Abstract

Fringe-based optical measurement techniques require reliable fringe analysis methods, where empirical mode decomposition (EMD) is an outstanding one due to its ability of analyzing complex signals and the merit of being data-driven. However, two challenging issues hinder the application of EMD in practical measurement. One is the tricky mode mixing problem (MMP), making the decomposed intrinsic mode functions (IMFs) have equivocal physical meaning; the other is the automatic and accurate extraction of the sinusoidal fringe from the IMFs when unpredictable and unavoidable background and noise exist in real measurements. Accordingly, in this paper, a novel bidimensional sinusoids-assisted EMD (BSEMD) is proposed to decompose a fringe pattern into mono-component bidimensional IMFs (BIMFs), with the MMP solved; properties of the resulted BIMFs are then analyzed to recognize and enhance the useful fringe component. The decomposition and the fringe recognition are integrated and the latter provides a feedback to the former, helping to automatically stop the decomposition to make the algorithm simpler and more reliable. A series of experiments show that the proposed method is accurate, efficient and robust to various fringe patterns even with poor quality, rendering it a potential tool for practical use.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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  1. X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 40(2), 191–204 (2010).
    [Crossref]
  2. Z. Zhang and J. Zhong, “Applicability analysis of wavelet-transform profilometry,” Opt. Express 21(16), 18777–18796 (2013).
    [Crossref] [PubMed]
  3. Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: A review,” Opt. Lasers Eng. 66, 67–73 (2015).
    [Crossref]
  4. 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(6), 723–729 (2007).
    [Crossref]
  5. 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(5), 1195–1201 (2009).
    [Crossref] [PubMed]
  6. C. Zhang, W. Ren, T. Mu, L. Fu, and C. Jia, “Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer,” Opt. Express 21(3), 2592–2605 (2013).
    [Crossref] [PubMed]
  7. G. Lagubeau, P. Cobelli, T. Bobinski, A. Maurel, V. Pagneux, and P. Petitjeans, “Empirical mode decomposition profilometry: small-scale capabilities and comparison to Fourier transform profilometry,” Appl. Opt. 54(32), 9409–9414 (2015).
    [Crossref] [PubMed]
  8. Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise-assisted data analysis method,” Adv. Adapt. Data Anal. 1(1), 1–41 (2009).
    [Crossref]
  9. X. Zhou, H. Zhao, and T. Jiang, “Adaptive analysis of optical fringe patterns using ensemble empirical mode decomposition algorithm,” Opt. Lett. 34(13), 2033–2035 (2009).
    [Crossref] [PubMed]
  10. C. Wang, Q. Kemao, and F. Da, “Regenerated phase-shifted sinusoids-assisted empirical mode decomposition,” IEEE Signal Process. Lett. 23(4), 556–560 (2016).
    [Crossref]
  11. C. Yi, Y. Lv, H. Xiao, G. Yao, and Z. Dang, “Research on the blind source separation method based on regenerated phase-shifted sinusoids-assisted EMD and its application in diagnosing rolling-bearing faults,” Appl. Sci. 7(4), 414 (2017).
    [Crossref]
  12. C. Wang, Q. Kemao, and F. Da, “Regenerated phase-shifted sinusoids-assisted EMD for adaptive analysis of fringe patterns,” Opt. Lasers Eng. 87, 176–184 (2016).
    [Crossref]
  13. Y. Zhou and H. Li, “Adaptive noise reduction method for DSPI fringes based on bi-dimensional ensemble empirical mode decomposition,” Opt. Express 19(19), 18207–18215 (2011).
    [Crossref] [PubMed]
  14. M. B. Bernini, A. Federico, and G. H. Kaufmann, “Phase measurement in temporal speckle pattern interferometry signals presenting low-modulated regions by means of the bidimensional empirical mode decomposition,” Appl. Opt. 50(5), 641–647 (2011).
    [Crossref] [PubMed]
  15. S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation,” EURASIP J. Adv. Signal Process. 2008(164), 725356 (2008).
  16. Y. Zhou and H. Li, “A denoising scheme for DSPI fringes based on fast bi-dimensional ensemble empirical mode decomposition and BIMF energy estimation,” Mech. Syst. Signal Process. 35(1-2), 369–382 (2013).
    [Crossref]
  17. M. B. Bernini, A. Federico, and G. H. Kaufmann, “Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform,” Appl. Opt. 48(36), 6862–6869 (2009).
    [Crossref] [PubMed]
  18. 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(28), 5513–5523 (2011).
    [Crossref] [PubMed]
  19. M. Trusiak, K. Patorski, and M. Wielgus, “Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform,” Opt. Express 20(21), 23463–23479 (2012).
    [Crossref] [PubMed]
  20. M. Trusiak, M. Wielgus, and K. Patorski, “Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition,” Opt. Lasers Eng. 52, 230–240 (2014).
    [Crossref]
  21. K. Patorski, M. Trusiak, and K. Pokorski, “Diffraction grating three-beam interferometry without self-imaging regime contrast modulations,” Opt. Lett. 40(6), 1089–1092 (2015).
    [Crossref] [PubMed]
  22. M. Trusiak, Ł. Służewski, and K. Patorski, “Single shot fringe pattern phase demodulation using Hilbert-Huang transform aided by the principal component analysis,” Opt. Express 24(4), 4221–4238 (2016).
    [Crossref] [PubMed]
  23. J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21(12), 1019–1026 (2003).
    [Crossref]
  24. G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Signal Process. 56(1), 85–95 (2008).
    [Crossref]
  25. Z. Wu and N. E. Huang, “A study of the characteristics of white noise using the empirical mode decomposition method,” Proc. R. Soc. Lond. A 460(2046), 1597–1611 (2004).
    [Crossref]
  26. K. G. Larkin, “Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18(8), 1871–1881 (2001).
    [Crossref] [PubMed]
  27. 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. R. Soc. Lond. A 454(1971), 903–995 (1998).
    [Crossref]
  28. X. Zhou, A. G. Podoleanu, Z. Yang, T. Yang, and H. Zhao, “Morphological Operation-based bi-dimensional empirical mode decomposition for automatic background removal of fringe patterns,” Opt. Express 20(22), 24247–24262 (2012).
    [Crossref] [PubMed]
  29. F. C. M. Alanís and J. A. M. Rodríguez, “Self-calibration of vision parameters via genetic algorithms with simulated binary crossover and laser line projection,” Opt. Eng. 54(5), 053115 (2015).
    [Crossref]
  30. L. Kai and Q. Kemao, “Fast frequency-guided sequential demodulation of a single fringe pattern,” Opt. Lett. 35(22), 3718–3720 (2010).
    [Crossref] [PubMed]
  31. X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
    [Crossref]

