Abstract

Fringe patterns produced by various optical interferometric techniques encode information such as shape, deformation, and refractive index. Noise affects further processing of the fringe patterns. Denoising is often needed before fringe pattern demodulation. Filtering along the fringe orientation is an effective option. Such filters include coherence enhancing diffusion, spin filtering with curve windows, second-order oriented partial-differential equations, and the regularized quadratic cost function for oriented fringe pattern filtering. These filters are analyzed to establish the relationships among them. Theoretical analysis shows that the four filters are largely equivalent to each other. Quantitative results are given on simulated fringe patterns to validate the theoretical analysis and to compare the performance of these filters.

© 2011 Optical Society of America

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References

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  1. Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D.W.Robinson and G.T.Reid, eds. (Institute of Physics1993).
  2. A. A. Shulev, I. R. Roussev, and V. Sainov, “New automatic FFT filtration technique for phase maps and its application in speckle interferometry,” Proc. SPIE 4933, 323–327 (2003).
    [CrossRef]
  3. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004).
    [CrossRef] [PubMed]
  4. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
    [CrossRef]
  5. G. H. Kaufmann and G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35, 9–14 (1996).
    [CrossRef]
  6. A. Federico and G. Kaufmann, “Comparative study of wavelet thresholding techniques for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
    [CrossRef]
  7. Q. Yu, X. Liu, and K. Andresen, “New spin filters for interferometric fringe patterns and grating patterns,” Appl. Opt. 33, 3705–3711 (1994).
    [CrossRef] [PubMed]
  8. Q. Yu, X. Sun, X. Liu, and Z. Qiu, “Spin filtering with curve windows for interferometric fringe patterns,” Appl. Opt. 41, 2650–2654 (2002).
    [CrossRef] [PubMed]
  9. Q. Yu, X. Sun, X. Liu, X. Ding, and Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
    [CrossRef]
  10. Q. Yu, X. Yang, S. Fu, X. Liu, and X. Sun, “An adaptive contoured window filter for interferometric synthetic aperture radar,” IEEE Geosci. Remote Sens. Lett. 4, 23–26 (2007).
    [CrossRef]
  11. C. Tang, L. Han, H. Ren, D. Zhou, Y. Chang, X. Wang, and X. Cui, “Second-order oriented partial-differential equations for denoising in electronic-speckle-pattern interferometry fringes,” Opt. Lett. 33, 2179–2181 (2008).
    [CrossRef] [PubMed]
  12. C. Tang, L. Han, H. Ren, T. Gao, Z. Wang, and K. Tang, “The oriented-couple partial differential equations for filtering in wrapped phase patterns,” Opt. Express 17, 5606–5617 (2009).
    [CrossRef] [PubMed]
  13. C. Tang, T. Gao, S. Yan, L. Wang, and J. Wu, “The oriented spatial filter masks for electronic speckle pattern interferometry phase patterns,” Opt. Express 18, 8942–8947 (2010).
    [CrossRef] [PubMed]
  14. J. Weickert, “Coherence-enhancing diffusion filtering,” Int. J. Comput. Vis. 31, 111–127 (1999).
    [CrossRef]
  15. H. Wang, Q. Kemao, W. Gao, S. H. Soon, and F. Lin, “Fringe pattern denoising using coherence enhancing diffusion,” Opt. Lett. 34, 1141–1143 (2009).
    [CrossRef] [PubMed]
  16. J. Villa, J. A. Quiroga, and I. Rosa, “Regularized quadratic cost function for oriented fringe-pattern filtering,” Opt. Lett. 34, 1741–1743 (2009).
    [CrossRef] [PubMed]
  17. J. Villa, R. Rodriguez-Vera, J. A. Quiroga, I. Rosa, and E. Gonzalez, “Anisotropic phase-map denoising using a regularized cost-function with complex-valued Markov-random-fields,” Opt. Lasers Eng. 48, 650–656 (2010).
    [CrossRef]
  18. H. Wang and Q. Kemao, “Coherence-enhancing diffusion and windowed Fourier filtering for fringe pattern denoising,” Proc. SPIE 7522, 752248 (2009).
    [CrossRef]
  19. H. Wang and Q. Kemao, “Coherence-enhancing diffusion and windowed Fourier filtering for fringe pattern denoising (II),” AIP Conf. Proc. 1236, 52–56 (2010).
    [CrossRef]
  20. X. Zhou, J. P. Baird, and J. F. Amold, “Fringe-orientation estimation by use of a Gaussian gradient filter and neighboring-direction averaging,” Appl. Opt. 38, 795–804 (1999).
    [CrossRef]
  21. X. Yang, Q. Yu, and S. Fu, “A combined technique for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66(2007).
    [CrossRef]
  22. K. G. Larkin, “Uniform estimation of orientation using local and nonlocal 2-D energy operators,” Opt. Express 13, 8097–8121 (2005).
    [CrossRef] [PubMed]
  23. X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286–292 (2007).
    [CrossRef]
  24. C. Tang, Z. Wang, L. Wang, J. Wu, T. Gao, and S. Yan, “Estimation of fringe orientation for optical fringe patterns with poor quality based on Fourier transform,” Appl. Opt. 49, 554–561 (2010).
    [CrossRef] [PubMed]
  25. J. Weickert and H. Scharr, “A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance,” J. Visual Commun. Image Represent. 13, 103–118 (2002).
    [CrossRef]
  26. Q. Yu, X. Yang, S. Fu, and X. Sun, “Two improved algorithms with which to obtain contoured windows for fringe patterns generated by electronic speckle-pattern interferometry,” Appl. Opt. 44, 7050–7054 (2005).
    [CrossRef] [PubMed]
  27. P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Machine Intell. 12, 629–639 (1990).
    [CrossRef]
  28. F. Catte, T. Coll, P. L. Lions, and J. M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
    [CrossRef]
  29. G. Aubert and K. Pierre, in Mathematical Problems in Image Processing (Springer, 2002).

