Abstract

High-speed panoramic three-dimensional (3D) shape measurement can be achieved by introducing plane mirrors into the traditional fringe projection profilometry (FPP) system because such a system simultaneously captures fringe patterns from three different perspectives (i.e., by a real camera and two virtual cameras in the plane mirrors). However, calibrating such a system is nontrivial due to the complicated setup. This work introduces a flexible new technique to calibrate such a system. We first present the mathematical representation of the plane mirror, and then mathematically prove that it only requires the camera to observe a set of feature point pairs (including real points and virtual points) to generate a solution to the reflection matrix of a plane mirror. By calibrating the virtual and real camera in the same world coordinate system, 3D point cloud data obtained from real and virtual perspectives can be automatically aligned to generate a panoramic 3D model of the object. Finally, we developed a system to verify the performance of the proposed calibration technique for panoramic 3D shape measurement.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
    [Crossref]
  2. C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
    [Crossref]
  3. S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Mea. Sci. Technol. 29(12), 122001 (2018).
    [Crossref]
  4. S. Zhang, “Absolute phase retrieval methods for digital fringe projection profilometry: A review,” Opt. Lasers Eng. 107, 28–37 (2018).
    [Crossref]
  5. S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
    [Crossref]
  6. C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
    [Crossref]
  7. Z. Zhang, “Review of single-shot 3d shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
    [Crossref]
  8. X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: a review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
    [Crossref]
  9. C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (µftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
    [Crossref]
  10. S. Zhang, “High-speed 3d shape measurement with structured light methods: A review,” Opt. Lasers Eng. 106, 119–131 (2018).
    [Crossref]
  11. W. Yin, S. Feng, T. Tao, L. Huang, M. Trusiak, Q. Chen, and C. Zuo, “High-speed 3d shape measurement using the optimized composite fringe patterns and stereo-assisted structured light system,” Opt. Express 27(3), 2411–2431 (2019).
    [Crossref]
  12. J.-S. Hyun, G. T.-C. Chiu, and S. Zhang, “High-speed and high-accuracy 3d surface measurement using a mechanical projector,” Opt. Express 26(2), 1474–1487 (2018).
    [Crossref]
  13. W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
    [Crossref]
  14. X. Liu, X. Peng, H. Chen, D. He, and B. Z. Gao, “Strategy for automatic and complete three-dimensional optical digitization,” Opt. Lett. 37(15), 3126–3128 (2012).
    [Crossref]
  15. L. Song, Y. Ru, Y. Yang, Q. Guo, X. Zhu, and J. Xi, “Full-view three-dimensional measurement of complex surfaces,” Opt. Eng. 57(10), 104106 (2018).
    [Crossref]
  16. M. Nießner, M. Zollhöfer, S. Izadi, and M. Stamminger, “Real-time 3d reconstruction at scale using voxel hashing,” ACM Trans. Graph. 32(6), 1–11 (2013).
    [Crossref]
  17. E. Epstein, M. Granger-Piché, and P. Potilin, “Exploiting mirrors in interactive reconstruction with structured light,” in VMV, (2004), pp. 125, 132.
  18. D. Lanman, D. Crispell, and G. Taubin, “Surround structured lighting: 3-d scanning with orthographic illumination,” Comput. Vis. Image Underst. 113(11), 1107–1117 (2009).
    [Crossref]
  19. B. Chen and B. Pan, “Mirror-assisted panoramic-digital image correlation for full-surface 360-deg deformation measurement,” Measurement 132, 350–358 (2019).
    [Crossref]
  20. P. J. Besl and N. D. McKay, “A method for registration of 3-d shapes,” IEEE Transactions on Pattern Analysis Mach. Intell. 14(2), 239–256 (1992).
  21. H. Mohammadzade and D. Hatzinakos, “Iterative closest normal point for 3d face recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 35(2), 381–397 (2013).
    [Crossref]
  22. G. L. Mariottini, S. Scheggi, F. Morbidi, and D. Prattichizzo, “Planar mirrors for image-based robot localization and 3-d reconstruction,” Mechatronics 22(4), 398–409 (2012).
    [Crossref]
  23. P. Wang, J. Wang, J. Xu, Y. Guan, G. Zhang, and K. Chen, “Calibration method for a large-scale structured light measurement system,” Appl. Opt. 56(14), 3995–4002 (2017).
    [Crossref]
  24. C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
    [Crossref]
  25. X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2d reference target,” Opt. Lasers Eng. 89, 131–137 (2017).
    [Crossref]
  26. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
    [Crossref]
  27. S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
    [Crossref]

