Abstract

Three-dimensional profilometric object reconstruction is a challenging topic; among the various methods available, we implement the line projection technique, which has superiorities over other methods. In order to increase the accuracy of measurement, a wavelet transform analysis is used in two stages of denoising and phase extraction. Because of the denoising capability and multiresolution characteristics of wavelet transforms, we employ an undecimated wavelet transform for noise reduction and a continuous wavelet transform in the phase extraction stage. The aim is to add a preprocessing stage of denoising based on the undecimated wavelet transform to enhance the accuracy of measurement in noisy patterns. The experimental results on the human face as a complex object demonstrate that the combination of undecimated and continuous wavelet transforms could increase measurement accuracy in noise-contaminated patterns.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Zhang, “High-resolution, real-time 3-D shape measurement,” Ph.D. dissertation (Stony Brook University, 2005).
  2. E. Stoykova, A. A. Alatan, P. Benzie, N. Grammalidis, S. Malassiotis, J. Ostermann, S. Piekh, V. Sainov, C. Theobalt, T. Thevar, and X. Zabulis, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits Syst. Video Technol. 17, 1568–1586 (2007).
    [CrossRef]
  3. D. C. Méndez, S. C. Méndez, A. L. Quezada, H. Rudolph, and M. Lehman, “Face recognition system using fringe projection and moiré: characterization with fractal parameters,” Int. J. Comput. Sci. Network Secur. 9, 78–84 (2009).
  4. L. Wu, H. Li, N. Yu, and M. Li, “Accurate 3D facial synthesis for plastic surgery simulation,” in Advances in Multimedia Modeling, Part II, T.-J. Cham, J. Cai, C. Dorai, D. Rajan, T.-S. Chua, and L.-T. Chia, eds. (Springer, 2006), pp. 269–278.
  5. W. S. Lee and N. M. Thalmann, “Fast head modeling for animation,” Image Vis. Comput. 18, 355–364 (2000).
    [CrossRef]
  6. H. H. S. Ip and L. Yin, “Constructing a 3D individualized head model from two orthogonal views,” Vis. Comput. 12, 254–266 (1996).
    [CrossRef]
  7. S. F. Wang and S. H. Lai, “Efficient 3D face reconstruction from a single 2D image by combining statistical and geometrical information,” in Computer Vision: ACCV 2006, Part II, P. J. Narayanan, S. K. Nayar, and H.-Y. Shum, eds. (Springer, 2006), 427–436 (2006).
  8. A. Hayasaka, T. Shibahara, K. Ito, T. Aoki, H. Nakajima, and K. Kobayashi, “A passive 3D face recognition system and its performance evaluation,” IEICE Transactions on Fundamentals E91-A, 1974–1981 (2008).
    [CrossRef]
  9. Y. Sui and F. Da, “Stereo vision based 3D reconstruction algorithm of human face,” in 2009 Chinese Conference on Pattern Recognition (IEEE, 2009), 196–200.
  10. N. D’Apuzzo, “3D Laser Scanning Systems,” http://www.hometrica.ch/docs/laserscanning.pdf .
  11. L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
    [CrossRef]
  12. P. S. Huang, F. Jin, and F. P Chiang, “Quantitative evaluation of corrosion by a digital fringe projection technique,” Opt. Lasers Eng. 31, 371–380 (1999).
    [CrossRef]
  13. S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
    [CrossRef]
  14. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  15. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
    [CrossRef]
  16. C. J. Tay, C. Quan, and L. Chen, “Phase retrieval with a three-frame phase-shifting algorithm with an unknown phase shift,” Appl. Opt. 44, 1401–1409 (2005).
    [CrossRef]
  17. E. H. Kim, J. Hahn, H. Kim, and B. Lee, “Profilometry without phase unwrapping using multifrequency and four-step phase-shift sinusoidal fringe projection,” Opt. Express 17, 7818–7830 (2009).
    [CrossRef]
  18. A. Z. A. Abid, “Fringe pattern analysis using wavelet transforms,” Ph.D. dissertation (Liverpool John Moores University, 2008).
  19. M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform,” Opt. Commun. 266, 482–489 (2006).
    [CrossRef]
  20. L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
    [CrossRef]
  21. Y.-F. Li, “Image denoising based on undecimated discrete wavelet transform,” in 2007 International Conference on Wavelet Analysis and Pattern Recognition (IEEE, 2007), pp. 527–531.
  22. C. Stein, “Estimation of the mean of a multivariate normal distribution,” Ann. Stat. 9, 1135–1151 (1981).
    [CrossRef]
  23. D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Am. Stat. Assoc. 90, 1200–1224 (1995).
    [CrossRef]
  24. D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika 81, 425–455 (1994).
    [CrossRef]
  25. D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, and D. Picard, “Wavelet shrinkage: asymptopia?” J. R. Stat. Soc. Ser. B 57, 301–369 (1995).
  26. D. L. Donoho and I. M. Johnstone, “Minimax estimation via wavelet shrinkage,” Ann. Stat. 26, 879–921 (1998).
    [CrossRef]
  27. H. Guo, “Theory and application of the shift invariant, time varying, and undecimated wavelet transform,” Master’s thesis (Rice University, 1995).
  28. D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995).
    [CrossRef]
  29. C. J. Tay, C. Quan, W. Sun, and X. Y. He, “Demodulation of a single interferogram based on continuous wavelet transform and phase derivative,” Opt. Commun. 280, 327–336 (2007).
    [CrossRef]
  30. M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
    [CrossRef]
  31. M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Spatial carrier fringe pattern demodulation using a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006).
    [CrossRef]
  32. H. Niu, C. Quan, and C. J. Tay, “Phase retrieval of speckle fringe pattern with carriers using 2D wavelet transform,” Opt. Laser Eng. 47, 1334–1339 (2009).
    [CrossRef]
  33. Q. Zhang, W. Chen, and Y. Tang, “Method of choosing the adaptive level of discrete wavelet decomposition to eliminate zero component,” Opt. Commun. 282, 778–785 (2009).
    [CrossRef]
  34. H. Liu, A. N. Cartwright, and C. Basaran, “Moiré interferogram phase extraction: a ridge detection algorithm for continuous wavelet transforms,” Appl. Opt. 43, 850–857 (2004).
    [CrossRef]
  35. E. M. Barj, M. Afifi, A. Idrissi, S. Rachafi, and K. Nassim, “Wavelet phase evaluation extended to digital speckle pattern interferometry,” Moroccan J. Cond. Matter 5, 163–167 (2004).
  36. D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. 11, 107–117 (1994).
    [CrossRef]
  37. Y. Lu, X. Wang, and X. Zhang, “Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map,” Optik 118, 62–66 (2007).
    [CrossRef]

