recursive estimation of motion structure and focal length presents a formulation for recursive recovery of motion pointwise structure and focal length from feature correspondences tracked through an image sequence in addition to adding focal length to the state vector several representational improvements are made over earlier structure from motion formulations yielding a stable and accurate estimation framework which applies uniformly to both true perspective and orthographic projection results on synthetic and real imagery illustrate the performance of the estimator

estimating multivariate latent structure models a constructive proof of identification of multilinear decompositions of multiway arrays is presented it can be applied to show identification in a variety of multivariate latent structures examples are finite mixture models and hidden markov models the key step to show identification is the joint diagonalization of a set of matrices in the same non orthogonal basis an estimator of the latent structure model may then be based on a sample version of this simultaneous diagonalization problem simple algorithms are available for computation asymptotic theory is derived for this joint approximate diagonalization estimator

estimating three dimensional motion parameters of a rigid planar patch ii singular value decomposition we show that the three dimensional 3 d motion parameters of a rigid planar patch can be determined by computing the singular value decomposition svd of a 3 3 matrix containing the eight so called pure parameters furthermore aside from a scale factor for the translation parameters the number of solutions is either one or two depending on the multiplicity of the singular values of the matrix

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

sharp upper bound on the blow up rate for the critical nonlinear schrodinger equation we consider the critical nonlinear schrodinger equation iu t delta u u 4 n with initial condition u 0 x u0

a comment on analysis of video image sequences using point and line correspondences abstract in this paper we would like to contest the results of y f wang n karandikar and j k aggarwal pattern recognition 24 1065 1085 1991 raising two fundamental claims a line does not contribute anything to recognition of motion parameters from two images four traceable points are not sufficient to recover motion parameters from two perspective projections to be constructive however we show that four traceable points are sufficient to recover motion parameters from two frames under orthogonal projection and that five points are sufficient to simplify the solution of the two frame problem under orthogonal projection to solving a linear equation system

determining motion parameters using intensity guided range sensing abstract this paper describes a method for the direct computation of rotation and translation parameters of an object using multisensory data gathered from intensity and range sensors intensity images which can be gathered rapidly are used as the basis for guiding the extraction of a small set of correspondent points whose three dimensional coordinates can be determined by a range sensing device library model centered motion transformations are computed using a least squares approach object centered motion parameters are derived by computing the transformation between successive positions of the object results are presented for range and intensity images of synthetic and laboratory scenes

tensor decompositions for learning latent variable models this work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models including gaussian mixture models hidden markov models and latent dirichlet allocation which exploits a certain tensor structure in their low order observable moments typically of second and third order specifically parameter estimation is reduced to the problem of extracting a certain orthogonal decomposition of a symmetric tensor derived from the moments this decomposition can be viewed as a natural generalization of the singular value decomposition for matrices although tensor decompositions are generally intractable to compute the decomposition of these specially structured tensors can be efficiently obtained by a variety of approaches including power iterations and maximization approaches similar to the case of matrices a detailed analysis of a robust tensor power method is provided establishing an analogue of wedin s perturbation theorem for the singular vectors of matrices this implies a robust and computationally tractable estimation approach for several popular latent variable models

the quantum beating and its numerical simulation abstract we examine the suppression of quantum beating in a one dimensional non linear double well potential made up of two focusing nonlinear point interactions the investigation of the schrodinger dynamics is reduced to the study of a system of coupled nonlinear volterra integral equations for various values of the geometric and dynamical parameters of the model we give analytical and numerical results on the way states which are initially confined in one well evolve we show that already for a nonlinearity exponent well below the critical value there is complete suppression of the typical beating behavior characterizing the linear quantum case

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

the point like limit for a nls equation with concentrated nonlinearity in dimension three abstract we consider a scaling limit of a nonlinear schrodinger equation nls with a nonlocal nonlinearity showing that it reproduces in the limit of cutoff removal a nls equation with nonlinearity concentrated at a point the regularized dynamics is described by the equation i t e t e t g e e e t 2 e e t e where e 0 weakly and the function g embodies the nonlinearity and the scaling and has to be fine tuned in order to have a nontrivial limit dynamics the limit dynamics is a nonlinear version of point interaction in dimension three and it has been previously studied in several papers as regards the well posedness blow up and asymptotic properties of solutions our result is the first justification of the model as the point limit of a regularized dynamics

