Abstract

Arbitrary two-dimensional (2-D) motion introduces coordinate errors and phase errors to three-dimensional (3-D) shape measurement of objects in phase-shifting profilometry (PSP). This paper presents a new robust 3-D reconstruction method for arbitrary 2-D moving objects by introducing an adaptive reference phase map and the motion estimation based on fence image. First, a composite fence image is used to track object motion. Second, to obtain the transformation matrixes and remove the coordinate errors among object images, the angle extraction technique and the 1-D hybrid phase correlation method (1-D HPCM) are integrated to automatically estimate the sub-pixel motion of objects. Third, the phase errors are compensated to obtain the rough absolute phase map of objects by combining the transformation matrixes with the reference phase map. Finally, the absolute phase map is refined to reconstruct the 3-D surfaces of moving objects with adaptive reference phase map. The proposed computational framework can accurately and automatically realize 3-D shape measurement of arbitrary objects with 2-D movement. The results of experiment verify the effectiveness of our computational framework.

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

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References

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2018 (9)

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]

Z. Liu, P. C. Zibley, and S. Zhang, “Motion-induced error compensation for phase shifting profilometry,” Opt. Express 26, 12632–12637 (2018).
[Crossref] [PubMed]

L. Lu, Y. Yin, Z. Su, X. Ren, Y. Luan, and J. Xi, “General model for phase shifting profilometry with an object in motion,” Appl. Opt. 57, 10364–10369 (2018).
[Crossref]

H. Li, Y. Hu, T. Tao, S. Feng, M. Zhang, Y. Zhang, and C. Zuo, “Optimal wavelength selection strategy in temporal phase unwrapping with projection distance minimization,” Appl. Opt. 57, 2352–2360 (2018).
[Crossref] [PubMed]

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. Lasers Eng. 103, 127–138 (2018).
[Crossref]

Y. Wang, Z. Liu, C. Jiang, and S. Zhang, “Motion induced phase error reduction using a hilbert transform,” Opt. Express 26, 34224–34235 (2018).
[Crossref]

Q. Guo, Y. Ruan, J. Xi, L. Song, X. Zhu, Y. Yu, and J. Tong, “3d shape measurement of moving object with fft-based spatial matching,” Opt. Laser Technol. 100, 325 – 331 (2018).
[Crossref]

Y. Xing and C. Quan, “Reference-plane-based fast pixel-by-pixel absolute phase retrieval for height measurement,” Appl. Opt. 57, 4901–4908 (2018).
[Crossref] [PubMed]

H. Wang, J. Zhao, J. Zhao, J. Song, Z. Pan, and X. Jiang, “A new rapid-precision position measurement method for a linear motor mover based on a 1-d epca,” IEEE Trans. Ind. Electron 65, 7485–7494 (2018).
[Crossref]

2017 (3)

2016 (5)

2015 (2)

J. L. Flores, J. A. Ferrari, G. G. Torales, R. Legarda-Saenz, and A. Silva, “Color-fringe pattern profilometry using a generalized phase-shifting algorithm,” Appl. Opt. 54, 8827–8834 (2015).
[Crossref] [PubMed]

S. Matthias, M. Kästner, and E. Reithmeier, “Evaluation of system models for an endoscopic fringe projection system,” Measurement 73, 239 – 246 (2015).
[Crossref]

2013 (2)

2011 (1)

F. Bruno, G. Bianco, M. Muzzupappa, S. Barone, and A. Razionale, “Experimentation of structured light and stereo vision for underwater 3d reconstruction,” ISPRS-J. Photogramm. Remote Sens. 66, 508 – 518 (2011).
[Crossref]

2009 (1)

Y. Hu, J. Xi, J. F. Chicharo, W. Cheng, and Z. Yang, “Inverse function analysis method for fringe pattern profilometry,” IEEE Trans. Instrum. Meas. 58, 3305–3314 (2009).
[Crossref]

2006 (1)

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 13602 (2006).
[Crossref]

2004 (2)

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recognit. 37, 827 – 849 (2004).
[Crossref]

Z. Wang and B. Han, “Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms,” Opt. Lett. 29, 1671–1673 (2004).
[Crossref] [PubMed]

2003 (1)

W. S. Hoge, “A subspace identification extension to the phase correlation method [mri application],” IEEE Trans. Med. Imaging 22, 277–280 (2003).
[Crossref] [PubMed]

1997 (1)

1994 (1)

1990 (1)

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

An, Y.

