3 d motion estimation using a sequence of noisy stereo images models estimation and uniqueness results a kinematic model based approach for the estimation of 3 d motion parameters from a sequence of noisy stereo images is discussed the approach is based on representing the constant acceleration translational motion and constant precession rotational motion in the form of a bilinear state space model using standard rectilinear states for translation and quaternions for rotation closed form solutions of the state transition equations are obtained to propagate the quaternions the measurements are noisy perturbations of 3 d feature points represented in an inertial coordinate system it is assumed that the 3 d feature points are extracted from the stereo images and matched over the frames owing to the nonlinearity in the state model nonlinear filters are designed for the estimation of motion parameters simulation results are included the cramer rao performance bounds for motion parameter estimates are computed a constructive proof for the uniqueness of motion parameters is given it is shown that with uniform sampling in time three noncollinear feature points in five consecutive binocular image pairs contain all the spatial and temporal information both nondegenerate and degenerate motions are analyzed a deterministic algorithm to recover motion parameters from a stereo image sequence is summarized from the constructive proof

recursive combination tests we present a method that extends the flexibility of adaptive designs to the number of interim analyses and to the choice of decision boundaries at each stage of the trial the design of the next stage can be determined using all of the information gathered so far additionally one can specify the next stage as the final stage or can plan a further interim analysis the method is based on a recursive application of the two stage combination tests for p values the crucial point is the appropriate definition of a p value function that combines p values from two separate stages to a single p value formally we start with a two stage combination test however the p value of the second stage can be replaced by the p value of a further combination test this applies if the experimenter decides in the first interim analysis to perform another interim analysis thereby extending the design to at least three stages obviously this can be also done in a recursive way in the following interim analyses the test

conditional properties of unconditional parametric bootstrap procedures for inference in exponential families higher order inference about a scalar parameter in the presence of nuisance parameters can be achieved by bootstrapping in circumstances where the parameter of interest is a component of the canonical parameter in a full exponential family the optimal test which is approximated is a conditional one based on conditioning on the sufficient statistic for the nuisance parameter a bootstrap procedure that ignores the conditioning is shown to have desirable conditional properties in providing third order relative accuracy in approximation of p values associated with the optimal test in both continuous and discrete models the bootstrap approach is equivalent to third order analytical approaches and is demonstrated in a number of examples to give very accurate approximations even for very small sample sizes

existence of lipschitz and semiconcave control lyapunov functions given a locally lipschitz control system which is globally asymptotically controllable at the origin we construct a control lyapunov function for the system which is lipschitz on bounded sets and we deduce the existence of another one which is semiconcave and so locally lipschitz outside the origin the proof relies on value functions and nonsmooth calculus

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

a stochastic jurdjevic quinn theorem the purpose of this paper is to state sufficient conditions for the stabilizability of stochastic differential systems when both the drift and diffusion terms are affine in the control this result extends to stochastic differential systems the well known theorem of jurdjevic quinn j differential equations 28 1978 pp 381 389 and incorporates earlier stabilization results proved in p florchinger stochastic anal appl 12 1994 pp 473 480 and r chabour and m oumoun stochastic anal appl 16 1998 pp 43 50

estimation of object motion parameters from noisy images an approach is presented for the estimation of object motion parameters based on a sequence of noisy images the problem considered is that of a rigid body undergoing unknown rotational and translational motion the measurement data consists of a sequence of noisy image coordinates of two or more object correspondence points by modeling the object dynamics as a function of time estimates of the model parameters including motion parameters can be extracted from the data using recursive and or batch techniques this permits a desired degree of smoothing to be achieved through the use of an arbitrarily large number of images some assumptions regarding object structure are presently made results are presented for a recursive estimation procedure the case considered here is that of a sequence of one dimensional images of a two dimensional object thus the object moves in one transverse dimension and in depth preserving the fundamental ambiguity of the central projection image model loss of depth information an iterated extended kalman filter is used for the recursive solution noise levels of 5 10 percent of the object image size are used approximate cramer rao lower bounds are derived for the model parameter estimates as a function of object trajectory and noise level this approach may be of use in situations where it is difficult to resolve large numbers of object match points but relatively long sequences of images 10 to 20 or more are available

