Abstract

Distortion correction or camera calibration for an imaging system which is highly configurable and requires frequent disassembly for maintenance or replacement of parts needs a speedy method for recalibration. Here we present direct techniques for calculating distortion parameters of a non-linear model based on the correct determination of the center of distortion. These techniques are fast, very easy to implement, and accurate at sub-pixel level. The implementation at the X-ray tomography system of the I12 beamline, Diamond Light Source, which strictly requires sub-pixel accuracy, shows excellent performance in the calibration image and in the reconstructed images.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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  2. M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
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  4. F. Remondino and C. Fraser, “Digital camera calibration methods: considerations and comparisons,” Int. Arch. Photogrammetry, Remote Sens. Spatial Inf. Sci. 36(5), 266–272 (2006).
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    [Crossref]
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  7. C. Hughes, P. Denny, E. Jones, and M. Glavin, “Accuracy of fish-eye lens models,” Appl. Opt. 49(17), 3338–3347 (2010).
    [Crossref] [PubMed]
  8. C. Ricolfe-Viala and A.-J. Sanchez-Salmeron, “Lens distortion models evaluation,” Appl. Opt. 49(30), 5914–5928 (2010).
    [Crossref] [PubMed]
  9. J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14(10), 965–980 (1992).
    [Crossref]
  10. J. Salvi, X. Armanguk, and J. Batlle, “A comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recognit. 35(7), 1617–1635 (2002).
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    [Crossref]
  14. C. Ishii, Y. Sudo, and H. Hashimoto, “An image conversion algorithm from fish eye image to perspective image for human eyes,” in Proc. of the IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics (2003), pp. 1009–1014.
    [Crossref]
  15. J. C. A. Fernandes, M. J. O. Ferreira, J. A. B. C. Neves, and C. A. C. Couto, “Fast correction of lens distortion for image applications,” in Proc. of the IEEE Int. Symposium on Industrial Electronics (1997), pp. 708–712.
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    [Crossref]
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    [Crossref]
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2015 (1)

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

2014 (1)

2010 (3)

2009 (1)

J. Park, S.-C. Byun, and B.-U. Lee, “Lens distortion correction using ideal image coordinates,” IEEE Trans. Consum. Electron. 55(3), 987–991 (2009).
[Crossref]

2006 (1)

F. Remondino and C. Fraser, “Digital camera calibration methods: considerations and comparisons,” Int. Arch. Photogrammetry, Remote Sens. Spatial Inf. Sci. 36(5), 266–272 (2006).

2002 (1)

J. Salvi, X. Armanguk, and J. Batlle, “A comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recognit. 35(7), 1617–1635 (2002).
[Crossref]

1999 (1)

K. V. Asari, S. Kumar, and D. Radhakrishnan, “A new approach for nonlinear distortion correction in endoscopic images based on least squares estimation,” IEEE Trans. Med. Imaging 18(4), 345–354 (1999).
[Crossref] [PubMed]

1998 (1)

T. A. Clarke and J. G. Fryer, “The development of camera calibration methods and models,” Photogramm. Rec. 16(91), 51–66 (1998).
[Crossref]

1995 (1)

H. Haneishi, Y. Yagihashi, and Y. Miyake, “A new method for distortion correction of electronic endoscope images,” IEEE Trans. Med. Imaging 14(3), 548–555 (1995).
[Crossref] [PubMed]

1992 (1)

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14(10), 965–980 (1992).
[Crossref]

Aggarwal, J. K.

S. Shah and J. K. Aggarwal, “A simple calibration procedure for fish-eye (high distortion) lens camera,” in Proc. 1994 IEEE Int. Conf. Robotics and Automation (1994), pp. 3422–3427.
[Crossref]

Armanguk, X.

J. Salvi, X. Armanguk, and J. Batlle, “A comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recognit. 35(7), 1617–1635 (2002).
[Crossref]

Asari, K. V.

K. V. Asari, S. Kumar, and D. Radhakrishnan, “A new approach for nonlinear distortion correction in endoscopic images based on least squares estimation,” IEEE Trans. Med. Imaging 18(4), 345–354 (1999).
[Crossref] [PubMed]

Atwood, R.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Atwood, R. C.

Bailey, D. G.

D. G. Bailey, “A new approach to lens disortion correction,” in Proceedings of Image and Vision Computing New Zealand Conference, (2002), pp. 59–64.

Basham, M.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Batlle, J.

J. Salvi, X. Armanguk, and J. Batlle, “A comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recognit. 35(7), 1617–1635 (2002).
[Crossref]

Byun, S.-C.

