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

critical phenomena in linear elliptic problems abstract in this article we consider the existence and nonexistence of principal eigenvalues for the linear elliptic equation u v x u in r n and u d 1 2 r n where n 3 and v l 1 loc r n with v 0 in r n we establish that when potential v has strong singularities phenomena which appear under critical exponent nonlinearities brezis and nirenberg are present in linear problems as well

nonlinear observers for perspective time invariant linear systems perspective dynamical systems arise in machine vision in which only perspective observation is available this paper proposes and studies a luenberger type nonlinear observer for perspective time invariant linear systems assuming a given perspective time invariant linear system to be lyapunov stable and to satisfy some sort of detectability condition it is shown that the estimation error converges exponentially to zero finally some simple numerical examples are presented to illustrate the result obtained

minimal mass blow up solutions for the l2 critical nls with inverse square potential abstract we study minimal mass blow up solutions of the focusing l 2 critical nonlinear schrodinger equation with inverse square potential i t u u c x 2 u u 4 n u 0 with n 3 and 0 c n 2 2 4 we first prove a sharp global well posedness result all h 1 solutions with a mass i e l 2 norm strictly below that of the ground states are global note that unlike the equation in free space we do not know if the ground state is unique in the presence of the inverse square potential nevertheless all ground states have the same minimal mass we then construct and classify finite time blow up solutions at the minimal mass threshold up to the symmetries of the equation every such solution is a pseudo conformal transformation of a ground state solution

canonical forms and parameter identification problems in perspective systems we introduce canonical forms for perspective dynamical systems under the action of a perspective group and illustrate their application to parameter identification with the aid of a single charged coupled device camera we show that the parameters in the canonical form can be identified uniquely using an extended kalman filter

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

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

lower semicontinuity of functionals via the concentration compactness principle in this paper we show the weak lower semicontinuity of some classes of functionals using the concentration compactness principle of p l lions these functionals involve an integral term and we do not know whether it can be handled by the de giorgi theorem the semicontinuity result allows us to prove several existence results for quasilinear elliptic equations

rigid affine and locally affine registration of free form surfaces in this paper we propose a new framework to perform nonrigid surface registration it is based on various extensions of an iterative algorithm recently presented by several researchers besl and mckay 1992 champleboux et al 1992 chen and medioni 1992 menq and lai 1992 zhang 1994 to rigidly register surfaces represented by a set of 3d points when a prior estimate of the displacement is available our framework consists of three stages first we search for the best rigid displacement to superpose the two surfaces we show how to efficiently use curvatures to superpose principal frames at possible corresponding points in order to find a prior rough estimate of the displacement and initialize the iterative algorithm second we search for the best affine transformation we introduce differential information in points coordinates this allows us to match locally similar points then we show how principal frames and curvatures are transformed by an affine transformation finally we introduce this differential information in a global criterion minimized by extended kalman filtering in order to ensure the convergence of the algorithm third we locally deform the surface instead of computing a global affine transformation we attach to each point a local affine transformation varying smoothly along the surface we call this deformation a locally affine deformation all these stages are illustrated with experiments on various real biomedical surfaces teeth faces skulls brains and hearts which demonstrate the validity of the approach

a realization theory for perspective systems with applications to parameter estimation problems in machine vision in this paper we introduce and study a linear dynamical system with a perspective observation function the study of these systems has been shown to be useful in motion and shape estimation problems in machine vision we introduce the notion of perspective observability and obtain under a special case a necessary and sufficient condition that would guarantee observability of the initial condition of the linear dynamical system up to a one parameter magnitude scaling subsequently a new realization theory is introduced which is useful for studying linear systems with perspective observation our main result is to show that parameters can be recovered up to orbits of a suitable perspective group a new rescaling algorithm is described to identify parameters up to orbits of the perspective system the identification problem is further analyzed in detail for various problems that are of interest in machine vision

a perspective theory for motion and shape estimation in machine vision in this paper we consider the problem of motion and shape estimation of a moving body with the aid of a monocular camera we show that the estimation problem reduces to a specific parameter estimation of a perspective dynamical system surprisingly the above reduction is independent of whether the data measured is the brightness pattern which the object produces on the image plane or whether the data observed are points lines or curves on the image plane produced as a result of discontinuities in the brightness pattern many cases of the perspective parameter estimation problem have been analyzed in this paper these cases include a fairly complete analysis of a planar textured surface undergoing a rigid flow and an affine flow these two cases have been analyzed for orthographic pseudo orthographic and image centered projections the basic procedure introduced for parameter estimation is to subdivide the problem into two modules one for spatial averaging and the other for time averaging the estimation procedure is carried out with the aid of a new realization theory for perspective systems introduced for systems described in discrete time and in continuous time finally much of our analysis has been substantiated by computer simulation of specific algorithms developed in order to explicitly compute the parameters detailed simulation that would answer the perspective realizability question is a subject of future research

state observer for a class of nonlinear systems and its application to machine vision in this note we consider the state observer problem for a class of nonlinear systems which are usually encountered in the machine vision study the formulation of the state observer is motivated by the sliding mode methods and adaptive control techniques the proposed observer is applied to the identification problems of the motion parameters and space position of a moving object by using the perspective observation of a single point it is clarified that the rotation parameters can be observed by using the observation of one camera and the position and translation parameters cannot be observed by using one camera and must appeal to stereo vision simulation results show that the proposed algorithm is effective

