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Linear Pushbroom Cameras
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1994
"... Modelling th# push broom sensors commonly used in satellite imagery is quite di#cult and computationally intensive due to th# complicated motion ofth# orbiting satellite with respect to th# rotating earth# In addition, th# math#46 tical model is quite complex, involving orbital dynamics, andh#(0k is ..."
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Cited by 140 (6 self)
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Modelling th# push broom sensors commonly used in satellite imagery is quite di#cult and computationally intensive due to th# complicated motion ofth# orbiting satellite with respect to th# rotating earth# In addition, th# math#46 tical model is quite complex, involving orbital dynamics, andh#(0k is di#cult to analyze. Inth#A paper, a simplified model of apush broom sensor(th# linear push broom model) is introduced. Ith as th e advantage of computational simplicity wh#A9 atth# same time giving very accurate results compared with th# full orbitingpush broom model. Meth# ds are given for solving th# major standardph# togrammetric problems for th e linear push broom sensor. Simple noniterative solutions are given for th# following problems : computation of th# model parameters from groundcontrol points; determination of relative model parameters from image correspondences between two images; scene reconstruction given image correspondences and groundcontrol points. In addition, th# linearpush broom model leads toth#0 retical insigh ts th# t will be approximately valid for th# full model as well.Th# epipolar geometry of linear push broom cameras in investigated and sh own to be totally di#erent from th at of a perspective camera. Neverth eless, a matrix analogous to th e essential matrix of perspective cameras issh own to exist for linear push broom sensors. Fromth#0 it is sh# wn th# t a scene is determined up to an a#ne transformation from two viewswith linearpush broom cameras. Keywords :push broom sensor, satellite image, essential matrixph# togrammetry, camera model The research describ ed in this paper hasb een supportedb y DARPA Contract #MDA97291 C0053 1 Real Push broom sensors are commonly used in satellite cameras, notably th# SPOT satellite forth# generatio...
Understanding noise sensitivity in structure from motion

, 1996
"... Solutions to the structure from motion problem have been shown to be very sensitive to measurement noise and the respective motion and geometry configuration. Statistical error analysis has become an invaluable tool in analyzing the sensitivity phenomenon. This paper presents a unifying approach to ..."
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Cited by 54 (5 self)
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Solutions to the structure from motion problem have been shown to be very sensitive to measurement noise and the respective motion and geometry configuration. Statistical error analysis has become an invaluable tool in analyzing the sensitivity phenomenon. This paper presents a unifying approach to the problems of statistical bias, correlated noise, choice of error metrics, geometric instabilities and information fusion exploring several assumptions commonly used in motion estimation and reviews several promising techniques for motion estimation. The techniques are based on a small number of principles of statistics and perturbation theory. The analyticity of the approach enables the design of alternatives overcoming the observed instabilities.
The Coupling of Rotation and Translation in Motion Estimation of Planar Surfaces
"... This paper studies the error sensitivity in the estimation of the 3Dmotion and the normal of a planar surface from an instantaneous motion field. We use the statistical theory of the CramerRao lower bound for the error covariance in the estimated motion and structure parameters which enables the d ..."
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Cited by 32 (0 self)
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This paper studies the error sensitivity in the estimation of the 3Dmotion and the normal of a planar surface from an instantaneous motion field. We use the statistical theory of the CramerRao lower bound for the error covariance in the estimated motion and structure parameters which enables the derivation of results valid for any unbiased estimator under the assumption of Gaussian noise in the motion eld. The obtained lowerboundmatrix is studied analytically with respect to the measurement noise, size of the field of view and the motiongeometry configuration. The main result of this analysis is the coupling between translation and rotation which is exacerbated if the field of view and the slant of the plane become smaller and the deviation of the translation from the viewing direction becomes larger. Byproducts of this study are the relationships of the uncertainty bounds for every unknown motion parameter to the angle between translation and the planenormal, the size of the field of view, the distance from the perceived plane and the translation magnitude.
Recursive Motion and Structure Estimation with Complete Error Characterization
, 1993
"... We present an algorithm that performs recursive estimation of egomotion and ambient structure from a stream of monocular perspective images of a number of feature points. The algorithm is based on an Extended Kalman Filter (EKF) that integrates over time the instantaneous motion and structure measu ..."
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Cited by 28 (8 self)
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We present an algorithm that performs recursive estimation of egomotion and ambient structure from a stream of monocular perspective images of a number of feature points. The algorithm is based on an Extended Kalman Filter (EKF) that integrates over time the instantaneous motion and structure measurements computed by a 2perspectiveviews step. Key features of our filter are (1) global observability of the model, (2) complete online characterization of the uncertainty of the measurements provided by the twoviews step. The filter is thus guaranteed to be wellbehaved regardless of the particular motion undergone by the observer. Regions of motion space that do not allow recovery of structure (e.g. pure rotation) may be crossed while maintaining good estimates of structure and motion; whenever reliable measurements are available they are exploited. The algorithm works well for arbitrary motions with minimal smoothness assumptions and no ad hoc tuning. Simulations are presented that il...
A multiframe structurefrommotion algorithm under perspective projection
 International Journal of Computer Vision
, 1999
"... Abstract. We present a fast, robust algorithm for multiframe 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 rea ..."