2019 (4)

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

B. Chen and B. Pan, “Mirror-assisted panoramic-digital image correlation for full-surface 360-deg deformation measurement,” Measurement 132, 350–358 (2019).
[Crossref]

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

W. Yin, S. Feng, T. Tao, L. Huang, M. Trusiak, Q. Chen, and C. Zuo, “High-speed 3d shape measurement using the optimized composite fringe patterns and stereo-assisted structured light system,” Opt. Express 27(3), 2411–2431 (2019).
[Crossref]

2018 (7)

J.-S. Hyun, G. T.-C. Chiu, and S. Zhang, “High-speed and high-accuracy 3d surface measurement using a mechanical projector,” Opt. Express 26(2), 1474–1487 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Mea. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

S. Zhang, “Absolute phase retrieval methods for digital fringe projection profilometry: A review,” Opt. Lasers Eng. 107, 28–37 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (µftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

S. Zhang, “High-speed 3d shape measurement with structured light methods: A review,” Opt. Lasers Eng. 106, 119–131 (2018).
[Crossref]

L. Song, Y. Ru, Y. Yang, Q. Guo, X. Zhu, and J. Xi, “Full-view three-dimensional measurement of complex surfaces,” Opt. Eng. 57(10), 104106 (2018).
[Crossref]

2017 (2)

P. Wang, J. Wang, J. Xu, Y. Guan, G. Zhang, and K. Chen, “Calibration method for a large-scale structured light measurement system,” Appl. Opt. 56(14), 3995–4002 (2017).
[Crossref]

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2d reference target,” Opt. Lasers Eng. 89, 131–137 (2017).
[Crossref]

2016 (1)

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

2013 (3)

H. Mohammadzade and D. Hatzinakos, “Iterative closest normal point for 3d face recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 35(2), 381–397 (2013).
[Crossref]

M. Nießner, M. Zollhöfer, S. Izadi, and M. Stamminger, “Real-time 3d reconstruction at scale using voxel hashing,” ACM Trans. Graph. 32(6), 1–11 (2013).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

2012 (3)

Z. Zhang, “Review of single-shot 3d shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
[Crossref]

G. L. Mariottini, S. Scheggi, F. Morbidi, and D. Prattichizzo, “Planar mirrors for image-based robot localization and 3-d reconstruction,” Mechatronics 22(4), 398–409 (2012).
[Crossref]

X. Liu, X. Peng, H. Chen, D. He, and B. Z. Gao, “Strategy for automatic and complete three-dimensional optical digitization,” Opt. Lett. 37(15), 3126–3128 (2012).
[Crossref]

2010 (2)

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: a review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

2009 (1)

D. Lanman, D. Crispell, and G. Taubin, “Surround structured lighting: 3-d scanning with orthographic illumination,” Comput. Vis. Image Underst. 113(11), 1107–1117 (2009).
[Crossref]

2006 (1)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

2000 (1)

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

1992 (1)

P. J. Besl and N. D. McKay, “A method for registration of 3-d shapes,” IEEE Transactions on Pattern Analysis Mach. Intell. 14(2), 239–256 (1992).

Asundi, A.

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (µftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Besl, P. J.

P. J. Besl and N. D. McKay, “A method for registration of 3-d shapes,” IEEE Transactions on Pattern Analysis Mach. Intell. 14(2), 239–256 (1992).

Cai, Z.

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2d reference target,” Opt. Lasers Eng. 89, 131–137 (2017).
[Crossref]

Chen, B.

B. Chen and B. Pan, “Mirror-assisted panoramic-digital image correlation for full-surface 360-deg deformation measurement,” Measurement 132, 350–358 (2019).
[Crossref]

Chen, H.

Chen, K.

Chen, Q.

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

W. Yin, S. Feng, T. Tao, L. Huang, M. Trusiak, Q. Chen, and C. Zuo, “High-speed 3d shape measurement using the optimized composite fringe patterns and stereo-assisted structured light system,” Opt. Express 27(3), 2411–2431 (2019).
[Crossref]

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Mea. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (µftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

Chiu, G. T.-C.

Crispell, D.

D. Lanman, D. Crispell, and G. Taubin, “Surround structured lighting: 3-d scanning with orthographic illumination,” Comput. Vis. Image Underst. 113(11), 1107–1117 (2009).
[Crossref]

Epstein, E.