estimating three dimensional motion parameters of a rigid planar patch iii finite point correspondences and the three view problem two results are presented in this paper first it is shown that in estimating three dimensional motion of a rigid planar patch the eight pure parameters used in 1 and 2 are uniquely determined from the image correspondences of four points no three collinear and can be estimated by solving a set of linear equations the second result concerns the three view problem it is proved that given four image point correspondences in three perspective views of a planar patch undergoing general three dimensional rigid body motion the number of solutions for the motion parameters is one as opposed to two 2 when only two perspective views are given

optimal visual motion estimation a note the problem of estimating 3d motion in an optimal manner using correspondences of features in two views is analyzed the importance of having an optimal estimator is twofold first for the estimation itself and second for the bound it offers on how much sensitivity one can expect from a two frame point based motion algorithm the optimal estimator turns out to be nonlinear and for that reason techniques that provide very good initial guesses for the iterative computation of the optimal estimator are developed

on wielandt s inequality and its application to the asymptotic distribution of the eigenvalues of a random symmetric matrix a relatively obscure eigenvalue inequality due to wielandt is used to give a simple derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix the asymptotic distributions are obtained under a fairly general setting an application of the general theory to the bootstrap distribution of the eigenvalues of the sample covariance matrix is given 1 introduction and summary the derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix arises in many papers in multivariate analysis although the main idea behind most of the derivations is quite basic i e the expansion of the sample roots about the population roots the derivations themselves are often quite involved these complications are primarily due to the mathematical rather than statistical nature of the eigenvalue problem one of the main objectives of this paper is to introduce a simple method for obtaining the asymptotic distribution of the eigenvalue of random symmetric matrices the method is based upon a relatively obscure eigenvalue inequality

motion parameter estimation from global flow field data presented are two methods for the determination of the parameters of motion of a sensor given the vector flow field induced by an imaging system governed by a perspective transformation of a rigid scene both algorithms integrate global data to determine motion parameters the first the flow circulation algorithm determines the rotational parameters the second the foe search algorithm determines the translational parameters of the motion independently of the first algorithm several methods for determining when the function has the appropriate form are suggested one method involves filtering the function by a collection of circular surround zero mean receptive fields the other methods project the function onto a linear space of quadratic polynomials and measures the distance between the two functions the error function for the first two methods is a quadratic polynomial of the candidate position yielding a very rapid search strategy

a class of nonlinear schrodinger equations with concentrated nonlinearity abstract we consider the nonlinear schrodinger equation in dimension one with a nonlinearity concentrated in a finite number of points detailed results on the local existence of the solution in fractional sobolev spaces h are given we also prove the conservation of the l 2 norm and the energy of the solution and give a global existence result for repulsive and weakly attractive interaction in the space h 1 finally we prove the existence of blow up solutions for strongly attractive interaction

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

scene segmentation from visual motion using global optimization this paper presents results from computer experiments with an algorithm to perform scene disposition and motion segmentation from visual motion or optic flow the maximum a posteriori map criterion is used to formulate what the best segmentation or interpretation of the scene should be where the scene is assumed to be made up of some fixed number of moving planar surface patches the bayesian approach requires first specification of prior expectations for the optic flow field which here is modeled as spatial and temporal markov random fields and secondly a way of measuring how well the segmentation predicts the measured flow field the markov random fields incorporate the physical constraints that objects and their images are probably spatially continuous and that their images are likely to move quite smoothly across the image plane to compute the flow predicted by the segmentation a recent method for reconstructing the motion and orientation of planar surface facets is used the search for the globally optimal segmentation is performed using simulated annealing

improving point and interval estimators of monotone functions by rearrangement suppose that a target function is monotonic and an available original estimate of this target function is not monotonic rearrangements univariate and multivariate transform the original estimate to a monotonic estimate that always lies closer in common metrics to the target function furthermore suppose an original confidence interval which covers the target function with probability at least 1 is defined by an upper and lower endpoint functions that are not monotonic then the rearranged confidence interval defined by the rearranged upper and lower endpoint functions is monotonic shorter in length in common norms than the original interval and covers the target function with probability at least 1 we illustrate the results with a growth chart example

the blow up dynamic and upper bound on the blow up rate for critical nonlinear schrodinger equation we consider the critical nonlinear schr odinger equation iut u u 4 n u with initial condition u 0 x u0 in dimension n 1 for u0 h1 local existence in the time of solutions on an interval 0 t is known and there exist finite time blow up solutions that is u0 such that limt t 1

