self calibration of a stereo rig using monocular epipolar geometries this paper addresses the problem of self calibration from one unknown motion of an uncalibrated stereo rig unlike the existing methods for stereo rig self calibration which have been focused on applying the autocalibration paradigm using both motion and stereo correspondences our method does not require the recovery of stereo correspondences our method combines purely algebraic constraints with implicit geometric constraints assuming that the rotational part of the stereo geometry has two unknown degrees of freedom i e the third dof is roughly known and that the principle point of each camera is known we first show that the computation of the intrinsic and extrinsic parameters of the stereo rig can be recovered from the motion correspondences only i e the monocular fundamental matrices we then provide an initialization procedure for the proposed non linear method we provide an extensive performance study for the method in the presence of image noise in addition we study some of the aspects related to the 3d motion that govern the accuracy of the proposed self calibration method experiments conducted on synthetic and real data images demonstrate the effectiveness and efficiency of the proposed method

efficient design sensitivities of structures subjected to dynamic loading calculation of design sensitivities often involves much computational effort particularly in large structural systems with many design variables approximation concepts which are often used to reduce the computational cost involved in repeated analysis are usually not sufficiently accurate for sensitivity analysis in this study approximate reanalysis is used to improve the efficiency of dynamic sensitivity analysis using modal analysis the response derivatives with respect to design variables are presented as a combination of sensitivities of the eigenvectors and the generalized displacements a procedure intended to reduce the number of differential equations that must be solved during the solution process is proposed efficient evaluation of the derivatives using finite difference and the recently developed combined approximations approach is presented numerical examples show that high accuracy of design sensitivities can be achieved efficiently

review of options for structural design sensitivity analysis part 1 linear systems the paper reviews options for structural design sensitivity analysis including global finite differences continuum derivatives discrete derivatives and computational or automated differentiation the objective is to put these different approaches to design sensitivity analysis in the context of accuracy and consistency computational cost and implementation options and effort linear static analysis and transient dynamic analysis are reviewed in a separate appendix special attention is paid to the semi analytical method a future paper will address design sensitivity analysis in nonlinear structural problems

sequential determination of estimator as well as sample size on considere certains problemes d estimation ponctuelle ou par intervalles et on propose des methodes sequentielles pour le choix d un estimateur et de la taille de l echantillon sur lequel sera base l estimateur

efficient sensitivity analysis for structural optimization abstract efficient sensitivity analysis based on high quality approximations of displacements is presented the improved approximations are achieved by combining the efficiency of local approximations series expansion and the quality of global approximations the reduced basis method three approximate sensitivity analysis methods are developed and compared the direct method the adjoint variable method and the finite difference method all the approximations are based on the results of a single exact analysis of the initial design and they can be used with a general finite element system the methods are easy to implement and suitable for different types of design variables and structures it is shown that high quality approximations of derivatives can be achieved with a relatively small computational effort for very large changes in the design variables

approximate vibration reanalysis of structures thecombinedapproximationsmethodisdevelopedforvibrationreanalysisofstructures inthesolution process the terms of local series approximations are used as basis vectors in global reduced basis approximations the solution steps are straightforward and the method can be readily used with a general e nite element system the computational effort needed by the method is usually much smaller than the effort needed for complete vibration analysis the efe ciency of the calculations and the accuracy of the results can be controlled by the amount of information considered efe cient solutions are obtained by low order approximations and accurate results can be achievedbyconsideringhigher orderterms numericalexamplesshowthataccurateresultsareachievedefe ciently for very large changes in the design nomenclature b matrix dee ned by eq 21 c matrix dee ned by eq 16 e modulus of elasticity i moment of inertia i identity matrix k stiffness matrix kr reduced stiffness matrix l length m mass matrix mr reduced mass matrix r right hand side vector r displacement vector rb matrix of basis vectors s number of basis vectors u upper triangular matrix y vector of coefe cients coefe cient dee ned by eq 35 angle between vectors 1k change in the stiffness matrix 1m change in the mass matrix kronecker delta eigenvalue circular frequency

