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Lines and Points in Three Views and the Trifocal Tensor

Author:

Richard I. HartleyAuthors Info & Claims

International Journal of Computer Vision, Volume 22, Issue 2

Pages 125 - 140

https://doi.org/10.1023/A:1007936012022

Published: 01 March 1997 Publication History

Abstract

This paper discusses the basic role of the trifocal tensor in scene reconstruction from three views. This 3\times 3\times 3 tensor plays a role in the analysis of scenes from three views analogous to the role played by the fundamental matrix in the two-view case. In particular, the trifocal tensor may be computed by a linear algorithm from a set of 13 line correspondences in three views. It is further shown in this paper, that the trifocal tensor is essentially identical to a set of coefficients introduced by Shashua to effect point transfer in the three view case. This observation means that the 13-line algorithm may be extended to allow for the computation of the trifocal tensor given any mixture of sufficiently many line and point correspondences. From the trifocal tensor the camera matrices of the images may be computed, and the scene may be reconstructed. For unrelated uncalibrated cameras, this reconstruction will be unique up to projectivity. Thus, projective reconstruction of a set of lines and points may be carried out linearly from three views.

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Cited By

Xu WPeng XKneip L(2024)Tight Fusion of Events and Inertial Measurements for Direct Velocity EstimationIEEE Transactions on Robotics10.1109/TRO.2023.333310840(240-256)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TRO.2023.3333108
Duff TKohn KLeykin APajdla T(2024)PLP: Point-Line Minimal Problems under Partial Visibility in Three ViewsInternational Journal of Computer Vision10.1007/s11263-024-01992-1132:8(3302-3323)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1007/s11263-024-01992-1
Agarwal SDuff TLieblich MThomas R(2024)An Atlas for the Pinhole CameraFoundations of Computational Mathematics10.1007/s10208-022-09592-624:1(227-277)Online publication date: 1-Feb-2024
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Index Terms

Lines and Points in Three Views and the Trifocal Tensor
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision problems
        Reconstruction
      2. Image and video acquisition
        3D imaging
  2. Computer graphics
    1. Animation

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Information & Contributors

Information

Published In

cover image International Journal of Computer Vision

International Journal of Computer Vision Volume 22, Issue 2

March 1997

79 pages

ISSN:0920-5691

Editors:
Takeo Kanade
Carnegie Mellon Univ., Pittsburgh, PA
,
Olivier Faugeras
INRIA, Valbonne, France

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Copyright © Copyright © 1997 Kluwer Academic Publishers.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 March 1997

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Cited By

Xu WPeng XKneip L(2024)Tight Fusion of Events and Inertial Measurements for Direct Velocity EstimationIEEE Transactions on Robotics10.1109/TRO.2023.333310840(240-256)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1109/TRO.2023.3333108
Duff TKohn KLeykin APajdla T(2024)PLP: Point-Line Minimal Problems under Partial Visibility in Three ViewsInternational Journal of Computer Vision10.1007/s11263-024-01992-1132:8(3302-3323)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1007/s11263-024-01992-1
Agarwal SDuff TLieblich MThomas R(2024)An Atlas for the Pinhole CameraFoundations of Computational Mathematics10.1007/s10208-022-09592-624:1(227-277)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1007/s10208-022-09592-6
Nong XHadfield S(2022)ASL-SLAM: An Asynchronous Formulation of Lines for SLAM with Event SensorsProceedings of the 2022 9th International Conference on Industrial Engineering and Applications (Europe)10.1145/3523132.3523146(84-91)Online publication date: 12-Jan-2022
https://dl.acm.org/doi/10.1145/3523132.3523146
Mariotti LEising C(2022)Spherical Formulation of Geometric Motion Segmentation Constraints in Fisheye CamerasIEEE Transactions on Intelligent Transportation Systems10.1109/TITS.2020.304275923:5(4201-4211)Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1109/TITS.2020.3042759
Guan JLi JXi J(2021)Robust Computation of Trifocal Tensor Based on Hybrid Particle Swarm OptimizationProceedings of the 2021 3rd International Conference on Image Processing and Machine Vision10.1145/3469951.3469958(35-41)Online publication date: 22-May-2021
https://dl.acm.org/doi/10.1145/3469951.3469958
Zhou YZhao JLuo C(2021)A novel method for reconstructing general 3D curves from stereo imagesThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-020-01959-637:7(2009-2021)Online publication date: 1-Jul-2021
https://dl.acm.org/doi/10.1007/s00371-020-01959-6
Duff TKohn KLeykin APajdla T(2020)PLP - Point-Line Minimal Problems Under Partial Visibility in Three ViewsComputer Vision – ECCV 202010.1007/978-3-030-58574-7_11(175-192)Online publication date: 23-Aug-2020
https://dl.acm.org/doi/10.1007/978-3-030-58574-7_11
Arrigoni FMagri LPajdla T(2020)On the Usage of the Trifocal Tensor in Motion SegmentationComputer Vision – ECCV 202010.1007/978-3-030-58565-5_31(514-530)Online publication date: 23-Aug-2020
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Zhang KChaumette FChen J(2019)Trifocal tensor-based 6-DOF visual servoingInternational Journal of Robotics Research10.1177/027836491987254438:10-11(1208-1228)Online publication date: 1-Sep-2019
https://dl.acm.org/doi/10.1177/0278364919872544
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