Abstract
Conics-based calibration has been widely inves- tigated in the past several years. The primary method is to utilize the generalized eigenvalue decomposition (GED) of conics. In this paper, we extend the GED method to deal with a general case: two enclosing ellipses. We construct a link between enclosing ellipses and confocal conics. The homography is, thus, decomposed to three components, each of which corresponds to a clear geometrical meaning. Other general conics cases including separate case, intersecting case and hyperbolas case are also discussed. Experiments with simulated and real data demonstrate the good performance of our camera calibration algorithms.
Similar content being viewed by others
References
Zhang Z.: A flexible new technique for camera calibration. IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1344 (2000)
Sturm, P., Maybank, S.: On plane-based camera calibration: A general algorithm, singularities, applications. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE (1999)
Hartley R., Zisserman A.: Multiple View Geometry in Computer Vision, 2 edn. Cambridge University Press, Cambridge (2003)
Chen, Q., Wu, H., Wada, T.: Camera calibration with two arbitrary coplanar circles. In: Proceedings of European Conference on Computer Vision (ECCV). IEEE (2004)
Wu, Y., Zhu, H., Hu, Z., Wu, F.: Camera calibration from the quasi-affine invariance of two parallel circles. In: Proceedings of European Conference on Computer Vision (ECCV). IEEE (2004)
Ying, X., Zha, H.: Camera calibration using principal-axes aligned conics. In: Proceedings of Asian Conference on Computer Vision (ACCV). IEEE (2007)
Gurdjos, P., Kim, J.S., Kweon, I.S.: Euclidean structure from confocal conics: Theory and application to camera calibration. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE (2006)
Gurdjos, P., Sturm, P., Wu, Y.: Euclidean structure from n ≥ 2 parallel circles: Theory and algorithms. In: Proceedings of European Conference on Computer Vision (ECCV). IEEE (2006)
Jiang, G., Quan, L.: Detection of concentric circles for camera calibration. In: Proceedings of International Conference on Computer Vision (ICCV). IEEE (2005)
Kim J.S., Gurdjos P., Kweon I.S.: Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration. IEEE Trans. Pattern Anal. Mach. Intell. 27(4), 637–642 (2005)
Zheng Y., Liu Y.: Camera calibration using one perspective view of two arbitrary coplanar circles. Opt. Eng. 47(6), 067203 (2008)
Rothwell C., Zisserman A., Marinos C., Forsyth D., Mundy J.: Relative motion and pose from arbitrary plane curves. Image Vis. Comput. 10(4), 250–262 (1992)
Semple J., Kneebone. G.: Algebraic Projective Geometry. Oxford Clarendon Press, New York (1952)
Mundy J.L., Zisserman A.: Geometric Invariance in Computer Vision. MIT Press, USA (1992)
Forsyth D., Mundy J., Zisserman A., Coelho C., Heller A., Rothwell C.: Invariant descriptors for 3-d object recognition and pose. IEEE Trans. Pattern Anal. Mach. Intell. 13(10), 971–991 (1991)
Fitzgibbon A.W., Pilu M., Fisher R.B.: Direct least-spuares fitting of ellipses. IEEE Trans. Pattern Anal. Mach. Intell. 21(5), 476–480 (1999)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cai, S., Zhao, Z., Huang, L. et al. Camera calibration with enclosing ellipses by an extended application of generalized eigenvalue decomposition. Machine Vision and Applications 24, 513–520 (2013). https://doi.org/10.1007/s00138-012-0446-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00138-012-0446-0