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]

Barone, S.

F. Bruno, G. Bianco, M. Muzzupappa, S. Barone, and A. Razionale, “Experimentation of structured light and stereo vision for underwater 3d reconstruction,” ISPRS-J. Photogramm. Remote Sens. 66, 508 – 518 (2011).
[Crossref]

Batlle, J.

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recognit. 37, 827 – 849 (2004).
[Crossref]

Bianco, G.

F. Bruno, G. Bianco, M. Muzzupappa, S. Barone, and A. Razionale, “Experimentation of structured light and stereo vision for underwater 3d reconstruction,” ISPRS-J. Photogramm. Remote Sens. 66, 508 – 518 (2011).
[Crossref]

Bruno, F.

F. Bruno, G. Bianco, M. Muzzupappa, S. Barone, and A. Razionale, “Experimentation of structured light and stereo vision for underwater 3d reconstruction,” ISPRS-J. Photogramm. Remote Sens. 66, 508 – 518 (2011).
[Crossref]

Chen, Q.

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, 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. Lasers Eng. 103, 127–138 (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]

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, 20253–20269 (2016).
[Crossref] [PubMed]

Chen, W.

Cheng, W.

Y. Hu, J. Xi, J. F. Chicharo, W. Cheng, and Z. Yang, “Inverse function analysis method for fringe pattern profilometry,” IEEE Trans. Instrum. Meas. 58, 3305–3314 (2009).
[Crossref]

Chiang, F.-P.

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 13602 (2006).
[Crossref]

Chicharo, J. F.

Y. Hu, J. Xi, J. F. Chicharo, W. Cheng, and Z. Yang, “Inverse function analysis method for fringe pattern profilometry,” IEEE Trans. Instrum. Meas. 58, 3305–3314 (2009).
[Crossref]

Corini, S.

Da, J.

Ding, Y.

Docchio, F.

Dong, F.

J. Zhao, J. Zhao, H. Wang, J. Song, and F. Dong, “Precision position measurement of linear motors mover based on temporal image correlation,” IEEE Trans. Instrum. Meas. pp. 1–10 (2018).

Feng, S.

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, 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. Lasers Eng. 103, 127–138 (2018).
[Crossref]

H. Li, Y. Hu, T. Tao, S. Feng, M. Zhang, Y. Zhang, and C. Zuo, “Optimal wavelength selection strategy in temporal phase unwrapping with projection distance minimization,” Appl. Opt. 57, 2352–2360 (2018).
[Crossref] [PubMed]

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, 20253–20269 (2016).
[Crossref] [PubMed]

Ferrari, J. A.

Flores, J. L.

Gu, G.

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. Lasers Eng. 103, 127–138 (2018).
[Crossref]

Guo, L.

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

Guo, Q.

Q. Guo, Y. Ruan, J. Xi, L. Song, X. Zhu, Y. Yu, and J. Tong, “3d shape measurement of moving object with fft-based spatial matching,” Opt. Laser Technol. 100, 325 – 331 (2018).
[Crossref]

L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the accuracy of 3-d shape measurement of moving object using phase shifting profilometry,” Opt. Express 21, 30610–30622 (2013).
[Crossref]

Han, B.

Hoge, W. S.

W. S. Hoge, “A subspace identification extension to the phase correlation method [mri application],” IEEE Trans. Med. Imaging 22, 277–280 (2003).
[Crossref] [PubMed]

Hu, Y.