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

stochastic versions of the lasalle theorem the main aim of this paper is to establish stochastic versions of the well known lasalle stability theorem from these stochastic versions follow many classical results on stochastic stability this shows clearly the power of our new results

asymptotic controllability implies feedback stabilization it is shown that every asymptotically controllable system can be globally stabilized by means of some discontinuous feedback law the stabilizing strategy is based on pointwise optimization of a smoothed version of a control lyapunov function iteratively sending trajectories into smaller and smaller neighborhoods of a desired equilibrium a major technical problem and one of the contributions of the present paper concerns the precise meaning of solution when using a discontinuous controller

comutations underlying the measuremnt of visual motion abstract the organization of movement in a changing image provides a valuable source of information for analyzing the environment in terms of objects their motion in space and their three dimensional structure a description of this movement is not provided to our visual system directly however it must be inferred from the pattern of changing intensity that reaches the eye this paper examines the problem of motion measurement which we formulate as the computation of an instantaneous two dimensional velocity field initial motion measurements occur at the location of significant intensity changes as suggested by marr and ullman 1 these measurements provide only one component of velocity and must be integrated to compute the two dimensional velocity field a fundamental problem for this integration is that motion is not determined uniquely from the changing image an additional constraint of smoothness of the velocity field is formulated based on the physical assumption that surfaces are generally smooth allowing the computation of a unique solution a theoretical analysis of the conditions under which this computation yields the correct velocity field suggests that the solution is physically plausible empirical studies show the results to be consistent with human motion perception

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

reducing structure from motion a general framework for dynamic vision 2 implementation and experimental assessment for pt 1 see ibid p 933 42 1998 a number of methods have been proposed in the literature for estimating scene structure and ego motion from a sequence of images using dynamical models despite the fact that all methods may be derived from a natural dynamical model within a unified framework from an engineering perspective there are a number of trade offs that lead to different strategies depending upon the applications and the goals one is targeting we want to characterize and compare the properties of each model such that the engineer may choose the one best suited to the specific application we analyze the properties of filters derived from each dynamical model under a variety of experimental conditions assess the accuracy of the estimates their robustness to measurement noise sensitivity to initial conditions and visual angle effects of the bas relief ambiguity and occlusions dependence upon the number of image measurements and their sampling rate

stability of dynamical systems with competitive controls the degenerate case abstract we study the stability of a dynamical system with two competitive controls to a general closed set the stability is proven to be equivalent to the continuity on such set of the value function of a differential game with maximum cost functional the existence of a suitably defined and continuous lyapunov function is proven to imply the stability our lyapunov function satisfies a differential inequality in the sense of the theory of viscosity solutions

interactive optimization of 3d shape and 2d correspondence using multiple geometric constraints via pocs the traditional approach of handling motion tracking and structure from motion sfm independently in successive steps exhibits inherent limitations in terms of achievable precision and incorporation of prior geometric constraints about the scene this paper proposes a projections onto convex sets pocs framework for iterative refinement of the measurement matrix in the well known factorization method to incorporate multiple geometric constraints about the scene thereby improving the accuracy of both 2d feature point tracking and 3d structure estimates regularities in the scene such as points on line and plane and parallel lines and planes that can be interactively identified and marked at each pocs iteration enforce rank and parallelism constraints on appropriately defined local measurement matrices one for each constraint the pocs framework allows for the integration of the information in each of these local measurement matrices into a single measurement matrix that is closest to the initial observed measurement matrix in frobenius norm which is then factored in the usual manner experimental results demonstrate that the proposed interactive pocs framework consistently improves both 2d correspondences and 3d shape motion estimates and similar results cannot be achieved by enforcing these constraints as either post or preprocessing

statistical bias in 3 d reconstruction from a monocular video the present state of the art in computing the error statistics in three dimensional 3 d reconstruction from video concentrates on estimating the error covariance a different source of error which has not received much attention is the fact that the reconstruction estimates are often significantly statistically biased in this paper we derive a precise expression for the bias in the depth estimate based on the continuous differentiable version of structure from motion sfm many sfm algorithms or certain portions of them can be posed in a linear least squares ls framework ax b examples include initialization procedures for bundle adjustment or algorithms that alternately estimate depth and camera motion it is a well known fact that the ls estimate is biased if the system matrix a is noisy in sfm the matrix a contains point correspondences which are always difficult to obtain precisely thus it is expected that the structure and motion estimates in such a formulation of the problem would be biased existing results on the minimum achievable variance of the sfm estimator are extended by deriving a generalized cramer rao lower bound a detailed analysis of the effect of various camera motion parameters on the bias is presented we conclude by presenting the effect of bias compensation on reconstructing 3 d face models from rendered images

