Abstract

In recent years, fringe projection has become an established and essential method for dynamic three-dimensional (3-D) shape measurement in different fields such as online inspection and real-time quality control. Numerous high-speed 3-D shape measurement methods have been developed by either employing high-speed hardware, minimizing the number of pattern projection, or both. However, dynamic 3-D shape measurement of arbitrarily-shaped objects with full sensor resolution without the necessity of additional pattern projections is still a big challenge. In this work, we introduce a high-speed 3-D shape measurement technique based on composite phase-shifting fringes and a multi-view system. The geometry constraint is adopted to search the corresponding points independently without additional images. Meanwhile, by analysing the 3-D position and the main wrapped phase of the corresponding point, pairs with an incorrect 3-D position or a considerable phase difference are effectively rejected. All of the qualified corresponding points are then corrected, and the unique one as well as the related period order is selected through the embedded triangular wave. Finally, considering that some points can only be captured by one of the cameras due to the occlusions, these points may have different fringe orders in the two views, so a left-right consistency check is employed to eliminate those erroneous period orders in this case. Several experiments on both static and dynamic scenes are performed, verifying that our method can achieve a speed of 120 frames per second (fps) with 25-period fringe patterns for fast, dense, and accurate 3-D measurement.

© 2016 Optical Society of America

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  1. S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Eng. 48, 133–140 (2010).
    [Crossref]
  2. X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: a review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
    [Crossref]
  3. S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
    [Crossref]
  4. S Van der Jeught and Joris J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. (2016 in press).
    [Crossref]
  5. Y. Gong and S. Zhang, “Ultrafast 3-D shape measurement with an off-the-shelf DLP projector,” Opt. Express 18(19), 19743–19754 (2010).
    [Crossref] [PubMed]
  6. K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
    [Crossref] [PubMed]
  7. C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
    [Crossref] [PubMed]
  8. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
    [Crossref] [PubMed]
  9. Q. Zhang and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13(8), 3110–3116 (2005).
    [Crossref] [PubMed]
  10. X. Su and W. Chen, “Fourier transform profilometry:: a review,” Opt. Lasers Eng 35(5), 263–284 (2001).
    [Crossref]
  11. L. Guo, X. Su, and J. Li, “Improved Fourier transform profilometry for the automatic measurement of 3D object shapes,” Opt. Eng. 29(12), 1439–1444 (1990).
    [Crossref]
  12. V. Srinivasan, H. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23(18), 3105–3108 (1984).
    [Crossref] [PubMed]
  13. J. Li, L. G. Hassebrook, and C. Guan, “Optimized two-frequency phase-measuring-profilometry light-sensor temporal-noise sensitivity,” J. Opt. Soc. Am. A 20(1), 106–115 (2003).
    [Crossref]
  14. X. Su, G. Von Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Optics Communications. 98(1–3), 141–150 (1993).
    [Crossref]
  15. H. S. Abdul-Rahman, M. A. Gdeisat, D. R. Burton, M. J. Lalor, F. Lilley, and C. J. Moore, “Fast and robust three-dimensional best path phase unwrapping algorithm,” Appl. Opt. 46(26), 6623–6635 (2007).
    [Crossref] [PubMed]
  16. G. Sansoni, M. Carocci, and R. Rodella, “Three-dimensional vision based on a combination of gray-code and phase-shift light projection: analysis and compensation of the systematic errors,” Appl. Opt. 38(31), 6565–6573 (1999).
    [Crossref]
  17. Y. Wang and S. Zhang, “Superfast multifrequency phase-shifting technique with optimal pulse width modulation,” Opt. Express 19(6), 5149–5155 (2011).
    [Crossref] [PubMed]
  18. Y. Zhang, Z. Xiong, and F. Wu, “Unambiguous 3D measurement from speckle-embedded fringe,” Appl. Opt. 52(32), 7797–7805 (2013).
    [Crossref] [PubMed]
  19. Y. Wang, K. Liu, Q. Hao, D. L. Lau, and L. G. Hassebrook, “Period coded phase shifting strategy for real-time 3-D structured light illumination,” IEEE Trans. Image Processing. 20(11), 3001–3013 (2011).
    [Crossref]
  20. T. Weise, B. Leibe, and L. Van Gool, “Fast 3d scanning with automatic motion compensation,” 2007 IEEE Conference on Computer Vision and Pattern Recognition. IEEE pp. 1–8 (2007).
  21. D. Li, H. Zhao, and H. Jiang, “Fast phase-based stereo matching method for 3D shape measurement,” Optomechatronic Technologies (ISOT), 2010 International Symposium on. IEEE pp. 1–5 (2010).
  22. C. BrÃd’uer-Burchardt, C. Munkelt, M. Heinze, P. KÃijhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3D measuring systems,” International Conference on Image Analysis and Processing. pp. 265–274 (2011).
  23. Z. Li, K. Zhong, Y. Li, X. Zhou, and Y. Shi, “Multiview phase shifting: a full-resolution and high-speed 3D measurement framework for arbitrary shape dynamic objects,” Opt. Lett. 38(9), 1389–1391 (2013).
    [Crossref] [PubMed]
  24. P. Fua, “A parallel stereo algorithm that produces dense depth maps and preserves image features,” Machine vision and applications 6(1), 35–49 (1993).
    [Crossref]
  25. S. Zhang and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Opt. Eng. 46(6), 063601 (2007).
    [Crossref]
  26. 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]
  27. S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
    [Crossref]
  28. S. Feng, Q. Chen, and C. Zuo, “Graphics processing unit–assisted real-time three-dimensional measurement using speckle-embedded fringe,” Appl. Opt. 54(22), 6865–6873 (2015).
    [Crossref] [PubMed]
  29. V. I. Gushov and Y. N. Solodkin, “Automatic processing of fringe patterns in integer interferometers,” Opt. Lasers Eng 14(4–5), 311–324 (1991).
    [Crossref]
  30. M. Takeda, Q. Gu, M. Kinoshita, H. Takai, and Y. Takahashi, “Frequency-multiplex Fourier-transform profilometry: a single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations,” Appl. Opt. 36(22), 5347–5354 (1997).
    [Crossref] [PubMed]
  31. J. Zhong and Y. Zhang, “Absolute phase-measurement technique based on number theory in multifrequency grating projection profilometry,” Appl. Opt. 40(4), 492–500 (2001).
    [Crossref]
  32. K. H. Rosen, Elementary Number Theory and its Applications (Pearson Education, 2005).
  33. 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]