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

directions of motion fields are hardly ever ambiguous if instead of the full motion field we consider only the direction of the motion field due to a rigid motion what can we say about the three dimensional motion information contained in it this paper provides a geometric analysis of this question based solely on the constraint that the depth of the surfaces in view is positive the motivation behind this analysis is to provide a theoretical foundation for image constraints employing only the sign of flow in various directions and justify their utilization for addressing 3d dynamic vision problems it is shown that considering as the imaging surface the whole sphere independently of the scene in view two different rigid motions cannot give rise to the same directional motion field if we restrict the image to half of a sphere or an infinitely large image plane two different rigid motions with instantaneous translational and rotational velocities t 1 1 and t 2 2 cannot give rise to the same directional motion field unless the plane through t 1 and t 2 is perpendicular to the plane through 1 and 2 i e t 1 t 2 1 2 e 0 in addition in order to give practical significance to these uniqueness results for the case of a limited field of view we also characterize the locations on the image where the motion vectors due to the different motions must have different directions if 1 2 t 1 t 2 e 0 and certain additional constraints are met then the two rigid motions could produce motion fields with the same direction for this to happen the depth of each corresponding surface has to be within a certain range defined by a second and a third order surface similar more restrictive constraints are obtained for the case of multiple motions consequently directions of motion fields are hardly ever ambiguous a byproduct of the analysis is that full motion fields are never ambiguous with a half sphere as the imaging surface

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

a general aperture problem for direct estimation of 3 d motion parameters the necessary and sufficient conditions that an object should satisfy so that motion can be uniquely determined by a direct method are discussed this direct method based on the temporal spatial gradient scheme can estimate the three dimensional 3 motion parameters of a rigid moving object from an image sequence by utilizing depth information of the object it is shown that the 3 d motion cannot be uniquely determined for only eight kinds of objects with special geometric structure and surface pattern

the action of volterra integral operators with highly singular kernels on holder continuous lebesgue and sobolev functions abstract for kernels which are positive and integrable we show that the operator g j g 0 x x s g s d s on a finite time interval enjoys a regularizing effect when applied to holder continuous and lebesgue functions and a contractive effect when applied to sobolev functions for holder continuous functions we establish that the improvement of the regularity of the modulus of continuity is given by the integral of the kernel namely by the factor n x 0 x s d s for functions in lebesgue spaces we prove that an improvement always exists and it can be expressed in terms of orlicz integrability finally for functions in sobolev spaces we show that the operator j shrinks the norm of the argument by a factor that as in the holder case depends on the function n whereas no regularization result can be obtained these results can be applied for instance to abel kernels and to the volterra function i x x 0 1 0 x s 1 s d s the latter being relevant for instance in the analysis of the schrodinger equation with concentrated nonlinearities in r 2

motion analysis of a homogeneously deformable object using subset correspondences abstract analysis of generalized motion parameters involves the estimation of translation rotation and the deformation parameters for a non rigid object most motion analysis methods require a preprocessing step of establishing the feature point correspondence between subsequent time frames such a preprocessing of data is computationally demanding and very often leads to erroneous results we explore the possibility of relaxing the above requirements for a homogeneously deformable object a computationally efficient method is proposed here that needs only subset correspondences between 3d feature points on the object at two different time instants instead of having explicit point correspondence the deformation parameters are obtained utilizing the changes in the euclidean distance for individual feature points belonging to different subsets under the proposed model the object may now be transformed into a rigid one utilizing the estimated deformation parameters the rotation parameters are estimated by considering the invariance properties of the principal moments simulation experiments are carried out to evaluate the performance of the proposed method the applicability of the method is also tested on a real data set

instrumental variable treatment of nonclassical measurement error models while the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors in variables models with continuously distributed variables our main identifying assumption is that conditional on the value of the true regressors some measure of location of the distribution of the measurement error e g its mean mode or median is equal to zero the proposed approach relies on the eigenvalue eigenfunction decomposition of an integral operator associated with specific joint probability densities the main identifying assumption is used to index the eigenfunctions so that the decomposition is unique we propose a convenient sieve based estimator derive its asymptotic properties and investigate its finite sample behavior through monte carlo simulations

recursive estimation of time varying motion and structure parameters we present a computational framework for recovering both first order motion parameters observer direction of translation and observer rotation second order motion parameters observer rotational acceleration and relative depth maps from time varying optical flow we recover translation speed and acceleration in units which are scaled relative to the distance to the object our assumption is that the observer rotational motion is no more than second order in other words observer motion is either constant or has at most constant acceleration we examine the effect of noise on the solution of the motion and structure parameters this ensemble of unknowns comprises a solution to the classical structure and motion from optic flow problem our complete framework utilizes a method for interpreting the bilinear image velocity equation by solving simple systems of linear equations since our noise analysis yields uncertainty measures for each parameter a kalman filter is employed to incrementally integrate new measurements as they become available as each additional frame in the sequence is processed we conclude by analysing this reduction of uncertainty over time as the system converges to a stable solution for both synthetic and real image sequences