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

an improved bonferroni procedure for multiple tests of significance summary a modification of the bonferroni procedure for testing multiple hypotheses is presented the method based on the ordered p values of the individual tests is less conservative than the classical bonferroni procedure but is still simple to apply a simulation study shows that the probability of a type i error of the procedure does not exceed the nominal significance level a for a variety of multivariate normal and multivariate gamma test statistics for independent tests the procedure has type i error probability equal to a the method appears particularly advantageous over the classical bonferroni procedure when several highly correlated test statistics are involved

p values maximized over a confidence set for the nuisance parameter abstract for testing problems of the form h 0 v v 0 with unknown nuisance parameter various methods are used to deal with the simplest approach is exemplified by the t test where the unknown variance is replaced by the sample variance and the t distribution accounts for estimation of the variance in other problems such as the 2 2 contingency table one conditions on a sufficient statistic for 0 and proceeds as in fisher s exact test because neither of these standard methods is appropriate for all situations this article suggests a new method for handling the unknown this new method is a simple modification of the formal definition of a p value that involves taking a maximum over the nuisance parameter space of a p value obtained for the case when is known the suggested modification is to restrict the maximization to a confidence set for the nuisance parameter after giving a brief justification we give various examples to show how this new method gives improved results for 2 2 tabl

motion estimation with more than two frames the development of a general motion estimation system based on using three or more frames is reported the relevant portion of the sequence is treated as a whole thus simplifying the process of estimating the motion parameters and making possible the computation of the motion parameters in terms of the natural center of motion a general description of this motion estimation method is presented with the derivation of motion equations for three cases three points in three frames two points in four frames and one point in five frames results are given for real and synthetic images for the case of one point in five and six frames on the average the program converged quickly to the right answer for noiseless data for noisy data the answers were reasonable and their accuracy was directly a function of the amount of noise in the disparity vector

a stochastic representation for mean curvature type geometric flows a smooth solution t t 0 t rd of a parabolic geometric flow is characterized as the reachability set of a stochastic target problem in this control problem the controller tries to steer the state process into a given deterministic set tc with probability one the reachability set v t for the target problem is the set of all initial data x from which the state process xx t tc for some control process this representation is proved by studying the squared distance function to t for the codimension k mean curvature flow the state process is dx t 2 pdw t where w t is a d dimensional brownian motion and the control p is any projection matrix onto a d k dimensional plane smooth solutions of the inverse mean curvature flow and a discussion of non smooth solutions are also given

lyapunov functions for infinite dimensional systems abstract we study lyapunov functions for infinite dimensional dynamical systems governed by general maximal monotone operators we obtain a characterization of lyapunov pairs by means of the associated hamilton jacobi partial differential equations whose solutions are meant in the viscosity sense as evolved in works of tataru and crandall lions our approach also leads to a new sufficient condition for lyapunov pairs generalizing a classical result of pazy

motion estimation via dynamic vision estimating the three dimensional motion of an object from a sequence of projections is of paramount importance in a variety of applications in control and robotics such as autonomous navigation manipulation servo tracking docking planning and surveillance although visual motion estimation is an old problem the first formulations date back to the beginning of the century only recently have tools from nonlinear systems estimation theory hinted at acceptable solutions in this paper the authors formulate the visual motion estimation problem in terms of identification of nonlinear implicit systems with parameters on a topological manifold and propose a dynamic solution either in the local coordinates or in the embedding space of the parameter manifold such a formulation has structural advantages over previous recursive schemes since the estimation of motion is decoupled from the estimation of the structure of the object being viewed and therefore it is possible to handle occlusions in a principled way

three dimensional modeling from two dimensional video this paper presents the surface based factorization method to recover three dimensional 3 d structure i e the 3 d shape and 3 d motion of a rigid object from a two dimensional 2 d video sequence the main ingredients of our approach are as follows 1 we describe the unknown shape of the 3 d rigid object by polynomial patches 2 projections of these patches in the image plane move according to parametric 2 d motion models 3 we recover the parameters describing the 3 d shape and 3 d motion from the 2 d motion parameters by factorizing a matrix that is rank 1 in a noiseless situation our method is simultaneously an extension and a simplification of the original factorization method of tomasi and kanade 1992 we track regions where the 2 d motion in the image plane is described by a single set of parameters avoiding the need to track a large number of pointwise features in general a difficult task then our method estimates the parameters describing the 3 d structure by factoring a rank 1 matrix not rank 3 as in tomasi and kanade this allows the use of fast iterative algorithms to compute the 3 d structure that best fits the data experimental results with real life video sequences illustrate the good performance of our approach

the simes method for multiple hypothesis testing with positively dependent test statistics abstract the simes method for testing intersection of more than two hypotheses is known to control the probability of type i error only when the underlying test statistics are independent although this method is more powerful than the classical bonferroni method it is not known whether it is conservative when the test statistics are dependent this article proves that for multivariate distributions exhibiting a type of positive dependence that arise in many multiple hypothesis testing situations the simes method indeed controls the probability of type i error this extends some results established very recently in the special case of two hypotheses

an adaptive confirmatory trial with interim treatment selection practical experiences and unbalanced randomization this article has been motivated by an ongoing international adaptive confirmatory trial at the interim analysis of this two stage trial none one or two active treatment regimens are selected for further study in the second stage a combination test approach is used in this practical setting with an extension of the theory to unbalanced randomization we show that a combination test with suitable weights can still preserve the overall type i error rate provided that the test statistic is chosen appropriately and the unpooled z test for proportions is not used the accuracy of stagewise p values is also discussed in a more general framework monte carlo simulations confirm the validity of the approach retained and evaluate the necessary sample size additional issues addressed during the design of the trial are also examined such as multiplicity due to testing hypotheses on key secondary endpoints a non inferiority comparison to an active treatment and covariate adjusted analyses for various types of outcome