2010 (1)

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[CrossRef]

2009 (5)

E. H. Kim, J. Hahn, H. Kim, and B. Lee, “Profilometry without phase unwrapping using multifrequency and four-step phase-shift sinusoidal fringe projection,” Opt. Express 17, 7818–7830 (2009).
[CrossRef]

D. C. Méndez, S. C. Méndez, A. L. Quezada, H. Rudolph, and M. Lehman, “Face recognition system using fringe projection and moiré: characterization with fractal parameters,” Int. J. Comput. Sci. Network Secur. 9, 78–84 (2009).

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

H. Niu, C. Quan, and C. J. Tay, “Phase retrieval of speckle fringe pattern with carriers using 2D wavelet transform,” Opt. Laser Eng. 47, 1334–1339 (2009).
[CrossRef]

Q. Zhang, W. Chen, and Y. Tang, “Method of choosing the adaptive level of discrete wavelet decomposition to eliminate zero component,” Opt. Commun. 282, 778–785 (2009).
[CrossRef]

2008 (1)

A. Hayasaka, T. Shibahara, K. Ito, T. Aoki, H. Nakajima, and K. Kobayashi, “A passive 3D face recognition system and its performance evaluation,” IEICE Transactions on Fundamentals E91-A, 1974–1981 (2008).
[CrossRef]

2007 (3)

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

C. J. Tay, C. Quan, W. Sun, and X. Y. He, “Demodulation of a single interferogram based on continuous wavelet transform and phase derivative,” Opt. Commun. 280, 327–336 (2007).
[CrossRef]

Y. Lu, X. Wang, and X. Zhang, “Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map,” Optik 118, 62–66 (2007).
[CrossRef]

2006 (4)

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Spatial carrier fringe pattern demodulation using a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006).
[CrossRef]

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
[CrossRef]

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform,” Opt. Commun. 266, 482–489 (2006).
[CrossRef]

2005 (1)

2004 (3)

2000 (1)

