Abstract
Kruppa equation based camera self-calibration is one of the classical problems in computer vision. Most state-of-the-art approaches directly solve the quadratic constraints derived from Kruppa equations, which are computationally intensive and difficult to obtain initial values. In this paper, we propose a new initialization algorithm by estimating the unknown scalar in the equation, thus the camera parameters can be computed linearly in a closed form and then refined iteratively via global optimization techniques. We prove that the scalar can be uniquely recovered from the infinite homography and propose a practical method to estimate the homography from a physical or virtual plane located at a far distance to the camera. Extensive experiments on synthetic and real images validate the effectiveness of the proposed method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Armstrong, M., Zisserman, A., Hartley, R.: Self-calibration from image triplets. In: Buxton, B.F., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1064, pp. 3–16. Springer, Heidelberg (1996)
Chandraker, M., et al.: Autocalibration via rank-constrained estimation of the absolute quadric. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2007)
Faugeras, O.D., Luong, Q.T., Maybank, S.J.: Camera self-calibration: Theory and experiments. In: European Conference on Computer Vision, pp. 321–334 (1992)
Hartley, R.: Self-calibration from multiple views with a rotating camera. In: European Conference on Computer Vision, pp. A: 471–478 (1994)
Hartley, R.: Self-calibration of stationary cameras. International Journal of Computer Vision 22(1), 5–23 (1997)
Hartley, R.: Kruppa’s equations derived from the fundamental matrix. IEEE Trans. Pattern Anal. Mach. Intell. 19(2), 133–135 (1997)
Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004)
Hemayed, E.: A survey of camera self-calibration. In: IEEE Conference on Advanced Video and Signal Based Surveillance, pp. 351–357 (2003)
Heyden, A., Åström, K.: Euclidean reconstruction from image sequences with varying and unknown focal length and principal point. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 438–443 (1997)
Heyden, A., Åström, K.: Minimal conditions on intrinsic parameters for euclidean reconstruction. In: Asian Conference on Computer Vision, pp. 169–176 (1998)
Knight, J., Zisserman, A., Reid, I.: Linear auto-calibration for ground plane motion. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. I: 503–510 (2003)
Lei, C., et al.: A new approach to solving Kruppa equations for camera self-calibration. In: International Conference on Pattern Recognition, pp. 308–311 (2002)
Luong, Q., Faugeras, O.: Self-calibration of a moving camera from point correspondences and fundamental matrices. International Journal of Computer Vision 22(3), 261–289 (1997)
Ma, S.: A self-calibration technique for active vision systems. IEEE Transactions on Robotics and Automation 12(1), 114–120 (1996)
Malis, E., Cipolla, R.: Camera self-calibration from unknown planar structures enforcing the multiview constraints between collineations. IEEE Trans. Pattern Anal. Mach. Intell. 24(9), 1268–1272 (2002)
Maybank, S., Faugeras, O.: A theory of self-calibration of a moving camera. International Journal of Computer Vision 8(2), 123–151 (1992)
Pollefeys, M., Gool, L.J.V., Proesmans, M.: Euclidean 3D reconstruction from image sequences with variable focal lenghts. In: Buxton, B.F., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1064, pp. 31–42. Springer, Heidelberg (1996)
Pollefeys, M., Koch, R., Van Gool, L.: Self-calibration and metric reconstruction in spite of varying and unknown intrinsic camera parameters. International Journal of Computer Vision 32(1), 7–25 (1999)
Pollefeys, M., Van Gool, L.: Stratified self-calibration with the modulus constraint. IEEE Trans. Pattern Anal. Mach. Intell. 21(8), 707–724 (1999)
Ronda, J., Valdes, A., Jaureguizar, F.: Camera autocalibration and horopter curves. International Journal of Computer Vision 57(3), 219–232 (2004)
Seo, Y., Heyden, A.: Auto-calibration by linear iteration using the DAC equation. Image and Vision Computing 22(11), 919–926 (2004)
Triggs, B.: Autocalibration and the absolute quadric. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 609–614 (1997)
Tsai, R.: An efficient and accurate camera calibration technique for 3-D machine vision. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 364–374 (1986)
Valdés, A., Ronda, J., Gallego, G.: The absolute line quadric and camera autocali-bration. International Journal of Computer Vision 66(3), 283–303 (2006)
Xu, G., Sugimoto, N.: Algebraic derivation of the Kruppa equations and a new algorithm for self-calibration of cameras. Journal of the Optical Society of America-A 16(10), 2419–2424 (1999)
Zhang, Z.: A flexible new technique for camera calibration. IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000)
Zhong, H., Hung, Y.: Self-calibration from one circular motion sequence and two images. Pattern Recognition 39(9), 1672–1678 (2006)
Zhong, Y., Zhang, H.: Control point based semi-dense matching. In: Asian Conference on Computer Vision, pp. 374–379 (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, G., Wu, Q.M.J., Zhang, W. (2008). Camera Self-calibration under the Constraint of Distant Plane. In: Sommer, G., Klette, R. (eds) Robot Vision. RobVis 2008. Lecture Notes in Computer Science, vol 4931. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78157-8_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-78157-8_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78156-1
Online ISBN: 978-3-540-78157-8
eBook Packages: Computer ScienceComputer Science (R0)