Abstract

This Letter proposes a new method for automatically removing radial lens distortion from image feature point correspondences of two views. Based on the projective geometric relationship between two views of a planar scene, we have derived a system of algebraic equations that relates the invariants to the distortion parameters to be found. We then propose a noniterative procedure to solve the equations system, and a kernel-voting scheme to select the best root. Being a noniterative approach, our method overcomes many problems with the conventional iterative approach. It also largely decouples the estimation of the distortion from the estimation of other camera parameters and, therefore, delivers more reliable results. Experiments on both synthetic data and real images have provided satisfactory results.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Ricolfe-Viala, A. J. Sanchez-Salmeron, and E. Martinez-Berti, Opt. Lett. 36, 3064 (2011).
    [CrossRef]
  2. A. W. Fitzgibbon, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2001), Vol. 1, pp. 125–132.
  3. Z. Zhang, IEEE Trans. Pattern Anal. Machine Intell. 22, 1330 (2000).
    [CrossRef]
  4. D. Claus and A. Fitzgibbon, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2005), Vol. 1, pp. 213–219.
  5. T. A. Clarke, X. Wang, and J. G. Fryer, Photogram. Record 16, 293 (1998).
    [CrossRef]
  6. R. Hartley and S. B. Kang, in Proceedings of IEEE International Conference on Computer Vision (2005), Vol. 2, pp. 1834–1831.
  7. D. D. Cox and J. Little, Using Algebraic Geometry(Springer-Verlag, 2005).
  8. H. Li and R. Hartley, in Proceedings of OMNIVIS 2005 (2005), pp. 1–8.

2011 (1)

2000 (1)

Z. Zhang, IEEE Trans. Pattern Anal. Machine Intell. 22, 1330 (2000).
[CrossRef]

1998 (1)

T. A. Clarke, X. Wang, and J. G. Fryer, Photogram. Record 16, 293 (1998).
[CrossRef]

Clarke, T. A.

T. A. Clarke, X. Wang, and J. G. Fryer, Photogram. Record 16, 293 (1998).
[CrossRef]

Claus, D.

D. Claus and A. Fitzgibbon, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2005), Vol. 1, pp. 213–219.

Cox, D. D.

D. D. Cox and J. Little, Using Algebraic Geometry(Springer-Verlag, 2005).

Fitzgibbon, A.

D. Claus and A. Fitzgibbon, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2005), Vol. 1, pp. 213–219.

Fitzgibbon, A. W.

A. W. Fitzgibbon, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2001), Vol. 1, pp. 125–132.

Fryer, J. G.

T. A. Clarke, X. Wang, and J. G. Fryer, Photogram. Record 16, 293 (1998).
[CrossRef]

Hartley, R.

R. Hartley and S. B. Kang, in Proceedings of IEEE International Conference on Computer Vision (2005), Vol. 2, pp. 1834–1831.

H. Li and R. Hartley, in Proceedings of OMNIVIS 2005 (2005), pp. 1–8.

Kang, S. B.

R. Hartley and S. B. Kang, in Proceedings of IEEE International Conference on Computer Vision (2005), Vol. 2, pp. 1834–1831.

Li, H.

H. Li and R. Hartley, in Proceedings of OMNIVIS 2005 (2005), pp. 1–8.

Little, J.

D. D. Cox and J. Little, Using Algebraic Geometry(Springer-Verlag, 2005).

Martinez-Berti, E.

Ricolfe-Viala, C.

Sanchez-Salmeron, A. J.

Wang, X.

T. A. Clarke, X. Wang, and J. G. Fryer, Photogram. Record 16, 293 (1998).
[CrossRef]

Zhang, Z.

Z. Zhang, IEEE Trans. Pattern Anal. Machine Intell. 22, 1330 (2000).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell. (1)

Z. Zhang, IEEE Trans. Pattern Anal. Machine Intell. 22, 1330 (2000).
[CrossRef]

Opt. Lett. (1)

Photogram. Record (1)

T. A. Clarke, X. Wang, and J. G. Fryer, Photogram. Record 16, 293 (1998).
[CrossRef]

Other (5)

R. Hartley and S. B. Kang, in Proceedings of IEEE International Conference on Computer Vision (2005), Vol. 2, pp. 1834–1831.

D. D. Cox and J. Little, Using Algebraic Geometry(Springer-Verlag, 2005).

H. Li and R. Hartley, in Proceedings of OMNIVIS 2005 (2005), pp. 1–8.

A. W. Fitzgibbon, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2001), Vol. 1, pp. 125–132.

D. Claus and A. Fitzgibbon, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2005), Vol. 1, pp. 213–219.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Plane algebraic curves intersection. Each curve corresponds to one of the five-point basic equations. The intersection points give all real roots of the two basic equations.

Fig. 2.
Fig. 2.

2D kernel-voting results in the [k,a] plane.

Fig. 3.
Fig. 3.

One-dimensional kernel-voting results on the k axis.

Fig. 4.
Fig. 4.

First row: two views with significant radial distortion. Second row: our correction result.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

I1=|M421||M532||M432||M521|,I2=|M421||M531||M431||M521|,
{f1(k,a)I1(k,a)I1(k,a)=0f2(k,a)I2(k,a)I2(k,a)=0.

Metrics