Abstract

This paper addresses the high-precision measurement of the distortion of a digital camera from photographs. Traditionally, this distortion is measured from photographs of a flat pattern that contains aligned elements. Nevertheless, it is nearly impossible to fabricate a very flat pattern and to validate its flatness. This fact limits the attainable measurable precisions. In contrast, it is much easier to obtain physically very precise straight lines by tightly stretching good quality strings on a frame. Taking literally “plumb-line methods,” we built a “calibration harp” instead of the classic flat patterns to obtain a high-precision measurement tool, demonstrably reaching 2/100 pixel precisions. The harp is complemented with the algorithms computing automatically from harp photographs two different and complementary lens distortion measurements. The precision of the method is evaluated on images corrected by state-of-the-art distortion correction algorithms, and by popular software. Three applications are shown: first an objective and reliable measurement of the result of any distortion correction. Second, the harp permits us to control state-of-the art global camera calibration algorithms: it permits us to select the right distortion model, thus avoiding internal compensation errors inherent to these methods. Third, the method replaces manual procedures in other distortion correction methods, makes them fully automatic, and increases their reliability and precision.

© 2012 Optical Society of America

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  1. C. Slama, Manual of Photogrammetry, 4th ed. (American Society of Photogrammetry, 1980).
  2. R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3, 323–344 (1987).
    [CrossRef]
  3. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
    [CrossRef]
  4. J. Lavest, M. Viala, and M. Dhome, “Do we really need accurate calibration pattern to achieve a reliable camera calibration?” in Computer Vision—ECCV’98, Vol. 1408 of Lecture Notes in Computer Science (Springer, 1998), pp. 158–174.
  5. M. H. J. Weng and P. Cohen, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
    [CrossRef]
  6. Z. Tang, “Calibration de caméra à haute précision,” Ph.D. dissertation (Ecole Normale Supérieure de Cachan, 2011).
  7. R. Grompone von Gioi, P. Monasse, J.-M. Morel, and Z. Tang, “Towards high-precision lens distortion correction,” in Proceedings of 17th IEEE International Conference on Image Processing (IEEE, 2010), pp. 4237–4240.
  8. G. P. Stein, “Lens distortion calibration using point correspondences,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 602–608.
  9. Z. Zhang, “On the epipolar geometry between two images with lens distortion,” in Proceedings of 13th International Conference on Pattern Recognition (IEEE, 1996), pp. 407–411.
  10. A. Fitzgibbon, “Simultaneous linear estimation of multiple view geometry and lens distortion,” in Proceedings of 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2001), pp. 125–132.
  11. B. Micusik and T. Pajdla, “Estimation of omnidirectional camera model from epipolar geometry,” in Proceedings of 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2003), pp. 485–490.
  12. H. Li and R. Hartley, “A non-iterative method for correcting lens distortion from nine-point correspondences,” in Proceedings OmniVision ’05, ICCV Workshop (2005).
  13. S. Thirthala and M. Pollefeys, “The radial trifocal tensor: a tool for calibrating the radial distortion of wide-angle cameras,” in Proceedings of 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 321–328.
  14. D. Claus and A. Fitzgibbon, “A rational function lens distortion model for general cameras,” in Proceedings of 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 213–219.
  15. J. Barreto and K. Daniilidis, “Fundamental matrix for cameras with radial distortion,” in Proceedings of Tenth IEEE International Conference on Computer Vision (IEEE, 2005), pp. 625–632.