J. Park, S.-C. Byun, and B.-U. Lee, “Lens distortion correction using ideal image coordinates,” IEEE Trans. Consum. Electron. 55(3), 987–991 (2009).
[Crossref]

Clarke, T. A.

T. A. Clarke and J. G. Fryer, “The development of camera calibration methods and models,” Photogramm. Rec. 16(91), 51–66 (1998).
[Crossref]

Cohen, P.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14(10), 965–980 (1992).
[Crossref]

Connolley, T.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Connor, L.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Couto, C. A. C.

J. C. A. Fernandes, M. J. O. Ferreira, J. A. B. C. Neves, and C. A. C. Couto, “Fast correction of lens distortion for image applications,” in Proc. of the IEEE Int. Symposium on Industrial Electronics (1997), pp. 708–712.
[Crossref]

Davies, S.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

De Maio, N.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Denny, P.

C. Hughes, P. Denny, E. Jones, and M. Glavin, “Accuracy of fish-eye lens models,” Appl. Opt. 49(17), 3338–3347 (2010).
[Crossref] [PubMed]

C. Hughes, M. Glavin, E. Jones, and P. Denny, “Review of geometric distortion compensation in fish-eye cameras,” in IET Irish Signals and Systems Conference (2008), pp. 162–167.
[Crossref]

Drakopoulos, M.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

N. T. Vo, M. Drakopoulos, R. C. Atwood, and C. Reinhard, “Reliable method for calculating the center of rotation in parallel-beam tomography,” Opt. Express 22(16), 19078–19086 (2014).
[Crossref] [PubMed]

Fernandes, J. C. A.

J. C. A. Fernandes, M. J. O. Ferreira, J. A. B. C. Neves, and C. A. C. Couto, “Fast correction of lens distortion for image applications,” in Proc. of the IEEE Int. Symposium on Industrial Electronics (1997), pp. 708–712.
[Crossref]

Ferreira, M. J. O.

J. C. A. Fernandes, M. J. O. Ferreira, J. A. B. C. Neves, and C. A. C. Couto, “Fast correction of lens distortion for image applications,” in Proc. of the IEEE Int. Symposium on Industrial Electronics (1997), pp. 708–712.
[Crossref]

Foster, A.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Fraser, C.

F. Remondino and C. Fraser, “Digital camera calibration methods: considerations and comparisons,” Int. Arch. Photogrammetry, Remote Sens. Spatial Inf. Sci. 36(5), 266–272 (2006).

Fryer, J. G.

T. A. Clarke and J. G. Fryer, “The development of camera calibration methods and models,” Photogramm. Rec. 16(91), 51–66 (1998).
[Crossref]

Glavin, M.

C. Hughes, P. Denny, E. Jones, and M. Glavin, “Accuracy of fish-eye lens models,” Appl. Opt. 49(17), 3338–3347 (2010).
[Crossref] [PubMed]

C. Hughes, M. Glavin, E. Jones, and P. Denny, “Review of geometric distortion compensation in fish-eye cameras,” in IET Irish Signals and Systems Conference (2008), pp. 162–167.
[Crossref]

Haneishi, H.

H. Haneishi, Y. Yagihashi, and Y. Miyake, “A new method for distortion correction of electronic endoscope images,” IEEE Trans. Med. Imaging 14(3), 548–555 (1995).
[Crossref] [PubMed]

Hart, M.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Hashimoto, H.

C. Ishii, Y. Sudo, and H. Hashimoto, “An image conversion algorithm from fish eye image to perspective image for human eyes,” in Proc. of the IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics (2003), pp. 1009–1014.
[Crossref]

Herniou, M.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14(10), 965–980 (1992).
[Crossref]

Hill, T.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Howell, G.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Hughes, C.

C. Hughes, P. Denny, E. Jones, and M. Glavin, “Accuracy of fish-eye lens models,” Appl. Opt. 49(17), 3338–3347 (2010).
[Crossref] [PubMed]

C. Hughes, M. Glavin, E. Jones, and P. Denny, “Review of geometric distortion compensation in fish-eye cameras,” in IET Irish Signals and Systems Conference (2008), pp. 162–167.
[Crossref]

Humphreys, B.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Ishii, C.

C. Ishii, Y. Sudo, and H. Hashimoto, “An image conversion algorithm from fish eye image to perspective image for human eyes,” in Proc. of the IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics (2003), pp. 1009–1014.
[Crossref]

Jones, E.

C. Hughes, P. Denny, E. Jones, and M. Glavin, “Accuracy of fish-eye lens models,” Appl. Opt. 49(17), 3338–3347 (2010).
[Crossref] [PubMed]

C. Hughes, M. Glavin, E. Jones, and P. Denny, “Review of geometric distortion compensation in fish-eye cameras,” in IET Irish Signals and Systems Conference (2008), pp. 162–167.
[Crossref]

Kumar, S.