W. S. Lee and N. M. Thalmann, “Fast head modeling for animation,” Image Vis. Comput. 18, 355–364 (2000).
[CrossRef]

1999 (1)

P. S. Huang, F. Jin, and F. P Chiang, “Quantitative evaluation of corrosion by a digital fringe projection technique,” Opt. Lasers Eng. 31, 371–380 (1999).
[CrossRef]

1998 (1)

D. L. Donoho and I. M. Johnstone, “Minimax estimation via wavelet shrinkage,” Ann. Stat. 26, 879–921 (1998).
[CrossRef]

1996 (1)

H. H. S. Ip and L. Yin, “Constructing a 3D individualized head model from two orthogonal views,” Vis. Comput. 12, 254–266 (1996).
[CrossRef]

1995 (3)

D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, and D. Picard, “Wavelet shrinkage: asymptopia?” J. R. Stat. Soc. Ser. B 57, 301–369 (1995).

D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Am. Stat. Assoc. 90, 1200–1224 (1995).
[CrossRef]

D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995).
[CrossRef]

1994 (2)

D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. 11, 107–117 (1994).
[CrossRef]

D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika 81, 425–455 (1994).
[CrossRef]

1982 (1)

1981 (1)

C. Stein, “Estimation of the mean of a multivariate normal distribution,” Ann. Stat. 9, 1135–1151 (1981).
[CrossRef]

Abid, A.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

Abid, A. Z. A.

A. Z. A. Abid, “Fringe pattern analysis using wavelet transforms,” Ph.D. dissertation (Liverpool John Moores University, 2008).

Afifi, M.

E. M. Barj, M. Afifi, A. Idrissi, S. Rachafi, and K. Nassim, “Wavelet phase evaluation extended to digital speckle pattern interferometry,” Moroccan J. Cond. Matter 5, 163–167 (2004).

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, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Aoki, T.

A. Hayasaka, T. Shibahara, K. Ito, T. Aoki, H. Nakajima, and K. Kobayashi, “A passive 3D face recognition system and its performance evaluation,” IEICE Transactions on Fundamentals E91-A, 1974–1981 (2008).
[CrossRef]

Asundi, A. K.

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[CrossRef]

Barj, E. M.

E. M. Barj, M. Afifi, A. Idrissi, S. Rachafi, and K. Nassim, “Wavelet phase evaluation extended to digital speckle pattern interferometry,” Moroccan J. Cond. Matter 5, 163–167 (2004).

Basaran, C.

Baurecht, H.

L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
[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, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Biemer, E.

L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
[CrossRef]

Brockmann, G.

L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
[CrossRef]

Burton, D. R.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Spatial carrier fringe pattern demodulation using a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006).
[CrossRef]

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform,” Opt. Commun. 266, 482–489 (2006).
[CrossRef]

Cartwright, A. N.

Chen, L.

Chen, W.

Q. Zhang, W. Chen, and Y. Tang, “Method of choosing the adaptive level of discrete wavelet decomposition to eliminate zero component,” Opt. Commun. 282, 778–785 (2009).
[CrossRef]

Chiang, F. P

P. S. Huang, F. Jin, and F. P Chiang, “Quantitative evaluation of corrosion by a digital fringe projection technique,” Opt. Lasers Eng. 31, 371–380 (1999).
[CrossRef]

Da, F.

Y. Sui and F. Da, “Stereo vision based 3D reconstruction algorithm of human face,” in 2009 Chinese Conference on Pattern Recognition (IEEE, 2009), 196–200.

Donoho, D. L.

D. L. Donoho and I. M. Johnstone, “Minimax estimation via wavelet shrinkage,” Ann. Stat. 26, 879–921 (1998).
[CrossRef]

D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, and D. Picard, “Wavelet shrinkage: asymptopia?” J. R. Stat. Soc. Ser. B 57, 301–369 (1995).

D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Am. Stat. Assoc. 90, 1200–1224 (1995).
[CrossRef]

D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995).
[CrossRef]

D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika 81, 425–455 (1994).
[CrossRef]

Gdeisat, M. A.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Spatial carrier fringe pattern demodulation using a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006).
[CrossRef]

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform,” Opt. Commun. 266, 482–489 (2006).
[CrossRef]

Ghiglia, D. C.

D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. 11, 107–117 (1994).
[CrossRef]

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, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Gühring, M.

L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
[CrossRef]

Guo, H.

