Abstract

This paper presents a pre-calibration-free 3D shape measurement method based on fringe projection. Unlike ordinary methods, it performs calibration and 3D shape measurement concurrently. The captured phase-coded fringe images are utilized to obtain homogenous control points from two camera viewpoints, and the rough 3D structure of these points can be retrieved. Further, a constrained non-linear least-squares optimization model is established to determine the in situ geometry of the optical components, and then, the 3D scene is reconstructed. This method provides an accurate 3D shape measurement capability even during disturbance of the optical geometry. Moreover, not requiring a preliminary calibration process makes the system ultra-flexible. The performance of this method was verified by experiments.

© 2016 Optical Society of America

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References

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  1. B. W. Li, Y. J. Wang, J. F. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
    [Crossref]
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    [Crossref]
  3. Z. W. Li, K. Zhong, Y. F. Li, X. H. Zhou, and Y. S. Shi, “Multi-view phase-shifting: a high-speed and full-resolution 3D measurement framework for arbitrary shape dynamic object,” Opt. Lett. 38(9), 1389–1391 (2013).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  17. C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimized multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43(7), 788–800 (2005).
    [Crossref]
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    [Crossref]
  20. J. Heikkilä and O. Silvén, “A four-step camera calibration procedure with implicit image correction,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 1106–1112.
    [Crossref]
  21. J. K. Seo, H. K. Hong, C. W. Jho, and M. H. Choi, “Two quantitative measures of inlier distributions for precise fundamental matrix estimation,” Pattern Recognit. Lett. 25(6), 733–741 (2004).
    [Crossref]
  22. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
    [Crossref]
  23. M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “A practical approach to 3D scanning in the presence of inter-reflections, subsurface scattering and defocus,” Int. J. Comput. Vis. 102(1-3), 33–55 (2013).
    [Crossref]
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    [Crossref]

2015 (2)

Z. Wang, “Removal of noise and radial lens distortion during calibration of computer vision systems,” Opt. Express 23(9), 11341–11356 (2015).
[Crossref] [PubMed]

H. J. Zhao, Z. Wang, H. Z. Jiang, Y. Xu, and C. Dong, “Calibration for stereo vision system based on phase matching and bundle adjustment algorithm,” Opt. Lasers Eng. 68, 203–213 (2015).
[Crossref]

2014 (2)

Y. Cui, F. Zhou, Y. Wang, L. Liu, and H. Gao, “Precise calibration of binocular vision system used for vision measurement,” Opt. Express 22(8), 9134–9149 (2014).
[Crossref] [PubMed]

B. W. Li, Y. J. Wang, J. F. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[Crossref]

2013 (5)

K. Zhong, Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Z. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Z. W. Li, K. Zhong, Y. F. Li, X. H. Zhou, and Y. S. Shi, “Multi-view phase-shifting: a high-speed and full-resolution 3D measurement framework for arbitrary shape dynamic object,” Opt. Lett. 38(9), 1389–1391 (2013).
[Crossref] [PubMed]

P. Garbacz and W. Mizak, “A novel approach for automation of stereo camera calibration process,” Pomiary Automatyka Robotyka 17(2), 234–238 (2013).

Y. L. Xiao, J. Xue, and X. Su, “Robust self-calibration three-dimensional shape measurement in fringe-projection photogrammetry,” Opt. Lett. 38(5), 694–696 (2013).
[Crossref] [PubMed]

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “A practical approach to 3D scanning in the presence of inter-reflections, subsurface scattering and defocus,” Int. J. Comput. Vis. 102(1-3), 33–55 (2013).
[Crossref]

2012 (2)

2011 (2)

2009 (1)

T. Dang, C. Hoffmann, and C. Stiller, “Continuous stereo self-calibration by camera parameter tracking,” IEEE Trans. Image Process. 18(7), 1536–1550 (2009).
[Crossref] [PubMed]

2008 (1)

Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

2005 (1)

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimized multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43(7), 788–800 (2005).
[Crossref]

2004 (1)

J. K. Seo, H. K. Hong, C. W. Jho, and M. H. Choi, “Two quantitative measures of inlier distributions for precise fundamental matrix estimation,” Pattern Recognit. Lett. 25(6), 733–741 (2004).
[Crossref]

2000 (1)

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Agrawal, A.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “A practical approach to 3D scanning in the presence of inter-reflections, subsurface scattering and defocus,” Int. J. Comput. Vis. 102(1-3), 33–55 (2013).
[Crossref]

Bräuer-Burchardt, C.