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. Lasers Eng. 103, 127–138 (2018).
[Crossref]

H. Li, Y. Hu, T. Tao, S. Feng, M. Zhang, Y. Zhang, and C. Zuo, “Optimal wavelength selection strategy in temporal phase unwrapping with projection distance minimization,” Appl. Opt. 57, 2352–2360 (2018).
[Crossref] [PubMed]

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, 20253–20269 (2016).
[Crossref] [PubMed]

Y. Hu, J. Xi, J. F. Chicharo, W. Cheng, and Z. Yang, “Inverse function analysis method for fringe pattern profilometry,” IEEE Trans. Instrum. Meas. 58, 3305–3314 (2009).
[Crossref]

Huang, L.

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, 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.

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 13602 (2006).
[Crossref]

Hyun, J.-S.

Jiang, C.

Jiang, X.

H. Wang, J. Zhao, J. Zhao, J. Song, Z. Pan, and X. Jiang, “A new rapid-precision position measurement method for a linear motor mover based on a 1-d epca,” IEEE Trans. Ind. Electron 65, 7485–7494 (2018).
[Crossref]

Kästner, M.

S. Matthias, M. Kästner, and E. Reithmeier, “Evaluation of system models for an endoscopic fringe projection system,” Measurement 73, 239 – 246 (2015).
[Crossref]

Lazzari, S.

Legarda-Saenz, R.

Li, B.

Li, H.

Li, J.

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

Li, X.

Li, Y. F.

Li, Z.

Liu, Q.

Liu, Z.

Lu, L.

Luan, Y.

Matthias, S.

S. Matthias, M. Kästner, and E. Reithmeier, “Evaluation of system models for an endoscopic fringe projection system,” Measurement 73, 239 – 246 (2015).
[Crossref]

Muzzupappa, M.

F. Bruno, G. Bianco, M. Muzzupappa, S. Barone, and A. Razionale, “Experimentation of structured light and stereo vision for underwater 3d reconstruction,” ISPRS-J. Photogramm. Remote Sens. 66, 508 – 518 (2011).
[Crossref]

Ni, K.

Pagès, J.

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recognit. 37, 827 – 849 (2004).
[Crossref]

Pan, J.

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 13602 (2006).
[Crossref]

Pan, Z.

H. Wang, J. Zhao, J. Zhao, J. Song, Z. Pan, and X. Jiang, “A new rapid-precision position measurement method for a linear motor mover based on a 1-d epca,” IEEE Trans. Ind. Electron 65, 7485–7494 (2018).
[Crossref]

Qiao, X.

Quan, C.

Y. Xing and C. Quan, “Reference-plane-based fast pixel-by-pixel absolute phase retrieval for height measurement,” Appl. Opt. 57, 4901–4908 (2018).
[Crossref] [PubMed]

Y. Xing, C. Quan, and C. Tay, “A modified phase-coding method for absolute phase retrieval,” Opt. Lasers Eng. 87, 97 – 102 (2016).
[Crossref]

Razionale, A.

F. Bruno, G. Bianco, M. Muzzupappa, S. Barone, and A. Razionale, “Experimentation of structured light and stereo vision for underwater 3d reconstruction,” ISPRS-J. Photogramm. Remote Sens. 66, 508 – 518 (2011).
[Crossref]

Reithmeier, E.

S. Matthias, M. Kästner, and E. Reithmeier, “Evaluation of system models for an endoscopic fringe projection system,” Measurement 73, 239 – 246 (2015).
[Crossref]

Ren, X.

Rodella, R.

Ruan, Y.

Q. Guo, Y. Ruan, J. Xi, L. Song, X. Zhu, Y. Yu, and J. Tong, “3d shape measurement of moving object with fft-based spatial matching,” Opt. Laser Technol. 100, 325 – 331 (2018).
[Crossref]

Salvi, J.

J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recognit. 37, 827 – 849 (2004).
[Crossref]

Sansoni, G.

Shi, Y.

Silva, A.

Song, J.

