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Linear npoint camera pose determination
 ieee Transactions on Pattern Analysis and Machine Intelligence
, 1999
"... AbstractÐThe determination of camera position and orientation from known correspondences of 3D reference points and their images is known as pose estimation in computer vision and space resection in photogrammetry. It is wellknown that from three corresponding points there are at most four algebraic ..."
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Cited by 81 (2 self)
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AbstractÐThe determination of camera position and orientation from known correspondences of 3D reference points and their images is known as pose estimation in computer vision and space resection in photogrammetry. It is wellknown that from three corresponding points there are at most four algebraic solutions. Less appears to be known about the cases of four and five corresponding points. In this paper, we propose a family of linear methods that yield a unique solution to 4 and 5point pose determination for generic reference points. We first review the 3point algebraic method. Then we present our twostep, 4point and onestep, 5point linear algorithms. The 5point method can also be extended to handle more than five points. Finally, we demonstrate our methods on both simulated and real images. We show that they do not degenerate for coplanar configurations and even outperform the special linear algorithm for coplanar configurations in practice. Index TermsÐPose estimation, space resection, 2D3D image orientation, exterior orientation determination, perspectivenpointproblem, four points, five points. 1
Appendix  Projective Geometry for Machine Vision
, 1992
"... Introduction The idea for this Appendix arose from our perception of a frustrating situation faced by vision researchers. For example, one is interested in some aspect of the theory of perspective image formation such as the epipolar line. The interested party goes to the library to check out a boo ..."
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Cited by 27 (0 self)
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Introduction The idea for this Appendix arose from our perception of a frustrating situation faced by vision researchers. For example, one is interested in some aspect of the theory of perspective image formation such as the epipolar line. The interested party goes to the library to check out a book on projective geometry filled with hope that the necessary mathematical machinery will be directly at hand. These expectations are quickly dashed. Upon opening the book, the expectant reader finds the presentation dominated by endless observations about harmonic relations and a few chapters which explore the minutiae of Pappus' theorem. Finally, as a last cruel twist of irony, the book ends in triumph with a rather exhilarating discourse on the conic pencil. All of the material is presented in the form of theorems defined on points, lines and conics without the use of coordinates, except perhaps for a quick pause to define barycentric coordinates just to taunt the reader. Dejected, the vis
Camera pose revisited: New linear algorithms
 In 14„eme Congr„es Francophone de Reconnaissance des Formes et Intelligence Artificielle. Paper in French
, 2002
"... Abstract. Camera pose estimation is the problem of determining the position and orientation of an internally calibrated camera from known 3D reference points and their images. We briefly survey several existing methods for pose estimation, then introduce four new linear algorithms. The first three g ..."
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Cited by 12 (0 self)
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Abstract. Camera pose estimation is the problem of determining the position and orientation of an internally calibrated camera from known 3D reference points and their images. We briefly survey several existing methods for pose estimation, then introduce four new linear algorithms. The first three give a unique linear solution from four points by SVD null space estimation. They are based on resultant matrices: the 24 × 24 method is the raw resultant matrix, and the 12 × 12 and 9 × 9 methods are compressed versions of this obtained by Gaussian elimination with pivoting on constant entries. The final method returns the four intrinsic solutions to the pose from 3 points problem. It is based on eigendecomposition of a 5 × 5 matrix. One advantage of all these methods is that they are simple to implement. In particular, the matrix entries are simple functions of the input data. Numerical experiments are given comparing the performance of the new algorithms with several existing algebraic and linear methods.
Fast and Reliable Object Pose Estimation from Line Correspondences
"... . In this paper, we describe a fast object pose estimation method from 3D to 2D line correspondences using a perspective camera model. The principle consists in iteratively improving the pose computed with an affine camera model (either weak perspective or paraperspective) to converge, at the limi ..."
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. In this paper, we describe a fast object pose estimation method from 3D to 2D line correspondences using a perspective camera model. The principle consists in iteratively improving the pose computed with an affine camera model (either weak perspective or paraperspective) to converge, at the limit, to a pose estimation computed with a perspective camera model. Thus, the advantage of the method is to reduce the problem to solving a linear system at each iteration step. The iterative algorithms that we describe in detail in this paper can deal with non coplanar or coplanar object models and have interesting properties both in terms of speed and rate of convergence. 1 Introduction and background The problem of object pose from 2D to 3D correspondences has received a lot of attention for the last years. The perspective camera model has associated with it, in general, non linear object pose computation techniques. This naturally leads to non linear minimization methods which require s...