E. Epstein, M. Granger-Piché, and P. Potilin, “Exploiting mirrors in interactive reconstruction with structured light,” in VMV, (2004), pp. 125, 132.

Feng, F.

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

Feng, S.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

W. Yin, S. Feng, T. Tao, L. Huang, M. Trusiak, Q. Chen, and C. Zuo, “High-speed 3d shape measurement using the optimized composite fringe patterns and stereo-assisted structured light system,” Opt. Express 27(3), 2411–2431 (2019).
[Crossref]

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Mea. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (µftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

Gao, B. Z.

Gorthi, S. S.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Granger-Piché, M.

E. Epstein, M. Granger-Piché, and P. Potilin, “Exploiting mirrors in interactive reconstruction with structured light,” in VMV, (2004), pp. 125, 132.

Gu, G.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Mea. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

Guan, Y.

Guo, Q.

L. Song, Y. Ru, Y. Yang, Q. Guo, X. Zhu, and J. Xi, “Full-view three-dimensional measurement of complex surfaces,” Opt. Eng. 57(10), 104106 (2018).
[Crossref]

Hatzinakos, D.

H. Mohammadzade and D. Hatzinakos, “Iterative closest normal point for 3d face recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 35(2), 381–397 (2013).
[Crossref]

He, D.

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2d reference target,” Opt. Lasers Eng. 89, 131–137 (2017).
[Crossref]

X. Liu, X. Peng, H. Chen, D. He, and B. Z. Gao, “Strategy for automatic and complete three-dimensional optical digitization,” Opt. Lett. 37(15), 3126–3128 (2012).
[Crossref]

He, W.

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2d reference target,” Opt. Lasers Eng. 89, 131–137 (2017).
[Crossref]

Hu, Y.

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

Huang, L.

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

W. Yin, S. Feng, T. Tao, L. Huang, M. Trusiak, Q. Chen, and C. Zuo, “High-speed 3d shape measurement using the optimized composite fringe patterns and stereo-assisted structured light system,” Opt. Express 27(3), 2411–2431 (2019).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (µftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Huang, P. S.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

Hyun, J.-S.

Izadi, S.

M. Nießner, M. Zollhöfer, S. Izadi, and M. Stamminger, “Real-time 3d reconstruction at scale using voxel hashing,” ACM Trans. Graph. 32(6), 1–11 (2013).
[Crossref]

Jiang, H.

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2d reference target,” Opt. Lasers Eng. 89, 131–137 (2017).
[Crossref]

Lanman, D.

D. Lanman, D. Crispell, and G. Taubin, “Surround structured lighting: 3-d scanning with orthographic illumination,” Comput. Vis. Image Underst. 113(11), 1107–1117 (2009).
[Crossref]

Li, R.

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

Liu, X.

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2d reference target,” Opt. Lasers Eng. 89, 131–137 (2017).
[Crossref]

X. Liu, X. Peng, H. Chen, D. He, and B. Z. Gao, “Strategy for automatic and complete three-dimensional optical digitization,” Opt. Lett. 37(15), 3126–3128 (2012).
[Crossref]

Ma, J.

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

Mariottini, G. L.

G. L. Mariottini, S. Scheggi, F. Morbidi, and D. Prattichizzo, “Planar mirrors for image-based robot localization and 3-d reconstruction,” Mechatronics 22(4), 398–409 (2012).
[Crossref]

McKay, N. D.

P. J. Besl and N. D. McKay, “A method for registration of 3-d shapes,” IEEE Transactions on Pattern Analysis Mach. Intell. 14(2), 239–256 (1992).

Mohammadzade, H.

H. Mohammadzade and D. Hatzinakos, “Iterative closest normal point for 3d face recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 35(2), 381–397 (2013).
[Crossref]

Morbidi, F.

G. L. Mariottini, S. Scheggi, F. Morbidi, and D. Prattichizzo, “Planar mirrors for image-based robot localization and 3-d reconstruction,” Mechatronics 22(4), 398–409 (2012).
[Crossref]

Nießner, M.

M. Nießner, M. Zollhöfer, S. Izadi, and M. Stamminger, “Real-time 3d reconstruction at scale using voxel hashing,” ACM Trans. Graph. 32(6), 1–11 (2013).
[Crossref]

Pan, B.

B. Chen and B. Pan, “Mirror-assisted panoramic-digital image correlation for full-surface 360-deg deformation measurement,” Measurement 132, 350–358 (2019).
[Crossref]

Peng, X.