2010

C. Tang, T. Gao, S. Yan, L. Wang, and J. Wu, “The oriented spatial filter masks for electronic speckle pattern interferometry phase patterns,” Opt. Express 18, 8942–8947 (2010).
[CrossRef] [PubMed]

J. Villa, R. Rodriguez-Vera, J. A. Quiroga, I. Rosa, and E. Gonzalez, “Anisotropic phase-map denoising using a regularized cost-function with complex-valued Markov-random-fields,” Opt. Lasers Eng. 48, 650–656 (2010).
[CrossRef]

H. Wang and Q. Kemao, “Coherence-enhancing diffusion and windowed Fourier filtering for fringe pattern denoising (II),” AIP Conf. Proc. 1236, 52–56 (2010).
[CrossRef]

C. Tang, Z. Wang, L. Wang, J. Wu, T. Gao, and S. Yan, “Estimation of fringe orientation for optical fringe patterns with poor quality based on Fourier transform,” Appl. Opt. 49, 554–561 (2010).
[CrossRef] [PubMed]

2009

2008

2007

Q. Yu, X. Yang, S. Fu, X. Liu, and X. Sun, “An adaptive contoured window filter for interferometric synthetic aperture radar,” IEEE Geosci. Remote Sens. Lett. 4, 23–26 (2007).
[CrossRef]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286–292 (2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “A combined technique for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66(2007).
[CrossRef]

2005

2004

2003

A. A. Shulev, I. R. Roussev, and V. Sainov, “New automatic FFT filtration technique for phase maps and its application in speckle interferometry,” Proc. SPIE 4933, 323–327 (2003).
[CrossRef]

Q. Yu, X. Sun, X. Liu, X. Ding, and Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

2002

Q. Yu, X. Sun, X. Liu, and Z. Qiu, “Spin filtering with curve windows for interferometric fringe patterns,” Appl. Opt. 41, 2650–2654 (2002).
[CrossRef] [PubMed]

J. Weickert and H. Scharr, “A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance,” J. Visual Commun. Image Represent. 13, 103–118 (2002).
[CrossRef]

2001

A. Federico and G. Kaufmann, “Comparative study of wavelet thresholding techniques for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
[CrossRef]

1999

1996

G. H. Kaufmann and G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35, 9–14 (1996).
[CrossRef]

1994

1992

F. Catte, T. Coll, P. L. Lions, and J. M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

1990

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Machine Intell. 12, 629–639 (1990).
[CrossRef]

Amold, J. F.

