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51
A Robust Technique for Matching Two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry
, 1994
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Determining the Epipolar Geometry and its Uncertainty: A Review
 International Journal of Computer Vision
, 1998
"... Two images of a single scene/object are related by the epipolar geometry, which can be described by a 3×3 singular matrix called the essential matrix if images' internal parameters are known, or the fundamental matrix otherwise. It captures all geometric information contained in two images, an ..."
Abstract

Cited by 320 (7 self)
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Two images of a single scene/object are related by the epipolar geometry, which can be described by a 3×3 singular matrix called the essential matrix if images' internal parameters are known, or the fundamental matrix otherwise. It captures all geometric information contained in two images, and its determination is very important in many applications such as scene modeling and vehicle navigation. This paper gives an introduction to the epipolar geometry, and provides a complete review of the current techniques for estimating the fundamental matrix and its uncertainty. A wellfounded measure is proposed to compare these techniques. Projective reconstruction is also reviewed. The software which we have developed for this review is available on the Internet.
Euclidean reconstruction from uncalibrated views
 Applications of Invariance in Computer Vision
, 1993
"... The possibility of calibrating a camera from image data alone, based on matched points identified in a series of images by a moving camera was suggested by Mayband and Faugeras. This result implies the possibility of Euclidean reconstruction from a series of images with a moving camera, or equivalen ..."
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Cited by 233 (14 self)
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The possibility of calibrating a camera from image data alone, based on matched points identified in a series of images by a moving camera was suggested by Mayband and Faugeras. This result implies the possibility of Euclidean reconstruction from a series of images with a moving camera, or equivalently, Euclidean structurefrommotion from an uncalibrated camera. No tractable algorithm for implementing their methods for more than three images have been previously reported. This paper gives a practical algorithm for Euclidean reconstruction from several views with the same camera. The algorithm is demonstrated on synthetic and real data and is shown to behave very robustly in the presence of noise giving excellent calibration and reconstruction results. 1
The development and comparison of robust methods for estimating the fundamental matrix
 International Journal of Computer Vision
, 1997
"... Abstract. This paper has two goals. The first is to develop a variety of robust methods for the computation of the Fundamental Matrix, the calibrationfree representation of camera motion. The methods are drawn from the principal categories of robust estimators, viz. case deletion diagnostics, Mest ..."
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Cited by 220 (9 self)
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Abstract. This paper has two goals. The first is to develop a variety of robust methods for the computation of the Fundamental Matrix, the calibrationfree representation of camera motion. The methods are drawn from the principal categories of robust estimators, viz. case deletion diagnostics, Mestimators and random sampling, and the paper develops the theory required to apply them to nonlinear orthogonal regression problems. Although a considerable amount of interest has focussed on the application of robust estimation in computer vision, the relative merits of the many individual methods are unknown, leaving the potential practitioner to guess at their value. The second goal is therefore to compare and judge the methods. Comparative tests are carried out using correspondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery. In contrast with previously reported methods the goodness of fit to the synthetic observations is judged not in terms of the fit to the observations per se but in terms of fit to the ground truth. A variety of error measures are examined. The experiments allow a statistically satisfying and quasioptimal method to be synthesized, which is shown to be stable with up to 50 percent outlier contamination, and may still be used if there are more than 50 percent outliers. Performance bounds are established for the method, and a variety of robust methods to estimate the standard deviation of the error and covariance matrix of the parameters are examined. The results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but also by gross outliers.
Canonic Representations for the Geometries of Multiple Projective Views
 Computer Vision and Image Understanding
, 1994
"... This work is in the context of motion and stereo analysis. It presents a new uni ed representation which will be useful when dealing with multiple views in the case of uncalibrated cameras. Several levels of information might be considered, depending on the availability of information. Among other t ..."
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Cited by 180 (8 self)
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This work is in the context of motion and stereo analysis. It presents a new uni ed representation which will be useful when dealing with multiple views in the case of uncalibrated cameras. Several levels of information might be considered, depending on the availability of information. Among other things, an algebraic description of the epipolar geometry of N views is introduced, as well as a framework for camera selfcalibration, calibration updating, and structure from motion in an image sequence taken by a camera which is zooming and moving at the same time. We show how a special decomposition of a set of two or three general projection matrices, called canonical enables us to build geometric descriptions for a system of cameras which are invariant with respect to a given group of transformations. These representations are minimal and capture completely the properties of each level of description considered: Euclidean (in the context of calibration, and in the context of structure from motion, which we distinguish clearly), a ne, and projective, that we also relate to each other. In the last case, a new decomposition of the wellknown fundamental matrix is obtained. Dependencies, which appear when three or more views are available, are studied in the context of the canonic decomposition, and new composition formulas are established. The theory is illustrated by tutorial examples with real images.