C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “Error compensation by sensor re-calibration in fringe projection based optical 3D stereo scanners,” in Proceedings of International Conference on Image Analysis and Processing Part II (Academic, 2011), pp. 363–373.
[Crossref]

Choi, M. H.

J. K. Seo, H. K. Hong, C. W. Jho, and M. H. Choi, “Two quantitative measures of inlier distributions for precise fundamental matrix estimation,” Pattern Recognit. Lett. 25(6), 733–741 (2004).
[Crossref]

Cui, Y.

Dai, J. F.

B. W. Li, Y. J. Wang, J. F. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[Crossref]

Dang, T.

T. Dang, C. Hoffmann, and C. Stiller, “Continuous stereo self-calibration by camera parameter tracking,” IEEE Trans. Image Process. 18(7), 1536–1550 (2009).
[Crossref] [PubMed]

Dong, C.

H. J. Zhao, Z. Wang, H. Z. Jiang, Y. Xu, and C. Dong, “Calibration for stereo vision system based on phase matching and bundle adjustment algorithm,” Opt. Lasers Eng. 68, 203–213 (2015).
[Crossref]

Gao, B. Z.

Gao, H.

Garbacz, P.

P. Garbacz and W. Mizak, “A novel approach for automation of stereo camera calibration process,” Pomiary Automatyka Robotyka 17(2), 234–238 (2013).

Guo, C. Z.

D. H. Xu, Q. Q. Zeng, H. J. Zhao, C. Z. Guo, K. Kidono, and Y. Kojima, “Online stereovision calibration using on-road markings,” in Proceedings of IEEE Conference on Intelligent Transportation Systems (IEEE, 2014), pp. 245–252.

Guo, T.

Gupta, M.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “A practical approach to 3D scanning in the presence of inter-reflections, subsurface scattering and defocus,” Int. J. Comput. Vis. 102(1-3), 33–55 (2013).
[Crossref]

Heikkilä, J.

J. Heikkilä and O. Silvén, “A four-step camera calibration procedure with implicit image correction,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 1106–1112.
[Crossref]

Hoffmann, C.

T. Dang, C. Hoffmann, and C. Stiller, “Continuous stereo self-calibration by camera parameter tracking,” IEEE Trans. Image Process. 18(7), 1536–1550 (2009).
[Crossref] [PubMed]

Hong, H. K.

J. K. Seo, H. K. Hong, C. W. Jho, and M. H. Choi, “Two quantitative measures of inlier distributions for precise fundamental matrix estimation,” Pattern Recognit. Lett. 25(6), 733–741 (2004).
[Crossref]

Jho, C. W.

J. K. Seo, H. K. Hong, C. W. Jho, and M. H. Choi, “Two quantitative measures of inlier distributions for precise fundamental matrix estimation,” Pattern Recognit. Lett. 25(6), 733–741 (2004).
[Crossref]

Jiang, H. Z.

H. J. Zhao, Z. Wang, H. Z. Jiang, Y. Xu, and C. Dong, “Calibration for stereo vision system based on phase matching and bundle adjustment algorithm,” Opt. Lasers Eng. 68, 203–213 (2015).
[Crossref]

Jones, J. D. C.

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimized multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43(7), 788–800 (2005).
[Crossref]

Kidono, K.

D. H. Xu, Q. Q. Zeng, H. J. Zhao, C. Z. Guo, K. Kidono, and Y. Kojima, “Online stereovision calibration using on-road markings,” in Proceedings of IEEE Conference on Intelligent Transportation Systems (IEEE, 2014), pp. 245–252.

Kojima, Y.

D. H. Xu, Q. Q. Zeng, H. J. Zhao, C. Z. Guo, K. Kidono, and Y. Kojima, “Online stereovision calibration using on-road markings,” in Proceedings of IEEE Conference on Intelligent Transportation Systems (IEEE, 2014), pp. 245–252.

Kühmstedt, P.

C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “Error compensation by sensor re-calibration in fringe projection based optical 3D stereo scanners,” in Proceedings of International Conference on Image Analysis and Processing Part II (Academic, 2011), pp. 363–373.
[Crossref]

Kutulakos, K. N.

