Abstract

In this paper, we propose a high-speed 3D shape measurement technique based on the optimized composite fringe patterns and stereo-assisted structured light system. Stereo phase unwrapping, as a new-fashioned method for absolute phase retrieval based on the multi-view geometric constraints, can eliminate the phase ambiguities and obtain a continuous phase map without projecting any additional patterns. However, in order to ensure the stability of phase unwrapping, the period of fringe is generally around 20, which limits the accuracy of 3D measurement. To solve this problem, we develop an optimized method for designing the composite pattern, in which the speckle pattern is embedded into the conventional 4-step phase-shifting fringe patterns without compromising the fringe modulation, and thus the phase measurement accuracy. We also present a simple and effective evaluation criterion for the correlation quality of the designed speckle pattern in order to improve the matching accuracy significantly. When the embedded speckle pattern is demodulated, the periodic ambiguities in the wrapped phase can be eliminated by combining the adaptive window image correlation with geometry constraint. Finally, some mismatched regions are further corrected based on the proposed regional diffusion compensation technique (RDC). These proposed techniques constitute a complete computational framework that allows to effectively recover an accurate, unambiguous, and distortion-free 3D point cloud with only 4 projected patterns. Experimental results verify that our method can achieve high-speed, high-accuracy, robust 3D shape measurement with dense (64-period) fringe patterns at 5000 frames per second.

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

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Corrections

12 March 2019: Corrections were made to the author affiliations and funding section.


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References

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2019 (1)

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. Laser Eng. 115, 21–31 (2019).
[Crossref]

2018 (8)

S. Heist, P. Dietrich, M. Landmann, P. Kühmstedt, G. Notni, and A. Tünnermann, “GOBO projection for 3D measurements at highest frame rates: a performance analysis,” Light: Science & Applications. 7(1), 71 (2018).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (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, “High-speed 3-D shape measurement with structured light methods: A review,” Opt. Laser Eng. 106, 119–131 (2018).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3-D 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. Laser Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier Transform Profilometry (μFTP): 3-D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

P. Zhou, J. Zhu, and H. Jing, “Optical 3-D surface reconstruction with color binary speckle pattern encoding,” Opt. Express 26(3), 3452–3465 (2018).
[Crossref]

2017 (3)

X. Liu and J. Kofman, “High-frequency background modulation fringe patterns based on a fringe-wavelength geometry-constraint model for 3-D surface-shape measurement,” Opt. Express 25(14), 16618–16628 (2017).
[Crossref] [PubMed]

T. Tao, Q. Chen, S. Feng, Y. Hu, M. Zhang, and C. Zuo, “High-precision real-time 3-D shape measurement based on a quad-camera system,” J. Optics 20(1), 014009 (2017).
[Crossref]

Y. Hu, Q. Chen, S. Feng, T. Tao, H. Li, and C. Zuo, “Real-time microscopic 3-D shape measurement based on optimized pulse-width-modulation binary fringe projection,” Mea Sci Technol 28(7), 075010 (2017).
[Crossref]

2016 (4)

2015 (2)

2014 (2)

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Laser Eng. 59, 56–71 (2014).
[Crossref]

W. Lohry and S. Zhang, “High-speed absolute three-dimensional shape measurement using three binary dithered patterns,” Opt. Express 22(22), 26752–26762 (2014).
[Crossref]

2013 (7)

W. Lohry and S. Zhang, “Genetic method to optimize binary dithering technique for high-quality fringe generation,” Opt. Lett. 38(4), 540–542 (2013).
[Crossref]

Z. Zhang, S. Huang, S. Meng, F. Gao, and X. Jiang, “A simple, flexible and automatic 3D calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21(10), 12218–12227 (2013).
[Crossref] [PubMed]

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

Z. Li, K. Zhong, Y. Li, X. Zhou, and Y. Shi, “Multiview phase shifting: a full-resolution and high-speed 3-D measurement framework for arbitrary shape dynamic objects,” Opt. Lett. 38(9), 1389–1391 (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. Laser Eng. 51(8), 953–960 (2013).
[Crossref]