H. Wang, J. Zhao, J. Zhao, J. Song, Z. Pan, and X. Jiang, “A new rapid-precision position measurement method for a linear motor mover based on a 1-d epca,” IEEE Trans. Ind. Electron 65, 7485–7494 (2018).
[Crossref]

J. Zhao, J. Zhao, H. Wang, J. Song, and F. Dong, “Precision position measurement of linear motors mover based on temporal image correlation,” IEEE Trans. Instrum. Meas. pp. 1–10 (2018).

Song, L.

Q. Guo, Y. Ruan, J. Xi, L. Song, X. Zhu, Y. Yu, and J. Tong, “3d shape measurement of moving object with fft-based spatial matching,” Opt. Laser Technol. 100, 325 – 331 (2018).
[Crossref]

Su, X.

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

Su, Z.

Tan, Y.

Tao, T.

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. Lasers 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. Lasers Eng. 109, 23 – 59 (2018).
[Crossref]

H. Li, Y. Hu, T. Tao, S. Feng, M. Zhang, Y. Zhang, and C. Zuo, “Optimal wavelength selection strategy in temporal phase unwrapping with projection distance minimization,” Appl. Opt. 57, 2352–2360 (2018).
[Crossref] [PubMed]

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, 20253–20269 (2016).
[Crossref] [PubMed]

Tay, C.

Y. Xing, C. Quan, and C. Tay, “A modified phase-coding method for absolute phase retrieval,” Opt. Lasers Eng. 87, 97 – 102 (2016).
[Crossref]

Tong, J.

Q. Guo, Y. Ruan, J. Xi, L. Song, X. Zhu, Y. Yu, and J. Tong, “3d shape measurement of moving object with fft-based spatial matching,” Opt. Laser Technol. 100, 325 – 331 (2018).
[Crossref]

Torales, G. G.

Wang, H.

H. Wang, J. Zhao, J. Zhao, J. Song, Z. Pan, and X. Jiang, “A new rapid-precision position measurement method for a linear motor mover based on a 1-d epca,” IEEE Trans. Ind. Electron 65, 7485–7494 (2018).
[Crossref]

J. Zhao, J. Zhao, H. Wang, J. Song, and F. Dong, “Precision position measurement of linear motors mover based on temporal image correlation,” IEEE Trans. Instrum. Meas. pp. 1–10 (2018).

Wang, X.

Wang, Y.

Wang, Z.

Xi, J.

Xing, Y.

Y. Xing and C. Quan, “Reference-plane-based fast pixel-by-pixel absolute phase retrieval for height measurement,” Appl. Opt. 57, 4901–4908 (2018).
[Crossref] [PubMed]

Y. Xing, C. Quan, and C. Tay, “A modified phase-coding method for absolute phase retrieval,” Opt. Lasers Eng. 87, 97 – 102 (2016).
[Crossref]

Yang, Z.

Y. Hu, J. Xi, J. F. Chicharo, W. Cheng, and Z. Yang, “Inverse function analysis method for fringe pattern profilometry,” IEEE Trans. Instrum. Meas. 58, 3305–3314 (2009).
[Crossref]

Yin, W.

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.

Yu, Y.

Q. Guo, Y. Ruan, J. Xi, L. Song, X. Zhu, Y. Yu, and J. Tong, “3d shape measurement of moving object with fft-based spatial matching,” Opt. Laser Technol. 100, 325 – 331 (2018).
[Crossref]

L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the accuracy of 3-d shape measurement of moving object using phase shifting profilometry,” Opt. Express 21, 30610–30622 (2013).
[Crossref]

Zhang, M.

H. Li, Y. Hu, T. Tao, S. Feng, M. Zhang, Y. Zhang, and C. Zuo, “Optimal wavelength selection strategy in temporal phase unwrapping with projection distance minimization,” Appl. Opt. 57, 2352–2360 (2018).
[Crossref] [PubMed]

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. Lasers Eng. 103, 127–138 (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]

Zhang, S.

Zhang, Y.

Zhao, H.