2017 (1)

C. Yi, Y. Lv, H. Xiao, G. Yao, and Z. Dang, “Research on the blind source separation method based on regenerated phase-shifted sinusoids-assisted EMD and its application in diagnosing rolling-bearing faults,” Appl. Sci. 7(4), 414 (2017).
[Crossref]

2016 (3)

C. Wang, Q. Kemao, and F. Da, “Regenerated phase-shifted sinusoids-assisted EMD for adaptive analysis of fringe patterns,” Opt. Lasers Eng. 87, 176–184 (2016).
[Crossref]

C. Wang, Q. Kemao, and F. Da, “Regenerated phase-shifted sinusoids-assisted empirical mode decomposition,” IEEE Signal Process. Lett. 23(4), 556–560 (2016).
[Crossref]

M. Trusiak, Ł. Służewski, and K. Patorski, “Single shot fringe pattern phase demodulation using Hilbert-Huang transform aided by the principal component analysis,” Opt. Express 24(4), 4221–4238 (2016).
[Crossref] [PubMed]

2015 (4)

K. Patorski, M. Trusiak, and K. Pokorski, “Diffraction grating three-beam interferometry without self-imaging regime contrast modulations,” Opt. Lett. 40(6), 1089–1092 (2015).
[Crossref] [PubMed]

G. Lagubeau, P. Cobelli, T. Bobinski, A. Maurel, V. Pagneux, and P. Petitjeans, “Empirical mode decomposition profilometry: small-scale capabilities and comparison to Fourier transform profilometry,” Appl. Opt. 54(32), 9409–9414 (2015).
[Crossref] [PubMed]

Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: A review,” Opt. Lasers Eng. 66, 67–73 (2015).
[Crossref]

F. C. M. Alanís and J. A. M. Rodríguez, “Self-calibration of vision parameters via genetic algorithms with simulated binary crossover and laser line projection,” Opt. Eng. 54(5), 053115 (2015).
[Crossref]

2014 (1)

M. Trusiak, M. Wielgus, and K. Patorski, “Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition,” Opt. Lasers Eng. 52, 230–240 (2014).
[Crossref]

2013 (3)

2012 (2)

2011 (3)

2010 (2)

L. Kai and Q. Kemao, “Fast frequency-guided sequential demodulation of a single fringe pattern,” Opt. Lett. 35(22), 3718–3720 (2010).
[Crossref] [PubMed]

X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 40(2), 191–204 (2010).
[Crossref]

2009 (4)

2008 (2)

G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Signal Process. 56(1), 85–95 (2008).
[Crossref]

S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation,” EURASIP J. Adv. Signal Process. 2008(164), 725356 (2008).

2007 (1)

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(6), 723–729 (2007).
[Crossref]

2004 (1)

Z. Wu and N. E. Huang, “A study of the characteristics of white noise using the empirical mode decomposition method,” Proc. R. Soc. Lond. A 460(2046), 1597–1611 (2004).
[Crossref]

2003 (1)

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21(12), 1019–1026 (2003).
[Crossref]

2001 (2)

1998 (1)

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. R. Soc. Lond. A 454(1971), 903–995 (1998).
[Crossref]

Adhami, R. R.

S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation,” EURASIP J. Adv. Signal Process. 2008(164), 725356 (2008).

Alanís, F. C. M.

F. C. M. Alanís and J. A. M. Rodríguez, “Self-calibration of vision parameters via genetic algorithms with simulated binary crossover and laser line projection,” Opt. Eng. 54(5), 053115 (2015).
[Crossref]

Bernini, M. B.

Bhuiyan, S. M. A.

S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation,” EURASIP J. Adv. Signal Process. 2008(164), 725356 (2008).

Bobinski, T.

Bouaoune, Y.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21(12), 1019–1026 (2003).
[Crossref]

Bunel, Ph.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21(12), 1019–1026 (2003).
[Crossref]

Chen, W.

Cobelli, P.

Da, F.

C. Wang, Q. Kemao, and F. Da, “Regenerated phase-shifted sinusoids-assisted EMD for adaptive analysis of fringe patterns,” Opt. Lasers Eng. 87, 176–184 (2016).
[Crossref]

C. Wang, Q. Kemao, and F. Da, “Regenerated phase-shifted sinusoids-assisted empirical mode decomposition,” IEEE Signal Process. Lett. 23(4), 556–560 (2016).
[Crossref]

Dang, Z.

C. Yi, Y. Lv, H. Xiao, G. Yao, and Z. Dang, “Research on the blind source separation method based on regenerated phase-shifted sinusoids-assisted EMD and its application in diagnosing rolling-bearing faults,” Appl. Sci. 7(4), 414 (2017).
[Crossref]

Delechelle, E.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21(12), 1019–1026 (2003).
[Crossref]

Federico, A.

Flandrin, P.

G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Signal Process. 56(1), 85–95 (2008).
[Crossref]

Fu, L.

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(6), 723–729 (2007).
[Crossref]

Huang, N. E.

Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise-assisted data analysis method,” Adv. Adapt. Data Anal. 1(1), 1–41 (2009).
[Crossref]

Z. Wu and N. E. Huang, “A study of the characteristics of white noise using the empirical mode decomposition method,” Proc. R. Soc. Lond. A 460(2046), 1597–1611 (2004).
[Crossref]

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. R. Soc. Lond. A 454(1971), 903–995 (1998).
[Crossref]

Jia, C.

Jiang, T.

Kai, L.

Kaufmann, G. H.

Kemao, Q.