Y. Zhang, Z. Xiong, and F. Wu, “Unambiguous 3D measurement from speckle-embedded fringe,” Appl. Opt. 52(32), 7797–7805 (2013).
[Crossref] [PubMed]

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3D shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Laser Eng. 84, 74–81 (2013).
[Crossref]

2012 (5)

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]

R.R. Garcia and A. Zakhor, “Consistent stereo-assisted absolute phase unwrapping methods for structured light systems,” IEEE Journal of Selected Topics in Signal Processing 26(5), 411–424 (2012).
[Crossref]

Y. Wang and S. Zhang, “Novel phase-coding method for absolute phase retrieval,” Opt. Lett. 37(11), 2067–2069 (2012).
[Crossref] [PubMed]

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

Y. Wang and S. Zhang, “Three-dimensional shape measurement with binary dithered patterns,” Appl. Opt. 51(27), 6631–6636 (2012).
[Crossref]

2011 (2)

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 Transactions on Image Processing 20(11), 3001–3013 (2011).
[Crossref]

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and K. Qian, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50(33), 6214–6224 (2011).
[Crossref] [PubMed]

2010 (4)

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]

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

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

B. Pan, Z. Lu, and H. Xie, “Mean intensity gradient: an effective global parameter for quality assessment of the speckle patterns used in digital image correlation,” Opt. Laser Eng. 48, 469–477 (2010).
[Crossref]

2009 (1)

2004 (1)

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Laser Eng. 42(3), 245–261 (2004).
[Crossref]

2001 (1)

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

1999 (1)

1997 (1)

1996 (1)

1984 (1)

1983 (1)

An, Y.

Asundi, A.

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier Transform Profilometry (μFTP): 3-D shape measurement at 10,000 frames per second,” Opt. Laser 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]

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and K. Qian, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50(33), 6214–6224 (2011).
[Crossref] [PubMed]

Cai, Z.

Carocci, M.

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. Laser Eng. 115, 21–31 (2019).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (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. Laser Eng. 109, 23–59 (2018).
[Crossref]

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

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier Transform Profilometry (μFTP): 3-D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

Y. Hu, Q. Chen, S. Feng, T. Tao, H. Li, and C. Zuo, “Real-time microscopic 3-D shape measurement based on optimized pulse-width-modulation binary fringe projection,” Mea Sci Technol 28(7), 075010 (2017).
[Crossref]

T. Tao, Q. Chen, S. Feng, Y. Hu, M. Zhang, and C. Zuo, “High-precision real-time 3-D shape measurement based on a quad-camera system,” J. Optics 20(1), 014009 (2017).
[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]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
[Crossref] [PubMed]

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]

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Laser Eng. 59, 56–71 (2014).
[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. Laser 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]

Chen, W.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Laser Eng. 42(3), 245–261 (2004).
[Crossref]

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

Chiu, G.T.C.

Da, J.

Dietrich, P.

S. Heist, P. Dietrich, M. Landmann, P. Kühmstedt, G. Notni, and A. Tünnermann, “GOBO projection for 3D measurements at highest frame rates: a performance analysis,” Light: Science & Applications. 7(1), 71 (2018).
[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. Laser 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]

Feng, S.

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. Laser Eng. 115, 21–31 (2019).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3-D 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. Laser Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier Transform Profilometry (μFTP): 3-D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

Y. Hu, Q. Chen, S. Feng, T. Tao, H. Li, and C. Zuo, “Real-time microscopic 3-D shape measurement based on optimized pulse-width-modulation binary fringe projection,” Mea Sci Technol 28(7), 075010 (2017).
[Crossref]

T. Tao, Q. Chen, S. Feng, Y. Hu, M. Zhang, and C. Zuo, “High-precision real-time 3-D shape measurement based on a quad-camera system,” J. Optics 20(1), 014009 (2017).
[Crossref]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
[Crossref] [PubMed]

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]

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Laser Eng. 59, 56–71 (2014).
[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. Laser 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]

Flynn, T. J.

Gao, B. Z.

Gao, F.

Garcia, R.R.

R.R. Garcia and A. Zakhor, “Consistent stereo-assisted absolute phase unwrapping methods for structured light systems,” IEEE Journal of Selected Topics in Signal Processing 26(5), 411–424 (2012).
[Crossref]

Ghiglia, D. C.

