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A General Solution to the P4P Problem for Camera with Unknown Focal Length

Martin Bujnak, Zuzana Kukelova, Tomás Pajdla
CVPR 2008
doi:10.1109/CVPR.2008.4587793 /cvpr/2008/bujnak2008cvpr-general/

Abstract

This paper presents a general solution to the determination of the pose of a perspective camera with unknown focal length from images of four 3D reference points. Our problem is a generalization of the P3P and P4P problems previously developed for fully calibrated cameras. Given four 2D-to-3D correspondences, we estimate camera position, orientation and recover the camera focal length. We formulate the problem and provide a minimal solution from four points by solving a system of algebraic equations. We compare the Hidden variable resultant and Grobner basis techniques for solving the algebraic equations of our problem. By evaluating them on synthetic and on real-data, we show that the Grobner basis technique provides stable results.

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Text

Bujnak et al. "A General Solution to the P4P Problem for Camera with Unknown Focal Length." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2008. doi:10.1109/CVPR.2008.4587793

Markdown

[Bujnak et al. "A General Solution to the P4P Problem for Camera with Unknown Focal Length." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2008.](https://mlanthology.org/cvpr/2008/bujnak2008cvpr-general/) doi:10.1109/CVPR.2008.4587793

BibTeX

@inproceedings{bujnak2008cvpr-general,
  title     = {{A General Solution to the P4P Problem for Camera with Unknown Focal Length}},
  author    = {Bujnak, Martin and Kukelova, Zuzana and Pajdla, Tomás},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {2008},
  doi       = {10.1109/CVPR.2008.4587793},
  url       = {https://mlanthology.org/cvpr/2008/bujnak2008cvpr-general/}
}