C. Wang, Q. Kemao, and F. Da, “Regenerated phase-shifted sinusoids-assisted empirical mode decomposition,” IEEE Signal Process. Lett. 23(4), 556–560 (2016).
[Crossref]

C. Wang, Q. Kemao, and F. Da, “Regenerated phase-shifted sinusoids-assisted EMD for adaptive analysis of fringe patterns,” Opt. Lasers Eng. 87, 176–184 (2016).
[Crossref]

Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: A review,” Opt. Lasers Eng. 66, 67–73 (2015).
[Crossref]

L. Kai and Q. Kemao, “Fast frequency-guided sequential demodulation of a single fringe pattern,” Opt. Lett. 35(22), 3718–3720 (2010).
[Crossref] [PubMed]

Khan, J. F.

S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation,” EURASIP J. Adv. Signal Process. 2008(164), 725356 (2008).

Lagubeau, G.

Larkin, K. G.

Li, H.

Y. Zhou and H. Li, “A denoising scheme for DSPI fringes based on fast bi-dimensional ensemble empirical mode decomposition and BIMF energy estimation,” Mech. Syst. Signal Process. 35(1-2), 369–382 (2013).
[Crossref]

Y. Zhou and H. Li, “Adaptive noise reduction method for DSPI fringes based on bi-dimensional ensemble empirical mode decomposition,” Opt. Express 19(19), 18207–18215 (2011).
[Crossref] [PubMed]

Li, S.

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. R. Soc. Lond. A 454(1971), 903–995 (1998).
[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. R. Soc. Lond. A 454(1971), 903–995 (1998).
[Crossref]

Lv, Y.

C. Yi, Y. Lv, H. Xiao, G. Yao, and Z. Dang, “Research on the blind source separation method based on regenerated phase-shifted sinusoids-assisted EMD and its application in diagnosing rolling-bearing faults,” Appl. Sci. 7(4), 414 (2017).
[Crossref]

Maurel, A.

Mu, T.

Niang, O.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21(12), 1019–1026 (2003).
[Crossref]

Nunes, J. C.

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21(12), 1019–1026 (2003).
[Crossref]

Pagneux, V.

Patorski, K.

Petitjeans, P.

Podoleanu, A. G.

Pokorski, K.

Ren, W.

Rilling, G.

G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Signal Process. 56(1), 85–95 (2008).
[Crossref]

Rodríguez, J. A. M.

F. C. M. Alanís and J. A. M. Rodríguez, “Self-calibration of vision parameters via genetic algorithms with simulated binary crossover and laser line projection,” Opt. Eng. 54(5), 053115 (2015).
[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. R. Soc. Lond. A 454(1971), 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. R. Soc. Lond. A 454(1971), 903–995 (1998).
[Crossref]

Sluzewski, L.

Su, X.

X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 40(2), 191–204 (2010).
[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(5), 1195–1201 (2009).
[Crossref] [PubMed]

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

Trusiak, M.

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. R. Soc. Lond. A 454(1971), 903–995 (1998).
[Crossref]

Wang, C.

C. Wang, Q. Kemao, and F. Da, “Regenerated phase-shifted sinusoids-assisted EMD for adaptive analysis of fringe patterns,” Opt. Lasers Eng. 87, 176–184 (2016).
[Crossref]

C. Wang, Q. Kemao, and F. Da, “Regenerated phase-shifted sinusoids-assisted empirical mode decomposition,” IEEE Signal Process. Lett. 23(4), 556–560 (2016).
[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. R. Soc. Lond. A 454(1971), 903–995 (1998).
[Crossref]

Wu, Z.

Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise-assisted data analysis method,” Adv. Adapt. Data Anal. 1(1), 1–41 (2009).
[Crossref]

Z. Wu and N. E. Huang, “A study of the characteristics of white noise using the empirical mode decomposition method,” Proc. R. Soc. Lond. A 460(2046), 1597–1611 (2004).
[Crossref]

Xiang, L.

Xiao, H.

C. Yi, Y. Lv, H. Xiao, G. Yao, and Z. Dang, “Research on the blind source separation method based on regenerated phase-shifted sinusoids-assisted EMD and its application in diagnosing rolling-bearing faults,” Appl. Sci. 7(4), 414 (2017).
[Crossref]

Yang, T.

