Abstract
We introduce new linear mathematical formulations to calculate the focal length of a camera in an active platform. Through mathematical derivations, we show that the focal lengths in each direction can be estimated using only one point correspondence that relates images taken before and after a degenerate rotation of the camera. The new formulations will be beneficial in robotic and dynamic surveillance environments when the camera needs to be calibrated while it freely moves and zooms. By establishing a correspondence between only two images taken after slightly panning and tilting the camera and a reference image, our proposed Simplified Calibration Method is able to calculate the focal length of the camera. We extensively evaluate the derived formulations on a simulated camera, 3D scenes and real-world images. Our error analysis over simulated and real images indicates that the proposed Simplified Active Calibration formulation estimates the parameters of a camera with low error rates.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Maybank, S.J., Faugeras, O.D.: A theory of self-calibration of a moving camera. Int. J. Comput. Vis. 8(2), 123–151 (1992)
Faugeras, O.D., Luong, Q.-T., Maybank, S.J.: Camera self-calibration: theory and experiments. In: Sandini, G. (ed.) ECCV 1992. LNCS, vol. 588, pp. 321–334. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55426-2_37
Basu, A.: Active calibration. In: Proceedings of 1993 IEEE International Conference on Robotics and Automation, pp. 764–769. IEEE (1993)
Basu, A.: Active calibration: alternative strategy and analysis. In: Proceedings of 1993 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 1993, pp. 495–500. IEEE (1993)
Basu, A.: Active calibration of cameras: theory and implementation. IEEE Trans. Syst. Man Cybern. 25(2), 256–265 (1995)
Basu, A., Ravi, K.: Active camera calibration using pan, tilt and roll. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 27(3), 559–566 (1997)
Junejo, I.N., Foroosh, H.: Optimizing PTZ camera calibration from two images. Mach. Vis. Appl. 23(2), 375–389 (2012)
Zhang, Z.: Flexible camera calibration by viewing a plane from unknown orientations. In: The Proceedings of the Seventh IEEE International Conference on Computer Vision, vol. 1, pp. 666–673. IEEE (1999)
Faraji, M., Shanbehzadeh, J., Nasrollahi, K., Moeslund, T.B.: Erel: extremal regions of extremum levels. In: 2015 IEEE International Conference on Image Processing (ICIP), pp. 681–685. IEEE (2015)
Faraji, M., Shanbehzadeh, J., Nasrollahi, K., Moeslund, T.: Extremal regions detection guided by maxima of gradient magnitude. IEEE Trans. Image Process. 24, 5401–5415 (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Faraji, M., Basu, A. (2018). A Simplified Active Calibration Algorithm for Focal Length Estimation. In: Basu, A., Berretti, S. (eds) Smart Multimedia. ICSM 2018. Lecture Notes in Computer Science(), vol 11010. Springer, Cham. https://doi.org/10.1007/978-3-030-04375-9_32
Download citation
DOI: https://doi.org/10.1007/978-3-030-04375-9_32
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-04374-2
Online ISBN: 978-3-030-04375-9
eBook Packages: Computer ScienceComputer Science (R0)