M. O’Toole, J. Mather, and K. N. Kutulakos, “3D shape and indirect appearance by structured light transport,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2014), pp. 3246–3253.
[Crossref]

Lei, Y. Z.

K. Zhong, Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Z. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Li, A.

Li, B. W.

B. W. Li, Y. J. Wang, J. F. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[Crossref]

Li, Y. F.

Li, Z. W.

Z. W. Li, K. Zhong, Y. F. Li, X. H. Zhou, and Y. S. Shi, “Multi-view phase-shifting: a high-speed and full-resolution 3D measurement framework for arbitrary shape dynamic object,” Opt. Lett. 38(9), 1389–1391 (2013).
[Crossref] [PubMed]

K. Zhong, Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Z. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Liu, L.

Liu, X.

Lohry, W.

B. W. Li, Y. J. Wang, J. F. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[Crossref]

Ma, H.

Mather, J.

M. O’Toole, J. Mather, and K. N. Kutulakos, “3D shape and indirect appearance by structured light transport,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2014), pp. 3246–3253.
[Crossref]

Mizak, W.

P. Garbacz and W. Mizak, “A novel approach for automation of stereo camera calibration process,” Pomiary Automatyka Robotyka 17(2), 234–238 (2013).

Narasimhan, S. G.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “A practical approach to 3D scanning in the presence of inter-reflections, subsurface scattering and defocus,” Int. J. Comput. Vis. 102(1-3), 33–55 (2013).
[Crossref]

Notni, G.

C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “Error compensation by sensor re-calibration in fringe projection based optical 3D stereo scanners,” in Proceedings of International Conference on Image Analysis and Processing Part II (Academic, 2011), pp. 363–373.
[Crossref]

O’Toole, M.

M. O’Toole, J. Mather, and K. N. Kutulakos, “3D shape and indirect appearance by structured light transport,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2014), pp. 3246–3253.
[Crossref]

Pan, B.

Pan, T. Y.

Peng, X.

Seo, J. K.

J. K. Seo, H. K. Hong, C. W. Jho, and M. H. Choi, “Two quantitative measures of inlier distributions for precise fundamental matrix estimation,” Pattern Recognit. Lett. 25(6), 733–741 (2004).
[Crossref]

Shi, Y. S.

K. Zhong, Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Z. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Z. W. Li, K. Zhong, Y. F. Li, X. H. Zhou, and Y. S. Shi, “Multi-view phase-shifting: a high-speed and full-resolution 3D measurement framework for arbitrary shape dynamic object,” Opt. Lett. 38(9), 1389–1391 (2013).
[Crossref] [PubMed]

Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Silvén, O.

J. Heikkilä and O. Silvén, “A four-step camera calibration procedure with implicit image correction,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 1106–1112.
[Crossref]

Stiller, C.

T. Dang, C. Hoffmann, and C. Stiller, “Continuous stereo self-calibration by camera parameter tracking,” IEEE Trans. Image Process. 18(7), 1536–1550 (2009).
[Crossref] [PubMed]

Su, X.

Towers, C. E.

Z. Zhang, H. Ma, S. Zhang, T. Guo, C. E. Towers, and D. P. Towers, “Simple calibration of a phase-based 3D imaging system based on uneven fringe projection,” Opt. Lett. 36(5), 627–629 (2011).
[Crossref] [PubMed]

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimized multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43(7), 788–800 (2005).
[Crossref]

Towers, D. P.

Z. Zhang, H. Ma, S. Zhang, T. Guo, C. E. Towers, and D. P. Towers, “Simple calibration of a phase-based 3D imaging system based on uneven fringe projection,” Opt. Lett. 36(5), 627–629 (2011).
[Crossref] [PubMed]

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimized multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43(7), 788–800 (2005).
[Crossref]

Veeraraghavan, A.

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “A practical approach to 3D scanning in the presence of inter-reflections, subsurface scattering and defocus,” Int. J. Comput. Vis. 102(1-3), 33–55 (2013).
[Crossref]

Vo, M.

Wang, C. J.

K. Zhong, Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Z. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Wang, Y.

Wang, Y. J.

B. W. Li, Y. J. Wang, J. F. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[Crossref]

Wang, Y. Y.

Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Wang, Z.