  16. Z. Kukelova and T. Pajdla, “Two minimal problems for cameras with radial distortion,” in Proceedings of 11th IEEE International Conference on Computer Vision (IEEE, 2007), pp. 1–8.
  17. Z. Kukelova, M. Bujnak, and T. Pajdla, “Automatic generator of minimal problem solvers,” in Computer Vision—ECCV 2008, Vol. 5304 of Lecture Notes in Computer Science (Springer, 2008), pp. 302–315.
  18. M. Byrod, Z. Kukelova, K. Josephson, T. Pajdla, and K. Astrom, “Fast and robust numerical solutions to minimal problems for cameras with radial distortion,” in Computer Vision—ECCV 2008, Vol. 5304 of Lecture Notes in Computer Science (Springer, 2008), pp. 1–8.
  19. Z. Kukelova and T. Pajdla, “A minimal solution to the autocalibration of radial distortion,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–7.
  20. K. Josephson and M. Byrod, “Pose estimation with radial distortion and unknown focal length,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2009), pp. 2419–2426.
  21. B. Triggs, P. Mclauchlan, R. Hartley, and A. Fitzgibbon, “Bundle adjustment—a modern synthesis,” Vision Algorithms: Theory and Practice, Vol. 1883 of Lecture Notes in Computer Science (Springer, 2000), pp. 298–372.
  22. D. Brown, “Close-range camera calibration,” Photogramm. Eng. 37, 855–866 (1971).
  23. L. Alvarez, L. Gomez, and J. Rafael Sendra, “An algebraic approach to lens distortion by line rectification,” J. Math. Imaging Vision 35, 36–50 (2009).
    [CrossRef]
  24. B. Prescott and G. McLean, “Line-based correction of radial lens distortion,” Graph. Mod. Image Process. 59, 39–47(1997).
    [CrossRef]
  25. T. Pajdla, T. Werner, and V. Hlavac, “Correcting radial lens distortion without knowledge of 3-D structure,” Research Report (Czech Technical University, 1997).
  26. F. Devernay and O. Faugeras, “Straight lines have to be straight,” Mach. Vision Appl. 13, 14–24 (2001).
    [CrossRef]
  27. D. Claus and A. Fitzgibbon, “A plumbline constraint for the rational function lens distortion model,” in Proceedings of British Machine Vision Conference (2005), pp. 99–108.
  28. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2004).
  29. E. Rosten and R. Loveland, “Camera distortion self-calibration using the plumb-line constraint and minimal hough entropy,” Mach. Vision Appl. 22, 77–85 (2011).
  30. F. Devernay, “A non-maxima suppression method for edge detection with sub-pixel accuracy,” Tech. Rep. 2724, (INRIA rapport de recherche, 1995).
  31. J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8, 679–698(1986).
    [CrossRef]
  32. R. Deriche, “Using Canny’s criteria to derive a recursively implemented optimal edge detector,” Int. J. Comput. Vis. 1, 167–187 (1987).
    [CrossRef]
  33. R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a fast line segment detector with a false detection control,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 722–732(2010).
    [CrossRef]
  34. R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a line segment detector,” IPOP (2012), doi: http://dx.doi.org/10.5201/ipol.2012.gjmr-lsd .
  35. J. Morel and G. Yu, “Is SIFT scale invariant?” Inverse Problems Imaging 5, 115–136 (2011).
    [CrossRef]
  36. L. G. Luis Alvarez and J. R. Sendra, “Algebraic lens distortion model estimation,” IPOP (2010), http://dx.doi.org/10.5201/ipol.2010.ags-alde .

2012 (1)

R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a line segment detector,” IPOP (2012), doi: http://dx.doi.org/10.5201/ipol.2012.gjmr-lsd .

2011 (2)

J. Morel and G. Yu, “Is SIFT scale invariant?” Inverse Problems Imaging 5, 115–136 (2011).
[CrossRef]

E. Rosten and R. Loveland, “Camera distortion self-calibration using the plumb-line constraint and minimal hough entropy,” Mach. Vision Appl. 22, 77–85 (2011).

2010 (2)

L. G. Luis Alvarez and J. R. Sendra, “Algebraic lens distortion model estimation,” IPOP (2010), http://dx.doi.org/10.5201/ipol.2010.ags-alde .