the feasibility of motion and structure from noisy time varying image velocity information this research addresses the problem of noise sensitivity inherent in motion and structure algorithms the motion and structure paradigm is a two step process first we measure image velocities and perhaps their spatial and temporal derivatives are obtained from time varying image intensity data and second we use these data to compute the motion of a moving monocular observer in a stationary environment under perspective projection relative to a single 3 d planar surface the first contribution of this article is an algorithm that uses time varying image velocity information to compute the observer s translation and rotation and the normalized surface gradient of the 3 d planar surface the use of time varying image velocity information is an important tool in obtaining a more robust motion and structure calculation the second contribution of this article is an extensive error analysis of the motion and structure problem any motion and structure algorithm that uses image velocity information as its input should exhibit error sensitivity behavior compatible with the results reported here we perform an average and worst case error analysis for four types of image velocity information full and normal image velocities and full and normal sets of image velocity and its derivatives these derivatives are simply the coefficients of a truncated taylor series expansion about some point in space and time the main issues we address here are just how sensitive is a motion and structure computation in the presence of noisy input or alternately how accurate must our image velocity information be how much and what type of input data is needed and under what circumstances is motion and structure feasible that is when can we be sure that a motion and structure computation will produce usable results we base our answers on a numerical error analysis we conduct for a large number of motions

on improving density estimators which are not bona fide functions in order to improve the rate of decrease of the imse for nonparametric kernel density estimators with nonrandom bandwidth beyond o n 4 5 all current methods must relax the constraint that the density estimate be a bona fide function that is be nonnegative and integrate to one in this paper we show how to achieve similar improvement without relaxing any of these constraints the method can also be applied for orthogonal series adaptive orthogonal series spline jackknife and other density estimators and assures an improvement of the imse for each sample size

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

nonparametric estimation of non exchangeable latent variable models we propose a two step method to nonparametrically estimate multivariate models in which the observed outcomes are independent conditional on a discrete latent variable applications include microeconometric models with unobserved types of agents regime switching models and models with misclassification error in the first step we estimate weights that transform moments of the marginal distribution of the data into moments of the conditional distribution of the data for given values of the latent variable in the second step these conditional moments are estimated as weighted sample averages we illustrate the method by estimating a model of wages with unobserved heterogeneity on psid data

pose determination from line to plane correspondences existence condition and closed form solutions a class of pose determination problems in which the sensory data are lines and the corresponding reference data are planes is discussed the lines considered are different from edge lines in that they are not the intersection of boundary faces of the object the author describes a polynomial approach that does not require a priori knowledge about the object location closed form solutions for orthogonal parallel and coplanar feature configurations of critical importance in real applications are derived findings concerning the necessary and sufficient conditions under which the line to plane pose determination problem can be solved are described

scattering for nls with a delta potential abstract we prove h 1 scattering for the mass supercritical defocusing nonlinear schrodinger equation perturbed by a repulsive delta potential

non parametric estimation of finite mixtures from repeated measurements this paper provides methods to estimate finite mixtures from data with repeated measurements non parametrically we present a constructive identification argument and use it to develop simple two step estimators of the component distributions and all their functionals we discuss a computationally efficient method for estimation and derive asymptotic theory simulation experiments suggest that our theory provides confidence intervals with good coverage in small samples

a diffusion mechanism for obstacle detection from size change information a mechanism fur the visual detection of obstacles is presented a new immediacy measure representing the imminence of collision between an object and a moving observer is defined a diffusion process on the image domain whose initial condition is determined by the motion field normal to the object s boundary is shown to converge asymptotically to the immediacy measure a network of locally connected cells derived from a finite difference approximation of the diffusion equation estimates the immediacy measure from normal velocity and boundary information provided by a motion measurement and segmentation stage the algorithm s performance on real image sequences is demonstrated

bayesian algorithms for simultaneous structure from motion estimation of multiple independently moving objects the problem of simultaneous structure from motion estimation for multiple independently moving objects from a monocular image sequence is addressed two bayesian algorithms are presented for solving this problem using the sequential importance sampling sis technique the empirical posterior distribution of object motion and feature separation parameters is approximated by weighted samples the first algorithm addresses the problem when only two moving objects are present a singular value decomposition svd based sample clustering algorithm is shown to be capable of separating samples related to different objects a pair of sis procedures is used to track the posterior distribution of the motion parameters in the second algorithm a balancing step is added into the sis procedure to preserve samples of low weights so that all objects have enough samples to propagate empirical motion distributions by using the proposed algorithms the relative motions of all the moving objects with respect to the camera can be simultaneously estimated both algorithms have been tested on synthetic and real image sequences improved results have been achieved