Yang, Z.

Yao, G.

C. Yi, Y. Lv, H. Xiao, G. Yao, and Z. Dang, “Research on the blind source separation method based on regenerated phase-shifted sinusoids-assisted EMD and its application in diagnosing rolling-bearing faults,” Appl. Sci. 7(4), 414 (2017).
[Crossref]

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. R. Soc. Lond. A 454(1971), 903–995 (1998).
[Crossref]

Yi, C.

C. Yi, Y. Lv, H. Xiao, G. Yao, and Z. Dang, “Research on the blind source separation method based on regenerated phase-shifted sinusoids-assisted EMD and its application in diagnosing rolling-bearing faults,” Appl. Sci. 7(4), 414 (2017).
[Crossref]

Zhang, C.

Zhang, Q.

X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 40(2), 191–204 (2010).
[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. R. Soc. Lond. A 454(1971), 903–995 (1998).
[Crossref]

Zhong, J.

Zhou, X.

Zhou, Y.

Y. Zhou and H. Li, “A denoising scheme for DSPI fringes based on fast bi-dimensional ensemble empirical mode decomposition and BIMF energy estimation,” Mech. Syst. Signal Process. 35(1-2), 369–382 (2013).
[Crossref]

Y. Zhou and H. Li, “Adaptive noise reduction method for DSPI fringes based on bi-dimensional ensemble empirical mode decomposition,” Opt. Express 19(19), 18207–18215 (2011).
[Crossref] [PubMed]

Adv. Adapt. Data Anal. (1)

Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise-assisted data analysis method,” Adv. Adapt. Data Anal. 1(1), 1–41 (2009).
[Crossref]

Appl. Opt. (4)

Appl. Sci. (1)

C. Yi, Y. Lv, H. Xiao, G. Yao, and Z. Dang, “Research on the blind source separation method based on regenerated phase-shifted sinusoids-assisted EMD and its application in diagnosing rolling-bearing faults,” Appl. Sci. 7(4), 414 (2017).
[Crossref]

EURASIP J. Adv. Signal Process. (1)

S. M. A. Bhuiyan, R. R. Adhami, and J. F. Khan, “Fast and adaptive bidimensional empirical mode decomposition using order-statistics filter based envelope estimation,” EURASIP J. Adv. Signal Process. 2008(164), 725356 (2008).

IEEE Signal Process. Lett. (1)

C. Wang, Q. Kemao, and F. Da, “Regenerated phase-shifted sinusoids-assisted empirical mode decomposition,” IEEE Signal Process. Lett. 23(4), 556–560 (2016).
[Crossref]

IEEE Trans. Signal Process. (1)

G. Rilling and P. Flandrin, “One or two frequencies? The empirical mode decomposition answers,” IEEE Trans. Signal Process. 56(1), 85–95 (2008).
[Crossref]

Image Vis. Comput. (1)

J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and Ph. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image Vis. Comput. 21(12), 1019–1026 (2003).
[Crossref]

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

Mech. Syst. Signal Process. (1)

Y. Zhou and H. Li, “A denoising scheme for DSPI fringes based on fast bi-dimensional ensemble empirical mode decomposition and BIMF energy estimation,” Mech. Syst. Signal Process. 35(1-2), 369–382 (2013).
[Crossref]

Opt. Eng. (1)

F. C. M. Alanís and J. A. M. Rodríguez, “Self-calibration of vision parameters via genetic algorithms with simulated binary crossover and laser line projection,” Opt. Eng. 54(5), 053115 (2015).
[Crossref]

Opt. Express (6)

Opt. Lasers Eng. (6)

M. Trusiak, M. Wielgus, and K. Patorski, “Advanced processing of optical fringe patterns by automated selective reconstruction and enhanced fast empirical mode decomposition,” Opt. Lasers Eng. 52, 230–240 (2014).
[Crossref]

C. Wang, Q. Kemao, and F. Da, “Regenerated phase-shifted sinusoids-assisted EMD for adaptive analysis of fringe patterns,” Opt. Lasers Eng. 87, 176–184 (2016).
[Crossref]