H. J. Zhao, Z. Wang, H. Z. Jiang, Y. Xu, and C. Dong, “Calibration for stereo vision system based on phase matching and bundle adjustment algorithm,” Opt. Lasers Eng. 68, 203–213 (2015).
[Crossref]

Z. Wang, “Removal of noise and radial lens distortion during calibration of computer vision systems,” Opt. Express 23(9), 11341–11356 (2015).
[Crossref] [PubMed]

Wang, Z. Y.

Xiao, Y. L.

Xu, D. H.

D. H. Xu, Q. Q. Zeng, H. J. Zhao, C. Z. Guo, K. Kidono, and Y. Kojima, “Online stereovision calibration using on-road markings,” in Proceedings of IEEE Conference on Intelligent Transportation Systems (IEEE, 2014), pp. 245–252.

Xu, Y.

H. J. Zhao, Z. Wang, H. Z. Jiang, Y. Xu, and C. Dong, “Calibration for stereo vision system based on phase matching and bundle adjustment algorithm,” Opt. Lasers Eng. 68, 203–213 (2015).
[Crossref]

Xue, J.

Yin, Y.

Zeng, Q. Q.

D. H. Xu, Q. Q. Zeng, H. J. Zhao, C. Z. Guo, K. Kidono, and Y. Kojima, “Online stereovision calibration using on-road markings,” in Proceedings of IEEE Conference on Intelligent Transportation Systems (IEEE, 2014), pp. 245–252.

Zhang, S.

B. W. Li, Y. J. Wang, J. F. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[Crossref]

Z. Zhang, H. Ma, S. Zhang, T. Guo, C. E. Towers, and D. P. Towers, “Simple calibration of a phase-based 3D imaging system based on uneven fringe projection,” Opt. Lett. 36(5), 627–629 (2011).
[Crossref] [PubMed]

Zhang, Z.

Zhang, Z. Y.

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Zhao, H. J.

H. J. Zhao, Z. Wang, H. Z. Jiang, Y. Xu, and C. Dong, “Calibration for stereo vision system based on phase matching and bundle adjustment algorithm,” Opt. Lasers Eng. 68, 203–213 (2015).
[Crossref]

D. H. Xu, Q. Q. Zeng, H. J. Zhao, C. Z. Guo, K. Kidono, and Y. Kojima, “Online stereovision calibration using on-road markings,” in Proceedings of IEEE Conference on Intelligent Transportation Systems (IEEE, 2014), pp. 245–252.

Zhong, K.

K. Zhong, Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Z. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

Z. W. Li, K. Zhong, Y. F. Li, X. H. Zhou, and Y. S. Shi, “Multi-view phase-shifting: a high-speed and full-resolution 3D measurement framework for arbitrary shape dynamic object,” Opt. Lett. 38(9), 1389–1391 (2013).
[Crossref] [PubMed]

Zhou, F.

Zhou, X. H.

Exp. Mech. (1)

B. Pan, “Recent progress in digital image correlation,” Exp. Mech. 51(7), 1223–1235 (2011).
[Crossref]

IEEE Trans. Image Process. (1)

T. Dang, C. Hoffmann, and C. Stiller, “Continuous stereo self-calibration by camera parameter tracking,” IEEE Trans. Image Process. 18(7), 1536–1550 (2009).
[Crossref] [PubMed]

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

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Int. J. Comput. Vis. (1)

M. Gupta, A. Agrawal, A. Veeraraghavan, and S. G. Narasimhan, “A practical approach to 3D scanning in the presence of inter-reflections, subsurface scattering and defocus,” Int. J. Comput. Vis. 102(1-3), 33–55 (2013).
[Crossref]

Opt. Eng. (1)

Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[Crossref]

Opt. Express (3)

Opt. Lasers Eng. (4)

B. W. Li, Y. J. Wang, J. F. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[Crossref]

K. Zhong, Z. W. Li, Y. S. Shi, C. J. Wang, and Y. Z. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Lasers Eng. 51(11), 1213–1222 (2013).
[Crossref]

H. J. Zhao, Z. Wang, H. Z. Jiang, Y. Xu, and C. Dong, “Calibration for stereo vision system based on phase matching and bundle adjustment algorithm,” Opt. Lasers Eng. 68, 203–213 (2015).
[Crossref]

C. E. Towers, D. P. Towers, and J. D. C. Jones, “Absolute fringe order calculation using optimized multi-frequency selection in full-field profilometry,” Opt. Lasers Eng. 43(7), 788–800 (2005).
[Crossref]

Opt. Lett. (4)

Pattern Recognit. Lett. (1)

J. K. Seo, H. K. Hong, C. W. Jho, and M. H. Choi, “Two quantitative measures of inlier distributions for precise fundamental matrix estimation,” Pattern Recognit. Lett. 25(6), 733–741 (2004).
[Crossref]

Pomiary Automatyka Robotyka (1)

P. Garbacz and W. Mizak, “A novel approach for automation of stereo camera calibration process,” Pomiary Automatyka Robotyka 17(2), 234–238 (2013).