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2d reference target,” Opt. Lasers Eng. 89, 131–137 (2017).
[Crossref]

X. Liu, X. Peng, H. Chen, D. He, and B. Z. Gao, “Strategy for automatic and complete three-dimensional optical digitization,” Opt. Lett. 37(15), 3126–3128 (2012).
[Crossref]

Potilin, P.

E. Epstein, M. Granger-Piché, and P. Potilin, “Exploiting mirrors in interactive reconstruction with structured light,” in VMV, (2004), pp. 125, 132.

Prattichizzo, D.

G. L. Mariottini, S. Scheggi, F. Morbidi, and D. Prattichizzo, “Planar mirrors for image-based robot localization and 3-d reconstruction,” Mechatronics 22(4), 398–409 (2012).
[Crossref]

Rastogi, P.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Ru, Y.

L. Song, Y. Ru, Y. Yang, Q. Guo, X. Zhu, and J. Xi, “Full-view three-dimensional measurement of complex surfaces,” Opt. Eng. 57(10), 104106 (2018).
[Crossref]

Scheggi, S.

G. L. Mariottini, S. Scheggi, F. Morbidi, and D. Prattichizzo, “Planar mirrors for image-based robot localization and 3-d reconstruction,” Mechatronics 22(4), 398–409 (2012).
[Crossref]

Shen, G.

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

Song, L.

L. Song, Y. Ru, Y. Yang, Q. Guo, X. Zhu, and J. Xi, “Full-view three-dimensional measurement of complex surfaces,” Opt. Eng. 57(10), 104106 (2018).
[Crossref]

Stamminger, M.

M. Nießner, M. Zollhöfer, S. Izadi, and M. Stamminger, “Real-time 3d reconstruction at scale using voxel hashing,” ACM Trans. Graph. 32(6), 1–11 (2013).
[Crossref]

Su, X.

X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: a review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

Tao, T.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

W. Yin, S. Feng, T. Tao, L. Huang, M. Trusiak, Q. Chen, and C. Zuo, “High-speed 3d shape measurement using the optimized composite fringe patterns and stereo-assisted structured light system,” Opt. Express 27(3), 2411–2431 (2019).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (µftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Mea. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

Taubin, G.

D. Lanman, D. Crispell, and G. Taubin, “Surround structured lighting: 3-d scanning with orthographic illumination,” Comput. Vis. Image Underst. 113(11), 1107–1117 (2009).
[Crossref]

Trusiak, M.

Wang, J.

Wang, P.

Xi, J.

L. Song, Y. Ru, Y. Yang, Q. Guo, X. Zhu, and J. Xi, “Full-view three-dimensional measurement of complex surfaces,” Opt. Eng. 57(10), 104106 (2018).
[Crossref]

Xu, J.

Yang, Y.

L. Song, Y. Ru, Y. Yang, Q. Guo, X. Zhu, and J. Xi, “Full-view three-dimensional measurement of complex surfaces,” Opt. Eng. 57(10), 104106 (2018).
[Crossref]

Yin, W.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

W. Yin, S. Feng, T. Tao, L. Huang, M. Trusiak, Q. Chen, and C. Zuo, “High-speed 3d shape measurement using the optimized composite fringe patterns and stereo-assisted structured light system,” Opt. Express 27(3), 2411–2431 (2019).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

Yin, Y.

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2d reference target,” Opt. Lasers Eng. 89, 131–137 (2017).
[Crossref]

Zhang, G.

Zhang, L.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Mea. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

Zhang, M.

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Zhang, Q.

X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: a review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

Zhang, S.

S. Zhang, “Absolute phase retrieval methods for digital fringe projection profilometry: A review,” Opt. Lasers Eng. 107, 28–37 (2018).
[Crossref]

S. Zhang, “High-speed 3d shape measurement with structured light methods: A review,” Opt. Lasers Eng. 106, 119–131 (2018).
[Crossref]

J.-S. Hyun, G. T.-C. Chiu, and S. Zhang, “High-speed and high-accuracy 3d surface measurement using a mechanical projector,” Opt. Express 26(2), 1474–1487 (2018).
[Crossref]

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

Zhang, Z.

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2d reference target,” Opt. Lasers Eng. 89, 131–137 (2017).
[Crossref]

Z. Zhang, “Review of single-shot 3d shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
[Crossref]

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

Zhu, X.

L. Song, Y. Ru, Y. Yang, Q. Guo, X. Zhu, and J. Xi, “Full-view three-dimensional measurement of complex surfaces,” Opt. Eng. 57(10), 104106 (2018).
[Crossref]

Zollhöfer, M.