Q. Kemao, “Applications of windowed Fourier fringe analysis in optical measurement: A review,” Opt. Lasers Eng. 66, 67–73 (2015).
[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(6), 723–729 (2007).
[Crossref]

X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 40(2), 191–204 (2010).
[Crossref]

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

Opt. Lett. (3)

Proc. R. Soc. Lond. A (2)

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. R. Soc. Lond. A 454(1971), 903–995 (1998).
[Crossref]

Z. Wu and N. E. Huang, “A study of the characteristics of white noise using the empirical mode decomposition method,” Proc. R. Soc. Lond. A 460(2046), 1597–1611 (2004).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 The structure of BSEMD.
Fig. 2
Fig. 2 A simulation of a closed fringe pattern.
Fig. 3
Fig. 3 The BIMFs by the: (a1)-(h1) EFEMD; (a2)-(i2): FBEEMD; (a3)-(i3): BSEMD.
Fig. 4
Fig. 4 Grouping parameters for all BIMFs of BSEMD: (a) the global energy E(k); (b) ratio values of global frequencies of two adjacent BIMFs; (c) the amplitude-frequency ratio Raf (k).
Fig. 5
Fig. 5 (a) The BIMF4 of BSEMD, namely Fig. 3(d3); (b) the instantaneous amplitude map by HST; (c) the segmentation performed on the amplitude map by Otsu’s n-thresholding (n = 4); the results after: (d) the morphological open operation, (e) the morphological close operation, and (f) the dilation operation; (g) the final result after removing the noise region.
Fig. 6
Fig. 6 The reconstructed PM signal of: (a) ASR-EFEMD, (b) FBEEMD, (c) our method; the normalized PM signal of: (d) ASR-EFEMD; (e) FBEEMD; (f) our method.
Fig. 7
Fig. 7 (a) A close fringe pattern with severe noise and background; the normalized PM signal of: (b) ASR-EFEMD with the central information reserving complete; (c) ASR-EFEMD with background removed thoroughly; (d) FBEEMD; (e) our method.
Fig. 8
Fig. 8 (a) A complex fringe pattern; (b)-(d): The PM signal by ASR-EFEMD, FBEEMD and our method respectively; (e)-(g): the normalized PM signal of ASR-EFEMD, FBEEMD and our method, respectively.
Fig. 9
Fig. 9 A real fringe pattern.
Fig. 10
Fig. 10 (a)-(c): the PM signal by ASR-EFEMD, FBEEMD and our method respectively; (d)-(f): the corresponding normalizeded PM signal.
Fig. 11
Fig. 11 Retrieved phases by FFSD [30] from the PM signals by using (a) ASR-EFEMD, (b) FBEEMD and (c) our method respectively, which are presented in Figs. 6(d)-6(f) correspondingly

Tables (3)

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Table 1 The error statistics of the three methods.

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Table 2 The error statistics of the three methods.

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Table 3 The OSB values and the processing time for reconstructing PM fringe signals.

Equations (13)

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I(x,y)= k=1 K BIMF k (x,y) +r(x,y),
T= MN P
s i (x,y)= a i cos(2π f i x)cos(2π f i y),
f m1 1.5 f m2 ,
a m1 f m1 > a m2 f m2 .
f i ={ 1/2, i=1 1.5 f av =1.5/ T i , i>1
a i =4×max( | BIMF 1 t | ).
I(x,y)=a(x,y)+b(x,y)cos[ φ(x,y) ]+n(x,y),
I(x,y)= k=1 k 1 BIMF k (x,y) + k= k 1 +1 k 2 BIMF k (x,y) +( k= k 2 +1 K BIMF k (x,y) +r(x,y) ),
A k ( τ 1 , τ 2 )= (x,y) [ BIMF k (x,y) BIMF k (x τ 1 ,y τ 2 ) ] .
f g = f 1g 2 + f 2g 2 .
R af (k)= a g (k)/ f g (k) ,
OSB= 1 M×N k=1 K1 [ (x,y) BIM F k (x,y)BIM F k+1 (x,y) ] .

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