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]

2015 (1)

2013 (3)

2012 (1)

2011 (2)

Y. Wang and S. Zhang, “Superfast multifrequency phase-shifting technique with optimal pulse width modulation,” Opt. Express 19(6), 5149–5155 (2011).
[Crossref] [PubMed]

Y. Wang, K. Liu, Q. Hao, D. L. Lau, and L. G. Hassebrook, “Period coded phase shifting strategy for real-time 3-D structured light illumination,” IEEE Trans. Image Processing. 20(11), 3001–3013 (2011).
[Crossref]

2010 (5)

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Eng. 48, 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]

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
[Crossref] [PubMed]

Y. Gong and S. Zhang, “Ultrafast 3-D shape measurement with an off-the-shelf DLP projector,” Opt. Express 18(19), 19743–19754 (2010).
[Crossref] [PubMed]

2007 (2)

H. S. Abdul-Rahman, M. A. Gdeisat, D. R. Burton, M. J. Lalor, F. Lilley, and C. J. Moore, “Fast and robust three-dimensional best path phase unwrapping algorithm,” Appl. Opt. 46(26), 6623–6635 (2007).
[Crossref] [PubMed]

S. Zhang and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Opt. Eng. 46(6), 063601 (2007).
[Crossref]

2006 (1)

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

2005 (1)

2003 (1)

2001 (2)

1999 (1)

1997 (1)

