Abstract

A triple-frequency color fringe-projected technique is presented to measure dynamic objects. Three fringe patterns with a carrier frequency ratio of 139 are encoded in red, green, and blue channels of a color fringe pattern and projected onto an object’s surface. Bidimensional empirical mode decomposition is used for decoupling the cross talk among color channels and for extracting the fundamental frequency components of the three fringe patterns. The unwrapped phase distribution of the high-frequency fringe is retrieved by a three-step phase unwrapping strategy to recover the object’s height distribution. Owing to its use of only a single snapshot, the technique is suitable for measuring dynamically changing objects with large discontinuity or spatially isolated surfaces.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
    [CrossRef]
  2. S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48, 149–158 (2010).
    [CrossRef]
  3. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
    [CrossRef]
  4. W.-H. Su and H. Liu, “Calibration-based two-frequency projected fringe profilometry: a robust, accurate, and single-shot measurement for objects with large depth discontinuities,” Opt. Express 14, 9178–9187 (2006).
    [CrossRef]
  5. 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, 5347–5354 (1997).
    [CrossRef]
  6. H.-M. Yue, X.-Y. Su, and Y.-Z. Liu, “Fourier transform profilometry based on composite structured light pattern,” Opt. Laser Technol. 39, 1170–1175 (2007).
    [CrossRef]
  7. J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 013602 (2006).
    [CrossRef]
  8. L. Kinell, “Multichannel method for absolute shape measurement using projected fringes,” Opt. Lasers Eng. 41, 57–71 (2004).
    [CrossRef]
  9. P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
    [CrossRef]
  10. Z. Zhang, D. P. Towers, and C. E. Towers, “Snapshot color fringe projection for absolute three-dimensional metrology of video sequences,” Appl. Opt. 49, 5947–5953 (2010).
    [CrossRef]
  11. Z. Zhang, C. E. Towers, and D. P. Towers, “Time efficient color fringe projection system for 3D shape and color using optimum 3-frequency selection,” Opt. Express 14, 6444–6455 (2006).
    [CrossRef]
  12. W.-H. Su, “Projected fringe profilometry using the area-encoded algorithm for spatially isolated and dynamic objects,” Opt. Express 16, 2590–2596 (2008).
    [CrossRef]
  13. W.-H. Su, “Color-encoded fringe projection for 3D shape measurements,” Opt. Express 15, 13167–13181 (2007).
    [CrossRef]
  14. P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
    [CrossRef]
  15. N. Karpinsky, S. Lei, and S. Zhang, “High-resolution, real-time fringe pattern profilometry,” Proc. SPIE 7522, 75220E (2009).
    [CrossRef]
  16. N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lond. Math. Phys. Sci. 454, 903–995 (1998).
    [CrossRef]
  17. M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723–729 (2007).
  18. S. Li, X. Su, W. Chen, and L. Xiang, “Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition,” J. Opt. Soc. Am. A 26, 1195–1201 (2009).
    [CrossRef]
  19. X. Zhou, T. Yang, H. H. Zou, and H. Zhao, “A multivariate empirical mode decomposition approach for adaptive denoising of fringe patterns,” Opt. Lett. 37, 1904–1906 (2012).
    [CrossRef]
  20. X. Zhou, H. Zhao, and T. Jiang, “Adaptive analysis of optical fringe patterns using ensemble empirical mode decomposition algorithm,” Opt. Lett. 34, 2033–2035 (2009).
    [CrossRef]
  21. M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47, 2592–2598 (2008).
    [CrossRef]
  22. M. Wielgus and K. Patorski, “Evaluation of amplitude encoded fringe patterns using the bidimensional empirical mode decomposition and the 2D Hilbert transform generalizations,” Appl. Opt. 50, 5513–5523 (2011).
    [CrossRef]
  23. J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21, 1019–1026 (2003).
    [CrossRef]
  24. J. C. Nunes, S. Guyot, and E. Deléchelle, “Texture analysis based on local analysis of the bidimensional empirical mode decomposition,” Mach. Vis. Appl. 16, 177–188 (2005).
    [CrossRef]
  25. L. Vincent, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE Trans. Image Process. 2, 176–201 (1993).
    [CrossRef]
  26. S. M. A. Bhuiyan, N. O. Attoh-okine, K. E. Barner, A. Y. Ayenu-prah, and R. R. Adhami, “Bidimensional empirical mode decomposition using various interpolation techniques,” Adv. Adapt. Data. Anal. 1, 309–338 (2009).
    [CrossRef]
  27. H. Zhao, W. Chen, and Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl. Opt. 33, 4497–4500 (1994).
    [CrossRef]

