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

recursive 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

a paraperspective factorization method for shape and motion recovery the factorization method first developed by tomasi and kanade 1992 recovers both the shape of an object and its motion from a sequence of images using many images and tracking many feature points to obtain highly redundant feature position information the method robustly processes the feature trajectory information using singular value decomposition svd taking advantage of the linear algebraic properties of orthographic projection however an orthographic formulation limits the range of motions the method can accommodate paraperspective projection first introduced by ohta et al 1981 is a projection model that closely approximates perspective projection by modeling several effects not modeled under orthographic projection while retaining linear algebraic properties our paraperspective factorization method can be applied to a much wider range of motion scenarios including image sequences containing motion toward the camera and aerial image sequences of terrain taken from a low altitude airplane

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

singular value decomposition eigenfaces and 3d reconstructions singular value decomposition svd is one of the most important and useful factoriza tions in linear algebra we describe how svd is applied to problems involving image processing in particular how svd aids the calculation of so called eigenfaces which pro vide an efficient representation of facial images in face recognition although the eigenface technique was developed for ordinary grayscale images the technique is not limited to these images imagine an image where the different shades of gray convey the physical three dimensional structure of a face although the eigenface technique can again be applied the problem is finding the three dimensional image in the first place we therefore also show how svd can be used to reconstruct three dimensional objects from a two dimensional video stream

model based brightness constraints on direct estimation of structure and motion we describe a direct method for estimating structure and motion from image intensities of multiple views we extend the direct methods of horn and weldon 1988 to three views adding the third view enables us to solve for motion and compute a dense depth map of the scene directly from image spatio temporal derivatives in a linear manner without first having to find point correspondences or compute optical flow we describe the advantages and limitations of this method which are then verified with experiments using real images

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

structure from motion causally integrated over time we describe an algorithm for reconstructing three dimensional structure and motion causally in real time from monocular sequences of images we prove that the algorithm is minimal and stable in the sense that the estimation error remains bounded with probability one throughout a sequence of arbitrary length we discuss a scheme for handling occlusions point features appearing and disappearing and drift in the scale factor these issues are crucial for the algorithm to operate in real time on real scenes we describe in detail the implementation of the algorithm which runs on a personal computer and has been made available to the community we report the performance of our implementation on a few representative long sequences of real and synthetic images the algorithm which has been tested extensively over the course of the past few years exhibits honest performance when the scene contains at least 20 40 points with high contrast when the relative motion is slow compared to the sampling frequency of the frame grabber 30 hz and the lens aperture is large enough typically more than 30 spl deg of visual field

linear and incremental acquisition of invariant shape models from image sequences we show how to automatically acquire euclidian shape representations of objects from noisy image sequences under weak perspective the proposed method is linear and incremental requiring no more than pseudoinverse a nonlinear but numerically sound preprocessing stage is added to improve the accuracy of the results even further experiments show that attention to noise and computational techniques improves the shape results substantially with respect to previous methods proposed for ideal images

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

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

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

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

robust ego motion estimation and 3 d model refinement using surface parallax we present an iterative algorithm for robustly estimating the ego motion and refining and updating a coarse depth map using parametric surface parallax models and brightness derivatives extracted from an image pair given a coarse depth map acquired by a range finder or extracted from a digital elevation map dem ego motion is estimated by combining a global ego motion constraint and a local brightness constancy constraint using the estimated camera motion and the available depth estimate motion of the three dimensional 3 d points is compensated we utilize the fact that the resulting surface parallax field is an epipolar field and knowing its direction from the previous motion estimates estimate its magnitude and use it to refine the depth map estimate the parallax magnitude is estimated using a constant parallax model cpm which assumes a smooth parallax field and a depth based parallax model dbpm which models the parallax magnitude using the given depth map we obtain confidence measures for determining the accuracy of the estimated depth values which are used to remove regions with potentially incorrect depth estimates for robustly estimating ego motion in subsequent iterations experimental results using both synthetic and real data both indoor and outdoor sequences illustrate the effectiveness of the proposed algorithm

brief paper observer forms for perspective systems the estimation of three dimensional position information from two dimensional images in computer vision systems can be formulated as a state estimation problem for a nonlinear perspective dynamic system the multi output state estimation problem has been treated by several authors using methods for nonlinear observer design this paper shows that a perspective system can be transformed to two observer forms and provides constructive methods for arriving at the transformations these observer forms lead to straightforward observer designs first it is shown that using an output transformation the system admits an observer form which leads to an observer with linear error dynamics a second observer design is based on a time scaled block triangular form both designs assume a commonly used observability condition the designs are demonstrated in simulation

