Cornea-reflection-based Extrinsic Camera Calibration without a Direct View

Kosuke Takahashi, Dan Mikami, Mariko Isogawa, Akira Kojima


In this paper, we propose a novel method to extrinsically calibrate a camera to a 3D reference object that is not directly visible from the camera. We use the spherical human cornea as a mirror and calibrate the extrinsic parameters from the reflections of the reference points. The main contribution of this paper is to present a cornea-reflection-based calibration algorithm with minimal configuration; there are five reference points on a single plane and one mirror pose. In this paper, we derive a linear equation and obtain a closed-form solution of extrinsic calibration by introducing two key ideas. The first is to model the cornea as a virtual sphere, which enables us to estimate the center of the cornea sphere from its projection. The second idea is to use basis vectors to represent the position of the reference points, which enables us to deal with 3D information of reference points compactly. Besides, in order to make our method robust to observation noise, we minimize the reprojection error while maintaining the valid 3D geometry of the solution based on the derived linear equation. We demonstrate the advantages of the proposed method with qualitative and quantitative evaluations using synthesized and real data.


  1. Agarwal, S., Furukawa, Y., Snavely, N., Curless, B., Seitz, S. M., and Szeliski, R. (2010). Reconstructing rome. IEEE Computer, 43:40-47.
  2. Agrawal, A. (2013). Extrinsic camera calibration without a direct view using spherical mirror. In Proc. of ICCV.
  3. Azuma, R., Baillot, Y., Behringer, R., Feiner, S., Julier, S., and MacIntyre, B. (2001). Recent advances in augmented reality. Computer Graphics and Applications, IEEE, 21(6):34 -47.
  4. Delaunoy, A., Li, J., Jacquet, B., and Pollefeys, M. (2014). Two cameras and a screen: How to calibrate mobile devices? In 3D Vision (3DV), 2014 2nd International Conference on, volume 1, pages 123-130. IEEE.
  5. Fitzgibbon, A. and Fisher, R. B. (1995). A buyer's guide to conic fitting.
  6. Francken, Y., Hermans, C., and Bekaert, P. (2007). Screencamera calibration using a spherical mirror. In 4th Canadian Conference on Computer and Robot Vision.
  7. Golub, G. and van Loan., C. (1996). Matrix Computations. The Johns Hopkins University Press, Baltimore, Maryland, third edition.
  8. Haralick, B. M., Lee, C.-N., Ottenberg, K., and N ölle, M. (1994). Review and analysis of solutions of the three point perspective pose estimation problem. IJCV, 13:331-356.
  9. Hartley, R. I. and Zisserman, A. (2004). Multiple View Geometry in Computer Vision. Cambridge University Press, second edition.
  10. Hesch, J., Mourikis, A., and Roumeliotis, S. (2010). Mirrorbased extrinsic camera calibration. In Algorithmic Foundation of Robotics VIII, volume 57, pages 285- 299.
  11. Hirayama, T., Dodane, J.-B., Kawashima, H., and Matsuyama, T. (2010). Estimates of user interest using timing structures between proactive content-display updates and eye movements. IEICE Trans. Information and Systems, 93(6):1470-1478.
  12. Kumar, R., Ilie, A., Frahm, J.-M., and Pollefeys, M. (2008). Simple calibration of non-overlapping cameras with a mirror. In Proc. of CVPR.
  13. Kuster, C., Popa, T., Bazin, J.-C., Gotsman, C., and Gross, M. (2012). Gaze correction for home video conferencing. ACM Trans. Graph., 31(6):174:1-174:6.
  14. Matsuyama, T., Nobuhara, S., Takai, T., and Tung, T. (2012). 3D Video and Its Applications. Springer Publishing Company, Incorporated.
  15. Moakher, M. (2002). Means and averaging in the group of rotations. SIAM J. Matrix Anal. Appl., 24:1-16.
  16. Nakazawa, A. and Nitschke, C. (2012). Point of gaze estimation through corneal surface reflection in an active illumination environment. In Proc. of ECCV.
  17. Nayar, S. (1997). Catadioptric omnidirectional camera. In Proc. of CVPR.
  18. Nitschke, C., Nakazawa, A., and Takemura, H. (2011). Display-camera calibration using eye reflections and geometry constraints. CVIU, 115(6):835 - 853.
  19. Richard S.Snell, M. A. L. (1997). Clinical Anatomy of the Eye. Wiley-Blackwell, second edition.
  20. Rodrigues, R., Barreto, P., and Nunes, U. (2010). Camera pose estimation using images of planar mirror reflections. In Proc. of ECCV, pages 382-395.
  21. Sturm, P. and Bonfort, T. (2006). How to compute the pose of an object without a direct view. In Proc. of ACCV.
  22. Takahashi, K., Nobuhara, S., and Matsuyama, T. (2012). A new mirror-based extrinsic camera calibration using an orthogonality constraint. In Proc. of CVPR.
  23. Triggs, B., McLauchlan, P., Hartley, R., and Fitzgibbon, A. (2000). Bundle adjustment a modern synthesis. In Triggs, B., Zisserman, A., and Szeliski, R., editors, Vision Algorithms: Theory and Practice, volume 1883 of Lecture Notes in Computer Science, pages 298- 372. Springer.
  24. Zhang, Z. (2000). A flexible new technique for camera calibration. TPAMI, pages 1330-1334.

Paper Citation

in Harvard Style

Takahashi K., Mikami D., Isogawa M. and Kojima A. (2016). Cornea-reflection-based Extrinsic Camera Calibration without a Direct View . In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2016) ISBN 978-989-758-175-5, pages 15-24. DOI: 10.5220/0005675300150024

in Bibtex Style

author={Kosuke Takahashi and Dan Mikami and Mariko Isogawa and Akira Kojima},
title={Cornea-reflection-based Extrinsic Camera Calibration without a Direct View},
booktitle={Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2016)},

in EndNote Style

JO - Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2016)
TI - Cornea-reflection-based Extrinsic Camera Calibration without a Direct View
SN - 978-989-758-175-5
AU - Takahashi K.
AU - Mikami D.
AU - Isogawa M.
AU - Kojima A.
PY - 2016
SP - 15
EP - 24
DO - 10.5220/0005675300150024