2012

2011

2010

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

Z. Zhang, D. P. Towers, and C. E. Towers, “Snapshot color fringe projection for absolute three-dimensional metrology of video sequences,” Appl. Opt. 49, 5947–5953 (2010).
[CrossRef]

2009

N. Karpinsky, S. Lei, and S. Zhang, “High-resolution, real-time fringe pattern profilometry,” Proc. SPIE 7522, 75220E (2009).
[CrossRef]

X. Zhou, H. Zhao, and T. Jiang, “Adaptive analysis of optical fringe patterns using ensemble empirical mode decomposition algorithm,” Opt. Lett. 34, 2033–2035 (2009).
[CrossRef]

S. M. A. Bhuiyan, N. O. Attoh-okine, K. E. Barner, A. Y. Ayenu-prah, and R. R. Adhami, “Bidimensional empirical mode decomposition using various interpolation techniques,” Adv. Adapt. Data. Anal. 1, 309–338 (2009).
[CrossRef]

S. Li, X. Su, W. Chen, and L. Xiang, “Eliminating the zero spectrum in Fourier transform profilometry using empirical mode decomposition,” J. Opt. Soc. Am. A 26, 1195–1201 (2009).
[CrossRef]

2008

2007

W.-H. Su, “Color-encoded fringe projection for 3D shape measurements,” Opt. Express 15, 13167–13181 (2007).
[CrossRef]

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723–729 (2007).

H.-M. Yue, X.-Y. Su, and Y.-Z. Liu, “Fourier transform profilometry based on composite structured light pattern,” Opt. Laser Technol. 39, 1170–1175 (2007).
[CrossRef]

2006

2005

J. C. Nunes, S. Guyot, and E. Deléchelle, “Texture analysis based on local analysis of the bidimensional empirical mode decomposition,” Mach. Vis. Appl. 16, 177–188 (2005).
[CrossRef]

2004

L. Kinell, “Multichannel method for absolute shape measurement using projected fringes,” Opt. Lasers Eng. 41, 57–71 (2004).
[CrossRef]

2003

P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21, 1019–1026 (2003).
[CrossRef]

1999

P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

1998

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lond. Math. Phys. Sci. 454, 903–995 (1998).
[CrossRef]

1997

1994

1993

L. Vincent, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE Trans. Image Process. 2, 176–201 (1993).
[CrossRef]

1983

Adhami, R. R.

S. M. A. Bhuiyan, N. O. Attoh-okine, K. E. Barner, A. Y. Ayenu-prah, and R. R. Adhami, “Bidimensional empirical mode decomposition using various interpolation techniques,” Adv. Adapt. Data. Anal. 1, 309–338 (2009).
[CrossRef]

Alatan, A. A.

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Attoh-okine, N. O.

S. M. A. Bhuiyan, N. O. Attoh-okine, K. E. Barner, A. Y. Ayenu-prah, and R. R. Adhami, “Bidimensional empirical mode decomposition using various interpolation techniques,” Adv. Adapt. Data. Anal. 1, 309–338 (2009).
[CrossRef]

Ayenu-prah, A. Y.

S. M. A. Bhuiyan, N. O. Attoh-okine, K. E. Barner, A. Y. Ayenu-prah, and R. R. Adhami, “Bidimensional empirical mode decomposition using various interpolation techniques,” Adv. Adapt. Data. Anal. 1, 309–338 (2009).
[CrossRef]

Barner, K. E.

S. M. A. Bhuiyan, N. O. Attoh-okine, K. E. Barner, A. Y. Ayenu-prah, and R. R. Adhami, “Bidimensional empirical mode decomposition using various interpolation techniques,” Adv. Adapt. Data. Anal. 1, 309–338 (2009).
[CrossRef]

Benzie, P.

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Bernini, M. B.

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47, 2592–2598 (2008).
[CrossRef]

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723–729 (2007).

Bhuiyan, S. M. A.

