The twisted cubic and camera calibration

Buchanan, Thomas

doi:10.1016/0734-189x(88)90146-6

Cited by 42 publications

(14 citation statements)

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“…Without noise in the data, the true model can be estimated without error (assuming we are not in a degenerate situation for the position of the calibration data, such as the twisted cubic for pinhole camera calibration [67]). Even with noise, the availability of infinitely many calibration data may allow a perfect calibration of the true camera model.…”

Section: So Many Models mentioning

confidence: 99%

Camera Models and Fundamental Concepts Used in Geometric Computer Vision

Sturm

2010

FNT in Computer Graphics and Vision

157

122

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A printed and bound version is available at a special discount price of US35 from Now Publishers. This can be obtained by entering the promotional code CGV006023 on https://www.nowpublishers.com/bookorder.aspx?doi=0600000023&product=CGVInternational audienceThis survey is mainly motivated by the increased availability and use of panoramic image acquisition devices, in computer vision and various of its applications. Different technologies and different computational models thereof exist and algorithms and theoretical studies for geometric computer vision ("structure-from-motion") are often re-developed without highlighting common underlying principles. One of the goals of this survey is to give an overview of image acquisition methods used in computer vision and especially, of the vast number of camera models that have been proposed and investigated over the years, where we try to point out similarities between different models. Results on epipolar and multi-view geometry for different camera models are reviewed as well as various calibration and self-calibration approaches, with an emphasis on non-perspective cameras. We finally describe what we consider are fundamental building blocks for geometric computer vision or structure-from-motion: epipolar geometry, pose and motion estimation, 3D scene modeling, and bundle adjustment. The main goal here is to highlight the main principles of these, which are independent of specific camera models

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Section: So Many Models mentioning

confidence: 99%

Camera Models and Fundamental Concepts Used in Geometric Computer Vision

Sturm

2010

FNT in Computer Graphics and Vision

157

122

View full text Add to dashboard Cite

show abstract

“…Let us consider extreme cases. Without noise in the data, the true model can be estimated without error (assuming we are not in a degenerate situation for the position of the calibration data, such as the twisted cubic for pinhole camera calibration [67]). Even with noise, the availability of infinitely many calibration data may allow a perfect calibration of the true camera model.…”

Section: So Many Models mentioning

confidence: 99%

Camera Models and Fundamental Concepts Used in Geometric Computer Vision

Sturm

Ramalingam²,

Tardif

et al. 2010

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This survey is mainly motivated by the increased availability and use of panoramic image acquisition devices, in computer vision and various of its applications. Different technologies and different computational models thereof exist and algorithms and theoretical studies for geometric computer vision ("structure-from-motion") are often redeveloped without highlighting common underlying principles. One of the goals of this survey is to give an overview of image acquisition methods used in computer vision and especially, of the vast number of camera models that have been proposed and investigated over the years, where we try to point out similarities between different models. Results on epipolar and multi-view geometry for different camera models are reviewed as well as various calibration and self-calibration approaches, with an emphasis on non-perspective cameras. We finally describe what we consider are fundamental building blocks for geometric computer vision or structure-from-motion: epipolar geometry, pose and motion estimation, 3D scene modeling, and bundle adjustment. The main goal here is to highlight the main principles of these, which are independent of specific camera models.

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“…The properties of a twisted cubic underlie many of the ambiguous cases which arise in reconstruction [1], [4], [10], [2], and underlie the invariants of points and lines in images and space [8], [9]. The invariant representation of a twisted cubic showed in Section 3 is free of coordinate systems, which implies that it can be conveniently used in computer vision.…”

Section: Application In Computer Visionmentioning

confidence: 99%

“…Our representation is both sufficient and necessary, and is free of choice of coordinate systems. Based on such a test, the ambiguous samples generated by six generic space points (see [1]) can be discarded by the initial reconstructed coordinates.…”

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confidence: 99%

The invariant representations of a quadric cone and a twisted cubic

2003

IEEE Trans. Pattern Anal. Machine Intell.

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Up to now, the shortest invariant representation of a quadric has 138 summands and there has been no invariant representation of a twisted cubic in 3D projective space, which limit to some extent the applications of invariants in 3D space. In this paper, we give a very short invariant representation of a quadric cone, a special quadric, which has only two summands similar to the invariant representation of a planar conic, and give a short invariant representation of a twisted cubic. Then, a completely linear algorithm for generating the parametric equations of a twisted cubic is provided also. Finally, we exemplify some applications of our proposed invariant representations in the fields of computer vision and automated geometric theorem proving.

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The twisted cubic and camera calibration

Abstract: We state a uniqueness theorem for camera calibration in terms of the twisted cubic. The theorem assumes the general linear model and is essentially a reformulation of Seydewitz's star generation theorem. 0 1988 Academic Press. Inc.

Cited by 42 publications

References 1 publication

Camera Models and Fundamental Concepts Used in Geometric Computer Vision

Camera Models and Fundamental Concepts Used in Geometric Computer Vision

Camera Models and Fundamental Concepts Used in Geometric Computer Vision

The invariant representations of a quadric cone and a twisted cubic

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