H. Guo, “Theory and application of the shift invariant, time varying, and undecimated wavelet transform,” Master’s thesis (Rice University, 1995).

Hahn, J.

Hayasaka, A.

A. Hayasaka, T. Shibahara, K. Ito, T. Aoki, H. Nakajima, and K. Kobayashi, “A passive 3D face recognition system and its performance evaluation,” IEICE Transactions on Fundamentals E91-A, 1974–1981 (2008).
[CrossRef]

He, X. Y.

C. J. Tay, C. Quan, W. Sun, and X. Y. He, “Demodulation of a single interferogram based on continuous wavelet transform and phase derivative,” Opt. Commun. 280, 327–336 (2007).
[CrossRef]

Huang, L.

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[CrossRef]

Huang, P. S.

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

P. S. Huang, F. Jin, and F. P Chiang, “Quantitative evaluation of corrosion by a digital fringe projection technique,” Opt. Lasers Eng. 31, 371–380 (1999).
[CrossRef]

Idrissi, A.

E. M. Barj, M. Afifi, A. Idrissi, S. Rachafi, and K. Nassim, “Wavelet phase evaluation extended to digital speckle pattern interferometry,” Moroccan J. Cond. Matter 5, 163–167 (2004).

Ina, H.

Ip, H. H. S.

H. H. S. Ip and L. Yin, “Constructing a 3D individualized head model from two orthogonal views,” Vis. Comput. 12, 254–266 (1996).
[CrossRef]

Ito, K.

A. Hayasaka, T. Shibahara, K. Ito, T. Aoki, H. Nakajima, and K. Kobayashi, “A passive 3D face recognition system and its performance evaluation,” IEICE Transactions on Fundamentals E91-A, 1974–1981 (2008).
[CrossRef]

Jin, F.

P. S. Huang, F. Jin, and F. P Chiang, “Quantitative evaluation of corrosion by a digital fringe projection technique,” Opt. Lasers Eng. 31, 371–380 (1999).
[CrossRef]

Johnstone, I. M.

D. L. Donoho and I. M. Johnstone, “Minimax estimation via wavelet shrinkage,” Ann. Stat. 26, 879–921 (1998).
[CrossRef]

D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, and D. Picard, “Wavelet shrinkage: asymptopia?” J. R. Stat. Soc. Ser. B 57, 301–369 (1995).

D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Am. Stat. Assoc. 90, 1200–1224 (1995).
[CrossRef]

D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika 81, 425–455 (1994).
[CrossRef]

Kemao, Q.

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[CrossRef]

Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
[CrossRef]

Kerkyacharian, G.

D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, and D. Picard, “Wavelet shrinkage: asymptopia?” J. R. Stat. Soc. Ser. B 57, 301–369 (1995).

Kim, E. H.

Kim, H.

Kobayashi, K.

A. Hayasaka, T. Shibahara, K. Ito, T. Aoki, H. Nakajima, and K. Kobayashi, “A passive 3D face recognition system and its performance evaluation,” IEICE Transactions on Fundamentals E91-A, 1974–1981 (2008).
[CrossRef]

Kobayashi, S.

Kovacs, L.

L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
[CrossRef]

Lai, S. H.

S. F. Wang and S. H. Lai, “Efficient 3D face reconstruction from a single 2D image by combining statistical and geometrical information,” in Computer Vision: ACCV 2006, Part II, P. J. Narayanan, S. K. Nayar, and H.-Y. Shum, eds. (Springer, 2006), 427–436 (2006).

Lalor, M. J.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Spatial carrier fringe pattern demodulation using a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006).
[CrossRef]

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform,” Opt. Commun. 266, 482–489 (2006).
[CrossRef]

Lee, B.

Lee, W. S.

W. S. Lee and N. M. Thalmann, “Fast head modeling for animation,” Image Vis. Comput. 18, 355–364 (2000).
[CrossRef]

Lehman, M.

D. C. Méndez, S. C. Méndez, A. L. Quezada, H. Rudolph, and M. Lehman, “Face recognition system using fringe projection and moiré: characterization with fractal parameters,” Int. J. Comput. Sci. Network Secur. 9, 78–84 (2009).

Li, H.

L. Wu, H. Li, N. Yu, and M. Li, “Accurate 3D facial synthesis for plastic surgery simulation,” in Advances in Multimedia Modeling, Part II, T.-J. Cham, J. Cai, C. Dorai, D. Rajan, T.-S. Chua, and L.-T. Chia, eds. (Springer, 2006), pp. 269–278.