R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a fast line segment detector with a false detection control,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 722–732(2010).
[CrossRef]

2009 (1)

L. Alvarez, L. Gomez, and J. Rafael Sendra, “An algebraic approach to lens distortion by line rectification,” J. Math. Imaging Vision 35, 36–50 (2009).
[CrossRef]

2001 (1)

F. Devernay and O. Faugeras, “Straight lines have to be straight,” Mach. Vision Appl. 13, 14–24 (2001).
[CrossRef]

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

1997 (1)

B. Prescott and G. McLean, “Line-based correction of radial lens distortion,” Graph. Mod. Image Process. 59, 39–47(1997).
[CrossRef]

1992 (1)

M. H. J. Weng and P. Cohen, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

1987 (2)

R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3, 323–344 (1987).
[CrossRef]

R. Deriche, “Using Canny’s criteria to derive a recursively implemented optimal edge detector,” Int. J. Comput. Vis. 1, 167–187 (1987).
[CrossRef]

1986 (1)

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8, 679–698(1986).
[CrossRef]

1971 (1)

D. Brown, “Close-range camera calibration,” Photogramm. Eng. 37, 855–866 (1971).

Alvarez, L.

L. Alvarez, L. Gomez, and J. Rafael Sendra, “An algebraic approach to lens distortion by line rectification,” J. Math. Imaging Vision 35, 36–50 (2009).
[CrossRef]

Alvarez, L. G. Luis

L. G. Luis Alvarez and J. R. Sendra, “Algebraic lens distortion model estimation,” IPOP (2010), http://dx.doi.org/10.5201/ipol.2010.ags-alde .

Astrom, K.

M. Byrod, Z. Kukelova, K. Josephson, T. Pajdla, and K. Astrom, “Fast and robust numerical solutions to minimal problems for cameras with radial distortion,” in Computer Vision—ECCV 2008, Vol. 5304 of Lecture Notes in Computer Science (Springer, 2008), pp. 1–8.

Barreto, J.

J. Barreto and K. Daniilidis, “Fundamental matrix for cameras with radial distortion,” in Proceedings of Tenth IEEE International Conference on Computer Vision (IEEE, 2005), pp. 625–632.

Brown, D.

D. Brown, “Close-range camera calibration,” Photogramm. Eng. 37, 855–866 (1971).

Bujnak, M.

Z. Kukelova, M. Bujnak, and T. Pajdla, “Automatic generator of minimal problem solvers,” in Computer Vision—ECCV 2008, Vol. 5304 of Lecture Notes in Computer Science (Springer, 2008), pp. 302–315.

Byrod, M.

M. Byrod, Z. Kukelova, K. Josephson, T. Pajdla, and K. Astrom, “Fast and robust numerical solutions to minimal problems for cameras with radial distortion,” in Computer Vision—ECCV 2008, Vol. 5304 of Lecture Notes in Computer Science (Springer, 2008), pp. 1–8.

K. Josephson and M. Byrod, “Pose estimation with radial distortion and unknown focal length,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2009), pp. 2419–2426.

Canny, J.

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8, 679–698(1986).
[CrossRef]

Claus, D.

D. Claus and A. Fitzgibbon, “A plumbline constraint for the rational function lens distortion model,” in Proceedings of British Machine Vision Conference (2005), pp. 99–108.

D. Claus and A. Fitzgibbon, “A rational function lens distortion model for general cameras,” in Proceedings of 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 213–219.

Cohen, P.

M. H. J. Weng and P. Cohen, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

Daniilidis, K.

J. Barreto and K. Daniilidis, “Fundamental matrix for cameras with radial distortion,” in Proceedings of Tenth IEEE International Conference on Computer Vision (IEEE, 2005), pp. 625–632.

Deriche, R.

R. Deriche, “Using Canny’s criteria to derive a recursively implemented optimal edge detector,” Int. J. Comput. Vis. 1, 167–187 (1987).
[CrossRef]

Devernay, F.