Andresen, K.

Aubert, G.

G. Aubert and K. Pierre, in Mathematical Problems in Image Processing (Springer, 2002).

Baird, J. P.

Catte, F.

F. Catte, T. Coll, P. L. Lions, and J. M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Chang, Y.

Coll, T.

F. Catte, T. Coll, P. L. Lions, and J. M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Cui, X.

Ding, X.

Q. Yu, X. Sun, X. Liu, X. Ding, and Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

Federico, A.

A. Federico and G. Kaufmann, “Comparative study of wavelet thresholding techniques for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
[CrossRef]

Fu, S.

Q. Yu, X. Yang, S. Fu, X. Liu, and X. Sun, “An adaptive contoured window filter for interferometric synthetic aperture radar,” IEEE Geosci. Remote Sens. Lett. 4, 23–26 (2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “A combined technique for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66(2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286–292 (2007).
[CrossRef]

Q. Yu, X. Yang, S. Fu, and X. Sun, “Two improved algorithms with which to obtain contoured windows for fringe patterns generated by electronic speckle-pattern interferometry,” Appl. Opt. 44, 7050–7054 (2005).
[CrossRef] [PubMed]

Galizzi, G. E.

G. H. Kaufmann and G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35, 9–14 (1996).
[CrossRef]

Gao, T.

Gao, W.

Gonzalez, E.

J. Villa, R. Rodriguez-Vera, J. A. Quiroga, I. Rosa, and E. Gonzalez, “Anisotropic phase-map denoising using a regularized cost-function with complex-valued Markov-random-fields,” Opt. Lasers Eng. 48, 650–656 (2010).
[CrossRef]

Han, L.

Kaufmann, G.

A. Federico and G. Kaufmann, “Comparative study of wavelet thresholding techniques for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
[CrossRef]

Kaufmann, G. H.

G. H. Kaufmann and G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35, 9–14 (1996).
[CrossRef]

Kemao, Q.

H. Wang and Q. Kemao, “Coherence-enhancing diffusion and windowed Fourier filtering for fringe pattern denoising (II),” AIP Conf. Proc. 1236, 52–56 (2010).
[CrossRef]

H. Wang and Q. Kemao, “Coherence-enhancing diffusion and windowed Fourier filtering for fringe pattern denoising,” Proc. SPIE 7522, 752248 (2009).
[CrossRef]

H. Wang, Q. Kemao, W. Gao, S. H. Soon, and F. Lin, “Fringe pattern denoising using coherence enhancing diffusion,” Opt. Lett. 34, 1141–1143 (2009).
[CrossRef] [PubMed]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
[CrossRef]

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

Larkin, K. G.

Lin, F.

Lions, P. L.

F. Catte, T. Coll, P. L. Lions, and J. M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Liu, X.

Q. Yu, X. Yang, S. Fu, X. Liu, and X. Sun, “An adaptive contoured window filter for interferometric synthetic aperture radar,” IEEE Geosci. Remote Sens. Lett. 4, 23–26 (2007).
[CrossRef]

Q. Yu, X. Sun, X. Liu, X. Ding, and Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

Q. Yu, X. Sun, X. Liu, and Z. Qiu, “Spin filtering with curve windows for interferometric fringe patterns,” Appl. Opt. 41, 2650–2654 (2002).
[CrossRef] [PubMed]

Q. Yu, X. Liu, and K. Andresen, “New spin filters for interferometric fringe patterns and grating patterns,” Appl. Opt. 33, 3705–3711 (1994).
[CrossRef] [PubMed]

Malik, J.

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Machine Intell. 12, 629–639 (1990).
[CrossRef]

Morel, J. M.

F. Catte, T. Coll, P. L. Lions, and J. M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Perona, P.

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Machine Intell. 12, 629–639 (1990).
[CrossRef]

Pierre, K.

G. Aubert and K. Pierre, in Mathematical Problems in Image Processing (Springer, 2002).

Qiu, Z.