some non existence results for the semilinear schrodinger equation without gauge invariance we consider the cauchy problem for the semilinear schrodinger equation nls i t u u p t x 0 t rd u 0 x f x x rd where u u t x is a c valued unknown function c 0 p 1 0 f f x is a c valued given function and t is a maximal existence time of the solution our first aim in the present paper is to prove a large data blow up result for nls in hs critical or hs subcritical case p ps 1 4 d 2s for some s 0 more precisely we show that in the case 1 0 such that for any 0 the following estimates t c and limt t 0 u t hs if1 p ps u ltr 0 t b 2s ifp ps hold where c 0 are constants independent of and r is an admissible pair see theorem 2 3 our second aim is to prove non existence local weak solution for nls in the hs supercritical case p ps which means that if p ps then there exists an hs function f such that if there exist t 0 and a weak solution u to nls on 0 t then 0 see theorem 2 5

non parametric identification and estimation of the number of components in multivariate mixtures this article analyzes the identiability of the number of components in k variate mcomponent nite mixture models in which each component distribution has independent marginals including models in latent class analysis without making parametric assumptions on the component distributions we investigate how one can identify the number of components from the distribution function of the observed data when k 2 a lower bound on the number of components m is nonparametrically identiable from the rank of a matrix constructed from the distribution function of the observed variables building on this identication condition we develop a procedure to consistently estimate a lower bound on the number of components

some properties of the e matrix in two view motion estimation in the eight point linear algorithm for determining 3d motion structure from two perspective views using point correspondences the e matrix plays a central role the e matrix is defined as a skew symmetrical matrix containing the translation components postmultiplied by a rotation matrix the authors show that a necessary and sufficient condition for a 3 3 matrix to be so decomposable is that one of its singular values is zero and the other two are equal several other forms of this property are presented some applications are briefly described

a new jacobi like method for joint diagonalization of arbitrary non defective matrices this paper addresses the problem of joint diagonalization of a set of matrices a new jacobi like method that has the advantages of computational efficiency and of generality is presented the proposed algorithm brings the general matrices into normal ones and performs a joint diagonalization by a combination of unitary and shears non unitary transformations it is based on the iterative minimization of an appropriate cost function using generalized jacobi rotation matrices

vehicle type motion estimation from multi frame images a model for vehicle type motion which assumes that the motion is a rotation around an axis through the vehicle center followed by a forward translation along the main axis of the vehicle is proposed when the rotation and the amplitude of translation are constant this type of motion is shown to be equivalent to a constant camera centered motion this indicates that a constant motion in the conventional camera centered model which is commonly considered to be artificial can in fact be a reasonable model in real life it is shown that a constant vehicle type motion can be interpreted as a constant screw motion a linear algorithm for estimating constant vehicle type motion is presented and experiments using real scene images are included as an extension vehicle type motion with constant rotation and constantly accelerated translation is discussed

rigidity checking of 3d point correspondences under perspective projection an algorithm is described which rapidly verifies the potential rigidity of three dimensional point correspondences from a pair of two dimensional views under perspective projection the output of the algorithm is a simple yes or no answer to the question could these corresponding points from two views be the projection of a rigid configuration potential applications include 3d object recognition from a single previous view and correspondence matching for stereo or motion over widely separated views the rigidity checking problem is different from the structure from motion problem because it is often the case that two views cannot provide an accurate structure from motion estimate due to ambiguity and ill conditioning whereas it is still possible to give an accurate yes no answer to the rigidity question rigidity checking verifies point correspondences using 3d recovery equations as a matching condition the proposed algorithm improves upon other methods that fall under this approach because it works with as few as six corresponding points under full perspective projection handles correspondences from widely separated views makes full use of the disparity of the correspondences and is integrated with a linear algorithm for 3d recovery due to kontsevich 1993 results are given for experiments with synthetic and real image data a complete implementation of this algorithm is being made publicly available

consistency of robust estimators in multi structural visual data segmentation a theoretical framework is presented to study the consistency of robust estimators used in vision problems involving extraction of fine details a strong correlation between asymptotic performance of a robust estimator and the asymptotic bias of its scale estimate is mathematically demonstrated where the structures are assumed to be linear corrupted by gaussian noise a new measure for the inconsistency of scale estimators is defined and formulated by deriving the functional forms of four recent high breakdown robust estimators for each estimator the inconsistency measures are numerically evaluated for a range of mutual distances between structures and inlier ratios and the minimum mutual distance between the structures for which each estimator returns a non bridging fit is calculated