F. Devernay and O. Faugeras, “Straight lines have to be straight,” Mach. Vision Appl. 13, 14–24 (2001).
[CrossRef]

F. Devernay, “A non-maxima suppression method for edge detection with sub-pixel accuracy,” Tech. Rep. 2724, (INRIA rapport de recherche, 1995).

Dhome, M.

J. Lavest, M. Viala, and M. Dhome, “Do we really need accurate calibration pattern to achieve a reliable camera calibration?” in Computer Vision—ECCV’98, Vol. 1408 of Lecture Notes in Computer Science (Springer, 1998), pp. 158–174.

Faugeras, O.

F. Devernay and O. Faugeras, “Straight lines have to be straight,” Mach. Vision Appl. 13, 14–24 (2001).
[CrossRef]

Fitzgibbon, A.

B. Triggs, P. Mclauchlan, R. Hartley, and A. Fitzgibbon, “Bundle adjustment—a modern synthesis,” Vision Algorithms: Theory and Practice, Vol. 1883 of Lecture Notes in Computer Science (Springer, 2000), pp. 298–372.

D. Claus and A. Fitzgibbon, “A plumbline constraint for the rational function lens distortion model,” in Proceedings of British Machine Vision Conference (2005), pp. 99–108.

A. Fitzgibbon, “Simultaneous linear estimation of multiple view geometry and lens distortion,” in Proceedings of 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2001), pp. 125–132.

D. Claus and A. Fitzgibbon, “A rational function lens distortion model for general cameras,” in Proceedings of 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 213–219.

Gomez, L.

L. Alvarez, L. Gomez, and J. Rafael Sendra, “An algebraic approach to lens distortion by line rectification,” J. Math. Imaging Vision 35, 36–50 (2009).
[CrossRef]

Grompone von Gioi, R.

R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a line segment detector,” IPOP (2012), doi: http://dx.doi.org/10.5201/ipol.2012.gjmr-lsd .

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2004).

B. Triggs, P. Mclauchlan, R. Hartley, and A. Fitzgibbon, “Bundle adjustment—a modern synthesis,” Vision Algorithms: Theory and Practice, Vol. 1883 of Lecture Notes in Computer Science (Springer, 2000), pp. 298–372.

H. Li and R. Hartley, “A non-iterative method for correcting lens distortion from nine-point correspondences,” in Proceedings OmniVision ’05, ICCV Workshop (2005).

Hlavac, V.

T. Pajdla, T. Werner, and V. Hlavac, “Correcting radial lens distortion without knowledge of 3-D structure,” Research Report (Czech Technical University, 1997).

Jakubowicz, J.

R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a line segment detector,” IPOP (2012), doi: http://dx.doi.org/10.5201/ipol.2012.gjmr-lsd .

R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a fast line segment detector with a false detection control,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 722–732(2010).
[CrossRef]

Josephson, K.

K. Josephson and M. Byrod, “Pose estimation with radial distortion and unknown focal length,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2009), pp. 2419–2426.

M. Byrod, Z. Kukelova, K. Josephson, T. Pajdla, and K. Astrom, “Fast and robust numerical solutions to minimal problems for cameras with radial distortion,” in Computer Vision—ECCV 2008, Vol. 5304 of Lecture Notes in Computer Science (Springer, 2008), pp. 1–8.

Kukelova, Z.

Z. Kukelova and T. Pajdla, “A minimal solution to the autocalibration of radial distortion,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–7.

M. Byrod, Z. Kukelova, K. Josephson, T. Pajdla, and K. Astrom, “Fast and robust numerical solutions to minimal problems for cameras with radial distortion,” in Computer Vision—ECCV 2008, Vol. 5304 of Lecture Notes in Computer Science (Springer, 2008), pp. 1–8.

