# EXTENSION OF THE GENERALIZED IMAGE RECTIFICATION - Catching the Infinity Cases

### Klaus Häming, Gabriele Peters

#### Abstract

This paper addresses the topic of image rectification, a widely used technique in 3D-reconstruction and stereo vision. The most popular algorithm uses a projective transformation to map the epipoles of the images to infinity. This algorithm fails whenever an epipole lies inside an image. To overcome this drawback, a rectification scheme known as polar rectification can be used. This, however, fails whenever an epipole lies at infinity. For autonomous systems exploring their environment, it can happen that successive camera positions constitute cases where we have an image pair with one epipole at infinity and the other inside an image. So neither of the previous algorithms can be applied directly. We present an extension to the polar rectification scheme. This extension allows the rectification of image pairs whose epipoles lie even at such difficult positions. Additionally, we discuss the necessary computation of the orientation of the epipolar geometry in terms of the fundamental matrix directly, avoiding the computation of a line homography as in the original polar rectification process.

#### References

- Hartley, R. I. and Zisserman, A. (2004). Multiple View Geometry in Computer Vision. Cambridge University Press, ISBN: 0521540518, second edition.
- Laveau, S. and Faugeras, O. D. (1996). Oriented projective geometry for computer vision. In ECCV 7896: Proceedings of the 4th European Conference on Computer Vision-Volume I, pages 147-156, London, UK. Springer.
- Peters, G. (2006). A Vision System for Interactive Object Learning. In IEEE International Conference on Computer Vision Systems (ICVS 2006), New York, USA.
- Pollefeys, M., Koch, R., and van Gool, L. J. (1999). A simple and efficient rectification method for general motion. In Proc. International Conference on Computer Vision (ICCV 1999), pages 496-501.

#### Paper Citation

#### in Harvard Style

Häming K. and Peters G. (2007). **EXTENSION OF THE GENERALIZED IMAGE RECTIFICATION - Catching the Infinity Cases** . In *Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO,* ISBN 978-972-8865-83-2, pages 275-279. DOI: 10.5220/0001620802750279

#### in Bibtex Style

@conference{icinco07,

author={Klaus Häming and Gabriele Peters},

title={EXTENSION OF THE GENERALIZED IMAGE RECTIFICATION - Catching the Infinity Cases},

booktitle={Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO,},

year={2007},

pages={275-279},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001620802750279},

isbn={978-972-8865-83-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 4: ICINCO,

TI - EXTENSION OF THE GENERALIZED IMAGE RECTIFICATION - Catching the Infinity Cases

SN - 978-972-8865-83-2

AU - Häming K.

AU - Peters G.

PY - 2007

SP - 275

EP - 279

DO - 10.5220/0001620802750279