K. V. Asari, S. Kumar, and D. Radhakrishnan, “A new approach for nonlinear distortion correction in endoscopic images based on least squares estimation,” IEEE Trans. Med. Imaging 18(4), 345–354 (1999).
[Crossref] [PubMed]

Lee, B.-U.

J. Park, S.-C. Byun, and B.-U. Lee, “Lens distortion correction using ideal image coordinates,” IEEE Trans. Consum. Electron. 55(3), 987–991 (2009).
[Crossref]

Magdysyuk, O.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Miyake, Y.

H. Haneishi, Y. Yagihashi, and Y. Miyake, “A new method for distortion correction of electronic endoscope images,” IEEE Trans. Med. Imaging 14(3), 548–555 (1995).
[Crossref] [PubMed]

Neves, J. A. B. C.

J. C. A. Fernandes, M. J. O. Ferreira, J. A. B. C. Neves, and C. A. C. Couto, “Fast correction of lens distortion for image applications,” in Proc. of the IEEE Int. Symposium on Industrial Electronics (1997), pp. 708–712.
[Crossref]

Park, J.

J. Park, S.-C. Byun, and B.-U. Lee, “Lens distortion correction using ideal image coordinates,” IEEE Trans. Consum. Electron. 55(3), 987–991 (2009).
[Crossref]

Pedersen, U.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Radhakrishnan, D.

K. V. Asari, S. Kumar, and D. Radhakrishnan, “A new approach for nonlinear distortion correction in endoscopic images based on least squares estimation,” IEEE Trans. Med. Imaging 18(4), 345–354 (1999).
[Crossref] [PubMed]

Reinhard, C.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

N. T. Vo, M. Drakopoulos, R. C. Atwood, and C. Reinhard, “Reliable method for calculating the center of rotation in parallel-beam tomography,” Opt. Express 22(16), 19078–19086 (2014).
[Crossref] [PubMed]

Remondino, F.

F. Remondino and C. Fraser, “Digital camera calibration methods: considerations and comparisons,” Int. Arch. Photogrammetry, Remote Sens. Spatial Inf. Sci. 36(5), 266–272 (2006).

Ricolfe-Viala, C.

C. Ricolfe-Viala and A.-J. Sanchez-Salmeron, “Lens distortion models evaluation,” Appl. Opt. 49(30), 5914–5928 (2010).
[Crossref] [PubMed]

C. Ricolfe-Viala and A. J. Sanchez-Salmeron, “Robust metric calibration of non-linear camera lens distortion,” Pattern Recognit. 43(4), 1688–1699 (2010).
[Crossref]

Salvi, J.

J. Salvi, X. Armanguk, and J. Batlle, “A comparative review of camera calibrating methods with accuracy evaluation,” Pattern Recognit. 35(7), 1617–1635 (2002).
[Crossref]

Sanchez-Salmeron, A. J.

C. Ricolfe-Viala and A. J. Sanchez-Salmeron, “Robust metric calibration of non-linear camera lens distortion,” Pattern Recognit. 43(4), 1688–1699 (2010).
[Crossref]

Sanchez-Salmeron, A.-J.

Shah, S.

S. Shah and J. K. Aggarwal, “A simple calibration procedure for fish-eye (high distortion) lens camera,” in Proc. 1994 IEEE Int. Conf. Robotics and Automation (1994), pp. 3422–3427.
[Crossref]

Sudo, Y.

C. Ishii, Y. Sudo, and H. Hashimoto, “An image conversion algorithm from fish eye image to perspective image for human eyes,” in Proc. of the IEEE/ASME Int. Conf. on Advanced Intelligent Mechatronics (2003), pp. 1009–1014.
[Crossref]

Vo, N.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Vo, N. T.

Wanelik, K.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Weng, J.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14(10), 965–980 (1992).
[Crossref]

Wilkin, G.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Yagihashi, Y.

H. Haneishi, Y. Yagihashi, and Y. Miyake, “A new method for distortion correction of electronic endoscope images,” IEEE Trans. Med. Imaging 14(3), 548–555 (1995).
[Crossref] [PubMed]

Yuan, F.