Z. Kukelova and T. Pajdla, “Two minimal problems for cameras with radial distortion,” in Proceedings of 11th IEEE International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

Z. Kukelova, M. Bujnak, and T. Pajdla, “Automatic generator of minimal problem solvers,” in Computer Vision—ECCV 2008, Vol. 5304 of Lecture Notes in Computer Science (Springer, 2008), pp. 302–315.

Lavest, J.

J. Lavest, M. Viala, and M. Dhome, “Do we really need accurate calibration pattern to achieve a reliable camera calibration?” in Computer Vision—ECCV’98, Vol. 1408 of Lecture Notes in Computer Science (Springer, 1998), pp. 158–174.

Li, H.

H. Li and R. Hartley, “A non-iterative method for correcting lens distortion from nine-point correspondences,” in Proceedings OmniVision ’05, ICCV Workshop (2005).

Loveland, R.

E. Rosten and R. Loveland, “Camera distortion self-calibration using the plumb-line constraint and minimal hough entropy,” Mach. Vision Appl. 22, 77–85 (2011).

Mclauchlan, P.

B. Triggs, P. Mclauchlan, R. Hartley, and A. Fitzgibbon, “Bundle adjustment—a modern synthesis,” Vision Algorithms: Theory and Practice, Vol. 1883 of Lecture Notes in Computer Science (Springer, 2000), pp. 298–372.

McLean, G.

B. Prescott and G. McLean, “Line-based correction of radial lens distortion,” Graph. Mod. Image Process. 59, 39–47(1997).
[CrossRef]

Micusik, B.

B. Micusik and T. Pajdla, “Estimation of omnidirectional camera model from epipolar geometry,” in Proceedings of 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2003), pp. 485–490.

Monasse, P.

R. Grompone von Gioi, P. Monasse, J.-M. Morel, and Z. Tang, “Towards high-precision lens distortion correction,” in Proceedings of 17th IEEE International Conference on Image Processing (IEEE, 2010), pp. 4237–4240.

Morel, J.

R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a line segment detector,” IPOP (2012), doi: http://dx.doi.org/10.5201/ipol.2012.gjmr-lsd .

J. Morel and G. Yu, “Is SIFT scale invariant?” Inverse Problems Imaging 5, 115–136 (2011).
[CrossRef]

R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a fast line segment detector with a false detection control,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 722–732(2010).
[CrossRef]

Morel, J.-M.

R. Grompone von Gioi, P. Monasse, J.-M. Morel, and Z. Tang, “Towards high-precision lens distortion correction,” in Proceedings of 17th IEEE International Conference on Image Processing (IEEE, 2010), pp. 4237–4240.

Pajdla, T.

B. Micusik and T. Pajdla, “Estimation of omnidirectional camera model from epipolar geometry,” in Proceedings of 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2003), pp. 485–490.

Z. Kukelova and T. Pajdla, “Two minimal problems for cameras with radial distortion,” in Proceedings of 11th IEEE International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

Z. Kukelova, M. Bujnak, and T. Pajdla, “Automatic generator of minimal problem solvers,” in Computer Vision—ECCV 2008, Vol. 5304 of Lecture Notes in Computer Science (Springer, 2008), pp. 302–315.

Z. Kukelova and T. Pajdla, “A minimal solution to the autocalibration of radial distortion,” in IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–7.

M. Byrod, Z. Kukelova, K. Josephson, T. Pajdla, and K. Astrom, “Fast and robust numerical solutions to minimal problems for cameras with radial distortion,” in Computer Vision—ECCV 2008, Vol. 5304 of Lecture Notes in Computer Science (Springer, 2008), pp. 1–8.

T. Pajdla, T. Werner, and V. Hlavac, “Correcting radial lens distortion without knowledge of 3-D structure,” Research Report (Czech Technical University, 1997).

Pollefeys, M.

S. Thirthala and M. Pollefeys, “The radial trifocal tensor: a tool for calibrating the radial distortion of wide-angle cameras,” in Proceedings of 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 321–328.