Q. Yu, X. Sun, X. Liu, X. Ding, and Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

Q. Yu, X. Sun, X. Liu, and Z. Qiu, “Spin filtering with curve windows for interferometric fringe patterns,” Appl. Opt. 41, 2650–2654 (2002).
[CrossRef] [PubMed]

Quiroga, J. A.

J. Villa, R. Rodriguez-Vera, J. A. Quiroga, I. Rosa, and E. Gonzalez, “Anisotropic phase-map denoising using a regularized cost-function with complex-valued Markov-random-fields,” Opt. Lasers Eng. 48, 650–656 (2010).
[CrossRef]

J. Villa, J. A. Quiroga, and I. Rosa, “Regularized quadratic cost function for oriented fringe-pattern filtering,” Opt. Lett. 34, 1741–1743 (2009).
[CrossRef] [PubMed]

Ren, H.

Rodriguez-Vera, R.

J. Villa, R. Rodriguez-Vera, J. A. Quiroga, I. Rosa, and E. Gonzalez, “Anisotropic phase-map denoising using a regularized cost-function with complex-valued Markov-random-fields,” Opt. Lasers Eng. 48, 650–656 (2010).
[CrossRef]

Rosa, I.

J. Villa, R. Rodriguez-Vera, J. A. Quiroga, I. Rosa, and E. Gonzalez, “Anisotropic phase-map denoising using a regularized cost-function with complex-valued Markov-random-fields,” Opt. Lasers Eng. 48, 650–656 (2010).
[CrossRef]

J. Villa, J. A. Quiroga, and I. Rosa, “Regularized quadratic cost function for oriented fringe-pattern filtering,” Opt. Lett. 34, 1741–1743 (2009).
[CrossRef] [PubMed]

Roussev, I. R.

A. A. Shulev, I. R. Roussev, and V. Sainov, “New automatic FFT filtration technique for phase maps and its application in speckle interferometry,” Proc. SPIE 4933, 323–327 (2003).
[CrossRef]

Sainov, V.

A. A. Shulev, I. R. Roussev, and V. Sainov, “New automatic FFT filtration technique for phase maps and its application in speckle interferometry,” Proc. SPIE 4933, 323–327 (2003).
[CrossRef]

Scharr, H.

J. Weickert and H. Scharr, “A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance,” J. Visual Commun. Image Represent. 13, 103–118 (2002).
[CrossRef]

Shulev, A. A.

A. A. Shulev, I. R. Roussev, and V. Sainov, “New automatic FFT filtration technique for phase maps and its application in speckle interferometry,” Proc. SPIE 4933, 323–327 (2003).
[CrossRef]

Soon, S. H.

Sun, X.

Q. Yu, X. Yang, S. Fu, X. Liu, and X. Sun, “An adaptive contoured window filter for interferometric synthetic aperture radar,” IEEE Geosci. Remote Sens. Lett. 4, 23–26 (2007).
[CrossRef]

Q. Yu, X. Yang, S. Fu, and X. Sun, “Two improved algorithms with which to obtain contoured windows for fringe patterns generated by electronic speckle-pattern interferometry,” Appl. Opt. 44, 7050–7054 (2005).
[CrossRef] [PubMed]

Q. Yu, X. Sun, X. Liu, X. Ding, and Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

Q. Yu, X. Sun, X. Liu, and Z. Qiu, “Spin filtering with curve windows for interferometric fringe patterns,” Appl. Opt. 41, 2650–2654 (2002).
[CrossRef] [PubMed]

Tang, C.

Tang, K.

Villa, J.

J. Villa, R. Rodriguez-Vera, J. A. Quiroga, I. Rosa, and E. Gonzalez, “Anisotropic phase-map denoising using a regularized cost-function with complex-valued Markov-random-fields,” Opt. Lasers Eng. 48, 650–656 (2010).
[CrossRef]

J. Villa, J. A. Quiroga, and I. Rosa, “Regularized quadratic cost function for oriented fringe-pattern filtering,” Opt. Lett. 34, 1741–1743 (2009).
[CrossRef] [PubMed]

Wang, H.