Gorthi, S. S.

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

Gu, G.

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

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (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. Laser 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]

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 Transactions on 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.

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 Transactions on Image Processing 20(11), 3001–3013 (2011).
[Crossref]

Hassebrook, L.G.

He, D.

Heist, S.

S. Heist, P. Dietrich, M. Landmann, P. Kühmstedt, G. Notni, and A. Tünnermann, “GOBO projection for 3D measurements at highest frame rates: a performance analysis,” Light: Science & Applications. 7(1), 71 (2018).
[Crossref]

Hu, S.

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3D shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Laser Eng. 84, 74–81 (2013).
[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. Laser Eng. 115, 21–31 (2019).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

T. Tao, Q. Chen, S. Feng, Y. Hu, M. Zhang, and C. Zuo, “High-precision real-time 3-D shape measurement based on a quad-camera system,” J. Optics 20(1), 014009 (2017).
[Crossref]

Y. Hu, Q. Chen, S. Feng, T. Tao, H. Li, and C. Zuo, “Real-time microscopic 3-D shape measurement based on optimized pulse-width-modulation binary fringe projection,” Mea Sci Technol 28(7), 075010 (2017).
[Crossref]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
[Crossref] [PubMed]

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. Laser Eng. 115, 21–31 (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. Laser Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier Transform Profilometry (μFTP): 3-D shape measurement at 10,000 frames per second,” Opt. Laser 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]

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and K. Qian, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50(33), 6214–6224 (2011).
[Crossref] [PubMed]

Huang, S.

Hyun, J. S.

Jiang, H.

Jiang, X.

Jing, H.

Kofman, J.

Kühmstedt, P.

S. Heist, P. Dietrich, M. Landmann, P. Kühmstedt, G. Notni, and A. Tünnermann, “GOBO projection for 3D measurements at highest frame rates: a performance analysis,” Light: Science & Applications. 7(1), 71 (2018).
[Crossref]

Landmann, M.

S. Heist, P. Dietrich, M. Landmann, P. Kühmstedt, G. Notni, and A. Tünnermann, “GOBO projection for 3D measurements at highest frame rates: a performance analysis,” Light: Science & Applications. 7(1), 71 (2018).
[Crossref]

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 Transactions on Image Processing 20(11), 3001–3013 (2011).
[Crossref]

Lau, D.L.

Lei, S.

Lei, Y.

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

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, A.

Li, H.

Y. Hu, Q. Chen, S. Feng, T. Tao, H. Li, and C. Zuo, “Real-time microscopic 3-D shape measurement based on optimized pulse-width-modulation binary fringe projection,” Mea Sci Technol 28(7), 075010 (2017).
[Crossref]

Li, R.

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Laser Eng. 59, 56–71 (2014).
[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. Laser Eng. 51(8), 953–960 (2013).
[Crossref]

Li, Y.

Li, Z.

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

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

Liu, H. C.

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 Transactions on 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]

Liu, X.

Lohry, W.

Lu, Z.

B. Pan, Z. Lu, and H. Xie, “Mean intensity gradient: an effective global parameter for quality assessment of the speckle patterns used in digital image correlation,” Opt. Laser Eng. 48, 469–477 (2010).
[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. Laser Eng. 115, 21–31 (2019).
[Crossref]

Meng, S.

Mutoh, K.

Notni, G.

S. Heist, P. Dietrich, M. Landmann, P. Kühmstedt, G. Notni, and A. Tünnermann, “GOBO projection for 3D measurements at highest frame rates: a performance analysis,” Light: Science & Applications. 7(1), 71 (2018).
[Crossref]

Pan, B.

B. Pan, Z. Lu, and H. Xie, “Mean intensity gradient: an effective global parameter for quality assessment of the speckle patterns used in digital image correlation,” Opt. Laser Eng. 48, 469–477 (2010).
[Crossref]

Peng, X.

Qian, K.

Rastogi, P.

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

Rodella, R.

Romero, L. A.

Sansoni, G.

Shen, G.

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Laser Eng. 59, 56–71 (2014).
[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. Laser Eng. 51(8), 953–960 (2013).
[Crossref]

Shi, Y.