Prescott, B.

B. Prescott and G. McLean, “Line-based correction of radial lens distortion,” Graph. Mod. Image Process. 59, 39–47(1997).
[CrossRef]

Randall, G.

R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a line segment detector,” IPOP (2012), doi: http://dx.doi.org/10.5201/ipol.2012.gjmr-lsd .

R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a fast line segment detector with a false detection control,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 722–732(2010).
[CrossRef]

Rosten, E.

E. Rosten and R. Loveland, “Camera distortion self-calibration using the plumb-line constraint and minimal hough entropy,” Mach. Vision Appl. 22, 77–85 (2011).

Sendra, J. R.

L. G. Luis Alvarez and J. R. Sendra, “Algebraic lens distortion model estimation,” IPOP (2010), http://dx.doi.org/10.5201/ipol.2010.ags-alde .

Sendra, J. Rafael

L. Alvarez, L. Gomez, and J. Rafael Sendra, “An algebraic approach to lens distortion by line rectification,” J. Math. Imaging Vision 35, 36–50 (2009).
[CrossRef]

Slama, C.

C. Slama, Manual of Photogrammetry, 4th ed. (American Society of Photogrammetry, 1980).

Stein, G. P.

G. P. Stein, “Lens distortion calibration using point correspondences,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 602–608.

Tang, Z.

R. Grompone von Gioi, P. Monasse, J.-M. Morel, and Z. Tang, “Towards high-precision lens distortion correction,” in Proceedings of 17th IEEE International Conference on Image Processing (IEEE, 2010), pp. 4237–4240.

Z. Tang, “Calibration de caméra à haute précision,” Ph.D. dissertation (Ecole Normale Supérieure de Cachan, 2011).

Thirthala, S.

S. Thirthala and M. Pollefeys, “The radial trifocal tensor: a tool for calibrating the radial distortion of wide-angle cameras,” in Proceedings of 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 321–328.

Triggs, B.

B. Triggs, P. Mclauchlan, R. Hartley, and A. Fitzgibbon, “Bundle adjustment—a modern synthesis,” Vision Algorithms: Theory and Practice, Vol. 1883 of Lecture Notes in Computer Science (Springer, 2000), pp. 298–372.

Tsai, R.

R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3, 323–344 (1987).
[CrossRef]

Viala, M.

J. Lavest, M. Viala, and M. Dhome, “Do we really need accurate calibration pattern to achieve a reliable camera calibration?” in Computer Vision—ECCV’98, Vol. 1408 of Lecture Notes in Computer Science (Springer, 1998), pp. 158–174.

von Gioi, R. Grompone

R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a fast line segment detector with a false detection control,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 722–732(2010).
[CrossRef]

R. Grompone von Gioi, P. Monasse, J.-M. Morel, and Z. Tang, “Towards high-precision lens distortion correction,” in Proceedings of 17th IEEE International Conference on Image Processing (IEEE, 2010), pp. 4237–4240.

Weng, M. H. J.

M. H. J. Weng and P. Cohen, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

Werner, T.

T. Pajdla, T. Werner, and V. Hlavac, “Correcting radial lens distortion without knowledge of 3-D structure,” Research Report (Czech Technical University, 1997).

Yu, G.

J. Morel and G. Yu, “Is SIFT scale invariant?” Inverse Problems Imaging 5, 115–136 (2011).
[CrossRef]

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

Z. Zhang, “On the epipolar geometry between two images with lens distortion,” in Proceedings of 13th International Conference on Pattern Recognition (IEEE, 1996), pp. 407–411.

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2004).