1993 (2)

X. Su, G. Von Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Optics Communications. 98(1–3), 141–150 (1993).
[Crossref]

P. Fua, “A parallel stereo algorithm that produces dense depth maps and preserves image features,” Machine vision and applications 6(1), 35–49 (1993).
[Crossref]

1991 (1)

V. I. Gushov and Y. N. Solodkin, “Automatic processing of fringe patterns in integer interferometers,” Opt. Lasers Eng 14(4–5), 311–324 (1991).
[Crossref]

1990 (1)

L. Guo, X. Su, and J. Li, “Improved Fourier transform profilometry for the automatic measurement of 3D object shapes,” Opt. Eng. 29(12), 1439–1444 (1990).
[Crossref]

1984 (1)

1983 (1)

Abdul-Rahman, H. S.

Asundi, A.

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]

BrÃd’uer-Burchardt, C.

C. BrÃd’uer-Burchardt, C. Munkelt, M. Heinze, P. KÃijhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3D measuring systems,” International Conference on Image Analysis and Processing. pp. 265–274 (2011).

Burton, D. R.

Carocci, M.

Chen, Q.

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]

S. Feng, Q. Chen, and C. Zuo, “Graphics processing unit–assisted real-time three-dimensional measurement using speckle-embedded fringe,” Appl. Opt. 54(22), 6865–6873 (2015).
[Crossref] [PubMed]

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]

C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
[Crossref] [PubMed]

Chen, W.

X. Su and W. Chen, “Fourier transform profilometry:: a review,” Opt. Lasers Eng 35(5), 263–284 (2001).
[Crossref]

Dirckx, Joris J. J.

S Van der Jeught and Joris J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. (2016 in press).
[Crossref]

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]

C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
[Crossref] [PubMed]

Feng, S.

Fua, P.

P. Fua, “A parallel stereo algorithm that produces dense depth maps and preserves image features,” Machine vision and applications 6(1), 35–49 (1993).
[Crossref]

Gdeisat, M. A.

Gong, Y.

Gorthi, S. S.

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

Gu, 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]

C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
[Crossref] [PubMed]

Gu, Q.

Guan, C.

Guo, L.

L. Guo, X. Su, and J. Li, “Improved Fourier transform profilometry for the automatic measurement of 3D object shapes,” Opt. Eng. 29(12), 1439–1444 (1990).
[Crossref]

Gushov, V. I.

V. I. Gushov and Y. N. Solodkin, “Automatic processing of fringe patterns in integer interferometers,” Opt. Lasers Eng 14(4–5), 311–324 (1991).
[Crossref]

Halioua, M.

Hao, Q.

Y. Wang, K. Liu, Q. Hao, D. L. Lau, and L. G. Hassebrook, “Period coded phase shifting strategy for real-time 3-D structured light illumination,” IEEE Trans. Image Processing. 20(11), 3001–3013 (2011).
[Crossref]

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
[Crossref] [PubMed]

Hassebrook, L. G.

Heinze, M.

C. BrÃd’uer-Burchardt, C. Munkelt, M. Heinze, P. KÃijhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3D measuring systems,” International Conference on Image Analysis and Processing. pp. 265–274 (2011).

Huang, L.

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, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Opt. Eng. 46(6), 063601 (2007).
[Crossref]

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

Jiang, H.

D. Li, H. Zhao, and H. Jiang, “Fast phase-based stereo matching method for 3D shape measurement,” Optomechatronic Technologies (ISOT), 2010 International Symposium on. IEEE pp. 1–5 (2010).

KÃijhmstedt, P.

C. BrÃd’uer-Burchardt, C. Munkelt, M. Heinze, P. KÃijhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3D measuring systems,” International Conference on Image Analysis and Processing. pp. 265–274 (2011).

Kinoshita, M.

Lalor, M. J.

Lau, D. L.

