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238
A Robust Technique for Matching Two Uncalibrated Images Through the Recovery of the Unknown Epipolar Geometry
, 1994
"... ..."
Camera SelfCalibration: Theory and Experiments
, 1992
"... . The problem of finding the internal orientation of a camera (camera calibration) is extremely important for practical applications. In this paper a complete method for calibrating a camera is presented. In contrast with existing methods it does not require a calibration object with a known 3D shap ..."
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Cited by 364 (28 self)
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. The problem of finding the internal orientation of a camera (camera calibration) is extremely important for practical applications. In this paper a complete method for calibrating a camera is presented. In contrast with existing methods it does not require a calibration object with a known 3D shape. The new method requires only point matches from image sequences. It is shown, using experiments with noisy data, that it is possible to calibrate a camera just by pointing it at the environment, selecting points of interest and then tracking them in the image as the camera moves. It is not necessary to know the camera motion. The camera calibration is computed in two steps. In the first step the epipolar transformation is found. Two methods for obtaining the epipoles are discussed, one due to Sturm is based on projective invariants, the other is based on a generalisation of the essential matrix. The second step of the computation uses the socalled Kruppa equations which link the epipolar...
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 ..."
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Cited by 322 (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.
Flexible camera calibration by viewing a plane from unknown orientations
 in ICCV
, 1999
"... We propose a flexible new technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled ..."
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Cited by 317 (6 self)
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We propose a flexible new technique to easily calibrate a camera. It only requires the camera to observe a planar pattern shown at a few (at least two) different orientations. Either the camera or the planar pattern can be freely moved. The motion need not be known. Radial lens distortion is modeled. The proposed procedure consists of a closedform solution, followed by a nonlinear refinement based on the maximum likelihood criterion. Both computer simulation and real data have been used to test the proposed technique, and very good results have been obtained. Compared with classical techniques which use expensive equipment such as two or three orthogonal planes, the proposed technique is easy to use and flexible. It advances 3D computer vision one step from laboratory environments to real world use. The corresponding software is available from the author’s Web page.
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 236 (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 Fundamental matrix: theory, algorithms, and stability analysis
 International Journal of Computer Vision
, 1995
"... In this paper we analyze in some detail the geometry of a pair of cameras, i.e. a stereo rig. Contrarily to what has been done in the past and is still done currently, for example in stereo or motion analysis, we do not assume that the intrinsic parameters of the cameras are known (coordinates of th ..."
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Cited by 234 (14 self)
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In this paper we analyze in some detail the geometry of a pair of cameras, i.e. a stereo rig. Contrarily to what has been done in the past and is still done currently, for example in stereo or motion analysis, we do not assume that the intrinsic parameters of the cameras are known (coordinates of the principal points, pixels aspect ratio and focal lengths). This is important for two reasons. First, it is more realistic in applications where these parameters may vary according to the task (active vision). Second, the general case considered here, captures all the relevant information that is necessary for establishing correspondences between two pairs of images. This information is fundamentally projective and is hidden in a confusing manner in the commonly used formalism of the Essential matrix introduced by LonguetHiggins [40]. This paper clarifies the projective nature of the correspondence problem in stereo and shows that the epipolar geometry can be summarized in one 3 \Theta 3 ma...
Autocalibration and the absolute quadric
 in Proc. IEEE Conf. Computer Vision, Pattern Recognition
, 1997
"... We describe a new method for camera autocalibration and scaled Euclidean structure and motion, from three or more views taken by a moving camera with fixed but unknown intrinsic parameters. The motion constancy of these is used to rectify an initial projective reconstruction. Euclidean scene structu ..."
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Cited by 213 (7 self)
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We describe a new method for camera autocalibration and scaled Euclidean structure and motion, from three or more views taken by a moving camera with fixed but unknown intrinsic parameters. The motion constancy of these is used to rectify an initial projective reconstruction. Euclidean scene structure is formulated in terms of the absolute quadric — the singular dual 3D quadric ( rank 3 matrix) giving the Euclidean dotproduct between plane normals. This is equivalent to the traditional absolute conic but simpler to use. It encodes both affine and Euclidean structure, and projects very simply to the dual absolute image conic which encodes camera calibration. Requiring the projection to be constant gives a bilinear constraint between the absolute quadric and image conic, from which both can be recovered nonlinearly from images, or quasilinearly from. Calibration and Euclidean structure follow easily. The nonlinear method is stabler, faster, more accurate and more general than the quasilinear one. It is based on a general constrained optimization technique — sequential quadratic programming — that may well be useful in other vision problems.
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 178 (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.
An ImageBased Approach to ThreeDimensional Computer Graphics
, 1997
"... The conventional approach to threedimensional computer graphics produces images from geometric scene descriptions by simulating the interaction of light with matter. My research explores an alternative approach that replaces the geometric scene description with perspective images and replaces the s ..."
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Cited by 167 (4 self)
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The conventional approach to threedimensional computer graphics produces images from geometric scene descriptions by simulating the interaction of light with matter. My research explores an alternative approach that replaces the geometric scene description with perspective images and replaces the simulation process with data interpolation. I derive an imagewarping equation that maps the visible points in a reference image to their correct positions in any desired view. This mapping from reference image to desired image is determined by the centerofprojection and pinholecamera model of the two images and by a generalized disparity value associated with each point in the reference image. This generalized disparity value, which represents the structure of the scene, can be determined from point correspondences between multiple reference images. The imagewarping equation alone is insufficient to synthesize desired images because multiple referenceimage points may map to a single point. I derive a new visibility algorithm that determines a drawing order for the image warp. This algorithm results in correct visibility for the desired image independent of the reference image’s contents. The utility of the imagebased approach can be enhanced with a more general pinholecamera
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