The Experts below are selected from a list of 5556 Experts worldwide ranked by ideXlab platform
Olivier Faugeras - One of the best experts on this subject based on the ideXlab platform.
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characterizing the uncertainty of the Fundamental Matrix
Computer Vision and Image Understanding, 1997Co-Authors: Gabriella Csurka, Cyril Zeller, Zhengyou Zhang, Olivier FaugerasAbstract: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 at the same time. We give 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. Alternatively, we propose a much simpler method which gives analytical results which are close to the results of the statistical method. Experiments with synthetic and real data have been conducted to validate the proposed methods. At the end of the paper, we provide three applications of the estimated uncertainty of the Fundamental Matrix: definition of the epipolar band for stereo matching, projective reconstruction, and self-calibration.
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the Fundamental Matrix theory algorithms and stability analysis
International Journal of Computer Vision, 1996Co-Authors: Quangtuan Luong, Olivier FaugerasAbstract: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 commonlyused formalism of the Essential Matrix introduced by Longuet-Higgins (1981). This paper clarifies the projective nature of the correspondence problem in stereo and shows that the epipolar geometry can be summarized in one 3 x 3 Matrix of rank 2 which we propose to call the Fundamental Matrix. After this theoretical analysis, we embark on the task of estimating the Fundamental Matrix from point corre- spondences, a task which is of practical importance. We analyze theoretically, and compare experimentally using synthetic and real data, several methods of estimation. The problem of the stability of the estimation is studied from two complementary viewpoints. First we show that there is an interesting relationship between the Fundamental Matrix and three-dimensional planes which induce homographies between the images and create unstabilities in the estimation procedures. Second, we point to a deep relation between the unstability of the estimation procedure and the presence in the scene of so-called critical surfaces which have been studied in the context of motion analysis. Finally we conclude by stressing the fact that we believe that the Fundamental Matrix will play a crucial role in future applications of three-dimensional Computer Vision by greatly increasing its versatility, robustness and hence applicability to real difficult problems.
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ECCV (1) - A stability analysis of the Fundamental Matrix
Computer Vision — ECCV '94, 1994Co-Authors: Q T Luong, Olivier FaugerasAbstract:The Fundamental Matrix is a key concept when working with uncalibrated images and multiple viewpoints. It contains all the available geometric information and enables to recover the epipolar geometry from uncalibrated perspective views. This paper is about a stability analysis for the Fundamental Matrix. We first present a probabilistic approach which works well. This approch, however, does not give insight into the causes of unstability. Two complementary explanations for unstability are the nature of the motions, and the interaction between motion and three-dimensional structure, which is characterized by a critical surface. Practical methods to characterize the proximity to the critical surface from image measurements, by estimating a quadratic transformation, are developped. They are then used for experiments which validate our observations. It turns out that surprisingly enough, the critical surface affects the stability of the Fundamental Matrix in a significant number of situations.
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a stability analysis of the Fundamental Matrix
European Conference on Computer Vision, 1994Co-Authors: Q T Luong, Olivier FaugerasAbstract:The Fundamental Matrix is a key concept when working with uncalibrated images and multiple viewpoints. It contains all the available geometric information and enables to recover the epipolar geometry from uncalibrated perspective views. This paper is about a stability analysis for the Fundamental Matrix. We first present a probabilistic approach which works well. This approch, however, does not give insight into the causes of unstability. Two complementary explanations for unstability are the nature of the motions, and the interaction between motion and three-dimensional structure, which is characterized by a critical surface. Practical methods to characterize the proximity to the critical surface from image measurements, by estimating a quadratic transformation, are developped. They are then used for experiments which validate our observations. It turns out that surprisingly enough, the critical surface affects the stability of the Fundamental Matrix in a significant number of situations.
R. Mohr - One of the best experts on this subject based on the ideXlab platform.
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Geometrical constraints of the synthetic method of estimating Fundamental Matrix and its analysing
Science China-technological Sciences, 1999Co-Authors: Peiyi Shen, Chengke Wu, Long Quan, Wei Wang, R. MohrAbstract:The new geometrical constraints, based on the geometrical analysing of synthetic method, are developed to estimate Fundamental Matrix (F Matrix). Applying the new constraints, the four parameters of Fundamental Matrix could be estimated firstly, and these four parameters are the coordinates of the two epipoles. The other four parameters of the Fundamental Matrix could be solved by solving the linear equations with the other new constraint secondly, and these parameters represent the homography between the two pencils of epipolar lines. The synthetic data and the real data are used to test the new method. And the method is of the advantages of obvious geometrical meaning, and high stability of the epipoles of the Fundamental Matrix.