second order approximation to the risk of a sequential procedure given x 1 x 2 cdots i i d with mean mu and variance sigma 2 suppose that at stage n one wishes to estimate mu by the sample mean bar x n subject to the loss function l n a bar x n mu 2 n a 0 if sigma is known the optimal fixed sample size n 0 approx a 1 2 sigma can be used with corresponding risk r n 0 but if sigma is unknown there is no fixed sample size procedure that will achieve the risk r n 0 for the sequential estimation procedure with stopping rule t inf n geq n a n 1 sum n 1 x i bar x n 2 leq a 1 n 2 the second order approximation of woodroofe 1977 to the risk r t for normal x i is extended to the distribution free case specifically if the x i have finite moments of order greater than eight and are non lattice under certain conditions on the delay n a it is shown that the regret r t r n 0 c o 1 as a rightarrow infty where c depends on the first four moments of the distribution of the x i for the lattice case bounds of the form c 1 o 1 leq r t r n 0 leq c 2 o 1 are obtained where the c j are c pm 3 it follows from these approximations that the regret can take arbitrarily large negative values as the distribution of the x i varies in contrast to previous results for normal and gamma cases

sequential estimation of the mean of a first order stationary autoregressive process on considere un estimateur ponctuel sequentiel base sur une moyenne d echantillon et on montre qu il est asymptotiquement efficace en risque lorsque le cout par observation tend vers zero

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

initialization method for self calibration using 2 views recently 3d structure recovery through self calibration of camera has been actively researched traditional calibration algorithm requires known 3d coordinates of the control points while self calibration only requires the corresponding points of images thus it has more flexibility in real application in general self calibration algorithm results in the nonlinear optimization problem using constraints from the intrinsic parameters of the camera thus it requires initial value for the nonlinear minimization traditional approaches get the initial values assuming they have the same intrinsic parameters while they are dealing with the situation where the intrinsic parameters of the camera may change in this paper we propose new initialization method using the minimum 2 images proposed method is based on the assumption that the least violation of the camera s intrinsic parameter gives more stable initial value synthetic and real experiment shows this result

self calibration of a moving camera from pointcorrespondences and fundamental matrices we address the problem of estimating three dimensional motion and structure from motion with an uncalibrated moving camera we show that point correspondences between three images and the fundamental matrices computed from these point correspondences are sufficient to recover the internal orientation of the camera its calibration the motion parameters and to compute coherent perspective projection matrices which enable us to reconstruct 3 d structure up to a similarity in contrast with other methods no calibration object with a known 3 d shape is needed and no limitations are put upon the unknown motions to be performed or the parameters to be recovered as long as they define a projective camera the theory of the method which is based on the constraint that the observed points are part of a static scene thus allowing us to link the intrinsic parameters and the fundamental matrix via the absolute conic is first detailed several algorithms are then presented and their performances compared by means of extensive simulations and illustrated by several experiments with real images

time sequential point estimation through estimating equations time sequential point estimation is studied in the model of fully parametric censored data and cox s regression model both are investigated in the context of counting processes through estimating equations defined by martingales the concept of information and a related inequality developed in estimating function theory by godambe are adapted to these models these suggest some optimality criteria for choosing stopping times as well as estimators these lead naturally to some sequential procedures which are shown to be asymptotically efficient with respect to the above criteria

efficient estimation in dynamic conditional quantile models in this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data we construct an m estimator which achieves the semiparametric efficiency bound recently derived by komunjer and vuong forthcoming our efficient m estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density the estimator is new and not yet seen in the literature we illustrate its performance through a monte carlo experiment

accuracy enhancement of fatigue damage counting using design sensitivity analysis abstract recent studies have suggested fatigue damage counting of a linear elastic system using only the output data design sensitivity analysis based on the transmissibility function was studied in order to identify the most sensitive response location under intact conditions the design sensitivity index was derived to be proportional to the response energy at the measured point through reformulation of the previous equation for the sensitivity index the accuracy of the damage counting method can be enhanced with design sensitivity analysis by selecting the location with the maximum response energy the method is optimally robust against unexpected noise in the output data simulation and testing of a notched simple specimen under uniaxial excitation were used to verify that sensitivity analysis enhances the accuracy of the predicted damage counting

efficient non linear reanalysis of skeletal structures using combined approximations non linear reanalysis of large scale structures usually involves much computational effort because the set of non linear equations must be solved repeatedly during the solution process various approximations that are often used for linear reanalysis are not sufficiently accurate for non linear problems in this study solution procedures based on the combined approximations approach are developed and compared in terms of efficiency and accuracy various path independent non linear analysis and reanalysis problems are considered including material non linearity geometric non linearity and buckling analysis numerical examples demonstrate the effectiveness of the procedures presented it is shown that in various cases accurate results can be achieved efficiently copyright 2007 john wiley sons ltd

