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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
On the Consistency of the Normalized EightPoint Algorithm
 J MATH IMAGING VIS (2007) 28: 19–27
, 2007
"... A recently proposed argument to explain the improved performance of the eightpoint algorithm that results from using normalized data (Chojnacki, W., et al. in IEEE Trans. Pattern Anal. Mach. Intell. 25(9):1172–1177, 2003) relies upon adoption of a certain model for statistical data distribution. U ..."
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A recently proposed argument to explain the improved performance of the eightpoint algorithm that results from using normalized data (Chojnacki, W., et al. in IEEE Trans. Pattern Anal. Mach. Intell. 25(9):1172–1177, 2003) relies upon adoption of a certain model for statistical data distribution
A Consistency Result for the Normalized EightPoint Algorithm
, 2007
"... A recently proposed argument to explain the improved performance of the eightpoint algorithm that results from using normalized data [IEEE Trans. Pattern Anal. Mach. Intell., 25(9):1172–1177, 2003] relies upon adoption of a certain model for statistical data distribution. Under this model, the cost ..."
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A recently proposed argument to explain the improved performance of the eightpoint algorithm that results from using normalized data [IEEE Trans. Pattern Anal. Mach. Intell., 25(9):1172–1177, 2003] relies upon adoption of a certain model for statistical data distribution. Under this model
Revisiting Hartley's Normalized EightPoint Algorithm
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2003
"... Abstract — Hartley’s eightpoint algorithm has maintained an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods. In this paper, a novel explanation is given for the improvement in performance of the e ..."
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Cited by 16 (4 self)
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Abstract — Hartley’s eightpoint algorithm has maintained an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods. In this paper, a novel explanation is given for the improvement in performance
Revisiting Hartley's Normalised EightPoint Algorithm
"... The eightpoint algorithm of Hartley has maintained an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods. In this paper, a novel explanation is given for the improvement in performance of the eightp ..."
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The eightpoint algorithm of Hartley has maintained an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods. In this paper, a novel explanation is given for the improvement in performance of the eightpoint
A statistical rationalisation of Hartley’s normalised eightpoint algorithm
 In Proc. 12th Int. Conf. Image Analysis and Processing
, 2003
"... The eightpoint algorithm of Hartley occupies an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods. In this paper, a novel explanation is given for the improvement in performance of the eightpoint al ..."
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Cited by 1 (1 self)
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The eightpoint algorithm of Hartley occupies an important place in computer vision, notably as a means of providing an initial value of the fundamental matrix for use in iterative estimation methods. In this paper, a novel explanation is given for the improvement in performance of the eightpoint
RankConstrained Fundamental Matrix Estimation by Polynomial Global Optimization Versus the EightPoint Algorithm
, 2012
"... The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eightpoint algorithm and twoview projective bundle adjustment. The eightpoint algorithm first computes a simple linear least squares solution by minimizing an algebraic cost and then computes ..."
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Cited by 2 (0 self)
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The fundamental matrix can be estimated from point matches. The current gold standard is to bootstrap the eightpoint algorithm and twoview projective bundle adjustment. The eightpoint algorithm first computes a simple linear least squares solution by minimizing an algebraic cost
Invariant fitting of two view geometry or ‘in defiance of the eight point algorithm
 In BMVC
, 2003
"... This paper describes the adaptation the Bookstein method for fitting conics to determination of epipolar geometry. The new method has the advantage that it exhibits the improved stability of previous methods for estimating the epipolar geometry, such as the preconditioning method of Hartley, whilst ..."
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Cited by 6 (1 self)
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This paper describes the adaptation the Bookstein method for fitting conics to determination of epipolar geometry. The new method has the advantage that it exhibits the improved stability of previous methods for estimating the epipolar geometry, such as the preconditioning method of Hartley, whilst also being invariant to equiform transformations. Within this paper it is proven that there is only one invariant norm to the set of Euclidean transformations of the image, and that this norm gives rise to a quadratic form allowing eigenvector methods to be used to find the essential matrix E, the fundamental matrix F, or an arbitrary homography H. This is a surprising result, as previously it had been thought that there was no more to say on the matter of linear estimation of epipolar geometry. The improved performance is justified by theory and verified by experiments on real images. 1
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
ThreeDimensional Structure Calculation: Achieving Accuracy without Calibration
, 2002
"... This paper addresses the problem of computing the camera motion and the threedimensional structure of a scene using two uncalibrated images as inputs. The camera motion is calculated by estimating the essential matrix and using approximate values, easily available, for the intrinsic parameters. The ..."
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Cited by 2 (0 self)
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. The classical eightpoint algorithm to calculate the essential matrix is known to be very sensitive to pixelnoise even when the intrinsic parameters are perfectly known. This paper shows that by using the normalized eightpoint algorithm, aimed at calculating the fundamental matrix, the pixelnoise sensitivity
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