maximum smoothed likelihood for multivariate mixtures summary we introduce an algorithm for estimating the parameters in a finite mixture of completely unspecified multivariate components in at least three dimensions under the assumption of conditionally independent coordinate dimensions we prove that this algorithm based on a majorization minimization idea possesses a desirable descent property just as any em algorithm does we discuss the similarities between our algorithm and a related one the so called nonlinearly smoothed em algorithm for the non mixture setting we also demonstrate via simulation studies that the new algorithm gives very similar results to another algorithm that has been shown empirically to be effective but that does not satisfy any descent property we provide code for implementing the new algorithm in a publicly available r package

estimating motion and structure from correspondences of line segments between two perspective images presents an algorithm for determining 3d motion and structure from correspondences of line segments between two perspective images to the author s knowledge this paper is the first investigation of use of line segments in motion and structure from motion classical methods use their geometric abstraction namely straight lines but then three images are necessary for the motion and structure determination process in this paper the author shows that it is possible to recover motion from two views when using line segments the assumption used is that two matched line segments contain the projection of a common part of the corresponding line segment in space i e they overlap indeed this is what the author uses to match line segments between different views this assumption constrains the possible motion between two views to an open set in motion parameter space a heuristic consisting of maximizing the overlap leads to a unique solution both synthetic and real data have been used to test the proposed algorithm and excellent results have been obtained with real data containing a relatively large set of line segments

blow up for the pointwise nls in dimension two absence of critical power abstract we consider the schrodinger equation in dimension two with a fixed pointwise focusing nonlinearity and show the occurrence of a blow up phenomenon with two peculiar features first the energy threshold under which all solutions blow up is strictly negative and coincides with the infimum of the energy of the standing waves second there is no critical power nonlinearity i e for every power there exist blow up solutions this last property is uncommon among the conservative schrodinger equations with local nonlinearity

paraperspective affine it is shown that the set of all paraperspective images with arbitrary reference point and the set of affine images of a 3 d object are identical consequently all uncalibrated paraperspective images of an object can be constructed from a 3 d model of the object by applying an affine transformation to the model and every affine image of the object represents some uncalibrated paraperspective image of the object it follows that the paraperspective images of an object can be expressed as linear combinations of any two non degenerate images of the object when the image position of the reference point is given the parameters of the affine transformation and likewise the coefficients of the linear combinations satisfy two quadratic constraints conversely when the values of parameters are given the image position of the reference point is determined by solving a bi quadratic equation

a correlation relaxation labeling framework for computing optical flow template matching from a new perspective optical flow estimation is discussed based on a model for time varying images more general than that implied by horn and schunk 1981 the emphasis is on applications where low contrast imagery nonrigid or evolving object patterns movement as well as large interframe displacements are encountered template matching is identified as having advantages over point correspondence and the gradient based approach in dealing with such applications the two fundamental uncertainties in feature matching whether template matching or feature point correspondences are discussed correlation template matching procedures are established based on likelihood measurement a method for determining optical flow is developed by combining template matching and relaxation labeling a number of candidate displacements for each template and their respective likelihood measures are determined then relaxation labeling is employed to iteratively update each candidate s likelihood by requiring smoothness within a motion field real cloud images from satellites are used to test the method

identifiability of parameters in latent structure models with many observed variables while hidden class models of various types arise in many statistical applications it is often difficult to establish the identifiability of their parameters focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones we demonstrate a general approach for establishing identifiability utilizing algebraic arguments a theorem of j kruskal for a simple latent class model with finite state space lies at the core of our results though we apply it to a diverse set of models these include mixtures of both finite and nonparametric product distributions hidden markov models and random graph mixture models and lead to a number of new results and improvements to old ones in the parametric setting this approach indicates that for such models the classical definition of identifiability is typically too strong instead generic identifiability holds which implies that the set of nonidentifiable parameters has measure zero so that parameter inference is still meaningful in particular this sheds light on the properties of finite mixtures of bernoulli products which have been used for decades despite being known to have nonidentifiable parameters in the nonparametric setting we again obtain identifiability only when certain restrictions are placed on the distributions that are mixed but we explicitly describe the conditions