On the geometry and algebra of the point and line correspondences between N images
, 1995
"... We explore the geometric and algebraic relations that exist between correspondences of points and lines in an arbitrary number of images. We propose to use the formalism of the GrassmannCayley algebra as the simplest way to make both geometric and algebraic statements in a very synthetic and effect ..."
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Cited by 149 (6 self)
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We explore the geometric and algebraic relations that exist between correspondences of points and lines in an arbitrary number of images. We propose to use the formalism of the GrassmannCayley algebra as the simplest way to make both geometric and algebraic statements in a very synthetic and effective way (i.e. allowing actual computation if needed). We have a fairly complete picture of the situation in the case of points: there are only three types of algebraic relations which are satisfied by the coordinates of the images of a 3D point: bilinear relations arising when we consider pairs of images among the N and which are the wellknown epipolar constraints, trilinear relations arising when we consider triples of images among the N , and quadrilinear relations arising when we consider fourtuples of images among the N . In the case of lines, we show how the traditional perspective projection equation can be suitably generalized and that in the case of three images there exist two in...
Selfcalibration from multiple views with a rotating camera
, 1994
"... Abstract. A newpractical method is given for the selfcalibration of a camera. In this method, at least three images are taken from the same point in space with different orientations of the camera and calibration is computed from an analysis of point matches between the images. The method requires ..."
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Cited by 148 (1 self)
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Abstract. A newpractical method is given for the selfcalibration of a camera. In this method, at least three images are taken from the same point in space with different orientations of the camera and calibration is computed from an analysis of point matches between the images. The method requires no knowledge of the orientations of the camera. Calibration is based on the image correspondences only. This method differs fundamentally from previous results by Maybank and Faugeras on selfcalibration using the epipolar structure of image pairs. In the method of this paper, there is no epipolar structure since all images are taken from the same point in space. Since the images are all taken from the same point in space, determination of point matches is considerably easier than for images taken with a moving camera, since problems of occlusion or change of aspect or illumination do not occur. The calibration method is evaluated on several sets of synthetic and real image data. 1
Euclidean Reconstruction from Image Sequences with Varying and Unknown Focal Length and Principal Point
"... In this paper the special case of reconstruction from image sequences taken by cameras with skew equal to 0 and aspect ratio equal to 1 has been treated. These type of cameras, here called cameras with Euclidean image planes, represent rigid projections where neither the principal point nor the foca ..."
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Cited by 105 (9 self)
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In this paper the special case of reconstruction from image sequences taken by cameras with skew equal to 0 and aspect ratio equal to 1 has been treated. These type of cameras, here called cameras with Euclidean image planes, represent rigid projections where neither the principal point nor the focal length is known. It will be shown that it is possible to reconstruct an unknown object from images taken by a camera with Euclidean image plane up to similarity transformations, i.e., Euclidean transformations plus changes in the global scale. An algorithm, using bundle adjustment techniques, has been implemented. The performance of the algorithm is shown on simulated data.
Robust Recovery of the Epipolar Geometry for an Uncalibrated Stereo Rig
, 1994
"... This paper addresses the problem of accurately and automatically recovering the epipolar geometry from an uncalibrated stereo rig and its application to the image matching problem. A robust correlation based approach that eliminates outliers is developped to produce a reliable set of correspondi ..."
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Cited by 88 (16 self)
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This paper addresses the problem of accurately and automatically recovering the epipolar geometry from an uncalibrated stereo rig and its application to the image matching problem. A robust correlation based approach that eliminates outliers is developped to produce a reliable set of corresponding high curvature points. These points are used to estimate the socalled Fundamental Matrix which is closely related to the epipolar geometry of the uncalibrated stereo rig. We show that an accurate determination of this matrix is a central problem. Using a linear criterion in the estimation of this matrix is shown to yield erroneous results. Different parametrization and nonlinear criteria are then developped to take into account the specific constraints of the Fundamental Matrix providing more accurate results. Various experimental results on real images illustates the approach.
Characterizing the Uncertainty of the Fundamental Matrix
 Computer Vision and Image Understanding
, 1995
"... This paper deals with the analysis of the uncertainty of the fundamental matrix. The basic idea is to compute the fundamental matrix and its uncertainty in the same time. We shall show two different methods. The first one is a statistical approach. As in all statistical methods the precision of the ..."
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Cited by 50 (5 self)
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This paper deals with the analysis of the uncertainty of the fundamental matrix. The basic idea is to compute the fundamental matrix and its uncertainty in the same time. We shall show two different methods. The first one is a statistical approach. As in all statistical methods the precision of the results depends on the number of analyzed samples. This means that we can always improve our results if we increase the number of samples but this process is very time consuming. We propose a much simpler method which gives results which are close to the results of the statistical methods. At the end of paper we shall show some experimental results obtained with synthetic and real data.