Y. Wang, K. Liu, Q. Hao, D. L. Lau, and L. G. Hassebrook, “Period coded phase shifting strategy for real-time 3-D structured light illumination,” IEEE Trans. Image Processing. 20(11), 3001–3013 (2011).
[Crossref]

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
[Crossref] [PubMed]

Leibe, B.

T. Weise, B. Leibe, and L. Van Gool, “Fast 3d scanning with automatic motion compensation,” 2007 IEEE Conference on Computer Vision and Pattern Recognition. IEEE pp. 1–8 (2007).

Li, D.

D. Li, H. Zhao, and H. Jiang, “Fast phase-based stereo matching method for 3D shape measurement,” Optomechatronic Technologies (ISOT), 2010 International Symposium on. IEEE pp. 1–5 (2010).

Li, J.

J. Li, L. G. Hassebrook, and C. Guan, “Optimized two-frequency phase-measuring-profilometry light-sensor temporal-noise sensitivity,” J. Opt. Soc. Am. A 20(1), 106–115 (2003).
[Crossref]

L. Guo, X. Su, and J. Li, “Improved Fourier transform profilometry for the automatic measurement of 3D object shapes,” Opt. Eng. 29(12), 1439–1444 (1990).
[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]

Li, Y.

Li, Z.

Lilley, F.

Liu, H.

Liu, K.

Y. Wang, K. Liu, Q. Hao, D. L. Lau, and L. G. Hassebrook, “Period coded phase shifting strategy for real-time 3-D structured light illumination,” IEEE Trans. Image Processing. 20(11), 3001–3013 (2011).
[Crossref]

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
[Crossref] [PubMed]

Moore, C. J.

Munkelt, C.

C. BrÃd’uer-Burchardt, C. Munkelt, M. Heinze, P. KÃijhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3D measuring systems,” International Conference on Image Analysis and Processing. pp. 265–274 (2011).

Mutoh, K.

Notni, G.

C. BrÃd’uer-Burchardt, C. Munkelt, M. Heinze, P. KÃijhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3D measuring systems,” International Conference on Image Analysis and Processing. pp. 265–274 (2011).

Rastogi, P.

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

Rodella, R.

Rosen, K. H.

K. H. Rosen, Elementary Number Theory and its Applications (Pearson Education, 2005).

Sansoni, G.

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]

Shi, Y.

Solodkin, Y. N.

V. I. Gushov and Y. N. Solodkin, “Automatic processing of fringe patterns in integer interferometers,” Opt. Lasers Eng 14(4–5), 311–324 (1991).
[Crossref]

Srinivasan, V.

Su, X.

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

Q. Zhang and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13(8), 3110–3116 (2005).
[Crossref] [PubMed]

X. Su and W. Chen, “Fourier transform profilometry:: a review,” Opt. Lasers Eng 35(5), 263–284 (2001).
[Crossref]

X. Su, G. Von Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Optics Communications. 98(1–3), 141–150 (1993).
[Crossref]

L. Guo, X. Su, and J. Li, “Improved Fourier transform profilometry for the automatic measurement of 3D object shapes,” Opt. Eng. 29(12), 1439–1444 (1990).
[Crossref]

Takahashi, Y.

Takai, H.

Takeda, M.

Van der Jeught, S

S Van der Jeught and Joris J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. (2016 in press).
[Crossref]

Van Gool, L.

T. Weise, B. Leibe, and L. Van Gool, “Fast 3d scanning with automatic motion compensation,” 2007 IEEE Conference on Computer Vision and Pattern Recognition. IEEE pp. 1–8 (2007).

Von Bally, G.

X. Su, G. Von Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Optics Communications. 98(1–3), 141–150 (1993).
[Crossref]

Vukicevic, D.

X. Su, G. Von Bally, and D. Vukicevic, “Phase-stepping grating profilometry: utilization of intensity modulation analysis in complex objects evaluation,” Optics Communications. 98(1–3), 141–150 (1993).
[Crossref]

Wang, Y.

Weise, T.