Li, M.

L. Wu, H. Li, N. Yu, and M. Li, “Accurate 3D facial synthesis for plastic surgery simulation,” in Advances in Multimedia Modeling, Part II, T.-J. Cham, J. Cai, C. Dorai, D. Rajan, T.-S. Chua, and L.-T. Chia, eds. (Springer, 2006), pp. 269–278.

Li, Y.-F.

Y.-F. Li, “Image denoising based on undecimated discrete wavelet transform,” in 2007 International Conference on Wavelet Analysis and Pattern Recognition (IEEE, 2007), pp. 527–531.

Lilley, F.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

Liu, H.

Lu, Y.

Y. Lu, X. Wang, and X. Zhang, “Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map,” Optik 118, 62–66 (2007).
[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, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Méndez, D. C.

D. C. Méndez, S. C. Méndez, A. L. Quezada, H. Rudolph, and M. Lehman, “Face recognition system using fringe projection and moiré: characterization with fractal parameters,” Int. J. Comput. Sci. Network Secur. 9, 78–84 (2009).

Méndez, S. C.

D. C. Méndez, S. C. Méndez, A. L. Quezada, H. Rudolph, and M. Lehman, “Face recognition system using fringe projection and moiré: characterization with fractal parameters,” Int. J. Comput. Sci. Network Secur. 9, 78–84 (2009).

Moore, C.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

Nakajima, H.

A. Hayasaka, T. Shibahara, K. Ito, T. Aoki, H. Nakajima, and K. Kobayashi, “A passive 3D face recognition system and its performance evaluation,” IEICE Transactions on Fundamentals E91-A, 1974–1981 (2008).
[CrossRef]

Nassim, K.

E. M. Barj, M. Afifi, A. Idrissi, S. Rachafi, and K. Nassim, “Wavelet phase evaluation extended to digital speckle pattern interferometry,” Moroccan J. Cond. Matter 5, 163–167 (2004).

Niu, H.

H. Niu, C. Quan, and C. J. Tay, “Phase retrieval of speckle fringe pattern with carriers using 2D wavelet transform,” Opt. Laser Eng. 47, 1334–1339 (2009).
[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, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Pan, B.

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[CrossRef]

Papadopulos, N. A.

L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
[CrossRef]

Picard, D.

D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, and D. Picard, “Wavelet shrinkage: asymptopia?” J. R. Stat. Soc. Ser. B 57, 301–369 (1995).

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, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Quan, C.

H. Niu, C. Quan, and C. J. Tay, “Phase retrieval of speckle fringe pattern with carriers using 2D wavelet transform,” Opt. Laser Eng. 47, 1334–1339 (2009).
[CrossRef]

C. J. Tay, C. Quan, W. Sun, and X. Y. He, “Demodulation of a single interferogram based on continuous wavelet transform and phase derivative,” Opt. Commun. 280, 327–336 (2007).
[CrossRef]

C. J. Tay, C. Quan, and L. Chen, “Phase retrieval with a three-frame phase-shifting algorithm with an unknown phase shift,” Appl. Opt. 44, 1401–1409 (2005).
[CrossRef]

Qudeisat, M.

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

Quezada, A. L.

D. C. Méndez, S. C. Méndez, A. L. Quezada, H. Rudolph, and M. Lehman, “Face recognition system using fringe projection and moiré: characterization with fractal parameters,” Int. J. Comput. Sci. Network Secur. 9, 78–84 (2009).

Rachafi, S.

E. M. Barj, M. Afifi, A. Idrissi, S. Rachafi, and K. Nassim, “Wavelet phase evaluation extended to digital speckle pattern interferometry,” Moroccan J. Cond. Matter 5, 163–167 (2004).

Romero, L. A.

D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. 11, 107–117 (1994).
[CrossRef]

Rudolph, H.

D. C. Méndez, S. C. Méndez, A. L. Quezada, H. Rudolph, and M. Lehman, “Face recognition system using fringe projection and moiré: characterization with fractal parameters,” Int. J. Comput. Sci. Network Secur. 9, 78–84 (2009).

Sader, R.

L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
[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, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Schwenzer-Zimmerer, K.

L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
[CrossRef]

Shibahara, T.