S. M. A. Bhuiyan, N. O. Attoh-okine, K. E. Barner, A. Y. Ayenu-prah, and R. R. Adhami, “Bidimensional empirical mode decomposition using various interpolation techniques,” Adv. Adapt. Data. Anal. 1, 309–338 (2009).
[CrossRef]

Bouaoune, Y.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21, 1019–1026 (2003).
[CrossRef]

Bunel, P.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21, 1019–1026 (2003).
[CrossRef]

Chen, W.

Chiang, F.-P.

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 013602 (2006).
[CrossRef]

P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Delechelle, E.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21, 1019–1026 (2003).
[CrossRef]

Deléchelle, E.

J. C. Nunes, S. Guyot, and E. Deléchelle, “Texture analysis based on local analysis of the bidimensional empirical mode decomposition,” Mach. Vis. Appl. 16, 177–188 (2005).
[CrossRef]

Federico, A.

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47, 2592–2598 (2008).
[CrossRef]

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723–729 (2007).

Galizzi, G. E.

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723–729 (2007).

Grammalidis, N.

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Gu, Q.

Guyot, S.

J. C. Nunes, S. Guyot, and E. Deléchelle, “Texture analysis based on local analysis of the bidimensional empirical mode decomposition,” Mach. Vis. Appl. 16, 177–188 (2005).
[CrossRef]

Hu, Q.

P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Huang, N. E.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lond. Math. Phys. Sci. 454, 903–995 (1998).
[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, 013602 (2006).
[CrossRef]

P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Jiang, T.

Jin, F.

P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Karpinsky, N.

N. Karpinsky, S. Lei, and S. Zhang, “High-resolution, real-time fringe pattern profilometry,” Proc. SPIE 7522, 75220E (2009).
[CrossRef]

Kaufmann, G. H.

M. B. Bernini, A. Federico, and G. H. Kaufmann, “Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition,” Appl. Opt. 47, 2592–2598 (2008).
[CrossRef]

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723–729 (2007).

Kinell, L.

L. Kinell, “Multichannel method for absolute shape measurement using projected fringes,” Opt. Lasers Eng. 41, 57–71 (2004).
[CrossRef]

Kinoshita, M.

Lei, S.

N. Karpinsky, S. Lei, and S. Zhang, “High-resolution, real-time fringe pattern profilometry,” Proc. SPIE 7522, 75220E (2009).
[CrossRef]

Li, S.

Liu, H.

Liu, H. H.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lond. Math. Phys. Sci. 454, 903–995 (1998).
[CrossRef]

Liu, Y.-Z.

H.-M. Yue, X.-Y. Su, and Y.-Z. Liu, “Fourier transform profilometry based on composite structured light pattern,” Opt. Laser Technol. 39, 1170–1175 (2007).
[CrossRef]

Long, S. R.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lond. Math. Phys. Sci. 454, 903–995 (1998).
[CrossRef]

Malassiotis, S.

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Mutoh, K.

Niang, O.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21, 1019–1026 (2003).
[CrossRef]

Nunes, J. C.

J. C. Nunes, S. Guyot, and E. Deléchelle, “Texture analysis based on local analysis of the bidimensional empirical mode decomposition,” Mach. Vis. Appl. 16, 177–188 (2005).
[CrossRef]

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21, 1019–1026 (2003).
[CrossRef]

Ostermann, J.

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Pan, J.

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 013602 (2006).
[CrossRef]

Patorski, K.

Piekh, S.

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Sainov, V.

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Shen, Z.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lond. Math. Phys. Sci. 454, 903–995 (1998).
[CrossRef]

Shih, H. H.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lond. Math. Phys. Sci. 454, 903–995 (1998).
[CrossRef]

Stoykova, E.

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Su, W.-H.

Su, X.

Su, X.-Y.

H.-M. Yue, X.-Y. Su, and Y.-Z. Liu, “Fourier transform profilometry based on composite structured light pattern,” Opt. Laser Technol. 39, 1170–1175 (2007).
[CrossRef]

Takahashi, Y.

Takai, H.

Takeda, M.

Tan, Y.

Theobalt, C.

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Thevar, T.

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Towers, C. E.

Towers, D. P.

Tung, C. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lond. Math. Phys. Sci. 454, 903–995 (1998).
[CrossRef]

Vincent, L.