T. Weise, B. Leibe, and L. Van Gool, “Fast 3d scanning with automatic motion compensation,” 2007 IEEE Conference on Computer Vision and Pattern Recognition. IEEE pp. 1–8 (2007).

Wu, F.

Xiong, Z.

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]

Q. Zhang and X. Su, “High-speed optical measurement for the drumhead vibration,” Opt. Express 13(8), 3110–3116 (2005).
[Crossref] [PubMed]

Zhang, S.

Y. Wang and S. Zhang, “Superfast multifrequency phase-shifting technique with optimal pulse width modulation,” Opt. Express 19(6), 5149–5155 (2011).
[Crossref] [PubMed]

Y. Gong and S. Zhang, “Ultrafast 3-D shape measurement with an off-the-shelf DLP projector,” Opt. Express 18(19), 19743–19754 (2010).
[Crossref] [PubMed]

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

S. Zhang and P. S. Huang, “Phase error compensation for a 3-D shape measurement system based on the phase-shifting method,” Opt. Eng. 46(6), 063601 (2007).
[Crossref]

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

Zhang, Y.

Zhao, H.

D. Li, H. Zhao, and H. Jiang, “Fast phase-based stereo matching method for 3D shape measurement,” Optomechatronic Technologies (ISOT), 2010 International Symposium on. IEEE pp. 1–5 (2010).

Zhong, J.

Zhong, K.

Zhou, X.

Zuo, C.

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]

S. Feng, Q. Chen, and C. Zuo, “Graphics processing unit–assisted real-time three-dimensional measurement using speckle-embedded fringe,” Appl. Opt. 54(22), 6865–6873 (2015).
[Crossref] [PubMed]

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]

C. Zuo, Q. Chen, G. Gu, S. Feng, and F. Feng, “High-speed three-dimensional profilometry for multiple objects with complex shapes,” Opt. Express 20(17), 19493–19510 (2012).
[Crossref] [PubMed]

Appl. Opt. (8)

M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
[Crossref] [PubMed]

V. Srinivasan, H. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23(18), 3105–3108 (1984).
[Crossref] [PubMed]

G. Sansoni, M. Carocci, and R. Rodella, “Three-dimensional vision based on a combination of gray-code and phase-shift light projection: analysis and compensation of the systematic errors,” Appl. Opt. 38(31), 6565–6573 (1999).
[Crossref]

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Supplementary Material (4)

NameDescription
» Visualization 1: MP4 (939 KB)      Measurement result of a moving palm
» Visualization 2: MP4 (1873 KB)      Measurement result of a moving palm
» Visualization 3: MP4 (2257 KB)      Measurement result of facial expressions
» Visualization 4: MP4 (1762 KB)      Measurement result of facial expressions

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Figures (10)

Fig. 1
Fig. 1 Illustration of distortion and deviation in multi-view system. (a) Speckle pattern derived from the composite patterns in the first camera; (b) Speckle pattern derived from the composite patterns in the second camera; (c) Subimage around point p in (a); (d)-(e) Subimages around corresponding points of p.

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Fig. 2
Fig. 2 Illustration of the influence of noise in composite patterns embedded with the triangular wave.

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Fig. 3
Fig. 3 Illustration of the geometry constraint.

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Fig. 4
Fig. 4 Information of an arbitrary point and its corresponding points in another camera. (a) A point in the first camera; (b) The corresponding projection points in the second camera; (c) Wrapped phase of sinusoidal signal and the intensity of the triangular wave of any point in the first camera; (d)-(i) Wrapped phase of sinusoidal signal and the intensity of the triangular wave of projection points in period 10, 11, 12, 13, 14, 15.

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Fig. 5
Fig. 5 Wrapped phase of sinusoidal signal and the intensity of triangular wave in line 330 of the first camera.

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Fig. 6
Fig. 6 The process of confirming period order for point p before left-right consistency.

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Fig. 7
Fig. 7 Performance of Step 2 and Step 3. (a) The period order after Step 2; (b) The period order after Step 3; (c) Line 333 of (a); (d) Line 333 of (b).