estimating three dimensional motion parameters of a rigid planar patch we present a new direct method of estimating the three dimensional motion parameters of a rigid planar patch from two time sequential perspective views image frames first a set of eight pure parameters are defined these parameters can be determined uniquely from the two given image frames by solving a set of linear equations then the actual motion parameters are determined from these pure parameters by a method which requires the solution of a sixth order polynomial of one variable only and there exists a certain efficient algorithm for solving a sixth order polynomial aside from a scale factor for the translation parameters the number of real solutions never exceeds two in the special case of three dimensional translation the motion parameters can be expressed directly as some simple functions of the eight pure parameters thus only a few arithmetic operations are needed

contour matching using epipolar geometry matching features computed in images is an important process in multiview image analysis when the motion between two images is large the matching problem becomes very difficult in this paper we propose a contour matching algorithm based on geometric constraints with the assumption that the contours are obtained from images taken from a moving camera with static scenes we apply the epipolar constraint between two sets of contours and compute the corresponding points on the contours from the initial epipolar constraints obtained from corner point matching candidate contours are selected according to the epipolar geometry contour end point constraints and contour distance measures in order to reduce the possibility of false matches the number of match points on a contour is also used as a selection measure the initial epipolar constraint is refined from the matched sets of contours the algorithm can be applied to a pair or two pairs of images all of the processes are fully automatic and successfully implemented and tested with various real images

epipolar line estimation and rectification for stereo image pairs the assumption that epipolar lines are parallel to image scan lines is made in many algorithms for stereo analysis if valid it enables the search for corresponding image features to be confined to one dimension and hence simplified an algorithm that generates a vertically aligned stereo pair by warped resampling is described the method uses grey scale image matching between the components of the stereo pair but confined to feature points

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

nonparametric estimation of component distributions in a multivariate mixture suppose k variate data are drawn from a mixture of two distributions each having independent components it is desired to estimate the univariate marginal distributions in each of the products as well as the mixing proportion this is the setting of two class fully parametrized latent models that has been proposed for estimating the distributions of medical test results when disease status is unavailable the problem is one of inference in a mixture of distributions without training data and until now it has been tackled only in a fully parametric setting we investigate the possibility of using nonparametric methods of course when k 1 the problem is not identifiable from a nonparametric viewpoint we show that the problem is almost identifiable when k 2 there the set of all possible representations can be expressed in terms of any one of those representations as a two parameter family furthermore it is proved that when k geq3 the problem is nonparametrically identifiable under particularly mild regularity conditions in this case we introduce root n consistent nonparametric estimators of the 2k univariate marginal distributions and the mixing proportion finite sample and asymptotic properties of the estimators are described

nonparametric identification of finite mixture models of dynamic discrete choices in dynamic discrete choice analysis controlling for unobserved heterogeneity is an important issue and finite mixture models provide flexible ways to account for it this paper studies nonparametric identifiability of type probabilities and type specific component distributions in finite mixture models of dynamic discrete choices we derive sucient conditions for nonparametric identification for various finite mixture models of dynamic discrete choices used in applied work under dierent assumptions on the markov property stationarity and type invariance in the transition process three elements emerge as the important determinants of identification the time dimension of panel data the number of values the covariates can take and the heterogeneity of the response of dierent types to changes in the co

a multi frame approach to visual motion perception one of the main issues in the area of motion estimation given the correspondences of some features in a sequence of images is sensitivity to error in the input the main way to attack the problem as with several other problems in science and engineering is redundancy in the data up to now all the algorithms developed either used two frames or depended on assumptions about the motion or the shape of the scene we present in this paper an algorithm based on multiple frames that employs only the rigidity assumption is simple and mathematically elegant and experimentally proves to be a major improvement over the two frame algorithms the algorithm does minimization of the squared error which we prove equivalent to an eigenvalue minimization problem one of the side effects of this mean square method is that the algorithm can have a very descriptive physical interpretation in terms of the loaded spring model

direct passive navigation in this correspondence we show how to recover the motion of an observer relative to a planar surface from image brightness derivatives we do not compute the optical flow as an intermediate step only the spatial and temporal brightness gradients at a minimum of eight points we first present two iterative schemes for solving nine nonlinear equations in terms of the motion and surface parameters that are derived from a least squares fomulation an initial pass over the relevant image region is used to accumulate a number of moments of the image brightness derivatives all of the quantities used in the iteration are efficiently computed from these totals without the need to refer back to the image we then show that either of two possible solutions can be obtained in closed form we first solve a linear matrix equation for the elements of a 3 3 matrix the eigenvalue decomposition of the symmetric part of the matrix is then used to compute the motion parameters and the plane orientation a new compact notation allows us to show easily that there are at most two planar solutions