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

experiments on estimating egomotion and structure parameters using long monocular image sequences this paper presents a simple but robust model based approach to estimating the kinematics of a moving camera and the structure of the objects in a stationary environment using long noisy monocular image sequences both batch and recursive algorithms are presented and the problem due to occlusion is addressed the approach is based on representing the constant translational velocity and constant angular velocity of the camera motion using nine rectilinear motion parameters which are 3 d vectors of the position of the rotation center linear and angular velocities the structure parameters are 3 d coordinates of the salient feature points in the inertial coordinate system due to redundancies in parameterization the total number of independent parameters to be estimated is 3m 7 wherem is the number of feature points the image plane coordinates of these feature points in each frame are first detected and matched over the frames these noisy image coordinates serve as the input to our algorithms due to the nonlinear nature of perspective projection a nonlinear least squares method is formulated for the batch algorithm and a conjugate gradient method is then applied to find the solution a recursive method using an iterated extended kalman filter iekf for incremental estimation of motion and structure is also presented since the plant model is simple in our formulation closed form solutions for the state and covariance transition equations are easily derived experimental results for simulated imagery as well as several real image sequences are included

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

some probability inequalities for ordered rm mtp sb 2 random variables a proof of the simes conjecture some new probability inequalities involving the ordered components of an mtp 2 random vector are derived which provide an analytical proof of an important conjecture in the field of multiple hypothesis testing this conjecture has been mostly validated so far using simulation

a unified approach for multi object triangulation tracking and camera calibration object triangulation 3 d object tracking feature correspondence and camera calibration are key problems for estimation from camera networks this paper addresses these problems within a unified bayesian framework for joint multi object tracking and camera calibration based on the finite set statistics methodology in contrast to the mainstream approaches an alternative parametrization is investigated for triangulation called disparity space the approach for feature correspondence is based on the probability hypothesis density phd filter and hence inherits the ability to handle the initialization of new tracks as well as the discrimination between targets and clutter within a bayesian paradigm the phd filtering approach then forms the basis of a camera calibration method from static or moving objects results are shown on simulated and real data

feedback stabilization of affine in the control stochastic differential systems by the control lyapunov function method the purpose of this paper is to study the asymptotic stability in probability of affine in the control stochastic differential systems sufficient conditions for the existence of control lyapunov functions leading to the existence of stabilizing feedback laws which are smooth except possibly at the equilibrium point of the system are provided

some experiments on estimating the 3 d motion parameters of a rigid body from two consecutive image frames this paper describes the results of some experiments on estimating the 3 d motion parameters of a rigid body from two consecutive tv images and discusses several factors which affect the accuracy of the results these factors include the sizes of the motion parameters themselves the accuracy of the raw data and the number of point correspondences in addition we address two related topics determining corner positions to subpixel accuracy and matching point patterns with different scales

a physics based analysis of image appearance models linear and multilinear models pca 3dmm aam asm and multilinear tensors of object shape appearance have been very popular in computer vision in this paper we analyze the applicability of these heuristic models from the fundamental physical laws of object motion and image formation we prove that under suitable conditions the image appearance space can be closely approximated to be multilinear with the illumination and texture subspaces being trilinearly combined with the direct sum of the motion and deformation subspaces this result provides a physics based understanding of many of the successes and limitations of the linear and multilinear approaches existing in the computer vision literature and also identifies some of the conditions under which they are valid it provides an analytical representation of the image space in terms of different physical factors that affect the image formation process numerical analysis of the accuracy of the physics based models is performed and tracking results on real data are presented

on the existence of optimal controls the optimal control problem where the state is governed by an ito stochastic differential equation possibly just an ordinary differential equation is formulated in martingale terms under a coercivity condition which is weaker than compactness of the control set a convexity condition and mild continuity hypotheses on the data it is shown by the direct method that optimal controls exist hard and soft constraints are allowed in the absence of soft constraints it is shown that there exists an optimal control that is a function only of the present time and state i e the synthesis problem has a solution the main tool here is krylov s markovian selection theorem

reducing structure from motion a general framework for dynamic vision 1 modeling the literature on recursive estimation of structure and motion from monocular image sequences comprises a large number of apparently unrelated models and estimation techniques we propose a framework that allows us to derive and compare all models by following the idea of dynamical system reduction the natural dynamic model derived from the rigidity constraint and the projection model is first reduced by explicitly decoupling structure depth from motion then implicit decoupling techniques are explored which consist of imposing that some function of the unknown parameters is held constant by appropriately choosing such a function not only can we account for models seen so far in the literature but we can also derive novel ones

asymptotics and the theory of inference asymptotic analysis has always been very useful for deriving distributions in statistics in cases where the exact distribution is unavailable more importantly asymptotic analysis can also provide insight into the inference process itself suggesting what information is available and how this information may be extracted the development of likelihood inference over the past twenty some years provides an illustration of the interplay between techniques of approximation and statistical theory