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Fig. 8
Fig. 8 Measurement result of the ceramic plate. (a) 3-D reconstruction; (b) Height in 300 column.

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Fig. 9
Fig. 9 Measurement results of several objects. (a) Desk fan; (b) Statue of David; (c) Tooth model; (d) Doraemon model.

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Fig. 10
Fig. 10 Dynamic measurement results (associated Visualization 1, Visualization 2, Visualization 3, and Visualization 4). (a) Palm measurement; (b) Facial expressions.

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Tables (1)

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Table 1 Accuracy results of the proposed method

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Equations (16)

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I 1 = r ( I d c + I a m 1 ) + I a m 2 + r I mod cos ( ϕ − θ ) , I 2 = r ( I d c + I a m 1 ) + I a m 2 + r I mod cos ( ϕ ) , I 3 = r ( I d c + I a m 1 ) + I a m 2 + r I mod cos ( ϕ + θ ) ,
ϕ = x p w 2 π N ,
ϕ ′ = a r c t a n ( t a n ( θ 2 ) ( I 1 − I 3 ) ( 2 I 2 − I 1 − I 3 ) ) .
ϕ ′ = a r c t a n 3 ( I 1 − I 3 ) ( 2 I 2 − I 1 − I 3 ) , r ( I d c + I a m 1 ) + I a m 2 = I 1 + I 2 + I 3 3 , r I mod = ( I 3 − I 1 ) 2 3 + ( 2 I 2 − I 1 − I 3 ) 2 9 ,
ϕ = ϕ ′ + 2 k π , k ∈ [ 0 , N − 1 ] ,
I 1 = r ( I d c + I a m 1 + I e ) + I a m 2 + r I mod cos ( ϕ − θ ) , I 2 = r ( I d c + I a m 1 + I e ) + I a m 2 + r I mod cos ( ϕ ) , I 3 = r ( I d c + I a m 1 + I e ) + I a m 2 + r I mod cos ( ϕ + θ ) ,
ϕ ′ = a r c t a n 3 ( I 1 − I 3 ) ( 2 I 2 − I 1 − I 3 ) , r ( I d c + I a m 1 + I e ) + I a m 2 = I 1 + I 2 + I 3 3 , r I mod = ( I 3 − I 1 ) 2 3 + ( 2 I 2 − I 1 − I 3 ) 2 9 ,
I e ′ = r ( I d c + I a m 1 + I e ) + I a m 2 r I mod .
c o r r = ∑ s , s c o r r ( I e ′ − I e ′ ¯ ) ( I e ′ ( p c o r r ) − I e ′ ( p c o r r ) ) ¯ ∑ s , s c o r r ( I e ′ − I e ′ ¯ ) 2 ∑ s , s c o r r ( I e ′ ( p c o r r ) − I e ′ ( p c o r r ) ) ¯ 2 ,
ϕ = ϕ ′ + 2 k π ϕ e = ϕ ′ e + 2 k e π ,
n e ϕ = n ϕ e .
( n ϕ ′ e − n e ϕ ′ ) / 2 π = k n e − k e n .
d ( p c o r r ( k ) ) = a b s ( ϕ ′ − ϕ ′ ( p c o r r ( k ) ) ) , d ( p c o r r ( k ) ) < t h 1 ∥ d ( p c o r r ( k ) ) > t h 2
f ( p c o r r ( k ) ′ ) = a b s ( I e ′ − I e ′ ( p c o r r ( k ) ′ ) ) .
f ( p c o r r ( k ) ′ ) = a b s ( ∑ s I e ′ − ∑ s I e ′ ( p c o r r ( k ) ′ ) ) .
f ( p c o r r ( k ) ′ ) = a b s ( ∑ l e f t I e ′ − ∑ l e f t I e ′ ( p c o r r ( k ) ′ ) ) + a b s ( ∑ r i g h t I e ′ − ∑ r i g h t I e ′ ( p c o r r ( k ) ′ ) ) .

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