L. Vincent, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE Trans. Image Process. 2, 176–201 (1993).
[CrossRef]

Wielgus, M.

Wu, M. C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lond. Math. Phys. Sci. 454, 903–995 (1998).
[CrossRef]

Xiang, L.

Yang, T.

Yen, N.-C.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lond. Math. Phys. Sci. 454, 903–995 (1998).
[CrossRef]

Yue, H.-M.

H.-M. Yue, X.-Y. Su, and Y.-Z. Liu, “Fourier transform profilometry based on composite structured light pattern,” Opt. Laser Technol. 39, 1170–1175 (2007).
[CrossRef]

Zabulis, X.

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Zhang, C.

P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

Zhang, S.

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

N. Karpinsky, S. Lei, and S. Zhang, “High-resolution, real-time fringe pattern profilometry,” Proc. SPIE 7522, 75220E (2009).
[CrossRef]

Zhang, Z.

Zhao, H.

Zheng, Q.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lond. Math. Phys. Sci. 454, 903–995 (1998).
[CrossRef]

Zhou, X.

Zou, H. H.

Adv. Adapt. Data. Anal.

S. M. A. Bhuiyan, N. O. Attoh-okine, K. E. Barner, A. Y. Ayenu-prah, and R. R. Adhami, “Bidimensional empirical mode decomposition using various interpolation techniques,” Adv. Adapt. Data. Anal. 1, 309–338 (2009).
[CrossRef]

Appl. Opt.

IEEE Trans. Circ. Syst. Video Technol.

E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3-D time-varying scene capture technologies—a survey,” IEEE Trans. Circ. Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

IEEE Trans. Image Process.

L. Vincent, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE Trans. Image Process. 2, 176–201 (1993).
[CrossRef]

Image Vis. Comput.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21, 1019–1026 (2003).
[CrossRef]

J. Opt. Soc. Am. A

Mach. Vis. Appl.

J. C. Nunes, S. Guyot, and E. Deléchelle, “Texture analysis based on local analysis of the bidimensional empirical mode decomposition,” Mach. Vis. Appl. 16, 177–188 (2005).
[CrossRef]

Opt. Eng.

J. Pan, P. S. Huang, and F.-P. Chiang, “Color phase-shifting technique for three-dimensional shape measurement,” Opt. Eng. 45, 013602 (2006).
[CrossRef]

P. S. Huang, C. Zhang, and F.-P. Chiang, “High-speed 3-D shape measurement based on digital fringe projection,” Opt. Eng. 42, 163–168 (2003).
[CrossRef]

P. S. Huang, Q. Hu, F. Jin, and F.-P. Chiang, “Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring,” Opt. Eng. 38, 1065–1071 (1999).
[CrossRef]

Opt. Express

Opt. Laser Technol.

H.-M. Yue, X.-Y. Su, and Y.-Z. Liu, “Fourier transform profilometry based on composite structured light pattern,” Opt. Laser Technol. 39, 1170–1175 (2007).
[CrossRef]

Opt. Lasers Eng.

L. Kinell, “Multichannel method for absolute shape measurement using projected fringes,” Opt. Lasers Eng. 41, 57–71 (2004).
[CrossRef]

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

M. B. Bernini, G. E. Galizzi, A. Federico, and G. H. Kaufmann, “Evaluation of the 1D empirical mode decomposition method to smooth digital speckle pattern interferometry fringes,” Opt. Lasers Eng. 45, 723–729 (2007).

Opt. Lett.

Proc. Roy. Soc. Lond. Math. Phys. Sci.

N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proc. Roy. Soc. Lond. Math. Phys. Sci. 454, 903–995 (1998).
[CrossRef]

Proc. SPIE

N. Karpinsky, S. Lei, and S. Zhang, “High-resolution, real-time fringe pattern profilometry,” Proc. SPIE 7522, 75220E (2009).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

Optical geometry.

Fig. 2.
Fig. 2.

Deformed color fringe pattern.

Fig. 3.
Fig. 3.

True (a) low; (b) medium; and (c) high fundamental frequency components; and (d) low; (e) medium and (f) high ones extracted by color decoupling algorithm based on BEMD.

Fig. 4.
Fig. 4.

Wrapped phase distribution of (a) low- (no phase wrap); (b) medium-; and (c) high-frequency fringes; unwrapped phase maps of (d) medium- and (e) high-frequency fringes; and (f) absolute error map.

