Abstract

In this paper novel approaches based on anisotropic coupled diffusion equations are presented to do filter and binarization for ESPI fringes. An advantageous characteristic associated with the proposed technique is that diffusion takes place mainly along the direction of the edge. Therefore, the proposed anisotropic coupled diffusion filter method can avoid blur of the fringe edge and protect the useful information of the fringe patterns. The anisotropic coupled diffusion binarization, which can repair the image boundary anisotropically, is able to avoid the redundant burr. More important, it can be directly applied to the noisy ESPI fringe patterns without much preprocessing, which is a significant advance in fringe analysis for ESPI. The effective of the proposed methods are tested by means of the computer-simulated and experimentally obtained fringe patterns, respectively.

© 2012 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  22. http://cgm.cs.mcgill.ca/~godfried/teaching/projects97/azar/skeleton.html .

2012 (3)

G. Rajshekhar and P. Rastogi, “Editorial, “Fringe analysis: Premise and perspectives,” Opt. Lasers Eng. 50(8), iii–x (2012).
[CrossRef]

C. Tang, L. Wang, H. Yan, and C. Li, “Comparison on performance of some representative and recent filtering methods in electronic speckle pattern interferometry,” Opt. Lasers Eng. 50(8), 1036–1051 (2012).
[CrossRef]

C. Tang, L. Wang, and H. Yan, “Overview of anisotropic filtering methods based on partial differential equations for electronic speckle pattern interferometry,” Appl. Opt. 51(20), 4916–4926 (2012).
[CrossRef] [PubMed]

2010 (2)

2009 (1)

2008 (1)

2006 (2)

C. Tang, F. Zhang, H. Yan, and Z. Chen, “Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations,” Opt. Commun. 260(1), 91–96 (2006).
[CrossRef]

C. Tang, F. Zhang, B. Li, and H. Yan, “Performance evaluation of partial differential equation models in electronic speckle pattern interferometry and the delta-mollification phase map method,” Appl. Opt. 45(28), 7392–7400 (2006).
[CrossRef] [PubMed]

2004 (1)

K. Genovese, L. Lamberti, and C. Pappalettere, “A comprehensive ESPI based system for combined measurement of shape and deformation of electronic components,” Opt. Lasers Eng. 42(5), 543–562 (2004).
[CrossRef]

2002 (1)

2001 (2)

Y. Chen, C. A. Z. Barcelos, and B. A. Mair, “Smoothing and edge detection by time-varying coupled nonlinear diffusion equations,” Comput. Vis. Image Underst. 82(2), 85–100 (2001).
[CrossRef]

P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC),” Opt. Eng. 40(8), 1613–1620 (2001).
[CrossRef]

1997 (1)

1996 (1)

A. Dávila, G. H. Kaufmann, and D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. 35(12), 3549–3554 (1996).
[CrossRef]

1994 (1)

B. Merriman, J. Bence, and S. Osher, “Motion of multiple junctions: A level set approach,” J. Comput. Phys. 112(2), 334–363 (1994).
[CrossRef]

1992 (2)

F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29(1), 182–193 (1992).
[CrossRef]

L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29(3), 845–866 (1992).
[CrossRef]

1990 (1)

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990).
[CrossRef]

1979 (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE T. Syst Man Cy. 9(1), 62–66 (1979).
[CrossRef]

Alvarez, L.

L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29(3), 845–866 (1992).
[CrossRef]

Barcelos, C. A. Z.

Y. Chen, C. A. Z. Barcelos, and B. A. Mair, “Smoothing and edge detection by time-varying coupled nonlinear diffusion equations,” Comput. Vis. Image Underst. 82(2), 85–100 (2001).
[CrossRef]

Bavigadda, V.

Bence, J.

B. Merriman, J. Bence, and S. Osher, “Motion of multiple junctions: A level set approach,” J. Comput. Phys. 112(2), 334–363 (1994).
[CrossRef]

Catté, F.

F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29(1), 182–193 (1992).
[CrossRef]

Chen, Y.

Y. Chen, C. A. Z. Barcelos, and B. A. Mair, “Smoothing and edge detection by time-varying coupled nonlinear diffusion equations,” Comput. Vis. Image Underst. 82(2), 85–100 (2001).
[CrossRef]

Chen, Z.

C. Tang, F. Zhang, H. Yan, and Z. Chen, “Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations,” Opt. Commun. 260(1), 91–96 (2006).
[CrossRef]

Coll, T.

F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29(1), 182–193 (1992).
[CrossRef]

Dai, Q.

Dávila, A.

A. Dávila, G. H. Kaufmann, and D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. 35(12), 3549–3554 (1996).
[CrossRef]

Gao, T.

Genovese, K.