Graph. Mod. Image Process. (1)

B. Prescott and G. McLean, “Line-based correction of radial lens distortion,” Graph. Mod. Image Process. 59, 39–47(1997).
[CrossRef]

IEEE J. Robot. Autom. (1)

R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Autom. 3, 323–344 (1987).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (4)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-8, 679–698(1986).
[CrossRef]

R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a fast line segment detector with a false detection control,” IEEE Trans. Pattern Anal. Mach. Intell. 32, 722–732(2010).
[CrossRef]

M. H. J. Weng and P. Cohen, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

Int. J. Comput. Vis. (1)

R. Deriche, “Using Canny’s criteria to derive a recursively implemented optimal edge detector,” Int. J. Comput. Vis. 1, 167–187 (1987).
[CrossRef]

Inverse Problems Imaging (1)

J. Morel and G. Yu, “Is SIFT scale invariant?” Inverse Problems Imaging 5, 115–136 (2011).
[CrossRef]

IPOP (2)

L. G. Luis Alvarez and J. R. Sendra, “Algebraic lens distortion model estimation,” IPOP (2010), http://dx.doi.org/10.5201/ipol.2010.ags-alde .

R. Grompone von Gioi, J. Jakubowicz, J. Morel, and G. Randall, “LSD: a line segment detector,” IPOP (2012), doi: http://dx.doi.org/10.5201/ipol.2012.gjmr-lsd .

J. Math. Imaging Vision (1)

L. Alvarez, L. Gomez, and J. Rafael Sendra, “An algebraic approach to lens distortion by line rectification,” J. Math. Imaging Vision 35, 36–50 (2009).
[CrossRef]

Mach. Vision Appl. (2)

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Figures (12)

Fig. 1.
Fig. 1.

DxO lens distortion measurement standard. Estimation of distortion from an image of a dot chart.

Fig. 2.
Fig. 2.

“Calibration harp.” Shadows can be observed in (a) and (c), while there is no shadow in (b) or (d).

Fig. 3.
Fig. 3.

Three types of strings. (a) sewing line, (b) tennis racket line, (c) opaque fishing line.

Fig. 4.
Fig. 4.

Intrinsic coordinate system of the edge points extracted on the distorted line. The red points are the distorted edge points. The x direction is determined by the direction of the regression line. The x -coordinate is the distance to the reference point along the regression line, and the y -coordinate is the signed distance from the edge points to the regression line.

Fig. 5.
Fig. 5.

The small oscillation of the corrected lines is related to the quality of the strings. The green (upper) curves show the signed distance (in pixels) from the edge points of a corrected line to its regression line. The red (lower) curves show the high frequency of the corresponding distorted line. The corrected line inherits the oscillation from the corresponding distorted line. (a) Sewing string, (b) tennis racket string, (c) opaque fishing line. The x -axis is the index of edge points. The range of the y -axis is from 0.3 pixels to 0.3 pixels. The almost superimposing high-frequency oscillation means that the high frequency of the distorted strings is not changed by the distortion correction. In such a case, the straightness error includes the high frequency of the distorted strings and does not really reflect the correction performance. So it is better to use a string that contains the smallest high-frequency oscillation. Among the three types of strings, the opaque fishing string shows the smallest such oscillations. The larger oscillation of the sewing string is due to a variation of the thickness related to its twisted structure, while the tennis racket string is simply too rigid to be stretched, even though this is not apparent in Fig. 3(b).

Fig. 6.
Fig. 6.

The quality of photos depends on the harp, its background, and the stability of camera for taking photos.

Fig. 7.
Fig. 7.

The LSD algorithm computes the level-line field of the image. The level-line field defines at each pixel the direction of the level line passing by this pixel. The image is then partitioned into connected groups that share roughly the same level-line direction. They are called line support regions. Only the validated regions are detected as line segments. Devernay’s edge points belonging to the same validated line support region are considered as the edge points of the corresponding line segment.

Fig. 8.
Fig. 8.

Line resampling. The black dots ( x 1 , y 1 ) , ( x 2 , y 2 ) , are the edge points extracted by Devernay’s detector. They are irregularly sampled along the line. The resampling (in white dots) is made along the line with the uniform length step d . Linear interpolation is used to compute the resampled points.

