Sensitivity of Calibration to Principal Point Position
A common practice when carrying out self-calibration and Euclidean reconstruction from one or more views is to start with a guess at the principal point of the camera. The general belief is that inaccuracies in the estimation of the principal point do not have a significant effect on the other calibration parameters, or on reconstruction accuracy. It is the purpose of this paper to refute that belief. Indeed, it is demonstrated that the determination of the focal length of the camera is tied up very closely with the estimate of the principal point. Small changes in the estimated (sometimes merely guessed) principal point can cause very large changes in the estimated focal length, and the accuracy of reconstruction. In fact, the relative uncertainty in the focal length is inversely proportional to the distance of the principal point to the epipolar line. This analysis is geometric and exact, rather than experimental.
KeywordsFocal Length Fundamental Matrix Principal Point Reconstruction Accuracy Epipolar Line
Unable to display preview. Download preview PDF.
- M. Armstrong, A. Zisserman, and R. Hartley. Self-calibration from image triplets. In Proc. 4th European Conference on Computer Vision, Cambridge, LNCS 1064/5, pages 3–16. Springer-Verlag, 1996.Google Scholar
- S. Bougnoux. From Projective to Euclidean space under any practical situation, a criticism of self-calibration. In Proc. 6th International Conference on Computer Vision, Bombay, India, pages 790–796, January 1998.Google Scholar
- R. Cipolla, D. P. Robertson, and E. G. Boyer. Photobuilder — 3D models of architectural scenes from uncalibrated images. In Proc. IEEE International Conference on Multimedia Computing and Systems, volume I, pages 25–31, June 1999.Google Scholar
- R. I. Hartley. Estimation of relative camera positions for uncalibrated cameras. In Proc. 2nd European Conference on Computer Vision, Santa Margharita Ligure, Italy, LNCS 588, pages 579–587. Springer-Verlag, 1992.Google Scholar
- R. I. Hartley and C Silpa-Anan. Visual navigation in a plane using the conformal point. In International Symposium on Robotics Research, pages to appear — available at http://www.anu.edu.au/ hartley, 2001.
- R. I. Hartley and C Silpa-Anan. Reconstruction from two views using approximate calibration. In ACCV, pages 338–343, 2002.Google Scholar
- R. I. Hartley and A. Zisserman. Multiple View Geometry in Computer Vision. Cambridge University Press, 2000.Google Scholar
- G. Newsam, D. Q. Huynh, M. Brooks, and H. P. Pan. Recovering unknown focal lengths in self-calibration: An essentially linear algorithm and degenerate configurations. In Int. Arch. Photogrammetry & Remote Sensing, volume XXXI-B3, pages 575–80, Vienna, 1996.Google Scholar
- M. Pollefeys, R. Koch, and L. Van Gool. Self calibration and metric reconstruction in spite of varying and unknown internal camera parameters. In Proc. 6th International Conference on Computer Vision, Bombay, India, pages 90–96, 1998.Google Scholar