M. Nießner, M. Zollhöfer, S. Izadi, and M. Stamminger, “Real-time 3d reconstruction at scale using voxel hashing,” ACM Trans. Graph. 32(6), 1–11 (2013).
[Crossref]

Zuo, C.

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

W. Yin, S. Feng, T. Tao, L. Huang, M. Trusiak, Q. Chen, and C. Zuo, “High-speed 3d shape measurement using the optimized composite fringe patterns and stereo-assisted structured light system,” Opt. Express 27(3), 2411–2431 (2019).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (µftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Mea. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

ACM Trans. Graph. (1)

M. Nießner, M. Zollhöfer, S. Izadi, and M. Stamminger, “Real-time 3d reconstruction at scale using voxel hashing,” ACM Trans. Graph. 32(6), 1–11 (2013).
[Crossref]

Adv. Photonics (1)

S. Feng, Q. Chen, G. Gu, T. Tao, L. Zhang, Y. Hu, W. Yin, and C. Zuo, “Fringe pattern analysis using deep learning,” Adv. Photonics 1(2), 025001 (2019).
[Crossref]

Appl. Opt. (1)

Comput. Vis. Image Underst. (1)

D. Lanman, D. Crispell, and G. Taubin, “Surround structured lighting: 3-d scanning with orthographic illumination,” Comput. Vis. Image Underst. 113(11), 1107–1117 (2009).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

H. Mohammadzade and D. Hatzinakos, “Iterative closest normal point for 3d face recognition,” IEEE Trans. Pattern Anal. Mach. Intell. 35(2), 381–397 (2013).
[Crossref]

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

IEEE Transactions on Pattern Analysis Mach. Intell. (1)

P. J. Besl and N. D. McKay, “A method for registration of 3-d shapes,” IEEE Transactions on Pattern Analysis Mach. Intell. 14(2), 239–256 (1992).

Mea. Sci. Technol. (1)

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3d measurements with fringe projection profilometry: a review,” Mea. Sci. Technol. 29(12), 122001 (2018).
[Crossref]

Measurement (1)

B. Chen and B. Pan, “Mirror-assisted panoramic-digital image correlation for full-surface 360-deg deformation measurement,” Measurement 132, 350–358 (2019).
[Crossref]

Mechatronics (1)

G. L. Mariottini, S. Scheggi, F. Morbidi, and D. Prattichizzo, “Planar mirrors for image-based robot localization and 3-d reconstruction,” Mechatronics 22(4), 398–409 (2012).
[Crossref]

Opt. Eng. (2)

L. Song, Y. Ru, Y. Yang, Q. Guo, X. Zhu, and J. Xi, “Full-view three-dimensional measurement of complex surfaces,” Opt. Eng. 57(10), 104106 (2018).
[Crossref]

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (11)

W. Yin, C. Zuo, S. Feng, T. Tao, Y. Hu, L. Huang, J. Ma, and Q. Chen, “High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping,” Opt. Lasers Eng. 115, 21–31 (2019).
[Crossref]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

X. Liu, Z. Cai, Y. Yin, H. Jiang, D. He, W. He, Z. Zhang, and X. Peng, “Calibration of fringe projection profilometry using an inaccurate 2d reference target,” Opt. Lasers Eng. 89, 131–137 (2017).
[Crossref]

S. Zhang, “Absolute phase retrieval methods for digital fringe projection profilometry: A review,” Opt. Lasers Eng. 107, 28–37 (2018).
[Crossref]

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, Q. Chen, G. Gu, S. Feng, F. Feng, R. Li, and G. Shen, “High-speed three-dimensional shape measurement for dynamic scenes using bi-frequency tripolar pulse-width-modulation fringe projection,” Opt. Lasers Eng. 51(8), 953–960 (2013).
[Crossref]

Z. Zhang, “Review of single-shot 3d shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
[Crossref]

X. Su and Q. Zhang, “Dynamic 3-d shape measurement method: a review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro fourier transform profilometry (µftp): 3d shape measurement at 10,000 frames per second,” Opt. Lasers Eng. 102, 70–91 (2018).
[Crossref]

S. Zhang, “High-speed 3d shape measurement with structured light methods: A review,” Opt. Lasers Eng. 106, 119–131 (2018).
[Crossref]

Opt. Lett. (1)

Other (1)

E. Epstein, M. Granger-Piché, and P. Potilin, “Exploiting mirrors in interactive reconstruction with structured light,” in VMV, (2004), pp. 125, 132.