estimating the heading direction using normal flow if an observer is moving rigidly with bounded rotation then normal flow measurements i e the spatiotemporal derivatives of the image intensity function give rise to a constraint on the oberver s translation this novel constraint gives rise to a robust qualitative solution to the problem of recovering the observer s heading direction by providing an area where the focus of expansion lies if the rotation of the observer is large then the solution area is large too while small rotation causes the solution area to be small thus giving rise to a robust solution in the paper the relationship between the solution area and the rotation and translation vectors is studied and experimental results using synthetic and real calibrated image sequences are presented this work demonstrates that the algorithm developed in horn and weldon 1987 for the case of pure translation if appropriately modified results in a robust algorithm that works in the case of general rigid motion with bounded rotation subsequently it has the potential to replace expensive accelerometers inertial systems and inaccurate odometers in practical navigational systems for the problem of kinetic stabilization which is a prerequisite for any other navigational ability

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

what can be seen in a noisy optical flow field projected by a moving planar patch in 3d space abstract in this paper we would like to propose a brand new interpretation to the so called structure from motion sfm problem the optical flow field projected by a moving rigid planar patch in 3d space is our main consideration instead of just obtaining an explicit 3d motion pose solution like the old approaches did before we focus our attention on analyzing its error sensitivity uncertainty and ambiguity from another point of view our new method can handle the above error analysis easily as known well before the optical flow field projected by a 3d moving planar patch can be completely expressed by eight coefficients two for second order four for first order and two for zeroth order based on these flow coefficients easily determined by a linear regression method or other similar approaches the error sensitivity of 3d estimates can be analyzed quantitatively and qualitatively in a coarse to fine way the concepts of camera fixation and singular value decomposition svd play important roles in our analysis there are three goals for our experiments 1 to prove the correctness of the algorithms simulated image 2 to show the tendency of error sensitivity when the 3d poses of the target planar patch are varied in a controlled manner simulated image 3 to show that our analysis is workable in the real world application real world image

identification and estimation of nonlinear models with misclassification error using instrumental variables a general solution abstract this paper provides a general solution to the problem of identification and estimation of nonlinear models with misclassification error in a general discrete explanatory variable using instrumental variables the misclassification error is allowed to be correlated with all the explanatory variables in the model it is not enough to identify the model by simply generalizing the identification in the binary case with a claim that the number of restrictions is no less than that of the unknowns such a claim requires solving a complicated nonlinear system of equations this paper introduces a matrix diagonalization technique which allows one to easily find the unique solution of the system the solution shows that the latent model can be expressed as an explicit function of directly observed distribution functions therefore the latent model is nonparametrically identifiable and directly estimable using instrumental variables the results show that certain monotonicity restrictions on the latent model may lead to its identification with virtually no restrictions on the misclassification probabilities an alternative identification condition suggests that the nonparametric identification may rely on the belief that people always have a higher probability of telling the truth than of misreporting the nonparametric identification in this paper directly leads to a n consistent semiparametric estimator the monte carlo simulation and empirical illustration show that the estimator performs well with a finite sample and real data

a review on egomotion by means of differential epipolar geometry applied to the movement of a mobile robot the estimation of camera egomotion is an old problem in computer vision since the 1980s many approaches based on both the discrete and the differential epipolar constraint have been proposed the discrete case is used mainly in self calibrated stereoscopic systems whereas the differential case deals with a single moving camera this article surveys several methods for 3d motion estimation unifying the mathematics convention which are then adapted to the common case of a mobile robot moving on a plane experimental results are given on synthetic data covering more than 0 5 million estimations these surveyed algorithms have been programmed and are available on the internet

on the problem of correspondence in range data and some inelastic uses for elastic nets in this work the authors propose a novel method to obtain correspondence between range data across image frames using neural like mechanisms the method is computationally efficient and tolerant of noise and missing points elastic nets which evolved out of research into mechanisms to establish ordered neural projections between structures of similar geometry are used to cast correspondence as an optimization problem this formulation is then used to obtain approximations to the motion parameters under the assumption of rigidity inelasticity these parameter scan be used to recover correspondence experimental results are presented to establish the veracity of the scheme and the method is compared to earlier attempts in this direction

direct computation of qualitative 3 d shape and motion invariants structure from motion often refers to the computation of three dimensional structure from a matched sequence of images however a depth map of a surface is difficult to compute and may not be a good representation for storage and recognition given matched images it is shown that the sign of the normal curvature in a given direction at a given point in the image can be computed from a simple difference of slopes of line segments in one image using this result local surface patches can be classified as convex concave cylindrical hyperbolic saddle point or planar at the same time the translational component of the optical flow from which the focus of expansion can be computed is obtained