on kineopsis and computation of structure and motion this correspondence deals with the computation of structure and motion of rigid objects in space from image positions and optical flow a test for rigid motion of objects in space is introduced which yields a new formulation of the problem assuming a central projection model for the viewing system it is shown that image positions and optical flow at four points can achieve this perception

the asymptotics of solutions of singularly perturbed functional differential equations distributed and concentrated delays are different abstract this paper illustrates the differences between systems with distributed delays and systems having only concentrated delays in what concerns the asymptotic rates of solutions of singularly perturbed linear retarded functional differential equations an example of a system with distributed delays shows that the introduction of a slow variable coupled with the fast variable may decrease the asymptotic rates of solutions observed when the perturbation parameter is close to zero such a situation cannot happen for ordinary differential equations or even for differential difference equations

convergence and boundary layers in singularly perturbed linear functional differential equations abstract the convergence of solutions of singularly perturbed systems of linear retarded functional differential equations to solutions of the associated degenerate problem is discussed in connection with the geometry of the flow in phase spaces defined in terms of square integrable functions

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

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

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

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

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

motion from flow along contours a note on robustness and ambiguous cases the projected contours of a rigid body in motion define a velocity field a flow in the image plane where the tangential components are invisible we investigate robustness when estimating motion parameters from the normal components of velocity along contours ambiguous curves are contours for which no unique motion can be recovered from normal flow we show that they are field lines of some extra velocity field which causes an invisible motion when added on top of the actual velocity field these field lines coincide with the contour this is an analytical description of what waxman and wohn 1984 called the aperture problem in the large which actually was studied by lie 1893 under the concept of self projective curves if we specialize to a planar surface patch we make a catalogue of the class of ambiguous curves we study the robustness of motion parameters obtained by least squares estimation by calculating the a mount by which noise in the normal flow is magnified for simple curves and a motion model with four unknowns two translation components rotation and expansion there are explicit formulas relating the robustness of motion parameters to how large a portion of the contour we use sometimes it helps to use more global information a larger portion of e g a closed contour and sometimes there is no way out because we are working with contour segments that too closely resemble ambiguous curves neither is there any hope to recover the true velocity field from normal flow locally since any contour falls into one of the ill conditioned contours

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

motion estimation based on multiple local constraints and nonlinear smoothing abstract a new algorithm for estimating motion from image sequences is presented initial motion estimates are determined based on a least squares solution to a set of independent linear constraints on the motion at a pixel these initial estimates are then improved by a nonlinear smoothing operation the results of this algorithm are compared with those obtained by the horn schunck algorithm on a number of image sequences

estimation of motion from sequential images using integral constraints abstract a novel method for estimating nonuniform motion from sequential images is presented which is based on integral brightness constancy constraints the equations which transform arbitrary integrals between sequential images are expressed as a function of the displacement field and intensity changes the apparent displacement field is then computed by iterative projections onto the solution space of each linearized transformation equation some properties of this technique are demonstrated on a synthetic image pair realistic motion estimation is also demonstrated using sequential tagged cine magnetic resonance images

uniqueness of solution of neumann problem for nonlinear elliptic equation abstract we prove under assumptions lg u concave and a x u u increasing in u existence and uniqueness of solutions u w 1 p l to equations of the form i 1 n x i u b i x u x a x u u x 0 x

robust optical flow estimation using semi invariant local features this paper presents a robust algorithm for computation of 2 d optical flow using the principle of conservation of a set of invariant local features that are representatives of local gray level properties in an image specifically a set of rotation invariant local orthogonal zernike moments is used as invariant features these are inherently integral based features and therefore are expected to be robust against possible variations of intensity values that may occur over a sequence of images due to sensor noise varying illumination etc the 2 d local optical flow field is obtained using singular value decomposition of an overdetermined set of linear equations of velocity field components resulting from the principle of conservation of invariant features in a small neighborhood the proposed moment based approach is compared with two existing optical flow techniques experimental results with synthetic as well as real sequences are presented to demonstrate the overall robustness of the proposed approach

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

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

optical flow by nonlinear relaxation abstract in this paper we present a local approach to the computation of raw optical flow fields based on nonlinear relaxation which is explicitly designed to be coupled with a nonlinear vector filtering technique so as to achieve an effective rejection of the outliers we derive the approach from a standard linear algorithm the one dimensional least squares this is split down into two steps first the linear algorithm is formulated as an iterative procedure in which image points in a suitable geometric neighborhood are made to interact each other second a nonlinearity term in the elementary interaction between neighbors is added which depends on the gaussian interaction of elements of a velocity neighborhood the results of a comparison with two linear local techniques show clearly the effectiveness of the approach both in terms of motion boundary preservation and of optical flow field density

asymptotic stability for a homogeneous singularly perturbed system of differential equations with unbounded delay sufficient conditions for equiasymptotic stability of the null solution of a homogeneous singularly perturbed system of differential equations with unbounded delay are obtained