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

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

Song, K.

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3D shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Laser Eng. 84, 74–81 (2013).
[Crossref]

Srinivasan, V.

Su, X.

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and K. Qian, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50(33), 6214–6224 (2011).
[Crossref] [PubMed]

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

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Laser Eng. 42(3), 245–261 (2004).
[Crossref]

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

Takeda, M.

Tao, T.

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. Laser Eng. 115, 21–31 (2019).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3-D 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. Laser Eng. 109, 23–59 (2018).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier Transform Profilometry (μFTP): 3-D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

Y. Hu, Q. Chen, S. Feng, T. Tao, H. Li, and C. Zuo, “Real-time microscopic 3-D shape measurement based on optimized pulse-width-modulation binary fringe projection,” Mea Sci Technol 28(7), 075010 (2017).
[Crossref]

T. Tao, Q. Chen, S. Feng, Y. Hu, M. Zhang, and C. Zuo, “High-precision real-time 3-D shape measurement based on a quad-camera system,” J. Optics 20(1), 014009 (2017).
[Crossref]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
[Crossref] [PubMed]

Tünnermann, A.

S. Heist, P. Dietrich, M. Landmann, P. Kühmstedt, G. Notni, and A. Tünnermann, “GOBO projection for 3D measurements at highest frame rates: a performance analysis,” Light: Science & Applications. 7(1), 71 (2018).
[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).

Wang, C.

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

Wen, X.

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3D shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Laser Eng. 84, 74–81 (2013).
[Crossref]

Wu, F.

Wu, J.

Xie, H.

B. Pan, Z. Lu, and H. Xie, “Mean intensity gradient: an effective global parameter for quality assessment of the speckle patterns used in digital image correlation,” Opt. Laser Eng. 48, 469–477 (2010).
[Crossref]

Xiong, Z.

Yan, Y.

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3D shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Laser Eng. 84, 74–81 (2013).
[Crossref]

Yin, W.

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. Laser Eng. 115, 21–31 (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. Laser Eng. 109, 23–59 (2018).
[Crossref]

Yin, Y.

Zakhor, A.

R.R. Garcia and A. Zakhor, “Consistent stereo-assisted absolute phase unwrapping methods for structured light systems,” IEEE Journal of Selected Topics in Signal Processing 26(5), 411–424 (2012).
[Crossref]

Zhang, L.

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

Zhang, M.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

T. Tao, Q. Chen, S. Feng, Y. Hu, M. Zhang, and C. Zuo, “High-precision real-time 3-D shape measurement based on a quad-camera system,” J. Optics 20(1), 014009 (2017).
[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]

Zhang, Q.

Zhang, S.

Zhang, Y.

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Laser Eng. 59, 56–71 (2014).
[Crossref]

Y. Zhang, Z. Xiong, and F. Wu, “Unambiguous 3D measurement from speckle-embedded fringe,” Appl. Opt. 52(32), 7797–7805 (2013).
[Crossref] [PubMed]

Zhang, Z.

Zhao, M.

Zhong, K.

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

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

Zhou, P.

Zhou, X.

Zhu, J.

Zuo, C.

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. Laser Eng. 115, 21–31 (2019).
[Crossref]

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-D measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

S. Feng, L. Zhang, C. Zuo, T. Tao, Q. Chen, and G. Gu, “High dynamic range 3-D 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. Laser Eng. 109, 23–59 (2018).
[Crossref]

C. Zuo, T. Tao, S. Feng, L. Huang, A. Asundi, and Q. Chen, “Micro Fourier Transform Profilometry (μFTP): 3-D shape measurement at 10,000 frames per second,” Opt. Laser Eng. 102, 70–91 (2018).
[Crossref]

Y. Hu, Q. Chen, S. Feng, T. Tao, H. Li, and C. Zuo, “Real-time microscopic 3-D shape measurement based on optimized pulse-width-modulation binary fringe projection,” Mea Sci Technol 28(7), 075010 (2017).
[Crossref]

T. Tao, Q. Chen, S. Feng, Y. Hu, M. Zhang, and C. Zuo, “High-precision real-time 3-D shape measurement based on a quad-camera system,” J. Optics 20(1), 014009 (2017).
[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]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
[Crossref] [PubMed]