H. Wang and Q. Kemao, “Coherence-enhancing diffusion and windowed Fourier filtering for fringe pattern denoising (II),” AIP Conf. Proc. 1236, 52–56 (2010).
[CrossRef]

H. Wang and Q. Kemao, “Coherence-enhancing diffusion and windowed Fourier filtering for fringe pattern denoising,” Proc. SPIE 7522, 752248 (2009).
[CrossRef]

H. Wang, Q. Kemao, W. Gao, S. H. Soon, and F. Lin, “Fringe pattern denoising using coherence enhancing diffusion,” Opt. Lett. 34, 1141–1143 (2009).
[CrossRef] [PubMed]

Wang, L.

Wang, X.

Wang, Z.

Weickert, J.

J. Weickert and H. Scharr, “A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance,” J. Visual Commun. Image Represent. 13, 103–118 (2002).
[CrossRef]

J. Weickert, “Coherence-enhancing diffusion filtering,” Int. J. Comput. Vis. 31, 111–127 (1999).
[CrossRef]

Wu, J.

Yan, S.

Yang, X.

X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286–292 (2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “A combined technique for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66(2007).
[CrossRef]

Q. Yu, X. Yang, S. Fu, X. Liu, and X. Sun, “An adaptive contoured window filter for interferometric synthetic aperture radar,” IEEE Geosci. Remote Sens. Lett. 4, 23–26 (2007).
[CrossRef]

Q. Yu, X. Yang, S. Fu, and X. Sun, “Two improved algorithms with which to obtain contoured windows for fringe patterns generated by electronic speckle-pattern interferometry,” Appl. Opt. 44, 7050–7054 (2005).
[CrossRef] [PubMed]

Yu, Q.

Q. Yu, X. Yang, S. Fu, X. Liu, and X. Sun, “An adaptive contoured window filter for interferometric synthetic aperture radar,” IEEE Geosci. Remote Sens. Lett. 4, 23–26 (2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “A combined technique for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66(2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286–292 (2007).
[CrossRef]

Q. Yu, X. Yang, S. Fu, and X. Sun, “Two improved algorithms with which to obtain contoured windows for fringe patterns generated by electronic speckle-pattern interferometry,” Appl. Opt. 44, 7050–7054 (2005).
[CrossRef] [PubMed]

Q. Yu, X. Sun, X. Liu, X. Ding, and Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

Q. Yu, X. Sun, X. Liu, and Z. Qiu, “Spin filtering with curve windows for interferometric fringe patterns,” Appl. Opt. 41, 2650–2654 (2002).
[CrossRef] [PubMed]

Q. Yu, X. Liu, and K. Andresen, “New spin filters for interferometric fringe patterns and grating patterns,” Appl. Opt. 33, 3705–3711 (1994).
[CrossRef] [PubMed]

Zhou, D.

Zhou, X.

AIP Conf. Proc.

H. Wang and Q. Kemao, “Coherence-enhancing diffusion and windowed Fourier filtering for fringe pattern denoising (II),” AIP Conf. Proc. 1236, 52–56 (2010).
[CrossRef]

Appl. Opt.

IEEE Geosci. Remote Sens. Lett.

Q. Yu, X. Yang, S. Fu, X. Liu, and X. Sun, “An adaptive contoured window filter for interferometric synthetic aperture radar,” IEEE Geosci. Remote Sens. Lett. 4, 23–26 (2007).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell.

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Machine Intell. 12, 629–639 (1990).
[CrossRef]

Int. J. Comput. Vis.

J. Weickert, “Coherence-enhancing diffusion filtering,” Int. J. Comput. Vis. 31, 111–127 (1999).
[CrossRef]

J. Visual Commun. Image Represent.

J. Weickert and H. Scharr, “A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance,” J. Visual Commun. Image Represent. 13, 103–118 (2002).
[CrossRef]

Opt. Commun.

X. Yang, Q. Yu, and S. Fu, “An algorithm for estimating both fringe orientation and fringe density,” Opt. Commun. 274, 286–292 (2007).
[CrossRef]

X. Yang, Q. Yu, and S. Fu, “A combined technique for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60–66(2007).
[CrossRef]

Opt. Eng.