Other (6)

D. H. Xu, Q. Q. Zeng, H. J. Zhao, C. Z. Guo, K. Kidono, and Y. Kojima, “Online stereovision calibration using on-road markings,” in Proceedings of IEEE Conference on Intelligent Transportation Systems (IEEE, 2014), pp. 245–252.

C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “Calibration of stereo 3D scanners with minimal number of views using plane targets and vanishing points,” in Proceedings of Computer Analysis of Images and Patterns: Part II (Academic, 2015), pp. 61–72.

C. Bräuer-Burchardt, P. Kühmstedt, and G. Notni, “Error compensation by sensor re-calibration in fringe projection based optical 3D stereo scanners,” in Proceedings of International Conference on Image Analysis and Processing Part II (Academic, 2011), pp. 363–373.
[Crossref]

R. I. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, 2nd ed. (Cambridge University Press, 2004).

J. Heikkilä and O. Silvén, “A four-step camera calibration procedure with implicit image correction,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 1106–1112.
[Crossref]

M. O’Toole, J. Mather, and K. N. Kutulakos, “3D shape and indirect appearance by structured light transport,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2014), pp. 3246–3253.
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Fringe projection and phase matching.
Fig. 2
Fig. 2 Homogenous control points selection.
Fig. 3
Fig. 3 Diagram of measurement procedure.
Fig. 4
Fig. 4 Measurement scene.
Fig. 5
Fig. 5 Accuracy and stability test: (a) Homogenous control points selection. (b) Reconstructed 3D point cloud.
Fig. 6
Fig. 6 Measurement error comparisons.
Fig. 7
Fig. 7 Measurement flexibility test: (a) Measurement scene of large scale range; (b) 3D point cloud of large scale range; (c) Measurement scene of small scale range; (d) 3D point cloud of small scale range.
Fig. 8
Fig. 8 Measurement test of various objects: (a) Measurement of packaging bag with richly textured surface; (b) Measurement of manufactured component with highly reflective surface; (c) Measurement of grape with translucent surface.

Equations (9)

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I n (x,y)=A(x,y)+B(x,y)cos[ϕ(x,y)+ δ n ],
ϕ=arctan( n=1 N I n sin( δ n ) / n=1 N I n cos( δ n ) ).
γ=B/A = 2 { [ n=1 N I n sin( δ n ) ] 2 + [ n=1 N I n cos( δ n ) ] 2 } 0.5 / n=1 N I n .
c= i=W W j=W W ( φ ij1 V φ ¯ 1 V ) 2 ( φ ij1 H φ ¯ 1 H ) 2 ( φ ij2 V φ ¯ 2 V ) 2 ( φ ij2 H φ ¯ 2 H ) 2 i=W W j=W W ( φ ij1 V φ ¯ 1 V ) 2 ( φ ij1 H φ ¯ 1 H ) 2 i=W W j=W W ( φ ij2 V φ ¯ 2 V ) 2 ( φ ij2 H φ ¯ 2 H ) 2 ,
{ s i m ˜ i = A i [ R i | t i ] M ˜ w m i = m i +θ( k i ; m i ) , with A i =[ a x i 0 u i 0 a y i v i 0 0 1 ],
{ R= R 2 R 1 1 t= t 2 R 2 R 1 1 t 1 .
m ˜ 2 T F m ˜ 1 =0, with F= A 2 T [t] x R A 1 1 ,
{ s 1 m ˜ 1 = A 1 [I|0] M ˜ c 1 s 2 m ˜ 2 = A 2 [R|t] M ˜ c 1 ,
Cst= i=1 L m 1 i m ^ 1 i ( A 1 , k 1 , M c 1 ) 2 + i=1 L m 2 i m ^ 2 i ( A 2 , k 2 ,R,t, M c 1 ) 2 ,

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