A. Hayasaka, T. Shibahara, K. Ito, T. Aoki, H. Nakajima, and K. Kobayashi, “A passive 3D face recognition system and its performance evaluation,” IEICE Transactions on Fundamentals E91-A, 1974–1981 (2008).
[CrossRef]

Stein, C.

C. Stein, “Estimation of the mean of a multivariate normal distribution,” Ann. Stat. 9, 1135–1151 (1981).
[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, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Sui, Y.

Y. Sui and F. Da, “Stereo vision based 3D reconstruction algorithm of human face,” in 2009 Chinese Conference on Pattern Recognition (IEEE, 2009), 196–200.

Sun, W.

C. J. Tay, C. Quan, W. Sun, and X. Y. He, “Demodulation of a single interferogram based on continuous wavelet transform and phase derivative,” Opt. Commun. 280, 327–336 (2007).
[CrossRef]

Takeda, M.

Tang, Y.

Q. Zhang, W. Chen, and Y. Tang, “Method of choosing the adaptive level of discrete wavelet decomposition to eliminate zero component,” Opt. Commun. 282, 778–785 (2009).
[CrossRef]

Tay, C. J.

H. Niu, C. Quan, and C. J. Tay, “Phase retrieval of speckle fringe pattern with carriers using 2D wavelet transform,” Opt. Laser Eng. 47, 1334–1339 (2009).
[CrossRef]

C. J. Tay, C. Quan, W. Sun, and X. Y. He, “Demodulation of a single interferogram based on continuous wavelet transform and phase derivative,” Opt. Commun. 280, 327–336 (2007).
[CrossRef]

C. J. Tay, C. Quan, and L. Chen, “Phase retrieval with a three-frame phase-shifting algorithm with an unknown phase shift,” Appl. Opt. 44, 1401–1409 (2005).
[CrossRef]

Thalmann, N. M.

W. S. Lee and N. M. Thalmann, “Fast head modeling for animation,” Image Vis. Comput. 18, 355–364 (2000).
[CrossRef]

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, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits 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, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Wang, S. F.

S. F. Wang and S. H. Lai, “Efficient 3D face reconstruction from a single 2D image by combining statistical and geometrical information,” in Computer Vision: ACCV 2006, Part II, P. J. Narayanan, S. K. Nayar, and H.-Y. Shum, eds. (Springer, 2006), 427–436 (2006).

Wang, X.

Y. Lu, X. Wang, and X. Zhang, “Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map,” Optik 118, 62–66 (2007).
[CrossRef]

Wu, L.

L. Wu, H. Li, N. Yu, and M. Li, “Accurate 3D facial synthesis for plastic surgery simulation,” in Advances in Multimedia Modeling, Part II, T.-J. Cham, J. Cai, C. Dorai, D. Rajan, T.-S. Chua, and L.-T. Chia, eds. (Springer, 2006), pp. 269–278.

Yin, L.

H. H. S. Ip and L. Yin, “Constructing a 3D individualized head model from two orthogonal views,” Vis. Comput. 12, 254–266 (1996).
[CrossRef]

Yu, N.

L. Wu, H. Li, N. Yu, and M. Li, “Accurate 3D facial synthesis for plastic surgery simulation,” in Advances in Multimedia Modeling, Part II, T.-J. Cham, J. Cai, C. Dorai, D. Rajan, T.-S. Chua, and L.-T. Chia, eds. (Springer, 2006), pp. 269–278.

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, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

Zeilhofer, H. F.

L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
[CrossRef]

Zhang, Q.

Q. Zhang, W. Chen, and Y. Tang, “Method of choosing the adaptive level of discrete wavelet decomposition to eliminate zero component,” Opt. Commun. 282, 778–785 (2009).
[CrossRef]

Zhang, S.

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

S. Zhang, “High-resolution, real-time 3-D shape measurement,” Ph.D. dissertation (Stony Brook University, 2005).

Zhang, X.

Y. Lu, X. Wang, and X. Zhang, “Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map,” Optik 118, 62–66 (2007).
[CrossRef]

Zimmermann, A.