Q. Yu, X. Sun, X. Liu, X. Ding, and Z. Qiu, “Removing speckle noise and extracting the skeletons from a single speckle fringe pattern by spin filtering with curved-surface windows,” Opt. Eng. 42, 68–74 (2003).
[CrossRef]

G. H. Kaufmann and G. E. Galizzi, “Speckle noise reduction in television holography fringes using wavelet thresholding,” Opt. Eng. 35, 9–14 (1996).
[CrossRef]

A. Federico and G. Kaufmann, “Comparative study of wavelet thresholding techniques for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

J. Villa, R. Rodriguez-Vera, J. A. Quiroga, I. Rosa, and E. Gonzalez, “Anisotropic phase-map denoising using a regularized cost-function with complex-valued Markov-random-fields,” Opt. Lasers Eng. 48, 650–656 (2010).
[CrossRef]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).
[CrossRef]

Opt. Lett.

Proc. SPIE

H. Wang and Q. Kemao, “Coherence-enhancing diffusion and windowed Fourier filtering for fringe pattern denoising,” Proc. SPIE 7522, 752248 (2009).
[CrossRef]

A. A. Shulev, I. R. Roussev, and V. Sainov, “New automatic FFT filtration technique for phase maps and its application in speckle interferometry,” Proc. SPIE 4933, 323–327 (2003).
[CrossRef]

SIAM J. Numer. Anal.

F. Catte, T. Coll, P. L. Lions, and J. M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29, 182–193 (1992).
[CrossRef]

Other

G. Aubert and K. Pierre, in Mathematical Problems in Image Processing (Springer, 2002).

Interferogram Analysis: Digital Fringe Pattern Measurement Techniques, D.W.Robinson and G.T.Reid, eds. (Institute of Physics1993).

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Figures (5)

Fig. 1
Fig. 1

CED denoising results. (a) Simulated fringe pattern. (b) Simulated noisy fringe pattern. (c) CED(0) result; (d) error map of (c). (e) CED(0.005) result; (f) error map of (e). (g) CED(adap) result; (h) error map of (g).

Fig. 2
Fig. 2

Involved pixels for denoising. (a) Involved pixels for SFCW(19); (b) weights of the pixels in (a). (c) Involved pixels for CED(0) after 50 iterations; (d) weights of the pixels in (c).

Fig. 3
Fig. 3

SFCW denoising results. (a) SFCW(19) result; (b) error map of (a). (c) SFCW(3) result; (d) error map of (c).

Fig. 4
Fig. 4

OPDE denoising results. (a) OPDE(0.0001) result; (b) error map of (a). (c) OPDE(0) result; (d) error map of (c).

Fig. 5
Fig. 5

RQCF denoising results. (a) RQCF(0.05) result; (b) error map of (a). (c) RQCF(0) result; (d) error map of (c).

Tables (1)

Tables Icon

Table 1 Fringe Pattern Denoising Results

Equations (40)