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

a comparison of rotational representations in structure and motion estimation for manoeuvring objects alternative methods are examined for estimating motion and structure of objects undergoing smooth maneuvers through measurements of feature positions in long multiple camera image sequences performance of extended kalman filters are compared for euler angle axis roll pitch yaw and quaternion parameterizations of rotational motion the angle axis method was found to give the best overall performance with a computationally efficient implementation

accurate p values for adaptive designs with binary endpoints adaptive designs encompass all trials allowing various types of design modifications over the course of the trial a key requirement for confirmatory adaptive designs to be accepted by regulators is the strong control of the family wise error rate this can be achieved by combining the p values for each arm and stage to account for adaptations including but not limited to treatment selection sample size adaptation and multiple stages while the theory for this is novel and well established in practice these methods can perform poorly especially for unbalanced designs and for small to moderate sample sizes the problem is that standard stagewise tests have inflated type i error rate especially but not only when the baseline success rate is close to the boundary and this is carried over to the adaptive tests seriously inflating the family wise error rate we propose to fix this problem by feeding the adaptive test with second order accurate p values in particular bootstrap p values secondly an adjusted version of the simes procedure for testing intersection hypotheses that reduces the built in conservatism is suggested numerical work and simulations show that unlike their standard counterparts the new approach preserves the overall error rate at or below the nominal level across the board irrespective of the baseline rate stagewise sample sizes or allocation ratio copyright 2017 john wiley sons ltd

evaluation of experiments with adaptive interim analyses summary a general method for statistical testing in experiments with an adaptive interim analysis is proposed the method is based on the observed error probabilities from the disjoint subsamples before and after the interim analysis formally an intersection of individual null hypotheses is tested by combining the twop values into a global test statistic stopping rules for fisher s product criterion in terms of critical limits for the p value in the first subsample are introduced including early stopping in the case of missing effects the control of qualitative treatment stage interactions is considered a generalization to three stages is outlined the loss of power when using the product criterion instead of the optimal classical test on the whole sample is calculated for the test of the mean of a normal distribution depending on increasing proportions of the first subsample in relation to the total sample size an upper bound on the loss of power due to early stopping is derived a general example is presented and rules for assessing the sample size in the second stage of the trial are given the problems of interpretation and precautions to be taken for applications are discussed finally the sources of bias for estimation in such designs are described

statistical analysis of effective singular values in matrix rank determination a major problem in using svd singular value decomposition as a tool in determining the effective rank of a perturbed matrix is that of distinguishing between significantly small and significantly large singular values to the end conference regions are derived for the perturbed singular values of matrices with noisy observation data the analysis is based on the theories of perturbations of singular values and statistical significance test threshold bounds for perturbation due to finite precision and i i d random models are evaluated in random models the threshold bounds depend on the dimension of the matrix the noisy variance and predefined statistical level of significance results applied to the problem of determining the effective order of a linear autoregressive system from the approximate rank of a sample autocorrelation matrix are considered various numerical examples illustrating the usefulness of these bounds and comparisons to other previously known approaches are given

3 d motion estimation understanding and prediction from noisy image sequences this paper presents an approach to understanding general 3 d motion of a rigid body from image sequences based on dynamics a locally constant angular momentum lcam model is introduced the model is local in the sense that it is applied to a limited number of image frames at a time specifically the model constrains the motion over a local frame subsequence to be a superposition of precession and translation thus the instantaneous rotation axis of the object is allowed to change through the subsequence the trajectory of the rotation center is approximated by a vector polynomial the parameters of the model evolve in time so that they can adapt to long term changes in motion characteristics the nature and parameters of short term motion can be estimated continuously with the goal of understanding motion through the image sequence the estimation algorithm presented in this paper is linear i e the algorithm consists of solving simultaneous linear equations based on the assumption that the motion is smooth object positions and motion in the near future can be predicted and short missing subsequences can be recovered noise smoothing is achieved by overdetermination and a leastsquares criterion the framework is flexible in the sense that it allows both overdetermination in number of feature points and the number of image frames