M. Drakopoulos, T. Connolley, C. Reinhard, R. Atwood, O. Magdysyuk, N. Vo, M. Hart, L. Connor, B. Humphreys, G. Howell, S. Davies, T. Hill, G. Wilkin, U. Pedersen, A. Foster, N. De Maio, M. Basham, F. Yuan, and K. Wanelik, “I12: the Joint Engineering, Environment and Processing (JEEP) beamline at Diamond Light Source,” J. Synchrotron Radiat. 22(3), 828–838 (2015).
[Crossref] [PubMed]

Appl. Opt. (2)

IEEE Trans. Consum. Electron. (1)

J. Park, S.-C. Byun, and B.-U. Lee, “Lens distortion correction using ideal image coordinates,” IEEE Trans. Consum. Electron. 55(3), 987–991 (2009).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 (a) Schematic of the camera system at I12. X-rays enter an optics module (bottom left). A visible light image is generated in the scintillator and imaged via visible light optics onto a commercial sensor (top right). The visible-light path is folded twice; (b) Visible light from a dot pattern is imaged with the camera system shown in (a) in which barrel distortion is clearly visible. A rectangle indicates the active field of view of the tomographic acquisition reflecting the borders of X-ray illumination.
Fig. 2
Fig. 2 (a) X-ray projection of a sample made of an assembly of spheres in which the center of rotation (CoR) is indicated by a vertical line, and the center of distortion (CoD) is indicated by a cross; (b) Part of of the reconstructed slice through the CoD (indicated by the white line numbered 1 in (a)) shows the distortion of spheres (arrows) increasing with their distance from CoD (indicated by a vertical line); (c) Sinogram at the top of a sphere, indicated by the white line numbered 2 in (a), shows the effect of vertical displacement (arrows).
Fig. 3
Fig. 3 Coordinates of the CoM of the dots. Parabolas are fitted to the horizontal gridlines (i-index) and the vertical gridlines (j-index). Only a small number of fitted parabolas are shown.
Fig. 4
Fig. 4 Deviation from the straight line of the points having minimum distance to the CoD (horizontal gridlines shown only) in two cases: (a) with the initial-estimate of the CoD; (b) with the refined CoD.
Fig. 5
Fig. 5 (a) Corrected image with vacant pixels (black lines). The area of negligible distortion around the CoD shows no missing pixels; (b) Magnified view of the areas indicated by the white square in (a); (c) Filled-in vacant pixels in (b) by super-sampling technique.
Fig. 6
Fig. 6 Magnified view of the part of the image having the highest distortion (bottom-left corner) with the overlay of the ideal gridlines: (a) Distorted image; (b) Corrected image from the BW model.
Fig. 7
Fig. 7 Residual of the corrected points against their ideal positions in x and y coordinates from different correction. (a, d) FW model; (b, e) BW-FW model; (c, f) BW model.
Fig. 8
Fig. 8 Reconstructed images from distorted data (a) and corrected data (b) with magnified views from areas indicated by the white frames: (c) Magnified view from frame 1 in (a); (d) Magnified view from frame 1 in (b); (e) Magnified view from frame 2 in (a); (f) Magnified view from frame 2 in (b). Note the poor reconstruction of features (arrowed) in case (c) in which the problem may not be immediately obvious to the eye. These features are clearly reconstructed in case (d).
Fig. 9
Fig. 9 (a) Part of the reconstructed image containing Ti-sphere (arrowed) and air-bubbles from the sinogram in Fig. 2(c); (b) Sinogram after correction; (c) Part of the reconstructed image from (b) where the shape of Ti-sphere is nicely recovered (arrowed) and the bubble no longer exhibits a distorted shape and bright arc artefacts.

Equations (12)

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y= a i x 2 + b i x+ c i ,
x= a j y 2 + b j y+ c j .
F f ( r d ) r u r d = k 0 + k 1 r + d k 2 r d 2 + k 3 r d 3 +... k n r d n
y d = a i x d 2 + b i x d + c i .
y u = b i x u + c i u
F f ( r d )= c i u a i x d 2 + c i .
[ ..... 1 r d r d 2 ..... r d n ..... 1 r d r d 2 ..... r d n ..... ][ k 0 k 1 k 2 k n ]=[ c i u / ( a i x d 2 + c i ) c j u / ( a j y d 2 + c j ) ]
F b ( r u ) r d r u = k 0 + k 1 r + u k 2 r u 2 + k 3 r u 3 +... k n r u n .
[ ..... 1 r d F f ( r d ) ..... r d n F f ( r d ) n ..... ][ k 0 k 1 k n ]=[ 1/ F f ( r d ) ]
F i a i x d 2 + c i c i u = F b ( r u )
F j a j y d 2 + c j c j u = F b ( r u ),
[ ..... 1 r d / F i ..... r d n / F i n ..... 1 r d / F j ..... r d n / F j n ..... ][ k 0 k 1 k n ]=[ F i F j ]

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