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Cited by 25 (2 self)
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Abstract. We present a fast, robust algorithm for multiframe 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 twoimage 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 basrelief ambiguity and exemplifies how such an analysis can be exploited to improve reconstruction. Also, we demonstrate a structurefrommotion 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 focallength variations strengthen the effects of the basrelief ambiguity. This paper includes extensive experimental studies of twoframe reconstruction and the Tomasi/Kanade approach in comparison to our algorithm. We find that twoframe algorithms are surprisingly robust and accurate, despite some problems with local minima. We demonstrate experimentally that a nearly optimal
Optimal Structure from Motion: Local Ambiguities and Global Estimates
, 2000
"... “Structure From Motion” (SFM) refers to the problem of estimating spatial properties of a threedimensional scene from the motion of its projection onto a twodimensional surface, such as the retina. We present an analysis of SFM which results in algorithms that are provably convergent and provably o ..."
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Cited by 23 (5 self)
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“Structure From Motion” (SFM) refers to the problem of estimating spatial properties of a threedimensional scene from the motion of its projection onto a twodimensional surface, such as the retina. We present an analysis of SFM which results in algorithms that are provably convergent and provably optimal with respect to a chosen norm. In particular, we cast SFM as the minimization of a highdimensional quadratic cost function, and show how it is possible to reduce it to the minimization of a twodimensional function whose stationary points are in onetoone correspondence with those of the original cost function. As a consequence, we can plot the reduced cost function and characterize the configurations of structure and motion that result in local minima. As an example, we discuss two local minima that are associated with wellknown visual illusions. Knowledge of the topology of the residual in the presence of such local minima allows us to formulate minimization algorithms that, in addition to provably converge to stationary points of the original cost function, can switch between different local extrema in order to converge to the global minimum, under suitable conditions. We also offer an experimental study of the distribution of the estimation error in the presence of noise in the measurements, and characterize the sensitivity of the algorithm using the structure of Fisher’s Information matrix.
Motion and structure from two perspective views: From essential parameters to euclidean motion via fundamental matrix
 Journal of the Optical Society of America A
, 1997
"... The standard approach consists of two stages: (i) using the 8point algorithm to estimate the 9 essential parameters defined up to a scale factor; (ii) refining the motion estimation based on some statistically optimal criteria, which is a nonlinear estimation problem on a fivedimensional space. Un ..."
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Cited by 23 (7 self)
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The standard approach consists of two stages: (i) using the 8point algorithm to estimate the 9 essential parameters defined up to a scale factor; (ii) refining the motion estimation based on some statistically optimal criteria, which is a nonlinear estimation problem on a fivedimensional space. Unfortunately, the results obtained are often not satisfactory. The problem is that the second stage is very sensitive to the initial guess, and that it is very difficult to obtain a precise initial estimate from the first stage. This is because we perform a projection of a set of quantities which are estimated in a space of 8 dimensions (by neglecting the constraints on the essential parameters), much higher than that of the real space which is fivedimensional. We propose in this paper a novel approach by introducing an intermediate stage which consists in estimating a 3 × 3 matrix defined up to a scale factor by imposing the rank2 constraint (the matrix has seven independent parameters, and is known as the fundamental matrix). The idea is to gradually project parameters estimated in a high dimensional space onto a slightly lower space, namely from 8 dimensions to 7 and finally to 5. The proposed approach has been tested with synthetic and real data, and a considerable improvement has been observed. Our conjecture from this work is that the imposition of the constraints arising from projective geometry should be used as an intermediate step in order to obtain reliable 3D Euclidean motion and structure estimation from multiple calibrated images. The software is available from the Internet.
A New Multistage Approach to Motion and Structure Estimation: From Essential Parameters to Euclidean Motion Via Fundamental Matrix
, 1996
"... The classical approach to motion and structure estimation problem from two perspective projections consists of two stages: (i) using the 8point algorithm to estimate the 9 essential parameters defined up to a scale factor, which is a linear estimation problem; (ii) refining the motion estimation ba ..."
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Cited by 20 (1 self)
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The classical approach to motion and structure estimation problem from two perspective projections consists of two stages: (i) using the 8point algorithm to estimate the 9 essential parameters defined up to a scale factor, which is a linear estimation problem; (ii) refining the motion estimation based on some statistically optimal criteria, which is a nonlinear estimation problem on a fivedimensional space. Unfortunately, the results obtained using this approach are often not satisfactory, especially when the motion is small or when the observed points are close to a degenerate surface (e.g. plane). The problem is that the second stage is very sensitive to the initial guess, and that it is very difficult to obtain a precise initial estimate from the first stage. This is because we perform a projection of a set of quantities which are estimated in a space of 8 dimensions, much higher than that of the real space which is fivedimensional. We propose in this paper a novel approach by introducing...
Recursive Motion and Structure Estimation with Complete Error Characterization
"... We present an algorithm that performs recursive estimation of egomotion and ambient structure from a stream of monocular perspective images of a number of feature points. The algorithm is based on an Extended Kalman Filter (EKF) that integrates over time the instantaneous motion and structure measu ..."
Abstract
 Add to MetaCart
We present an algorithm that performs recursive estimation of egomotion and ambient structure from a stream of monocular perspective images of a number of feature points. The algorithm is based on an Extended Kalman Filter (EKF) that integrates over time the instantaneous motion and structure measurements computed by a 2perspectiveviews step. Key features of our filter are (1) global observability of the model, (2) complete online characterization of the uncertainty of the measurements provided by the twoviews step. The filter is thus guaranteed to be wellbehaved regardless of the particular motion undergone by the observer. Regions of motion space that do not allow recovery of structure (e.g. pure rotation) may be crossed while maintaining good estimates of structure and motion; whenever reliable measurements are available they are exploited. The algorithm works well for arbitrary motions with minimal smoothness assumptions and no ad hoc tuning. Simulations are presented that illustrate these characteristics.