Abstract

A novel phase extraction method for single electronic speckle pattern interferometry (ESPI) fringes is proposed. The partial differential equations (PDEs) are used to extract the skeletons of the gray-scale fringe and to interpolate the whole-field phase values based on skeleton map. Firstly, the gradient vector field (GVF) of the initial fringe is adjusted by an anisotropic PDE. Secondly, the skeletons of the fringe are extracted combining the divergence property of the adjusted GVF. After assigning skeleton orders, the whole-field phase information is interpolated by the heat conduction equation. The validity of the proposed method is verified by computer-simulated and experimentally obtained poor-quality ESPI fringe patterns.

© 2015 Optical Society of America

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  1. V. Bavigadda, R. Jallapuram, E. Mihaylova, and V. Toal, “Electronic speckle-pattern interferometer using holographic optical elements for vibration measurements,” Opt. Lett. 35(19), 3273–3275 (2010).
    [Crossref] [PubMed]
  2. G. Pedrini, W. Osten, and M. E. Gusev, “High-speed digital holographic interferometry for vibration measurement,” Appl. Opt. 45(15), 3456–3462 (2006).
    [Crossref] [PubMed]
  3. C. Quan, C. J. Tay, F. Yang, and X. He, “Phase extraction from a single fringe pattern based on guidance of an extreme map,” Appl. Opt. 44(23), 4814–4821 (2005).
    [Crossref] [PubMed]
  4. L. Lam, S. W. Lee, and C. Y. Suen, “Thinning methodologies-a comprehensive survey,” IEEE Trans. Pattern Anal. Mach. Intell. 14(9), 869–885 (1992).
    [Crossref]
  5. C. Direkoglu, Feature extraction via heat flow analogy (Dissertation, University of Southampton, 2009).
  6. C. Tang, W. Lu, Y. Cai, L. Han, and G. Wang, “Nearly preprocessing-free method for skeletonization of gray-scale electronic speckle pattern interferometry fringe patterns via partial differential equations,” Opt. Lett. 33(2), 183–185 (2008).
    [Crossref] [PubMed]
  7. T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999).
    [Crossref] [PubMed]
  8. C. Tang, W. Lu, S. Chen, Z. Zhang, B. Li, W. Wang, and L. Han, “Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry,” Appl. Opt. 46(30), 7475–7484 (2007).
    [Crossref] [PubMed]
  9. G. Wang, Y. J. Li, and H. C. Zhou, “Application of the radial basis function interpolation to phase extraction from a single electronic speckle pattern interferometric fringe,” Appl. Opt. 50(19), 3110–3117 (2011).
    [Crossref] [PubMed]
  10. Y. Wang, X. Ji, and Q. Dai, “Fourth-order oriented partial-differential equations for noise removal of two-photon fluorescence images,” Opt. Lett. 35(17), 2943–2945 (2010).
    [Crossref] [PubMed]
  11. F. Zhang, Z. Xiao, J. Wu, L. Geng, H. Li, J. Xi, and J. Wang, “Anisotropic coupled diffusion filter and binarization for the electronic speckle pattern interferometry fringes,” Opt. Express 20(20), 21905–21916 (2012).
    [Crossref] [PubMed]
  12. J. H. Jang and K. S. Hong, “A pseudo-distance map for the segmentation-free skeletonization of gray-scale images,” IEEE International Conference on Computer Vision, 2, 18–23 (2001).
  13. Z. Yu and C. Bajaj, “A segmentation-free approach for skeletonization of gray-scale images via anisotropic vector diffusion,” IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1, 415–420 (2004).
  14. J. Zhou and J. Gu, “A model-based method for the computation of fingerprints’ orientation field,” IEEE Trans. Image Process. 13(6), 821–835 (2004).
    [Crossref] [PubMed]
  15. 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(4), 554–561 (2010).
    [Crossref] [PubMed]
  16. V. Espinosa-Duro, “Mathematical morphology approaches for fingerprint thinning,” International Carnahan Conference on Security Technology, 1, 43–45 (2002).

2012 (1)

2011 (1)

2010 (3)

2008 (1)

2007 (1)

2006 (1)

2005 (1)

2004 (1)

J. Zhou and J. Gu, “A model-based method for the computation of fingerprints’ orientation field,” IEEE Trans. Image Process. 13(6), 821–835 (2004).
[Crossref] [PubMed]

1999 (1)

T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999).
[Crossref] [PubMed]

1992 (1)

L. Lam, S. W. Lee, and C. Y. Suen, “Thinning methodologies-a comprehensive survey,” IEEE Trans. Pattern Anal. Mach. Intell. 14(9), 869–885 (1992).
[Crossref]

Bajaj, C.

Z. Yu and C. Bajaj, “A segmentation-free approach for skeletonization of gray-scale images via anisotropic vector diffusion,” IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1, 415–420 (2004).

Bavigadda, V.

Cai, Y.

Chen, S.

Dai, Q.

Gao, T.

Geng, L.

Gönner, C.