dynamic occlusion analysis in optical flow fields optical flow can be used to locate dynamic occlusion boundaries in an image sequence we derive an edge detection algorithm sensitive to changes in flow fields likely to be associated with occlusion the algorithm is patterned after the marr hildreth zero crossing detectors currently used to locate boundaries in scalar fields zero crossing detectors are extended to identify changes in direction and or magnitude in a vector valued flow field as a result the detector works for flow boundaries generated due to the relative motion of two overlapping surfaces as well as the simpler case of motion parallax due to a sensor moving through an otherwise stationary environment we then show how the approach can be extended to identify which side of a dynamic occlusion boundary corresponds to the occluding surface the fundamental principal involved is that at an occlusion boundary the image of the surface boundary moves with the image of the occluding surface such information is important in interpreting dynamic scenes results are demonstrated on optical flow fields automatically computed from real image sequences

unbiased estimation and statistical analysis of 3 d rigid motion from two views the problem of estimating 3d rigid motion from point correspondences over two views is formulated as nonlinear least squares ls optimization and the statistical behaviors of the errors in the solution are analyzed by introducing a realistic model of noise described in terms of the covariance matrices of n vectors it is shown that the ls solution based on the epipolar constraint is statistically biased the geometry of this bias is described in both quantitative and qualitative terms finally an unbiased estimation scheme is presented and random number simulations are conducted to observe its effectiveness

stochastic approximation and rate distortion analysis for robust structure and motion estimation recent research on structure and motion recovery has focused on issues related to sensitivity and robustness of existing techniques one possible reason is that in practical applications the underlying assumptions made by existing algorithms are often violated in this paper we propose a framework for 3d reconstruction from short monocular video sequences taking into account the statistical errors in reconstruction algorithms detailed error analysis is especially important for this problem because the motion between pairs of frames is small and slight perturbations in its estimates can lead to large errors in 3d reconstruction we focus on the following issues physical sources of errors their experimental and theoretical analysis robust estimation techniques and measures for characterizing the quality of the final reconstruction we derive a precise relationship between the error in the reconstruction and the error in the image correspondences the error analysis is used to design a robust recursive multi frame fusion algorithm using stochastic approximation as the framework since it is capable of dealing with incomplete information about errors in observations rate distortion analysis is proposed for evaluating the quality of the final reconstruction as a function of the number of frames and the error in the image correspondences finally to demonstrate the effectiveness of the algorithm examples of depth reconstruction are shown for different video sequences

almost sure stabilizability of controlled degenerate diffusions we develop a direct lyapunov method for the almost sure open loop stabilizability and asymptotic stabilizability of controlled degenerate diffusion processes the infinitesimal decrease condition for a lyapunov function is a new form of hamilton jacobi bellman partial differential inequality of second order we give local and global versions of the first and second lyapunov theorems assuming the existence of a lower semicontinuous lyapunov function satisfying such an inequality in the viscosity sense an explicit formula for a stabilizing feedback is provided for affine systems with smooth lyapunov function several examples illustrate the theory

3 d structure from visual motion modeling representation and observability abstract the problem of structure from motion concerns the reconstruction of the three dimensional structure of a scene from its projection onto a moving two dimensional surface such a problem is solved effectively by the human visual system judging from the ease with which we perform delicate control tasks involving vision as a sensor such as reaching for objects in the environment or driving a car in this paper we study structure from motion from the point of view of dynamical systems we first formalize the problem of 3 d structure and motion reconstruction as the estimation of the state of certain nonlinear dynamical models then we study the feasibility of structure from motion by analyzing the observability of such models the models that define the visual motion estimation problem for feature points in the euclidean 3 d space are not locally observable however the non observable manifold can be easily isolated by imposing metric constraints on the state space one of the peculiarities of vision as a sensor is its richness which can be a disadvantage when we are interested only in few of the unknown parameters for instance if we want to control the direction of heading of our car by measuring brightness values on our retina we have to overcome the effects that the shape of the environment its reflectance properties illumination and other quantities have on our measurements invariance to undesired parameters can be achieved by appropriate modeling or by choice of representation of the parameter space we propose and analyze models for 3 d structure that are independent of 3 d motion and vice versa estimating unknown parameters from such models amounts to the identification of nonlinear and implicit systems with parameters on differentiable manifolds such as a sphere or the so called essential manifold 1997 elsevier science ltd

filtering image sequences from a moving object and the edge detection problem in this paper we consider the problem of filtering sequences of images taken from moving objects with the aim of recovering information about the object itself as well as its underlying motion we first provide a formal description of the admissible classes of images and possibly nonrigid motions and of the functional relationship between the original image and the observed one blurring and noisy effects we then focus on the problem of edge detection assuming full information about the motion we propose a procedure that includes a preliminary preprocessing of the measured image aimed to localize the detection problem and to improve the signal to noise ratio then the edge identification is accomplished by an algorithm which implements recursive linear quadratic estimation and hypothesis testing finally the procedure is tested against simulated and real data