Fig. 9.
Fig. 9.

Distance from a set of points to their global linear regression line.

Fig. 10.
Fig. 10.

Left: traditional distortion measure: the maximal distance to the line defined by the extremities of the edge. Right: the regression line crosses the distorted line; the difference between the maximal and minimal signed distance to the line measures the full width of the distorted line.

Fig. 11.
Fig. 11.

Distorted photos of the “calibration harp.”

Fig. 12.
Fig. 12.

Images used in the Alvarez et al. method [23].

Tables (2)

Tables Icon

Table 1. Distortion Correction Performance of Three Algorithms, Measured by RMS Distance d and Maximal Distance d max

Tables Icon

Table 2. Distortion Correction Performance of the Alvarez et al. Method [23] on Four Kinds of Input Edge Points: Manual Clicks on Natural Image, Manual Clicks on a Grid Pattern Image, Manual Clicks on a Calibration Harp Image, and Automatic Edge Points Extraction on the Calibration Harp Imagea

Equations (20)

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

x = b a + b x 1 + a a + b x 2 , y = b a + b y 1 + a a + b y 2 ,
α x + β y γ = 0
α = sin θ , β = cos θ , γ = A x sin θ + A y cos θ ,
A x = 1 N i = 1 N x i , A y = 1 N i = 1 N y i , V x x = 1 N i = 1 N ( x i A x ) 2 , V x y = 1 N i = 1 N ( x i A x ) ( y i A y ) , V y y = 1 N i = 1 N ( y i A y ) 2 , tan 2 θ = 2 V x y V x x V y y .
S i = α x i + β y i γ .
S = l = 1 L i = 1 N l | S l i | 2 = l = 1 L i = 1 N l ( α l x l i + β l y l i γ l ) 2 .
d = S N T ,
d max = l = 1 L | max i S l i min i S l i | 2 L .
max l | max i S l i min i S l i | ,
x u x c = f ( r d ) ( x d x c ) ,
y u y c = f ( r d ) ( y d y c ) ,
f ( r d ) = k 0 + k 1 r + k 2 r 2 + + k N r N
D = 1 L l = 1 L 1 N l i = 1 N l S l i 2 = 1 L l = 1 L 1 N l i = 1 N l ( α l x u l i + β l y u l i + γ l ) 2 α l 2 + β l 2
E = 1 L l = 1 L ( S x x l S y y l ( S x y l ) 2 ) ,
S l = ( S x x l S x y l S x y l S y y l ) = 1 N l ( i = 1 N l ( x u l , i x ¯ u l , i ) 2 i = 1 N l ( x u l , i x ¯ u l , i ) ( y u l , i y ¯ u l , i ) i = 1 N l ( x u l , i x ¯ u l , i ) ( y u l , i y ¯ u l , i ) i = 1 N l ( y u l , i y ¯ u l , i ) 2 ) ,
E ( k ) = 1 L l = 1 L k T A l k k T B l k k T C l k k T C l k ,
A m , n l = 1 N l i = 1 N l ( ( r d l , i ) m x d l , i ( r d l , i ) m x d l , i ¯ ) ( ( r d l , i ) n x d l , i ( r d l , i ) n x d l , i ¯ ) ,
B m , n l = 1 N l i = 1 N l ( ( r d l , i ) m y d l , i ( r d l , i ) m y d l , i ¯ ) ( ( r d l , i ) n y d l , i ( r d l , i ) n y d l , i ¯ ) ,
C m , n l = 1 N l i = 1 N l ( ( r d l , i ) m x d l , i ( r d l , i ) m x d l , i ¯ ) ( ( r d l , i ) n y d l , i ( r d l , i ) n y d l , i ¯ ) ,
E ( k ) k i = 0 , i = 1 , 2 , , N .

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