L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
[CrossRef]

Ann. Stat. (2)

C. Stein, “Estimation of the mean of a multivariate normal distribution,” Ann. Stat. 9, 1135–1151 (1981).
[CrossRef]

D. L. Donoho and I. M. Johnstone, “Minimax estimation via wavelet shrinkage,” Ann. Stat. 26, 879–921 (1998).
[CrossRef]

Appl. Opt. (4)

Biometrika (1)

D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika 81, 425–455 (1994).
[CrossRef]

IEEE Trans. Circuits Syst. Video Technol. (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, “3DTV: 3D time-varying scene capture technologies—a survey,” IEEE Trans. Circuits Syst. Video Technol. 17, 1568–1586 (2007).
[CrossRef]

IEEE Trans. Inf. Theory (1)

D. L. Donoho, “De-noising by soft-thresholding,” IEEE Trans. Inf. Theory 41, 613–627 (1995).
[CrossRef]

IEICE Transactions on Fundamentals (1)

A. Hayasaka, T. Shibahara, K. Ito, T. Aoki, H. Nakajima, and K. Kobayashi, “A passive 3D face recognition system and its performance evaluation,” IEICE Transactions on Fundamentals E91-A, 1974–1981 (2008).
[CrossRef]

Image Vis. Comput. (1)

W. S. Lee and N. M. Thalmann, “Fast head modeling for animation,” Image Vis. Comput. 18, 355–364 (2000).
[CrossRef]

Int. J. Comput. Sci. Network Secur. (1)

D. C. Méndez, S. C. Méndez, A. L. Quezada, H. Rudolph, and M. Lehman, “Face recognition system using fringe projection and moiré: characterization with fractal parameters,” Int. J. Comput. Sci. Network Secur. 9, 78–84 (2009).

J. Am. Stat. Assoc. (1)

D. L. Donoho and I. M. Johnstone, “Adapting to unknown smoothness via wavelet shrinkage,” J. Am. Stat. Assoc. 90, 1200–1224 (1995).
[CrossRef]

J. Opt. Soc. Am. (2)

D. C. Ghiglia and L. A. Romero, “Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods,” J. Opt. Soc. Am. 11, 107–117 (1994).
[CrossRef]

M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
[CrossRef]

J. Plast. Reconstr. Aesthet. Surg. (1)

L. Kovacs, A. Zimmermann, G. Brockmann, M. Gühring, H. Baurecht, N. A. Papadopulos, K. Schwenzer-Zimmerer, R. Sader, E. Biemer, and H. F. Zeilhofer, “Three-dimensional recording of the human face with a 3D laser scanner,” J. Plast. Reconstr. Aesthet. Surg. 59, 1193–1202 (2006).
[CrossRef]

J. R. Stat. Soc. Ser. B (1)

D. L. Donoho, I. M. Johnstone, G. Kerkyacharian, and D. Picard, “Wavelet shrinkage: asymptopia?” J. R. Stat. Soc. Ser. B 57, 301–369 (1995).

Moroccan J. Cond. Matter (1)

E. M. Barj, M. Afifi, A. Idrissi, S. Rachafi, and K. Nassim, “Wavelet phase evaluation extended to digital speckle pattern interferometry,” Moroccan J. Cond. Matter 5, 163–167 (2004).

Opt. Commun. (3)

Q. Zhang, W. Chen, and Y. Tang, “Method of choosing the adaptive level of discrete wavelet decomposition to eliminate zero component,” Opt. Commun. 282, 778–785 (2009).
[CrossRef]

C. J. Tay, C. Quan, W. Sun, and X. Y. He, “Demodulation of a single interferogram based on continuous wavelet transform and phase derivative,” Opt. Commun. 280, 327–336 (2007).
[CrossRef]

M. A. Gdeisat, D. R. Burton, and M. J. Lalor, “Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform,” Opt. Commun. 266, 482–489 (2006).
[CrossRef]

Opt. Eng. (1)

S. Zhang and P. S. Huang, “High-resolution, real-time three-dimensional shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

Opt. Express (1)

Opt. Laser Eng. (1)

H. Niu, C. Quan, and C. J. Tay, “Phase retrieval of speckle fringe pattern with carriers using 2D wavelet transform,” Opt. Laser Eng. 47, 1334–1339 (2009).
[CrossRef]

Opt. Lasers Eng. (3)

M. A. Gdeisat, A. Abid, D. R. Burton, M. J. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009).
[CrossRef]

L. Huang, Q. Kemao, B. Pan, and A. K. Asundi, “Comparison of Fourier transform, windowed Fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48, 141–148 (2010).
[CrossRef]

P. S. Huang, F. Jin, and F. P Chiang, “Quantitative evaluation of corrosion by a digital fringe projection technique,” Opt. Lasers Eng. 31, 371–380 (1999).
[CrossRef]