iterative point matching for registration of free form curves and surfaces a heuristic method has been developed for registering two sets of 3 d curves obtained by using an edge based stereo system or two dense 3 d maps obtained by using a correlation based stereo system geometric matching in general is a difficult unsolved problem in computer vision fortunately in many practical applications some a priori knowledge exists which considerably simplifies the problem in visual navigation for example the motion between successive positions is usually approximately known from this initial estimate our algorithm computes observer motion with very good precision which is required for environment modeling e g building a digital elevation map objects are represented by a set of 3 d points which are considered as the samples of a surface no constraint is imposed on the form of the objects the proposed algorithm is based on iteratively matching points in one set to the closest points in the other a statistical method based on the distance distribution is used to deal with outliers occlusion appearance and disappearance which allows us to do subset subset matching a least squares technique is used to estimate 3 d motion from the point correspondences which reduces the average distance between points in the two sets both synthetic and real data have been used to test the algorithm and the results show that it is efficient and robust and yields an accurate motion estimate

motion and shape identification with vision and range in this paper we consider the problem of motion and shape estimation using a camera and a laser range finder the object considered is a plane which is undergoing a riccati motion the camera observes features on the moving plane perspectively the range finder camera is capable of obtaining the range of the plane along a given laser plane which can either be kept fixed or can be altered in time finally we assume that the identification is carried out as soon as the visual and range data is available or after a suitable temporal integration in each of these various cases we derive to what extent the motion and shape parameters are identifiable and characterize the results as an orbit of a suitable group the paper does not emphasize any specific choice of algorithm

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

range identification for perspective vision systems in this note a new observer is developed to determine range information and hence the three dimensional 3 d coordinates of an object feature moving with affine motion dynamics or the more general ricatti motion dynamics with known motion parameters the unmeasurable range information is determined from a single camera provided an observability condition is satisfied that has physical significance to develop the observer the perspective system is expressed in terms of the nonlinear feature dynamics the structure of the proposed observer is inspired by recent disturbance observer results the proposed technique facilitates a lyapunov based analysis that is less complex than the sliding mode based analysis derived for recent observer designs the analysis demonstrates that the 3 d task space coordinates of the feature point can be asymptotically identified simulation results are provided that illustrate the performance of the observer in the presence of noise

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

motion recovery by using stereo perspective observation the motion recovery for a class of movements in the space is considered in this note by using the stereo perspective observation of at least three points the motion equation that is considered can cover a wide class of practical movements in the space the asymptotic estimation of the motion parameters which are all time dependent variables is developed based on the second method of lyapunov furthermore the proposed algorithm can be modified to deal with occlusion phenomenon to illustrate the performance of the proposed algorithm it is compared with the extended kalman filter ekf by computer simulations

homogeneous dynamical systems theory we study controlled homogeneous dynamical systems and derive conditions under which the system is perspective controllable we also derive conditions under which the system is observable in the presence of a control over the complex base field in the absence of any control input we derive a necessary and sufficient condition for observability of a homogeneous dynamical system over the real base field the observability criterion obtained generalizes a well known popov belevitch hautus rank criterion to check the observability of a linear dynamical system finally we introduce rational exponential interpolation problems as an important step toward solving the problem of realizing homogeneous dynamical systems with minimum state dimensions

identification of riccati dynamics under perspective and orthographic observations the problem of identifying motion and shape parameters of a planar object undergoing a riccati motion from the associated optical flow generated on the image plane of a single ccd camera is studied the optical flow is generated by projecting feature points on the object onto the image plane via perspective and orthographic projections an important result we show is that under perspective projection the parameters of a specific riccati dynamics that extend the well known rigid motion can be identified up to choice of a sign the paper also discusses other riccati equations obtained from quadratic extension of a rigid motion and affine motion for each of the various motion models considered and for each of the two projection models we show that the extent to which motion and shape parameters can be recovered from optical flow can in fact be recovered from the linear approximation of the optical flow we also extend our analysis to a pair of cameras

a new state observer for perspective systems in this note we consider the problem of estimating the state of a class of perspective systems the problem can be converted into the observation of a dynamical system with nonlinearities a new discontinuous state observer which is motivated by the sliding mode control method and adaptive techniques is proposed for the obtained dynamical system the assumptions are reasonable and the convergence conditions are intuitive and have apparently physical interpretations the attraction of the new method is that the algorithm is very simple and easy to be implemented and it is robust to measurement noises further minor a priori knowledge of the system is required in the new formulation simulation results show the superiority of the new method to the traditional ones

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

motion from point matches multiple of solutions in this paper we study the multiplicity of solutions of the motion problem given n point matches between two frames how many solutions are there to the motion problem we show that the maximum number of solutions is 10 when 5 point matches are available this settles a question that has been around in the computer vision community for a while we follow two tracks we show that the two approaches are compatible and yield the same result we then describe a computer implementation of the second approach that uses maple a language for symbolic computation the program allows us to compute exactly the solutions for any configuration of 5 points some experiments are described