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]

S. Feng, Y. Zhang, Q. Chen, C. Zuo, R. Li, and G. Shen, “General solution for high dynamic range three-dimensional shape measurement using the fringe projection technique,” Opt. Laser Eng. 59, 56–71 (2014).
[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. Laser 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]

Appl. Opt. (7)

IEEE Journal of Selected Topics in Signal Processing (1)

R.R. Garcia and A. Zakhor, “Consistent stereo-assisted absolute phase unwrapping methods for structured light systems,” IEEE Journal of Selected Topics in Signal Processing 26(5), 411–424 (2012).
[Crossref]

IEEE Transactions on Image Processing (1)

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 Transactions on Image Processing 20(11), 3001–3013 (2011).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Optics (1)

T. Tao, Q. Chen, S. Feng, Y. Hu, M. Zhang, and C. Zuo, “High-precision real-time 3-D shape measurement based on a quad-camera system,” J. Optics 20(1), 014009 (2017).
[Crossref]

Light: Science & Applications. (1)

S. Heist, P. Dietrich, M. Landmann, P. Kühmstedt, G. Notni, and A. Tünnermann, “GOBO projection for 3D measurements at highest frame rates: a performance analysis,” Light: Science & Applications. 7(1), 71 (2018).
[Crossref]

Mea Sci Technol (2)

Y. Hu, Q. Chen, S. Feng, T. Tao, H. Li, and C. Zuo, “Real-time microscopic 3-D shape measurement based on optimized pulse-width-modulation binary fringe projection,” Mea Sci Technol 28(7), 075010 (2017).
[Crossref]

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

Opt. Express (11)

Z. Cai, X. Liu, H. Jiang, D. He, X. Peng, S. Huang, and Z. Zhang, “Flexible phase error compensation based on Hilbert transform in phase shifting profilometry,” Opt. Express 23(19), 25171–25181 (2015).
[Crossref]

Z. Zhang, S. Huang, S. Meng, F. Gao, and X. Jiang, “A simple, flexible and automatic 3D calibration method for a phase calculation-based fringe projection imaging system,” Opt. Express 21(10), 12218–12227 (2013).
[Crossref] [PubMed]

Z. Cai, X. Liu, X. Peng, Y. Yin, A. Li, J. Wu, and B. Z. Gao, “Structured light field 3D imaging,” Opt. Express 24(18), 20324–20334 (2016).
[Crossref] [PubMed]

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]

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]

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]

Y. An, J. S. Hyun, and S. Zhang, “Pixel-wise absolute phase unwrapping using geometric constraints of structured light system,” Opt. Express 24(16), 18445–18459 (2016).
[Crossref]

X. Liu and J. Kofman, “High-frequency background modulation fringe patterns based on a fringe-wavelength geometry-constraint model for 3-D surface-shape measurement,” Opt. Express 25(14), 16618–16628 (2017).
[Crossref] [PubMed]

P. Zhou, J. Zhu, and H. Jing, “Optical 3-D surface reconstruction with color binary speckle pattern encoding,” Opt. Express 26(3), 3452–3465 (2018).
[Crossref]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
[Crossref] [PubMed]

W. Lohry and S. Zhang, “High-speed absolute three-dimensional shape measurement using three binary dithered patterns,” Opt. Express 22(22), 26752–26762 (2014).
[Crossref]

Opt. Laser Eng. (15)

B. Pan, Z. Lu, and H. Xie, “Mean intensity gradient: an effective global parameter for quality assessment of the speckle patterns used in digital image correlation,” Opt. Laser Eng. 48, 469–477 (2010).
[Crossref]

K. Song, S. Hu, X. Wen, and Y. Yan, “Fast 3D shape measurement using fourier transform profilometry without phase unwrapping,” Opt. Laser Eng. 84, 74–81 (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. Laser Eng. 51(8), 953–960 (2013).
[Crossref]

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

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Opt. Lasers Eng. (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]

Opt. Lett. (4)

Other (1)

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).