Optik (1)

Y. Lu, X. Wang, and X. Zhang, “Weighted least-squares phase unwrapping algorithm based on derivative variance correlation map,” Optik 118, 62–66 (2007).
[CrossRef]

Vis. Comput. (1)

H. H. S. Ip and L. Yin, “Constructing a 3D individualized head model from two orthogonal views,” Vis. Comput. 12, 254–266 (1996).
[CrossRef]

Other (8)

S. F. Wang and S. H. Lai, “Efficient 3D face reconstruction from a single 2D image by combining statistical and geometrical information,” in Computer Vision: ACCV 2006, Part II, P. J. Narayanan, S. K. Nayar, and H.-Y. Shum, eds. (Springer, 2006), 427–436 (2006).

L. Wu, H. Li, N. Yu, and M. Li, “Accurate 3D facial synthesis for plastic surgery simulation,” in Advances in Multimedia Modeling, Part II, T.-J. Cham, J. Cai, C. Dorai, D. Rajan, T.-S. Chua, and L.-T. Chia, eds. (Springer, 2006), pp. 269–278.

Y. Sui and F. Da, “Stereo vision based 3D reconstruction algorithm of human face,” in 2009 Chinese Conference on Pattern Recognition (IEEE, 2009), 196–200.

N. D’Apuzzo, “3D Laser Scanning Systems,” http://www.hometrica.ch/docs/laserscanning.pdf .

Y.-F. Li, “Image denoising based on undecimated discrete wavelet transform,” in 2007 International Conference on Wavelet Analysis and Pattern Recognition (IEEE, 2007), pp. 527–531.

S. Zhang, “High-resolution, real-time 3-D shape measurement,” Ph.D. dissertation (Stony Brook University, 2005).

A. Z. A. Abid, “Fringe pattern analysis using wavelet transforms,” Ph.D. dissertation (Liverpool John Moores University, 2008).

H. Guo, “Theory and application of the shift invariant, time varying, and undecimated wavelet transform,” Master’s thesis (Rice University, 1995).

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 (15)

Fig. 1.
Fig. 1.

Optical measurement setup.

Fig. 2.
Fig. 2.

Complex Morlet wavelet.

Fig. 3.
Fig. 3.

(a) Simulation fringe for a step shape; (b) version of (a) contaminated with 0.3 standard deviation Gaussian white noise; (c) denoised frame based on Fourier transform method; (d) denoised frame based on UWT method.

Fig. 4.
Fig. 4.

Comparison between cross sections of the step shape obtained based on Fourier and CWT+UWT methods.

Fig. 5.
Fig. 5.

Line projection on human face.

Fig. 6.
Fig. 6.

Graph of intensity versus pixel position for row 945, indicated by red line in Fig. 5.

Fig. 7.
Fig. 7.

(a) Modulus and (b) phase of wavelet transform on row 945.

Fig. 8.
Fig. 8.

(a) Wrapped phase value for row 945; (b) unwrapped phase value for row 945 based on UWT+CWT analysis.

Fig. 9.
Fig. 9.

(a) Wrapped phase value, (b) unwrapped phase value, and (c) 3D reconstruction of human face.

Fig. 10.
Fig. 10.

Noisy image of human face with Gaussian white noise.

Fig. 11.
Fig. 11.

Comparison of extracted phase between CWT analysis alone and CWT with UWT preprocessing.

Fig. 12.
Fig. 12.

Power spectrum of extracted unwrapped phase value of the human face based on (a) CWT and (b) UWT+CWT analysis.

Fig. 13.
Fig. 13.

Comparison of extracted unwrapped phase value from (a) CWT, (b) the original signal, (c) FTP, and (d) UWT+CWT.

Fig. 14.
Fig. 14.

Optical setup based on single-point laser scanning.

Fig. 15.
Fig. 15.

Comparison between cross-sectional measurements of human face based on UWT+CWT analysis and single-point laser scanning.

Equations (8)

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

TU=2logN,
TM={0,N32,0.3936+0.1829log2N,N>32.
I(x,y)=a(x,y)+b(x,y)cos(ϕ(x,y)),
+ψ(x)dx=0.
ψa,b(x)=1aψ(xba),
ψ(x)=1xfbexp(2πifcx)exp(x2fb),
W(a,b)=+ψ*(xba)g(x)dx,
φ(a,b)=tan1[ImW(a,b)ReW(a,b)],

Metrics