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Epipole and Fundamental Matrix estimation using virtual parallax
Proceedings of IEEE International Conference on Computer Vision, 1995Co-Authors: B. Boufama, R. MohrAbstract:The paper addresses the problem of computing the Fundamental Matrix which describes a geometric relationship between a pair of stereo images: the epipolar geometry. We propose a novel method based on virtual parallax. Instead of computing directly the 3/spl times/3 Fundamental Matrix, we compute a homography with one epipole position, and show that this is equivalent to computing the Fundamental Matrix. Simple equations are derived by reducing the number of parameters to estimate. As a consequence, we obtain an accurate Fundamental Matrix of rank two with a stable linear computation. Experiments with simulated and real images validate our method and clearly show the improvement over existing methods.
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ICCV - Epipole and Fundamental Matrix estimation using virtual parallax
Proceedings of IEEE International Conference on Computer Vision, 1995Co-Authors: B. Boufama, R. MohrAbstract:The paper addresses the problem of computing the Fundamental Matrix which describes a geometric relationship between a pair of stereo images: the epipolar geometry. We propose a novel method based on virtual parallax. Instead of computing directly the 3/spl times/3 Fundamental Matrix, we compute a homography with one epipole position, and show that this is equivalent to computing the Fundamental Matrix. Simple equations are derived by reducing the number of parameters to estimate. As a consequence, we obtain an accurate Fundamental Matrix of rank two with a stable linear computation. Experiments with simulated and real images validate our method and clearly show the improvement over existing methods. >
Y S Hung - One of the best experts on this subject based on the ideXlab platform.
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DICTA - A Robust Method for Estimating the Fundamental Matrix
2020Co-Authors: C L Feng, Y S HungAbstract:In this paper, we propose a robust method to estimate the Fundamental Matrix in the presence of outliers. The new method uses random minimum subsets as a search engine to find inliers. The Fundamental Matrix is computed from a minimum subset and subsequently evaluated over the entire data set by means of the same measure, namely minimization of 2D reprojection error. A mixture model of Gaussian and Uniform distributions is used to describe the image errors. An iterative algorithm is developed for estimating the outlier percentage and noise level in the mixture model. Simulation results are provided to illustrate the performance of the proposed method.
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a robust method for estimating the Fundamental Matrix
Digital Image Computing: Techniques and Applications, 2003Co-Authors: C L Feng, Y S HungAbstract:In this paper, we propose a robust method to estimate the Fundamental Matrix in the presence of outliers. The new method uses random minimum subsets as a search engine to find inliers. The Fundamental Matrix is computed from a minimum subset and subsequently evaluated over the entire data set by means of the same measure, namely minimization of 2D reprojection error. A mixture model of Gaussian and Uniform distributions is used to describe the image errors. An iterative algorithm is developed for estimating the outlier percentage and noise level in the mixture model. Simulation results are provided to illustrate the performance of the proposed method.
Rujin Zhao - One of the best experts on this subject based on the ideXlab platform.
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a robust Fundamental Matrix estimation method based on epipolar geometric error criterion
IEEE Access, 2019Co-Authors: Rujin ZhaoAbstract:In this paper, a robust Fundamental Matrix estimation method based on epipolar geometric error criterion is proposed. First, the method removes outliers into the computation of the Fundamental Matrix instead of taking it as an independent processing step. The potential error corresponding points are eliminated by iteration to achieve the stable estimation of the Fundamental Matrix. Then, the epipolar geometry error criterion is used to identify outliers and the estimation results of the Fundamental Matrix are obtained during each iteration. The iterative process can converge quickly. Even if a large number of matched outliers are present, the calculated values will soon become stable. Experiments have been carried out for synthetic and real image pairs, which show that the proposed method performs very well in terms of robustness to noises and outliers. Additionally it has a low computational cost and is convenient for use in practical applications.
C L Feng - One of the best experts on this subject based on the ideXlab platform.
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DICTA - A Robust Method for Estimating the Fundamental Matrix
2020Co-Authors: C L Feng, Y S HungAbstract:In this paper, we propose a robust method to estimate the Fundamental Matrix in the presence of outliers. The new method uses random minimum subsets as a search engine to find inliers. The Fundamental Matrix is computed from a minimum subset and subsequently evaluated over the entire data set by means of the same measure, namely minimization of 2D reprojection error. A mixture model of Gaussian and Uniform distributions is used to describe the image errors. An iterative algorithm is developed for estimating the outlier percentage and noise level in the mixture model. Simulation results are provided to illustrate the performance of the proposed method.
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a robust method for estimating the Fundamental Matrix
Digital Image Computing: Techniques and Applications, 2003Co-Authors: C L Feng, Y S HungAbstract:In this paper, we propose a robust method to estimate the Fundamental Matrix in the presence of outliers. The new method uses random minimum subsets as a search engine to find inliers. The Fundamental Matrix is computed from a minimum subset and subsequently evaluated over the entire data set by means of the same measure, namely minimization of 2D reprojection error. A mixture model of Gaussian and Uniform distributions is used to describe the image errors. An iterative algorithm is developed for estimating the outlier percentage and noise level in the mixture model. Simulation results are provided to illustrate the performance of the proposed method.