T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999).
[Crossref] [PubMed]

Gu, J.

J. Zhou and J. Gu, “A model-based method for the computation of fingerprints’ orientation field,” IEEE Trans. Image Process. 13(6), 821–835 (2004).
[Crossref] [PubMed]

Gusev, M. E.

Han, L.

He, X.

Hong, K. S.

J. H. Jang and K. S. Hong, “A pseudo-distance map for the segmentation-free skeletonization of gray-scale images,” IEEE International Conference on Computer Vision, 2, 18–23 (2001).

Jallapuram, R.

Jang, J. H.

J. H. Jang and K. S. Hong, “A pseudo-distance map for the segmentation-free skeletonization of gray-scale images,” IEEE International Conference on Computer Vision, 2, 18–23 (2001).

Ji, X.

Lam, L.

L. Lam, S. W. Lee, and C. Y. Suen, “Thinning methodologies-a comprehensive survey,” IEEE Trans. Pattern Anal. Mach. Intell. 14(9), 869–885 (1992).
[Crossref]

Lee, S. W.

L. Lam, S. W. Lee, and C. Y. Suen, “Thinning methodologies-a comprehensive survey,” IEEE Trans. Pattern Anal. Mach. Intell. 14(9), 869–885 (1992).
[Crossref]

Lehmann, T. M.

T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999).
[Crossref] [PubMed]

Li, B.

Li, H.

Li, Y. J.

Lu, W.

Mihaylova, E.

Osten, W.

Pedrini, G.

Quan, C.

Spitzer, K.

T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999).
[Crossref] [PubMed]

Suen, C. Y.

L. Lam, S. W. Lee, and C. Y. Suen, “Thinning methodologies-a comprehensive survey,” IEEE Trans. Pattern Anal. Mach. Intell. 14(9), 869–885 (1992).
[Crossref]

Tang, C.

Tay, C. J.

Toal, V.

Wang, G.

Wang, J.

Wang, L.

Wang, W.

Wang, Y.

Wang, Z.

Wu, J.

Xi, J.

Xiao, Z.

Yan, S.

Yang, F.

Yu, Z.

Z. Yu and C. Bajaj, “A segmentation-free approach for skeletonization of gray-scale images via anisotropic vector diffusion,” IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1, 415–420 (2004).

Zhang, F.

Zhang, Z.

Zhou, H. C.

Zhou, J.

J. Zhou and J. Gu, “A model-based method for the computation of fingerprints’ orientation field,” IEEE Trans. Image Process. 13(6), 821–835 (2004).
[Crossref] [PubMed]

Appl. Opt. (5)

IEEE Trans. Image Process. (1)

J. Zhou and J. Gu, “A model-based method for the computation of fingerprints’ orientation field,” IEEE Trans. Image Process. 13(6), 821–835 (2004).
[Crossref] [PubMed]

IEEE Trans. Med. Imaging (1)

T. M. Lehmann, C. Gönner, and K. Spitzer, “Survey: interpolation methods in medical image processing,” IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

L. Lam, S. W. Lee, and C. Y. Suen, “Thinning methodologies-a comprehensive survey,” IEEE Trans. Pattern Anal. Mach. Intell. 14(9), 869–885 (1992).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Other (4)

C. Direkoglu, Feature extraction via heat flow analogy (Dissertation, University of Southampton, 2009).

J. H. Jang and K. S. Hong, “A pseudo-distance map for the segmentation-free skeletonization of gray-scale images,” IEEE International Conference on Computer Vision, 2, 18–23 (2001).

Z. Yu and C. Bajaj, “A segmentation-free approach for skeletonization of gray-scale images via anisotropic vector diffusion,” IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1, 415–420 (2004).

V. Espinosa-Duro, “Mathematical morphology approaches for fingerprint thinning,” International Carnahan Conference on Security Technology, 1, 43–45 (2002).

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Figures (7)