stabilization by artificial wiener processes in this technical note we restage the positive effects of gaussian white noises for continuous time driftless input affine nonholonomic systems compared with previous studies we found that the positive effects are hidden in the shadows of nonuniqueness of stochastic integrals over multi dimensional wiener processes furthermore we found that the positive effects are artificially restaged by numerical calculations with use of euler scheme for ordinary differential equations our results demonstrate that the positive effects act as hidden independent control inputs for nonholonomic systems this implies that our results provide a constructive procedure for designing control inputs such that the origins become p th moment exponentially or finite time stable

a multi frame structure from motion algorithm under perspective projection we present a fast robust algorithm for multi frame structure from motion from point features which works for general motion and large perspective effects the algorithm is for point features but easily extends to a direct method based on image intensities experiments on synthetic and real sequences show that the algorithm gives results nearly as accurate as the maximum likelihood estimate in a couple of seconds on an iris 10000 the results are significantly better than those of an optimal two image estimate when the camera projection is close to scaled orthographic the accuracy is comparable to that of the tomasi kanade algorithm and the algorithms are comparably fast the algorithm incorporates a quantitative theoretical analysis of the bas relief ambiguity and exemplifies how such an analysis can be exploited to improve reconstruction also we demonstrate a structure from motion algorithm for partially calibrated cameras with unknown focal length varying from image to image unlike the projective approach this algorithm fully exploits the partial knowledge of the calibration it is given by a simple modification of our algorithm for calibrated sequences and is insensitive to errors in calibrating the camera center theoretically we show that unknown focal length variations strengthen the effects of the bas relief ambiguity this paper includes extensive experimental studies of two frame reconstruction and the tomasi kanade approach in comparison to our algorithm we find that two frame algorithms are surprisingly robust and accurate despite some problems with local minima we demonstrate experimentally that a nearly optimal two frame reconstruction can be computed quickly by a minimization in the motion parameters alone lastly we show that a well known problem with the tomasi kanade algorithm is often not a significant one

identification of a moving object s velocity with a fixed camera in this paper a continuous estimator strategy is utilized to asymptotically identify the six degree of freedom velocity of a moving object using a single fixed camera the design of the estimator is facilitated by the fusion of homography based techniques with lyapunov design methods similar to the stereo vision paradigm the proposed estimator utilizes different views of the object from a single camera to calculate 3d information from 2d images in contrast to some of the previous work in this area no explicit model is used to describe the movement of the object rather the estimator is constructed based on bounds on the object s velocity acceleration and jerk

estimating the kinematics and structure of a rigid object from a sequence of monocular images the problem considered involves the use of a sequence of noisy monocular images of a three dimensional moving object to estimate both its structure and kinematics the object is assumed to be rigid and its motion is assumed to be smooth a set of object match points is assumed to be available consisting of fixed features on the object the image plane coordinates of which have been extracted from successive images in the sequence structure is defined as the 3 d positions of these object feature points relative to each other rotational motion occurs about the origin of an object centered coordinate system while translational motion is that of the origin of this coordinate system in this work which is a continuation of the research done by the authors and reported previously ibid vol pami 8 p 90 9 jan 1986 results of an experiment with real imagery are presented involving estimation of 28 unknown translational rotational and structural parameters based on 12 images with seven feature points

saddlepoint test in measurement error models we develop second order hypothesis testing procedures in functional measurement error models for small or moderate sample sizes where the classical first order asymptotic analysis often fails to provide accurate results in functional models no distributional assumptions are made on the unobservable covariates and this leads to semiparametric models our testing procedure is derived using saddlepoint techniques and is based on an empirical distribution estimation subject to the null hypothesis constraints in combination with a set of estimating equations which avoid a distribution approximation the validity of the method is proved in theorems for both simple and composite hypothesis tests and is demonstrated through simulation and a farm size data analysis

stochastic lyapunov functions without differentiability at supposed equilibria abstract stochastic calculus indicates that allowing a lyapunov candidate function to be non differentiable at the origin helps its expected value to decrease to utilize this observation this paper investigates stability of stochastic systems supposing that the origin of the state space is an equilibrium before influenced by gaussian white noises for identifying such stability properties notions of instantaneous points and almost sure equilibria which are mutually exclusive are introduced this paper clarifies the relationship between the stability properties and develops their lyapunov type characterizations without differentiability at the origin discussions are given in relation to the notion of noise to state stability and this paper proposes a method to address both transient and global in time properties simultaneously with a single positive definite function even when stochastic noises prevent the origin from being an equilibrium

