee function due to total knee replacement surgery and subsequent recovery the visual representation enables a simple clinical interpretation of the results from the quantitative analysis

a subspace approach for matching 2d shapes under affine distortions this paper presents a subspace approach to matching a pair of 2d shapes and estimating the affine transformation that aligns the two 2d shapes in the proposed method by considering each shape as a 2d signal one shape is projected onto the subspace spanned by the other and the affine transformation is estimated by minimizing the projection error in the subspace the proposed method is fast easy to implement and with a clear physical interpretation furthermore it is robust to noise due to the merit of the subspace method the proposed approach has been tested for registration accuracy computation time and robustness to noise its performance on synthetic and real images is compared with the state of the art reference algorithms the experimental results show that our approach compares favorably to the reference methods in terms of registration accuracy computation speed and robustness