Zhao, J.

H. Wang, J. Zhao, J. Zhao, J. Song, Z. Pan, and X. Jiang, “A new rapid-precision position measurement method for a linear motor mover based on a 1-d epca,” IEEE Trans. Ind. Electron 65, 7485–7494 (2018).
[Crossref]

H. Wang, J. Zhao, J. Zhao, J. Song, Z. Pan, and X. Jiang, “A new rapid-precision position measurement method for a linear motor mover based on a 1-d epca,” IEEE Trans. Ind. Electron 65, 7485–7494 (2018).
[Crossref]

J. Zhao, J. Zhao, H. Wang, J. Song, and F. Dong, “Precision position measurement of linear motors mover based on temporal image correlation,” IEEE Trans. Instrum. Meas. pp. 1–10 (2018).

J. Zhao, J. Zhao, H. Wang, J. Song, and F. Dong, “Precision position measurement of linear motors mover based on temporal image correlation,” IEEE Trans. Instrum. Meas. pp. 1–10 (2018).

Zhong, K.

Zhou, Q.

Zhou, X.

Zhu, X.

Q. Guo, Y. Ruan, J. Xi, L. Song, X. Zhu, Y. Yu, and J. Tong, “3d shape measurement of moving object with fft-based spatial matching,” Opt. Laser Technol. 100, 325 – 331 (2018).
[Crossref]

Zibley, P. C.

Zuo, C.

H. Li, Y. Hu, T. Tao, S. Feng, M. Zhang, Y. Zhang, and C. Zuo, “Optimal wavelength selection strategy in temporal phase unwrapping with projection distance minimization,” Appl. Opt. 57, 2352–2360 (2018).
[Crossref] [PubMed]

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, 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. Lasers Eng. 103, 127–138 (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]

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, 20253–20269 (2016).
[Crossref] [PubMed]

Appl. Opt. (6)

IEEE Trans. Ind. Electron (1)

H. Wang, J. Zhao, J. Zhao, J. Song, Z. Pan, and X. Jiang, “A new rapid-precision position measurement method for a linear motor mover based on a 1-d epca,” IEEE Trans. Ind. Electron 65, 7485–7494 (2018).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

Y. Hu, J. Xi, J. F. Chicharo, W. Cheng, and Z. Yang, “Inverse function analysis method for fringe pattern profilometry,” IEEE Trans. Instrum. Meas. 58, 3305–3314 (2009).
[Crossref]

IEEE Trans. Med. Imaging (1)

W. S. Hoge, “A subspace identification extension to the phase correlation method [mri application],” IEEE Trans. Med. Imaging 22, 277–280 (2003).
[Crossref] [PubMed]

ISPRS-J. Photogramm. Remote Sens. (1)

F. Bruno, G. Bianco, M. Muzzupappa, S. Barone, and A. Razionale, “Experimentation of structured light and stereo vision for underwater 3d reconstruction,” ISPRS-J. Photogramm. Remote Sens. 66, 508 – 518 (2011).
[Crossref]

Measurement (1)

S. Matthias, M. Kästner, and E. Reithmeier, “Evaluation of system models for an endoscopic fringe projection system,” Measurement 73, 239 – 246 (2015).
[Crossref]

Opt. Eng. (2)

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

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 13602 (2006).
[Crossref]

Opt. Express (9)

Y. Wang, Z. Liu, C. Jiang, and S. Zhang, “Motion induced phase error reduction using a hilbert transform,” Opt. Express 26, 34224–34235 (2018).
[Crossref]

L. Lu, J. Xi, Y. Yu, and Q. Guo, “New approach to improve the accuracy of 3-d shape measurement of moving object using phase shifting profilometry,” Opt. Express 21, 30610–30622 (2013).
[Crossref]

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

L. Lu, Y. Ding, Y. Luan, Y. Yin, Q. Liu, and J. Xi, “Automated approach for the surface profile measurement of moving objects based on psp,” Opt. Express 25, 32120–32131 (2017).
[Crossref] [PubMed]