scalable extrinsic calibration of omni directional image networks we describe a linear time algorithm that recovers absolute camera orientations and positions along with uncertainty estimates for networks of terrestrial image nodes spanning hundreds of meters in outdoor urban scenes the algorithm produces pose estimates globally consistent to roughly 0 1 2 milliradians and 5 centimeters on average or about four pixels of epipolar alignment we assume that adjacent nodes observe overlapping portions of the scene and that at least two distinct vanishing points are observed by each node the algorithm decouples registration into pure rotation and translation stages the rotation stage aligns nodes to commonly observed scene line directionss the translation stage assigns node positions consistent with locally estimated motion directions then registers the resulting network to absolute earth coordinates the paper s principal contributions include extension of classic registration methods to large scale and dimensional extents a consistent probabilistic framework for modeling projective uncertaintys and a new hybrid of hough transform and expectation maximization algorithms we assess the algorithm s performance on synthetic and real data and draw several conclusions first by fusing thousands of observations the algorithm achieves accurate registration even in the face of significant lighting variations low level feature noise and error in initial pose estimates second the algorithm s robustness and accuracy increase with image field of view third the algorithm surmounts the usual tradeoff between speed and accuracys it is both faster and more accurate than manual bundle adjustment

generating mapping class groups with elements of fixed finite order abstract we show that for k 6 and g sufficiently large the mapping class group of a surface of genus g can be generated by three elements of order k we also show that this can be done with four elements of order 5 when g is at least 8

adaptive visual servoing using common image features with unknown geometric parameters this paper generalizes the concept of the depth independent interaction matrix developed for point and line features in our early work to generalized image features we derive the conditions under which the depth independent interaction matrix can be linearly parameterized by the geometric parameters of the generalized image features and propose an adaptive visual servo controller for robot manipulators using the generalized image features whose geometric parameters are unknown to estimate the unknown parameters on line we propose new error functions that are linear to estimation errors of the parameters and an algorithm that minimizes the error functions using multiple images the lyapunov theory is used to prove asymptotic stability of the proposed controller based on the nonlinear dynamics of the manipulator it is also shown that in addition to points and lines other common image features like distances angles areas and centroids all satisfy the conditions for the linear parameterization experiments have been conducted to validate the proposed control method

optimal motion and structure estimation the causes of existing linear algorithms exhibiting various high sensitivities to noise are analyzed it is shown that even a small pixel level perturbation may override the epipolar information that is essential for the linear algorithms to distinguish different motions this analysis indicates the need for optimal estimation in the presence of noise methods are introduced for optimal motion and structure estimation under two situations of noise distribution known and unknown computationally the optimal estimation amounts to minimizing a nonlinear function for the correct convergence of this nonlinear minimization a two step approach is used the first step is using a linear algorithm to give a preliminary estimate for the parameters the second step is minimizing the optimal objective function starting from that preliminary estimate as an initial guess a remarkable accuracy improvement has been achieved by this two step approach over using the linear algorithm alone

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

absolute motion and structure from stereo image sequences without stereo correspondence and analysis of degenerate cases this paper deals with the estimation of motion and structure with an absolute scale factor from stereo image sequences without stereo correspondence we show that the absolute motion and structure can be determined using only motion correspondences this property is very useful in two aspects first motion correspondence is easier to solve than stereo correspondence because sequences of images can be taken at short time intervals second it is not necessary that the rigid scene be included in the intersection of the field of view of the two cameras it is also shown that the degenerate cases reported in this paper constitute all of the degenerate cases for the scheme and can be easily avoided

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

every mapping class group is generated by 6 involutions abstract let mod g b denote the mapping class group of a surface of genus g with b punctures luo asked in torsion elements in the mapping class group of a surface math gt 0004048 v1 8apr2000 if there is a universal upper bound independent of genus for the number of torsion elements needed to generate mod g b we answer luo s question by proving that 3 torsion elements suffice to generate mod g 0 we also prove the more delicate result that there is an upper bound independent of genus not only for the number of torsion elements needed to generate mod g b but also for the order of those elements in particular our main result is that 6 involutions i e orientation preserving diffeomorphisms of order two suffice to generate mod g b for every genus g 3 b 0 and g 4 b 1

