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157
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 i ..."
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Cited by 401 (9 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&times;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.
View morphing
 In Computer Graphics (SIGGRAPH’96
, 1996
"... Image morphing techniques can generate compelling 2D transitions between images. However, differences in object pose or viewpoint often cause unnatural distortions in image morphs that are difficult to correct manually. Using basic principles of projective geometry, this paper introduces a simple ex ..."
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Cited by 279 (20 self)
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Image morphing techniques can generate compelling 2D transitions between images. However, differences in object pose or viewpoint often cause unnatural distortions in image morphs that are difficult to correct manually. Using basic principles of projective geometry, this paper introduces a simple extension to image morphing that correctly handles 3D projective camera and scene transformations. The technique, called view morphing, works by prewarping two images prior to computing a morph and then postwarping the interpolated images. Because no knowledge of 3D shape is required, the technique may be applied to photographs and drawings, as well as rendered scenes. The ability to synthesize changes both in viewpoint and image structure affords a wide variety of interesting 3D effects via simple image transformations.
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 254 (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.
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 206 (6 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
In Defense of the EightPoint Algorithm
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... Abstract—The fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras, and the eightpoint algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches. It has the advantage of simplicity of implementati ..."
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Cited by 203 (1 self)
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Abstract—The fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras, and the eightpoint algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches. It has the advantage of simplicity of implementation. The prevailing view is, however, that it is extremely susceptible to noise and hence virtually useless for most purposes. This paper challenges that view, by showing that by preceding the algorithm with a very simple normalization (translation and scaling) of the coordinates of the matched points, results are obtained comparable with the best iterative algorithms. This improved performance is justified by theory and verified by extensive experiments on real images. Index Terms—Fundamental matrix, eightpoint algorithm, condition number, epipolar structure, stereo vision.
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 172 (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...
Sequential updating of projective and affine structure from motion
 International Journal of Computer Vision
, 1997
"... A structure from motion algorithm is described which recovers structure and camera position, modulo a projective ambiguity. Camera calibration is not required, and camera parameters such as focal length can be altered freely during motion. The structure is updated sequentially over an image sequenc ..."
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Cited by 161 (4 self)
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A structure from motion algorithm is described which recovers structure and camera position, modulo a projective ambiguity. Camera calibration is not required, and camera parameters such as focal length can be altered freely during motion. The structure is updated sequentially over an image sequence, in contrast to schemes which employ a batch process. A specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described, together with a method to periodically update the affine coordinate frame to prevent drift over time. We describe the constraint used to obtain this specialisation. Structure is recovered from image corners detected and matched automatically and reliably in real image sequences. Results are shown for reference objects and indoor environments, and accuracy of recovered structure is fully evaluated and compared for a number of reconstruction schemes. A specific application of the work is demonstrated  affine structure is used to compute free space maps enabling navigation through unstructured environments and avoidance of obstacles. The path planning involves only affine constructions.
Autocalibration from planar scenes
 European Conference on Computer Vision
, 1998
"... This paper describes a theory and a practical algorithm for the autocalibration of a moving projective camera, from views of a planar scene. The unknown camera calibration, and (up to scale) the unknown scene geometry and camera motion are recovered from the hypothesis that the camera’s internal par ..."
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Cited by 148 (2 self)
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This paper describes a theory and a practical algorithm for the autocalibration of a moving projective camera, from views of a planar scene. The unknown camera calibration, and (up to scale) the unknown scene geometry and camera motion are recovered from the hypothesis that the camera’s internal parameters remain constant during the motion. This work extends the various existing methods for nonplanar autocalibration to a practically common situation in which it is not possible to bootstrap the calibration from an intermediate projective reconstruction. It also extends Hartley’s method for the internal calibration of a rotating camera, to allow camera translation and to provide 3D as well as calibration information. The basic constraint is that the projections of orthogonal direction vectors (points at infinity) in the plane must be orthogonal in the calibrated camera frame of each image. Abstractly, since the two circular points of the 3D plane (representing its Euclidean structure) lie on the 3D absolute conic, their projections into each image must lie on the absolute conic’s image (representing the camera calibration). The resulting numerical algorithm optimizes this constraint over all circular points and projective calibration parameters, using the interimage homographies as a projective scene representation.
Factorization methods for projective structure and motion
 In IEEE Conf. Computer Vision & Pattern Recognition
, 1996
"... This paper describes a family of factorizationbased algorithms that recover 3D projective structure and motion from multiple uncalibrated perspective images of 3D points and lines. They can be viewed as generalizations of the TomasiKanade algorithm from affine to fully perspective cameras, and fro ..."
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Cited by 116 (5 self)
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This paper describes a family of factorizationbased algorithms that recover 3D projective structure and motion from multiple uncalibrated perspective images of 3D points and lines. They can be viewed as generalizations of the TomasiKanade algorithm from affine to fully perspective cameras, and from points to lines. They make no restrictive assumptions about scene or camera geometry, and unlike most existing reconstruction methods they do not rely on ‘privileged’ points or images. All of the available image data is used, and each feature in each image is treated uniformly. The key to projective factorization is the recovery of a consistent set of projective depths (scale factors) for the image points: this is done using fundamental matrices and epipoles estimated from the image data. We compare the performance of the new techniques with several existing ones, and also describe an approximate factorization method that gives similar results to SVDbased factorization, but runs much more quickly for large problems.