Fig. 5.
Fig. 5.

(a) Experimental setup and (b) deformed color fringe pattern.

Fig. 6.
Fig. 6.

(a) Red; (b) green; and (c) blue fringe patterns from the captured image; and (d) low; (e) medium; and (f) high fundamental frequency components extracted by color decoupling algorithm based on BEMD.

Fig. 7.
Fig. 7.

Wrapped phase maps of (a) low- (with little phase wraps); (b) medium-; and (c) high-frequency fringes, and unwrapped phase maps of (d) low-; (e) medium-; and (f) high-frequency fringes.

Fig. 8.
Fig. 8.

Restored phase distribution by (a) four-step-shifting method and (b) the proposed method; (c) the results of the 256th column by the two methods; and (d) a detailed view of A in (c).

Fig. 9.
Fig. 9.

(a) Surprised, (b) sad, and (c) chuckle expressions; 3D reconstruction results of (d) surprised, (e) sad, and (f) chuckle expressions.

Equations (16)

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

[R(x,y)G(x,y)B(x,y)]=[aragab]+[brcos(2πfrx)bgcos(2πfgx)bbcos(2πfbx)],
[gr(x,y)gg(x,y)gb(x,y)]=[CrrCrgCrbCgrCggCgbCbrCbgCbb][rr(x,y)·{ar+brcos[2πfrx+Φr(x,y)]}rg(x,y)·{ag+bgcos[2πfgx+Φg(x,y)]}rb(x,y)·{ab+bbcos[2πfbx+Φb(x,y)]}]+[nr(x,y)ng(x,y)nb(x,y)],
[gr(x,y)gg(x,y)gb(x,y)]=[CrrCrgCrbCgrCggCgbCbrCbgCbb][Ar(x,y)+Brcos[2πfrx+Φr(x,y)]Ag(x,y)+Bgcos[2πfgx+Φg(x,y)]Ab(x,y)+Bbcos[2πfbx+Φb(x,y)]]+[nr(x,y)ng(x,y)nb(x,y)].
h(x,y)=LΔΦi(x,y)2πfid=L2πfid[Φi(x,y)Φ0i(x,y)],(i=r,g,b),
s(x)=pm(x)+i=1NλiΦ(xxi),xRd,λiR,
Φ(r)=r2log(r).
[CrrCrgCrb]T[Ar(x,y)Ag(x,y)Ab(x,y)][CgrCggCgb]T[Ar(x,y)Ag(x,y)Ab(x,y)][CbrCbgCbb]T[Ar(x,y)Ag(x,y)Ab(x,y)].
[fMid_Low(x,y)fHigh_Low(x,y)]=[gg(x,y)gr(x,y)gb(x,y)gr(x,y)][CgrCrrCggCrgCgbCrbCbrCrrCbgCrgCbbCrb][Br(x,y)·cos[2πfr+Φr(x,y)]Bg(x,y)·cos[2πfg+Φg(x,y)]Bb(x,y)·cos[2πfb+Φb(x,y)]]+[ng(x,y)nr(x,y)nb(x,y)nr(x,y)].
[g¯r(x,y)g¯g(x,y)g¯b(x,y)]=[(CgrCrr)Br(x,y)·cos[2πfrx+Φr(x,y)](CggCrg)Bg(x,y)·cos[2πfgx+Φg(x,y)](CbbCrb)Bb(x,y)·cos[2πfbx+Φb(x,y)]].
ΔΦr(x,y)=Δφr(x,y),
ΔΦi(x,y)=Δφi(x,y)+2ni(x,y)π,(i=g,b).
nG(x,y)=INT[ΔΦg(x,y)2π]=INT[krΔΦr(x,y)/kgΔφg(x,y)2π],
Δ(m)=kg[Δφg(x,y)+2mπ]krΔΦr(x,y),[m=nG(x,y),nG(x,y)±1],
ΔΦg(x,y)=Δφg(x,y)+2m0g(x,y)π.
Φr(x,y)=P(x,y),Φg(x,y)=3P(x,y),Φb(x,y)=9P(x,y),
P(x,y)=3[3(1x)2ex2(y+1)210(x5x3y5)ex2y213e(x+1)2y2]/8,(x,y=1,2512),

Metrics