Supplementary Material (2)

NameDescription
» Visualization 1       The 3D reconstruction results for a one-time transient event: the statue of Voltaire and a free-falling balloon filled with water
» Visualization 2       The high-speed 3D reconstruction results for the rip of paper

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Figures (16)

Fig. 1
Fig. 1 The principle of Zhang’s method [36]. (a) The three-step phase-shifting patterns. (b) The speckle pattern. (c) The intensity of the speckle signal in conventional three-step phase-shifting patterns. (d) The three-step speckle-embedded phase-shifting patterns. (e) The embedded speckle pattern.
Fig. 2
Fig. 2 (a) The slope signal D ( x , y ) is designed within the range of [ 0.5 , 0.5 ] . (b) The designed coding signals C 0 ( x , y ) and C 1 ( x , y ) , where C 0 ( x , y ) = C 2 ( x , y ) , and C 1 ( x , y ) = C 3 ( x , y ) .
Fig. 3
Fig. 3 The proposed speckle-embedded phase-shifting algorithm. (a) The four-step speckle-embedded phase-shifting patterns. (b) The embedded speckle pattern.
Fig. 4
Fig. 4 The diagram of the optimized design method of the speckle pattern.
Fig. 5
Fig. 5 (a) A speckle pattern is designed using the proposed method. (b) The period order map based on (a) is obtained using the proposed test method. (c) The error rate for phase unwrapping on the designed speckle patterns with different speckle size.
Fig. 6
Fig. 6 Illustration of an arbitrary point p in the camera and its corresponding points in 3D space and the projector using depth constraint.
Fig. 7
Fig. 7 The operation process of confirming period order based on geometry constraint and the adaptive window image correlation. (a) The wrapped phase obtained from main camera. (b) The speckle pattern obtained from main camera. (c) The wrapped phase obtained from auxiliary camera. (d) The speckle pattern obtained from auxiliary camera. (e) The correlation result obtained using the smaller L (5 pixels). (f) The period order map obtained using the smaller L (5 pixels). (g) The correlation result obtained using the larger L (10 pixels). (h) The period order map obtained using the larger L (10 pixels). (i) The enlarged detail of the region in (f). (j) The enlarged detail of the region in (h).
Fig. 8
Fig. 8 The flowchart of the compensation procedure of RDC.
Fig. 9
Fig. 9 (a) The elementary absolute phase map obtained from auxiliary camera. (b) The final absolute phase map obtained using the left-right consistency check. (c) The 3D reconstruction result obtained using (b). (d) The enlarged detail of the region in (c). (e) The elementary absolute phase map obtained from main camera. (f) The final absolute phase map obtained using RDC. (g) The 3D reconstruction result obtained using (f). (h) The enlarged detail of the region in (g).
Fig. 10
Fig. 10 (a) The diagram of the traditional multi-view system. (b) The diagram of our multi-view system.
Fig. 11
Fig. 11 This system includes two high-speed CMOS cameras and a DLP projection system.
Fig. 12
Fig. 12 The phase measurement results of a standard ceramic plate. (a) The ceramic plate to be measured. (b) The 2D camera image (one of the four-step phase-shifting patterns) from main camera. (c) The wrapped phase is obtained using Eq. (12). (d) The demodulated speckle pattern is obtained using Eq. (15). (e) The phase order map based on geometry constraint. (f) The phase order map based on geometry constraint and the adaptive window image correlation. (g) The phase order map using left-right consistency check. (h) The phase order map using RDC. (i)-(l) The corresponding absolute phase map of (e)-(h).
Fig. 13
Fig. 13 The 3D measurement results of a standard ceramic plate. (a) The 3D reconstruction results of the plate. (b) The distribution of the errors of (a). (c) The histogram of (b).
Fig. 14
Fig. 14 The measurement results of several objects. (a) A girl statue with a ceramic plate. (b) A Voltaire model and a statue of the Goddess with discontinuous surfaces. (c) The statue of Skadi. (d)-(f) The corresponding 3D reconstruction results of (a)-(c). (g)-(i) The corresponding enlarged detail of the region in (d)-(f).
Fig. 15
Fig. 15 The 3D reconstruction results for a one-time transient event: the statue of Voltaire and a free-falling balloon filled with water ( Visualization 1).
Fig. 16
Fig. 16 The high-speed 3D reconstruction results for the rip of paper ( Visualization 2).