Q. Zhou, X. Qiao, K. Ni, X. Li, and X. Wang, “Depth detection in interactive projection system based on one-shot black-and-white stripe pattern,” Opt. Express 25, 5341–5351 (2017).
[Crossref] [PubMed]

Z. Liu, P. C. Zibley, and S. Zhang, “Motion-induced error compensation for phase shifting profilometry,” Opt. Express 26, 12632–12637 (2018).
[Crossref] [PubMed]

B. Li and S. Zhang, “Superfast high-resolution absolute 3d recovery of a stabilized flapping flight process,” Opt. Express 25, 27270–27282 (2017).
[Crossref] [PubMed]

B. Li, Z. Liu, and S. Zhang, “Motion-induced error reduction by combining fourier transform profilometry with phase-shifting profilometry,” Opt. Express 24, 23289–23303 (2016).
[Crossref] [PubMed]

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, 20253–20269 (2016).
[Crossref] [PubMed]

Opt. Laser Technol. (1)

Q. Guo, Y. Ruan, J. Xi, L. Song, X. Zhu, Y. Yu, and J. Tong, “3d shape measurement of moving object with fft-based spatial matching,” Opt. Laser Technol. 100, 325 – 331 (2018).
[Crossref]

Opt. Lasers Eng. (4)

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. Lasers Eng. 103, 127–138 (2018).
[Crossref]

Y. Xing, C. Quan, and C. Tay, “A modified phase-coding method for absolute phase retrieval,” Opt. Lasers Eng. 87, 97 – 102 (2016).
[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, 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. (2)

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J. Salvi, J. Pagès, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recognit. 37, 827 – 849 (2004).
[Crossref]

Other (1)

J. Zhao, J. Zhao, H. Wang, J. Song, and F. Dong, “Precision position measurement of linear motors mover based on temporal image correlation,” IEEE Trans. Instrum. Meas. pp. 1–10 (2018).

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Figures (12)

Fig. 1
Fig. 1 A schematic diagram of a typical DFP system with one camera.
Fig. 2
Fig. 2 DFP system with one reference phase map. (a) A reference plane is placed in front of the object; (b) A reference plane is placed behind the object.
Fig. 3
Fig. 3 The phase relationship between reference planes and object. (a) The pixel-to-pixel absolute phase unwrapping method; (b) The adaptive reference phase map P3.
Fig. 4
Fig. 4 The principle of extracting the rotation angle and the translation vector.
Fig. 5
Fig. 5 Workflow of our proposed 1-D HPCM.
Fig. 6
Fig. 6 The overall computational framework. The framework measures moving objects based on sub-pixel motion estimation and three-step PSP. The marker consists of a horizontal fence and a vertical fence, which moves with the object. The phase map of the reference plane is calculated and absolutely unwrapped by Gray-code phase unwrapping [7]. The two rectangular windows of projection fringe image is used to automatically extract the marking fence images, which are defined by red rectangles in the fringe images. The top window and bottom window are applied to crop different direction fence images.
Fig. 7
Fig. 7 Reconstructed results of the moving mask with four methods in 2-D translation. (a) Reconstructed 3-D shape using traditional three-step PSP. (b) Reconstructed 3-D shape using FTP. (c) Reconstructed 3-D shape using RPECM. (d) Reconstructed 3-D shape using ARPECM. (e-h) The corresponding enlarged detail of the region in Figs. 7(a)-7(d).
Fig. 8
Fig. 8 The height curves comparison of Figs. 7(a)-7(d), where x = 80 mm. (a) The height curves of results using traditional three-step PSP and FTP. (b) The height curves of results corrected by RPECM and ARPECM. (c) Absolute error comparison of four methods.
Fig. 9
Fig. 9 Reconstructed results of the moving mask with four methods in 2-D hybrid motion. (a) Reconstructed 3-D shape using traditional three-step PSP. (b) Reconstructed 3-D shape using FTP. (c) Reconstructed 3-D shape using RPECM. (d) Reconstructed 3-D shape using ARPECM. (e-h) The corresponding enlarged detail of the region in Figs. 9(a)-9(d).
Fig. 10
Fig. 10 The height curves comparison of Figs. 9(a)-9(d), where x = 80 mm. (a) The height curves of results using traditional three-step PSP and FTP. (b) The height curves of results corrected by RPECM and ARPECM. (c) Absolute error comparison of four methods.
Fig. 11
Fig. 11 Reconstructed results of three moving geometries with four methods in 2-D translation. (a) Reconstructed 3-D surface profile using traditional three-step PSP. (b) Reconstructed 3-D surface profile using FTP. (c) Reconstructed 3-D surface profile using the RPECM. (d) Reconstructed 3-D surface profile using the ARPECM.
Fig. 12
Fig. 12 Reconstructed results of three moving geometries with four methods in 2-D hybrid motion. (a) Reconstructed 3-D surface profile using traditional three-step PSP. (b) Reconstructed 3-D surface profile using FTP. (c) Reconstructed 3-D surface profile using the RPECM. (d) Reconstructed 3-D surface profile using the ARPECM.