determining the epipolar geometry and its uncertainty a review two images of a single scene object are related by the epipolar geometry which can be described by a 3 3 singular matrix called the essential matrix if images internal parameters are known or the fundamental matrix otherwise it captures all geometric information contained in two images and its determination is very important in many applications such as scene modeling and vehicle navigation this paper gives an introduction to the epipolar geometry and provides a complete review of the current techniques for estimating the fundamental matrix and its uncertainty a well founded measure is proposed to compare these techniques projective reconstruction is also reviewed the software which we have developed for this review is available on the internet

efficient finite difference design sensitivities the problem considered in this study is to evaluate efficiently displacement derivatives using global finite differences given the displacements for an initial design the displacements for various modified designs are evaluated by the recently developed combined approximations method calculations of finite difference sensitivity coefficients are demonstrated for static problems and eigenproblems the presented solution procedure is easy to implement efficient and can be used to calculate derivatives for various designs where the exact displacements are not known some numerical examples show that the accuracy of the results is similar to the accuracy obtained by finite difference calculations based on exact analysis

nonlinear dynamic sensitivities of structures using combined approximations calculation of design sensitivities involves much computational effort particularly for nonlinear dynamic response of large structures modal analysis is often not effective for such problems because eigenproblems must be solved many times approximation concepts which are used to reduce the computational cost involved in structural analysis are usually not sufficiently accurate for sensitivity analysis in this study approximate reanalysis concepts are used to improve the efficiency of nonlinear dynamic sensitivity analysis efficient evaluation of the derivatives using modal analysis finite difference of eigenpairs and the recently developed combined approximations approach is presented several approximate solution procedures are developed and compared in terms of the efficiency and the accuracy of the results it is shown that some of the approximations presented reduce significantly the computational effort and provide sufficiently accurate results i introduction design sensitivity analysis of structures deals with the calculation of the response derivatives with respect to the design variables these derivatives are used in the solution of various problems such as design optimization generation of response approximations including approximate reanalysis models and explicit approximations of the constraint functions in terms of the structural parameters sensitivities are required also for assessing the effects of uncertainties in the structural properties on the system response calculation of design sensitivities involves much computational effort particularly for nonlinear dynamic response of large structures as a result there has been much interest in efficient procedures for calculating the sensitivity coefficients early and recent developments in methods for sensitivity analysis are discussed in various studies 1 4 methods of sensitivity analysis for discretized systems can be divided into the following classes a finite difference methods which are easy to implement but might involve numerous repeated analyses and high computational cost particularly in large problems the efficiency can be improved by using fast reanalysis techniques but finite difference approximations might have accuracy problems b analytical methods which provide exact solutions but might not be easy to implement in some problems c semi analytical methods which are based on a compromise between finite difference methods and analytical methods these methods are easy to implement but might provide inaccurate results in general the main factors considered in choosing a suitable sensitivity analysis method for a specific application include the accuracy the computational effort and the ease of implementation the quality of the results and efficiency of the calculations are usually two conflicting factors that is higher accuracy is often achieved at the expense of more computational effort dynamic sensitivity analysis has been demonstrated by several authors in ref 5 the mode superposition approach has been considered for linear response assuming harmonic loading the response sensitivities were evaluated by direct differentiation of the equations of motion in several studies

accurate displacement derivatives for structural optimization using approximate reanalysis a unified approach for accurate approximations of displacements and displacement derivatives with respect to design variables is presented the solution procedure is based on results of a single exact analysis at an initial design unlike common approximations of the structural response the approach presented is not based on calculation of derivatives rather approximations of displacements are used to evaluate displacement derivatives at various modified designs it is shown that similar computational procedures are employed for evaluating displacements first and second order derivatives of displacements the procedure presented is suitable for different types of design variables and structures numerical results show that accurate approximations of derivatives can be achieved with a small computational effort for designs obtained by very large changes in the initial structure

relative sensitivity analysis of responses using transmissibility abstract to identify the most effective position for solving vibrational problems it is necessary to analyze the system sensitivities in this study new sensitivity indices based on the concept of transmissibility are proposed for analyzing the relative sensitivities of the responses with respect to the design variables that are used to indicate the sensitive positions where small design modifications can be applied and analyze the effect of these modifications on the responses the transmissibility concept is applied after differentiating the equation of motion to consider the crosstalk effects more important information regarding the relative sensitivity characteristics of a system with easily measured response data to reduce unintended responses can be acquired by using the proposed indices further the proposed indices are applicable to the variables of mass stiffness and damping the indices are validated analytically and numerically and the results demonstrate the effectiveness of the proposed indices