Tables (1)

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Table 1 Accuracy results of the proposed method

Equations (17)

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  I n ( x , y ) = A ( x , y ) + B ( x , y ) cos  ( Φ ( x , y ) 2 π n / N )
  I n p ( x , y ) = I n ( x , y ) + C n ( x , y )
ϕ ( x , y ) = tan 1 I 1 p ( x , y ) I 3 p ( x , y ) I 0 p ( x , y ) I 2 p ( x , y ) = tan 1 2 B ( x , y ) sin  Φ ( x , y ) + C 1 ( x , y ) C 3 ( x , y ) 2 B ( x , y ) cos  Φ ( x , y ) + C 0 ( x , y ) C 2 ( x , y )
C 0 ( x , y ) = C 2 ( x , y ) C 1 ( x , y ) = C 3 ( x , y )
  I n ( x , y ) C n ( x , y ) 1 I n ( x , y )
m a x ( I 0 ( x , y ) , I 2 ( x , y ) ) C 0 ( x , y ) m i n ( 1 I 0 ( x , y ) , 1 I 2 ( x , y ) ) m a x ( I 1 ( x , y ) , I 3 ( x , y ) ) C 1 ( x , y ) m i n ( 1 I 1 ( x , y ) , 1 I 3 ( x , y ) )
D ( x , y ) = ( I 0 p ( x , y ) + I 2 p ( x , y ) ) ( I 1 p ( x , y ) + I 3 p ( x , y ) ) = 2 ( C 0 ( x , y ) C 1 ( x , y ) )
{ D i n f ( x , y ) D ( x , y ) D s u p ( x , y ) D i n f ( x , y ) = 2 [ m a x ( I 0 ( x , y ) , I 2 ( x , y ) ) m i n ( 1 I 1 ( x , y ) , 1 I 3 ( x , y ) ) ] D s u p ( x , y ) = 2 [ m i n ( 1 I 0 ( x , y ) , 1 I 2 ( x , y ) ) m a x ( I 1 ( x , y ) , I 3 ( x , y ) ) ]
Δ δ c S Δ δ p
c o r r = i , j = M M ( I r ( x r + i , y r + j ) I r ¯ ) ( I t ( x t + i , y t + j ) I t ¯ ) i , j = M M ( I r ( x r + i , y r + j ) I r ¯ ) 2 i , j = M M ( I t ( x t + i , y t + j ) I t ¯ ) 2
I 0 c ( x , y ) = A c ( x , y ) + B c ( x , y ) cos  ( Φ c ( x , y ) ) + C 0 c ( x , y ) I 1 c ( x , y ) = A c ( x , y ) + B c ( x , y ) cos  ( Φ c ( x , y ) π / 2 ) + C 1 c ( x , y ) I 2 c ( x , y ) = A c ( x , y ) + B c ( x , y ) cos  ( Φ c ( x , y ) π ) + C 0 c ( x , y ) I 3 c ( x , y ) = A c ( x , y ) + B c ( x , y ) cos  ( Φ c ( x , y ) 3 π / 2 ) + C 1 c ( x , y )
  ϕ c ( x , y ) = tan 1 I 1 c ( x , y ) I 3 c ( x , y ) I 0 c ( x , y ) I 2 c ( x , y )
  B c ( x , y ) = 1 2 [ n = 0 3 I n c sin  n π 2 ] 2 + [ n = 0 3 I n c cos  n π 2 ] 2
M a s k v c ( x , y ) = B c ( x , y ) > T h r 1
I s p k c ( x , y ) = ( I 0 c ( x , y ) + I 2 c ( x , y ) ) ( I 1 c ( x , y ) + I 3 c ( x , y ) ) 4 B c ( x , y )
  0 < Φ c ( x + 1 , y ) Φ c ( x , y ) < π for the horizontal direction   0 < a b s ( Φ c ( x , y + 1 ) Φ c ( x , y ) ) < π for the vertical direction
  Φ s m a l l c ( x , y ) = Φ s m a l l c ( x , y ) + 2 π × R o u n d ( Φ l a r g e c ( x , y ) Φ s m a l l c ( x , y ) 2 π )

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