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f ( x , y ) = a ( x , y ) + b ( x , y ) cos [ φ ( x , y ) ] ,
θ ( x , y ) = arctan [ f x ( x , y ) / f y ( x , y ) ] [ π / 2 , π / 2 ] .
θ ( x , y ) = 1 2 arctan 2 { u = x ε x + ε v = y ε y + ε 2 f x σ ( u , v ) f y σ ( u , v ) , u = x ε x + ε v = y ε y + ε [ f y σ 2 ( u , v ) f x σ 2 ( u , v ) ] } [ π / 2 , π / 2 ] ,
f ( x , y ; t + 1 ) = f ( x , y ; t ) + β × f t ( x , y ; t ) , f ( x , y ; 0 ) = f 0 ( x , y ) ,
f t = · ( D f ) ,
J 0 ( f σ ) = f σ f σ T .
J ρ ( f σ ) = K ρ * [ J 0 ( f σ ) ] = [ K ρ * f x σ 2 K ρ * ( f x σ f y σ ) K ρ * ( f x σ f y σ ) K ρ * f y σ 2 ] [ j 11 j 12 j 12 j 22 ] ,
ω 1 = [ 2 j 12 ( j 22 j 11 + ( j 11 j 22 ) 2 + 4 j 12 2 ) 2 + 4 j 12 2 ( j 11 j 22 ) + ( j 11 j 22 ) 2 + 4 j 12 2 ( j 22 j 11 + ( j 11 j 22 ) 2 + 4 j 12 2 ) 2 + 4 j 12 2 ] T , ω 2 = [ ( j 11 j 22 ) + ( j 11 j 22 ) 2 + 4 j 12 2 ( j 22 j 11 + ( j 11 j 22 ) 2 + 4 j 12 2 ) 2 + 4 j 12 2 2 j 12 ( j 22 j 11 + ( j 11 j 22 ) 2 + 4 j 12 2 ) 2 + 4 j 12 2 ] T ,
μ 1 , 2 = ( j 11 + j 22 ) ± ( j 11 j 22 ) 2 + 4 j 12 2 2 .
D = [ ω 1 | ω 2 ] [ λ 1 0 0 λ 2 ] [ ω 1 T ω 2 T ] ,
D = λ 1 [ ( j 11 j 22 ) + ( j 11 j 22 ) 2 + 4 j 12 2 2 ( j 11 j 22 ) 2 + 4 j 12 2 j 12 ( j 11 j 22 ) 2 + 4 j 12 2 j 12 ( j 11 j 22 ) 2 + 4 j 12 2 ( j 11 j 22 ) + ( j 11 j 22 ) 2 + 4 j 12 2 2 ( j 11 j 22 ) 2 + 4 j 12 2 ] + λ 2 [ ( j 11 j 22 ) + ( j 11 j 22 ) 2 + 4 j 12 2 2 ( j 11 j 22 ) 2 + 4 j 12 2 j 12 ( j 11 j 22 ) 2 + 4 j 12 2 j 12 ( j 11 j 22 ) 2 + 4 j 12 2 ( j 11 j 22 ) + ( j 11 j 22 ) 2 + 4 j 12 2 2 ( j 11 j 22 ) 2 + 4 j 12 2 ] .
λ 1 = { α t N 0 max [ α , ( d thr ) / max ( d ) ] N 0 < t N ,
θ ( x , y ) = 1 2 arctan 2 [ 2 K ρ * f x σ f y σ , K ρ * ( f y σ 2 f x σ 2 ) ] .
θ ( x , y ) = 1 2 arctan 2 ( 2 j 12 , j 22 j 11 ) ,
D = λ 1 ( sin 2 θ sin θ cos θ sin θ cos θ cos 2 θ ) + λ 2 ( cos 2 θ sin θ cos θ sin θ cos θ sin 2 θ ) .
f t = λ 1 ( f x x sin 2 θ + f y y cos 2 θ 2 f x y sin θ cos θ ) + λ 2 ( f x x cos 2 θ + f y y sin 2 θ + 2 f x y sin θ cos θ ) + r ( f x , f y , θ , θ x , θ y ) ,
r ( f x , f y , θ , θ x , θ y ) = θ x ( λ 2 λ 1 ) ( f y cos 2 θ f x sin 2 θ ) + θ y ( λ 2 λ 1 ) ( f x cos 2 θ + f y sin 2 θ ) ,
x i + 1 = x i + cos θ i , y i + 1 = y i + sin θ i , x i 1 = x i cos θ i , y i 1 = y i sin θ i ,
f ( x + γ , y + η ) = ( 1 | η | ) { ( 1 | γ | ) f ( x , y ) + | γ | f [ x + sign ( γ ) , y ] } + | η | { ( 1 | γ | ) f [ x , y + sign ( η ) ] + | γ | f [ x + sign ( γ ) , y + sign ( η ) ] } ,