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

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

the structure of the torelli group i a finite set of generators for j this is the first of three papers concerning the so called torelli group let m mg be a compact orientable surface of genus g having n boundary components and let 9 xg be its mapping class group that is the group of orientation preserving diffeomorphisms of m which are 1 on the boundary am modulo isotopies which fix 3m pointwise this group is also known to the complex analysts as the teichmuller group or modular group if n 0 or 1 let further 4 jg be the subgroup of d1 which acts trivially on h1 m z the topologists have no traditional name for a but the analysts tell me it was known classically and is called the torelli group several interesting problems and conjectures exist concerning f the principal one can be found in kirby s problem list k and asks if gg is finitely generated in this first paper we shall answer the question affirmatively for both gg 0 and fgg when g 3 and shall give a fairly simple set of generators two other conjectures were made by the author the first involves the subgroup j of f which is generated by twists on nulhomologous simple closed curves ji produces a surjective homomorphism t fgg 1 a3h1 m z which kills c and it is conjectured there that in fact 5y ker t the proof of this is the content of the second paper in the third paper we use the results of the second to compute the abelianization f f explicitly thereby verifying another conjecture in ji the first reasonably simple but infinite set of generators for fg0 was produced by powell in p his generators consist of two types a twists on bounding simple closed curves b opposite twists on a bounding pair of disjoint homologous simple closed curves each of which are nonbounding using his result the author showed in j2 that the maps of the second type which we call bp maps for bounding pair are actually sufficient to generate both kg 0 and fg 1 for g 3 and in fact that we need only those whose two curves bound a genus one subsurface of m note that for g 2 all bp maps are trivial and hence the result fails in this case in the finite set of generators produced in this paper only

shape ambiguities in structure from motion this paper examines the fundamental ambiguities and uncertainties inherent in recovering structure from motion by examining the eigenvectors associated with null or small eigenvalues of the hessian matrix we can quantify the exact nature of these ambiguities and predict how they affect the accuracy of the reconstructed shape our results for orthographic cameras show that the bas relief ambiguity is significant even with many images unless a large amount of rotation is present similar results for perspective cameras suggest that three or more frames and a large amount of rotation are required for metrically accurate reconstruction

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

continuous stereo self calibration by camera parameter tracking this paper presents a consistent framework for continuous stereo self calibration based on a practical analysis of the sensitivity of stereo reconstruction to camera calibration uncertainties we identify important parameters for self calibration we evaluate different geometric constraints for estimation and tracking of these parameters bundle adjustment with reduced structure representation relating corresponding points in image sequences the epipolar constraint between stereo image pairs and trilinear constraints between image triplets continuous recursive calibration refinement is obtained with a robust adapted iterated extended kalman filter to achieve high accuracy physically relevant geometric optimization criteria are formulated in a gauss helmert type model the self calibration framework is tested on an active stereo system experiments with synthetic data as well as on natural indoor and outdoor imagery indicate that the different constraints are complementing each other and thus a method combining two of the above constraints is proposed while reduced order bundle adjustment gives by far the most accurate results and might suffice on its own in some environments the epipolar constraint yields instantaneous calibration that is not affected by independently moving objects in the scene hence it expedites and stabilizes the calibration process

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

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

generating the surface mapping class group by two elements wajnryb proved in 1996 that the mapping class group of an orientable surface is generated by two elements we prove that one of these generators can be taken as a dehn twist we also prove that the extended mapping class group is generated by two elements again one of which is a dehn twist another result we prove is that the mapping class groups are also generated by two elements of finite order

recursive estimation of 3d motion and surface structure from local affine flow parameters a recursive structure from motion algorithm based on optical flow measurements taken from an image sequence is described it provides estimates of surface normal in addition to 3d motion and depth the measurements are affine motion parameters which approximate the local flow fields associated with near planar surface patches in the scene these are integrated over time to give estimates of the 3d parameters using an extended kalman filter this also estimates the camera focal length and so the 3d estimates are metric the use of parametric measurements means that the algorithm is computationally less demanding than previous optical flow approaches and the recursive filter builds in a degree of noise robustness results of experiments on synthetic and real image sequences demonstrate that the algorithm performs well

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

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

calculation of the hidden symmetry operator in symmetric quantum mechanics in a recent paper it was shown that if a hamiltonian h has an unbroken symmetry then it also possesses a hidden symmetry represented by the linear operator the operator commutes with both h and the inner product with respect to is associated with a positive norm and the quantum theory built on the associated hilbert space is unitary in this paper it is shown how to construct the operator for the non hermitian symmetric hamiltonian h 1 2p2 1 2x2 ix3 using perturbative techniques it is also shown how to construct the operator for h 1 2p2 1 2x2 x4 using nonperturbative methods

risk sensitive filters for recursive estimation of motion from images in this paper an extended risk sensitive filter ersf is used to estimate the motion parameters of an object recursively from a sequence of monocular images the effect of varying the risk factor spl theta on the estimation error is examined the performance of the filter is compared with the extended kalman filter ekf and the theoretical cramer rao lower bound when the risk factor spl theta and the uncertainty in the measurement noise are large the initial estimation error of the ersf is less than that of the corresponding ekf the ersf is also found to converge to the steady state value of the error faster than the ekf in situations when the uncertainty in the initial estimate is large and the ekf diverges the ersf converges with small errors in confirmation with the theory as spl theta tends to zero the behavior of the ersf is the same as that of the ekf