Supplementary Material (3)

NameDescription
» Visualization 1       The 3D measurement results of a standard ceramic sphere.
» Visualization 2       The measurement results of a Voltaire model.
» Visualization 3       The measurement results of a Venus model.

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Figures (7)

Fig. 1.
Fig. 1. The schematic diagram of the ideal reflection model for the plane mirror.
Fig. 2.
Fig. 2. The diagram of the mirror-assisted FPP system.
Fig. 3.
Fig. 3. The process of obtaining panoramic 3D shape measurements of objects with complex surfaces.
Fig. 4.
Fig. 4. The measurement result of the circular calibration board. (a) One pose data of the circular calibration board can provide ${15}$ feature point pairs. (b) The 3D data of virtual points. (c) The 3D data of real points.
Fig. 5.
Fig. 5. The 3D measurement results of a standard ceramic sphere (Visualization 1). (a)-(c) The single-view 3D measurement results. (d)-(f) The corresponding distribution of the errors of (a)-(c). (g)-(i) The full-surface 3D measurement results. (j)-(l) The corresponding distribution of the errors of (g)-(i).
Fig. 6.
Fig. 6. The measurement results of a Voltaire model (Visualization 2). (a) The full-surface 3D reconstruction results of a Voltaire model. (b)-(d) The corresponding results of (a) from three different views.
Fig. 7.
Fig. 7. The measurement results of a Venus model (Visualization 3). (a) The full-surface 3D reconstruction results of a Venus model. (b)-(d) The corresponding results of (a) from three different views.

Tables (1)

Tables Icon

Table 1. Comparison of calibration residual errors at different steps.

Equations (24)

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

O X r = O X o + X o X r .
O X r = O X o + 2 d o r n r .
d o r = d w r O X o n r ,
O X r = O X o + 2 d w r n r 2 n r ( O X o n r ) .
X r = ( I 2 n r ( n r ) T ) X o + 2 d w r n r ,
[ X r 1 ] = D r [ X o 1 ] .
D r = [ I 2 n r ( n r ) T 2 d w r n r 0 1 ] .
D r [ X r 1 ] = [ X o 1 ] .
[ 1 2 ( a r ) 2 ] x r 2 a r b r y r 2 a r c r z r + 2 a r d w r = x o ,
2 a r b r x r + [ 1 2 ( b r ) 2 ] y r 2 b r c r z r + 2 b r d w r = y o ,
2 a r c r x r 2 b r c r y r + [ 1 2 ( c r ) 2 ] z r + 2 c r d w r = z o .
a r ( y r y o ) + b r ( x o x r ) = 0.
a r ( z r z o ) + c r ( x o x r ) = 0 ,
b r ( z r z o ) + c r ( y o y r ) = 0.
[ y r y o x o x r 0 z r z o 0 x o x r 0 z r z o y o y r ] [ a r b r c r ] = 0.
f ( d w r ) = n = 1 N r 1 2 ( d w r ) + r 2 2 ( d w r ) + r 3 2 ( d w r ) ,
r 1 ( d w r ) = 2 a 0 r d w r + [ 1 2 ( a 0 r ) 2 ] x r 2 a 0 r b 0 r y r 2 a 0 r c 0 r z r x o ,
r 2 ( d w r ) = 2 b 0 r d w r 2 a 0 r b 0 r x r + [ 1 2 ( b 0 r ) 2 ] y r 2 b 0 r c 0 r z r y o ,
r 3 ( d w r ) = 2 c 0 r d w r 2 a 0 r c 0 r x r 2 b 0 r c 0 r y r + [ 1 2 ( c 0 r ) 2 ] z r z o ,
n = 1 N g 1 2 ( G ) + g 2 2 ( G ) + g 3 2 ( G ) ,
g 1 ( G ) = [ 1 2 ( a r ) 2 ] x r 2 a r b r y r 2 a r c r z r + 2 a r d w r x o ,
g 2 ( G ) = 2 a r b r x r + [ 1 2 ( b r ) 2 ] y r 2 b r c r z r + 2 b r d w r y o ,
g 3 ( G ) = 2 a r c r x r 2 b r c r y r + [ 1 2 ( c r ) 2 ] z r + 2 c r d w r z o ,
n = 1 N g 1 2 ( G , X n r ) + g 2 2 ( G , X n r ) + g 3 2 ( G , X n r ) .