stochastic target problems dynamic programming and viscosity solutions in this paper we define and study a new class of optimal stochastic control problems which is closely related to the theory of backward sdes and forward backward sdes the controlled process x nu y nu takes values in mathbb r d times mathbb r and a given initial data for x nu 0 then the control problem is to find the minimal initial data for y nu so that it reaches a stochastic target at a specified terminal time t the main application is from financial mathematics in which the process x nu is related to stock price y nu is the wealth process and nu is the portfolio we introduce a new dynamic programming principle and prove that the value function of the stochastic target problem is a discontinuous viscosity solution of the associated dynamic programming equation the boundary conditions are also shown to solve a first order variational inequality in the discontinuous viscosity sense this provides a unique characterization of the value function which is the minimal initial data for y nu

finding trajectories of feature points in a monocular image sequence identifying the same physical point in more than one image the correspondence problem is vital in motion analysis most research for establishing correspondence uses only two frames of a sequence to solve this problem by using a sequence of frames it is possible to exploit the fact that due to inertia the motion of an object cannot change instantaneously by using smoothness of motion it is possible to solve the correspondence problem for arbitrary motion of several nonrigid objects in a scene we formulate the correspondence problem as an optimization problem and propose an iterative algorithm to find trajectories of points in a monocular image sequence a modified form of this algorithm is useful in case of occlusion also we demonstrate the efficacy of this approach considering synthetic laboratory and real scenes

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

adaptive sample size calculations in group sequential trials a method for group sequential trials that is based on the inverse normal method for combining the results of the separate stages is proposed without exaggerating the type i error rate this method enables data driven sample size reassessments during the course of the study it uses the stopping boundaries of the classical group sequential tests furthermore exact test procedures may be derived for a wide range of applications the procedure is compared with the classical designs in terms of power and expected sample size

lyapunov s second method for random dynamical systems abstract the method of lyapunov functions lyapunov s second or direct method was originally developed for studying the stability of a fixed point of an autonomous or non autonomous differential equation it was then extended from fixed points to sets from differential equations to dynamical systems and to stochastic differential equations we go one step further and develop lyapunov s second method for random dynamical systems and random sets together with matching notions of attraction and stability as a consequence lyapunov functions will also be random our test is that the extension be coherent in the sense that it reduces to the deterministic theory in case the noise is absent and that we can prove that a random set is asymptotically stable if and only if it has a lyapunov function several examples are treated including the stochastic lorenz system

bootstrap and second order tests of risk difference clinical trials data often come in the form of low dimensional tables of small counts standard approximate tests such as score and likelihood ratio tests are imperfect in several respects first they can give quite different answers from the same data second the actual type 1 error can differ significantly from nominal even for quite large sample sizes third exact inferences based on these can be strongly nonmonotonic functions of the null parameter and lead to confidence sets that are discontiguous there are two modern approaches to small sample inference one is to use so called higher order asymptotics reid 2003 annal of statistics 31 1695 1731 to provide an explicit adjustment to the likelihood ratio statistic the theory for this is complex but the statistic is quick to compute the second approach is to perform an exact calculation of significance assuming the nuisance parameters equal their null estimate lee and young 2005 statistic and probability letters 71 143 153 which is a kind of parametric bootstrap the purpose of this article is to explain and evaluate these two methods for testing whether a difference in probabilities p 2 p 1 exceeds a prechosen noninferiority margin 0 on the basis of an extensive numerical study we recommend bootstrap p values as superior to all other alternatives first they produce practically identical answers regardless of the basic test statistic chosen second they have excellent size accuracy and higher power third they vary much less erratically with the null parameter value 0

robust estimation of three dimensional motion parameters from a sequence of image frames using regularization in this paper we look at the issue of accurate estimation of the three dimensional motion parameters of a rigid body from a sequence of synthetic images and relate the effect of some parameters to the shape of an error function we first consider the case where only a small set of corresponding points is identified and suggest that a technique called regularization improves the quality and stability of a solution we then observe that if more pairs of corresponding points are available the error function becomes smooth and the solution stable finally we try to improve the quality of estimation by considering more than two consecutive frames for a moving camera looking at a stationary scene and summing the error functions obtained for any two consecutive frames surprisingly enough this technique does not improve stability unless we use regularization again

optimal brightness functions for optical flow estimation of deformable motion estimation accuracy of horn and schunck s 1981 classical optical flow algorithm depends on many factors including the brightness pattern of the measured images since some applications can select brightness functions with which to paint the object it is desirable to know what patterns will lead to the best motion estimates the paper presents a method for determining this pattern a priori using mild assumptions about the velocity field and imaging process the method is based on formulating horn and schunck s algorithm as a linear smoother and rigorously deriving an expression for the corresponding error covariance function the authors then specify a scalar performance measure and develop an approach to select an optimal brightness function which minimizes this performance measure from within a parametrized class conditions for existence of an optimal brightness function are also given the resulting optimal performance is demonstrated using simulations and a discussion of these results and potential future research is given