f ( x , y ; t + 1 ) = 1 3 [ f ( x 1 , y 1 ; t ) + f ( x , y ; t ) + f ( x + 1 , y + 1 ; t ) ] .
f ( t + 1 ) = f ( t ) + 1 3 ( f x x | cos θ | + f y y | sin θ | + 2 f x y | sin θ cos θ | ) ,
f x x ( x , y ) = f ( x + 1 , y ) + f ( x 1 , y ) 2 f ( x , y ) ,
f y y ( x , y ) = f ( x , y + 1 ) + f ( x , y 1 ) 2 f ( x , y ) ,
f x y ( x , y ) = 1 2 { [ f ( x + 1 , y + 1 ) f ( x , y + 1 ) ] [ f ( x + 1 , y ) f ( x , y ) ] + [ f ( x , y ) f ( x 1 , y ) ] [ f ( x , y 1 ) f ( x 1 , y 1 ) ] } .
f ( t + 1 ) = f ( t ) + 1 3 ( f x x | cos θ | + f y y | sin θ | 2 f x y | sin θ cos θ | ) ,
f x y ( x , y ) = 1 2 { [ f ( x + 1 , y ) f ( x , y ) ] [ f ( x + 1 , y 1 ) f ( x , y 1 ) ] + [ f ( x , y + 1 ) f ( x 1 , y + 1 ) ] [ f ( x , y ) f ( x 1 , y ) ] } .
f ( t + 1 ) = f ( t ) + 1 3 ( f x x | cos θ | + f y y | sin θ | + 2 f x y sin θ cos θ ) ,
f t = f x x | cos θ | + f y y | sin θ | + 2 f x y sin θ cos θ ,
f = cos [ ω ( sin θ 0 x cos θ 0 y ) ] ,
f t ( x , y ) = 2 f ( x , y ) ( cos θ 0 ( 1 | sin θ 0 | ) { cos [ ω ( sin θ 0 ) ] 1 } + | sin θ 0 | ( 1 cos θ 0 ) { cos [ ω ( cos θ 0 ) ] 1 } + | sin θ 0 | cos θ 0 { cos [ ω ( cos θ 0 | sin θ 0 | ) ] 1 } ) .
f t ( x , y ) = 2 f ( x , y ) ( ( cos 2 θ 0 | sin θ 0 | cos θ 0 ) { cos [ ω ( sin θ 0 ) ] 1 } + ( sin 2 θ 0 | sin θ 0 | cos θ 0 ) { cos [ ω ( cos θ 0 ) ] 1 } + | sin θ 0 | cos θ 0 { cos [ ω ( cos θ 0 | sin θ 0 | ) ] 1 } ) .
f T T = 1 | f | 2 ( f x 2 f y y + f y 2 f x x 2 f x f y f x y ) ,
f N N = 1 | f | 2 ( f x 2 f x x + f y 2 f y y + 2 f x f y f x y ) ,
N ( x , y ) = f ( x , y ) / | f ( x , y ) | , | T ( x , y ) | = 1 , T ( x , y ) N ( x , y ) ,
f T T = f x x cos 2 θ + f y y sin 2 θ + 2 f x y sin θ cos θ ,
f t = g ( | f | ) ( f x x cos 2 θ + f y y sin 2 θ + 2 f x y sin θ cos θ ) ,
U ( f m ) = μ m L ( f m f 0 m ) 2 + m , h , v L [ ( f m f h ) cos θ m + ( f m f v ) sin θ m ] 2 ,
f t ( x , y ) = μ [ f ( x , y ) f 0 ( x , y ) ] { [ f ( x , y ) f ( x 1 , y ) ] cos [ θ ( x , y ) ] + [ f ( x , y ) f ( x , y 1 ) ] sin [ θ ( x , y ) ] } { cos [ θ ( x , y ) ] + sin [ θ ( x , y ) ] } + { [ f ( x + 1 , y ) f ( x , y ) ] cos [ θ ( x + 1 , y ) ] + [ f ( x + 1 , y ) f ( x + 1 , y 1 ) ] sin [ θ ( x + 1 , y ) ] } cos [ θ ( x + 1 , y ) ] + { [ f ( x , y + 1 ) f ( x 1 , y + 1 ) ] cos [ θ ( x , y + 1 ) ] + [ f ( x , y + 1 ) f ( x , y ) ] sin [ θ ( x , y + 1 ) ] } sin [ θ ( x , y + 1 ) ] .
θ ( x , y ) = θ ( x + 1 , y ) = θ ( x , y + 1 ) ,
f t = f x x cos 2 θ + f y y sin 2 θ + 2 f x y sin θ cos θ + μ ( f 0 f ) ,

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