Fig. 1
Fig. 1 The inner orthogonal coordinate system based on the features of fringe patterns.
Fig. 2
Fig. 2 Experimentally-obtained ESPI fringe pattern (which comes from Ref [6].) and its skeletons. (a) Initial image; (b) Black fringe skeletons of (a) in Ref [6]; (c) Superimposition of white fringe skeletons of (a) on to (a) in Ref [6]; (d) White fringe skeletons of (a) by our method; (e) Black fringe skeletons of (a) by our method; (f) Superimposition of the white and black fringe skeletons onto (a).
Fig. 3
Fig. 3 Order assignment and phase interpolation for an experimentally-obtained fringe pattern. (a) Order assigned image; (b) Gray-phase image of (a) by our method; (c) Gray-phase image of (a) by BP Neural Networks; (d) and (e) The three-dimensional phase graph of (b) and (c).
Fig. 4
Fig. 4 Order assignment and phase interpolation for a computer-simulated fringe pattern. (a) A simulated original speckle fringe image; (b) Order assigned image for the skeletons of (a); (c) Three-dimensional graph of real phase; (d) Pseudo-color image of real phase; (e) Pseudo-color phase image by our method; (f), (g) and (h) are the pseudo-color phase image by BP Neural Network interpolation method (which come from three network training with the same parameters, respectively).
Fig. 5
Fig. 5 Phase extraction results. (a) Initial ESPI fringe pattern (comes from Ref [9].); (b) Skeleton map of bright fringes from Ref [9]; (c) Skeleton map of bright fringes by our method; (d) Gray image of evaluated phase from Ref [9]. based on (b); (e) Gray image of evaluated phase obtained by our method based on (b); (f) Gray image of evaluated phase obtained by our method based on (c).
Fig. 6
Fig. 6 Order assignment and phase interpolation for computer-simulated dense and sparse fringes. (a-1) and (a-2) Initial images; (b-1) and (b-2) Order assignment for skeletons; (c-1) and (c-2) Three-dimensional phase graphs by our method.
Fig. 7
Fig. 7 skeleton extraction and phase interpolation for experimentally-obtained ESPI fringe pattern with poor quality. (a-1) and (a-2) The unloaded speckle pattern; (b-1) and (b-2) The loaded speckle pattern; (c-1) and (c-2) Fringe pattern with poor quality; (d-1) and (d-2) The skeleton images; (e-1) and (e-2) Gray-phase images by our method; (f-1) and (f-2) Three-dimensional phase graph.

Equations (21)

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F 0 (x,y)= u 0 (x,y) i + v 0 (x,y) j
{ u t = u ηη +C u ξξ u(x,y,0)= u 0 (x,y) v t = v ηη +C v ξξ v(x,y,0)= v 0 (x,y)
θ( x,y )= 1 2 arctan[ ( i,j )Α 2 u 0 ( i,j ) v 0 ( i,j ) ( i,j )Α ( u 0 2 ( i,j ) v 0 2 ( i,j ) ) ]
{ u ξξ = u yy cos 2 θ+ u xx sin 2 θ2 u xy sinθcosθ u ηη = u xx cos 2 θ+ u yy sin 2 θ+2 u xy sinθcosθ
F ( x,y )=u(x,y) i +v(x,y) j
A (x,y)= P(x,y) x + Q(x,y) y
φ(x,y)= F (x,y)= u(x,y) x + v(x,y) y
φ D (x,y)={ 1φ(x,y)>0 0φ(x,y)<0 , φ B (x,y)={ 0φ(x,y)>0 1φ(x,y)<0
t I p = 2 I p , I p (x,y,0)= I a (x,y)
I p ( x s , y s , t n )= I a ( x s , y s ),( x s , y s )S
( u t ) i,j n = u i,j n+1 u i,j n Δt
( u xx ) i,j n = u i+1,j n 2 u i,j n + u i1,j n
( u yy ) i,j n = u i,j+1 n 2 u i,j n + u i,j1 n
( u xy ) i,j n = ( u i+1,j+1 n u i1,j+1 n u i+1,j1 n + u i1,j1 n ) /4
{ u i,j n+1 = u i,j n +Δt[ ( u ηη ) i,j n +C ( u ξξ ) i,j n ] v i,j n+1 = v i,j n +Δt[ ( v ηη ) i,j n +C ( v ξξ ) i,j n ]
{ ( u ηη ) i,j n = ( u xx ) i,j n cos 2 ( θ i,j )+2 ( u xy ) i,j n cos( θ i,j )sin( θ i,j )+ ( u yy ) i,j n sin 2 ( θ i,j ) ( u ξξ ) i,j n = ( u yy ) i,j n cos 2 ( θ i,j )2 ( u xy ) i,j n cos( θ i,j )sin( θ i,j )+ ( u xx ) i,j n sin 2 ( θ i,j ) ( v ηη ) i,j n = ( v xx ) i,j n cos 2 ( θ i,j )+2 ( v xy ) i,j n cos( θ i,j )sin( θ i,j )+ ( v yy ) i,j n sin 2 ( θ i,j ) ( v ξξ ) i,j n = ( v yy ) i,j n cos 2 ( θ i,j )2 ( v xy ) i,j n cos( θ i,j )sin( θ i,j )+ ( v xx ) i,j n sin 2 ( θ i,j )
u i,0 n = u i,1 n , u i,N+1 n = u i,N n , v i,0 n = v i,1 n , v i,N+1 n = v i,N n ,i=1,2,,M
u 0,j n = u 1,j n , u M+1,j n = u M,j n , v 0,j n = v 1,j n , v M+1,j n = v M,j n ,j=1,2,,N
( I p ) i,j n+1 = ( I p ) i,j n +Δt( ( I p ) i+1,j n + ( I p ) i1,j n + ( I p ) i,j+1 n + ( I p ) i,j1 n 4 ( I p ) i,j n )
( I p ) i,0 n = ( I p ) i,1 n , ( I p ) i,N+1 n = ( I p ) i,N n ,i=1,2,,M
( I p ) 0,j n = ( I p ) 1,j n , ( I p ) M+1,j n = ( I p ) M,j n ,j=1,2,,N

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