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

experiments in computing optical flow with the gradient based multiconstraint method abstract in this paper we present results on experiments in computing optical flow with the multiconstraint approach this approach relies on the gradient equation which relates spatial and temporal changes in the image to optical flow and the use of various image functions the experiments reported here are performed on camera acquired pictures and use feature operators to derive image functions from the original luminance function results indicate that this approach is promising

a model and tracking algorithm for a class of video targets algorithms are developed for a real time automatic system capable of tracking two dimensional 2 d targets in complex scenes a mathematical model of 2 d image spatial and temporal evolution applicable to certain classes of targets and target perturbations is developed it is shown that for small target perturbations the 2 d tracking problem may be approximated as a 1 d time varying parameter estimation problem a ccd implementable solution is developed which is particularly useful when considering target rotation and dilation and target background separation results of system simulation and suggestions for future research are presented

analysis of video image sequences using point and line correspondences abstract in this research we investigate the problem of analyzing time varying imagery using a feature based approach we assume a scenario where the imaged objects remain stationary while the camera moves the goal is to compute the structure of the imaged objects and the motion of the camera from a sequence of video images the proposed method exploits the principle of the invariance of rigid configurations during motion using the rigidity constraints we specify equations based on distance and angular invariance to compute the structural parameters of the imaged 3d objects independently of the camera s motion once the structural parameters are recovered the motion parameters can be computed the strength of our approach is in the decomposition of the computations of structure and motion and in the use of point and line correspondences simultaneously the main advantage of using both points and lines is that our approach is not limited to objects whose images have only a particular type of feature in abundance in this research we consider the special case of four points and one line which are the minimum feature sets required for computing the structure and motion parameters we then consider additional features in an overdetermined system of equations to improve the reliability and accuracy of the computation we present computer simulation results as well as results from real image sequences to demonstrate the algorithm s validity

computation and analysis of image motion a synopsis of current problems and methods the goal of this paper is to offer a structured synopsis of the problems in image motion computation and analysis and of the methods proposed exposing the underlying models and supporting assumptions a sufficient number of pointers to the literature will be given concentrating mostly on recent contributions emphasis will be on the detection measurement and segmentation of image motion tracking and deformable motion issues will be also addressed finally a number of related questions which could require more investigations will be presented

asymptotic stability of the solutions of a linear singularly perturbed system with unbounded delay abstract sufficient conditions for asymptotic stability of the solutions of a linear singularly perturbed system of differential equations with unbounded delay have been found under the same conditions it is proved that for a locally lipschitz initial function the initial value problem for the system degenerates regularly

to the uniqueness problem for nonlinear elliptic equations we prove existence and uniqueness of solutions u w1 2 l to equations of the form i 1n xi u bi x u x a x u u x 0 x our nonstandard assumptions on the coefficients are such that log u is concave and a x u u is increasing in u such assumptions are natural in view of drift diffusion processes for example in semiconductors and chemotaxis

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

optical flow from constraint lines parametrization abstract optical flow is a measure of the change of image brightness in a frame sequence and is commonly used as an approximation of the velocity field which is the perspective projection of the three dimensional 3d real velocity on the image plane one method for evaluating optical flow is based on the optical flow constraint ofc equation such an equation is associated with each image pixel under the assumption that in the immediate neighbourhood of a pixel the optical flow field is smooth the constraint equations in that neighbourhood should have a common solution least squares techniques are commonly used to derive the solution which typically is very sensitive to discontinuities a new method of evaluating the optical flow from the ofc equation is presented which performs well in the presence of discontinuities the method proposes to accumulate evidence from the solution of all pairs of constraints in each image segment to provide the most probable value for optical flow rather than adopting least squares techniques the proposed accumulation of evidence is performed using a variant of the hough transform the combinatorial hough transform experimental results under different types of motion are presented an efficient implementation of the algorithm is discussed on a highly parallel architecture

multiconstraint wiener based motion compensation using wavelet pyramids we have investigated an original motion estimation method that exploits several frequency subbands of wavelet pyramids using a multigrid multiconstraint strategy a recursive and iterative solution based on the wiener approach allows to take into account the reconstruction quality criterion that is crucial to image coding experiments show its performances in terms of compression ratio reconstruction quality and reduction of implementation complexity compared to a monoresolution case

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

exponential estimates for singularly perturbed linear fuctional differential equations abstract exponential estimates on the fundamental matrix uniform on the perturbation parameter are obtained for singularly perturbed systems of linear retarded functional differential equations under the assumption that the eigenvalues of a certain coefficient matrix in the system have negative real parts the exponential rates in the estimates are computable from upper bounds on the real parts of the characteristic values of the system or of associated simpler equations differences between differential difference equations and equations with distributed delays are emphasized

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