Tables (1)

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Table 1 The MSEs of 3-D shape measurements with four methods

Equations (20)

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I n ( x , y ) = a ( x , y ) + b ( x , y ) c o s [ ϕ ( x , y ) + 2 π ( n 1 ) / N ] ,
ϕ ( x , y ) = tan  1 { n = 1 N I n ( x , y ) sin  [ 2 π ( n 1 ) / N ] n = 1 N I n ( x , y ) cos  [ 2 π ( n 1 ) / N ] } .
I n ( p n , q n ) = A n ( p n , q n ) + B n ( p n , q n ) cos  [ ϕ ( p n , q n ) + 2 π ( n 1 ) / N ] ,
{ I 1 ( x , y ) = A 1 ( p 1 , q 1 ) + B 1 ( p 1 , q 1 ) cos  [ ϕ ( x , y ) + Δ φ ( p 1 , q 1 ) ] , I 2 ( x , y ) = A 2 ( p 2 , q 2 ) + B 2 ( p 2 , q 2 ) cos  [ ϕ ( x , y ) + Δ φ ( p 2 , q 2 ) + 2 π / N ] , I N ( x , y ) = A N ( p N , q N ) + B N ( p N , q N ) cos  [ ϕ ( x , y ) + Δ φ ( p N , q N ) + 2 π ( N 1 ) / N ] ,  
[ x y 1 ] T = [ p n q n 1 ] T [ cos  θ n sin  θ n T x n sin  θ n cos  θ n T y n 0 0 1 ]
{ A n ( p n , q n ) = a ( x , y ) , B n ( p n , q n ) = b ( x , y ) .
Φ ( x , y ) = ϕ ( x , y ) + 2 π × k ( x , y ) ,
k ( x , y ) = c e i l [ Φ P 1 ( x , y ) ϕ ( x , y ) 2 π ] ,
Φ P 3 = ω Φ P 1 + ( 1 ω ) Φ P 2 ,
ω = arg min  [ ( Φ Φ P 3 ) 2 ] .
g 2 ( y ) = g 1 ( y T y ) .
G 2 ( ν ) = G 1 ( ν ) exp  [ j ( ν T y ) ] .
Q ( ν ) = G 1 ( ν ) G 2 ( ν ) * | G 1 ( ν ) G 2 ( ν ) * | = exp  [ j ( ν T y ) ] ,
q ( y ) = δ ( y T y ) .
W [ μ c ] = u n w r a p { υ } ,
[ μ c ] = ( W T W ) 1 W T u n w r a p { υ } .
T y = μ M / 2 π .
T y 1 = 10 f l o o r ( T y 0 / 10 ) ,
T = T y 1 + T y 2 .
Δ φ ^ ( p n , q n ) = Φ P 3 ( p n , q n ) Φ P 3 ( x , y ) ,

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