K. Genovese, L. Lamberti, and C. Pappalettere, “A comprehensive ESPI based system for combined measurement of shape and deformation of electronic components,” Opt. Lasers Eng. 42(5), 543–562 (2004).
[CrossRef]

Goodson, K. E.

P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC),” Opt. Eng. 40(8), 1613–1620 (2001).
[CrossRef]

Han, L.

Jallapuram, R.

Ji, X.

Kaufmann, G. H.

A. Dávila, G. H. Kaufmann, and D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. 35(12), 3549–3554 (1996).
[CrossRef]

Kerr, D.

A. Dávila, G. H. Kaufmann, and D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. 35(12), 3549–3554 (1996).
[CrossRef]

Lamberti, L.

K. Genovese, L. Lamberti, and C. Pappalettere, “A comprehensive ESPI based system for combined measurement of shape and deformation of electronic components,” Opt. Lasers Eng. 42(5), 543–562 (2004).
[CrossRef]

Li, B.

Li, C.

C. Tang, L. Wang, H. Yan, and C. Li, “Comparison on performance of some representative and recent filtering methods in electronic speckle pattern interferometry,” Opt. Lasers Eng. 50(8), 1036–1051 (2012).
[CrossRef]

Lions, P.-L.

F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29(1), 182–193 (1992).
[CrossRef]

L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29(3), 845–866 (1992).
[CrossRef]

Liu, W.

Liu, X.

Mair, B. A.

Y. Chen, C. A. Z. Barcelos, and B. A. Mair, “Smoothing and edge detection by time-varying coupled nonlinear diffusion equations,” Comput. Vis. Image Underst. 82(2), 85–100 (2001).
[CrossRef]

Malik, J.

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990).
[CrossRef]

Marroquin, J. L.

Merriman, B.

B. Merriman, J. Bence, and S. Osher, “Motion of multiple junctions: A level set approach,” J. Comput. Phys. 112(2), 334–363 (1994).
[CrossRef]

Mihaylova, E.

Morel, J.-M.

L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29(3), 845–866 (1992).
[CrossRef]

F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29(1), 182–193 (1992).
[CrossRef]

Osher, S.

B. Merriman, J. Bence, and S. Osher, “Motion of multiple junctions: A level set approach,” J. Comput. Phys. 112(2), 334–363 (1994).
[CrossRef]

Otsu, N.

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE T. Syst Man Cy. 9(1), 62–66 (1979).
[CrossRef]

Pappalettere, C.

K. Genovese, L. Lamberti, and C. Pappalettere, “A comprehensive ESPI based system for combined measurement of shape and deformation of electronic components,” Opt. Lasers Eng. 42(5), 543–562 (2004).
[CrossRef]

Perona, P.

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990).
[CrossRef]

Qiu, Z.

Rajshekhar, G.

G. Rajshekhar and P. Rastogi, “Editorial, “Fringe analysis: Premise and perspectives,” Opt. Lasers Eng. 50(8), iii–x (2012).
[CrossRef]

Rastogi, P.

G. Rajshekhar and P. Rastogi, “Editorial, “Fringe analysis: Premise and perspectives,” Opt. Lasers Eng. 50(8), iii–x (2012).
[CrossRef]

Ren, H.

Ren, L.

Rodriguez-Vera, R.

Servin, M.

Sun, X.

Tang, C.

Tang, K.

Toal, V.

Wang, J.

Wang, L.

C. Tang, L. Wang, and H. Yan, “Overview of anisotropic filtering methods based on partial differential equations for electronic speckle pattern interferometry,” Appl. Opt. 51(20), 4916–4926 (2012).
[CrossRef] [PubMed]

C. Tang, L. Wang, H. Yan, and C. Li, “Comparison on performance of some representative and recent filtering methods in electronic speckle pattern interferometry,” Opt. Lasers Eng. 50(8), 1036–1051 (2012).
[CrossRef]

Wang, Y.

Wang, Z.

Yan, H.

C. Tang, L. Wang, H. Yan, and C. Li, “Comparison on performance of some representative and recent filtering methods in electronic speckle pattern interferometry,” Opt. Lasers Eng. 50(8), 1036–1051 (2012).
[CrossRef]

C. Tang, L. Wang, and H. Yan, “Overview of anisotropic filtering methods based on partial differential equations for electronic speckle pattern interferometry,” Appl. Opt. 51(20), 4916–4926 (2012).
[CrossRef] [PubMed]

C. Tang, F. Zhang, H. Yan, and Z. Chen, “Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations,” Opt. Commun. 260(1), 91–96 (2006).
[CrossRef]

C. Tang, F. Zhang, B. Li, and H. Yan, “Performance evaluation of partial differential equation models in electronic speckle pattern interferometry and the delta-mollification phase map method,” Appl. Opt. 45(28), 7392–7400 (2006).
[CrossRef] [PubMed]

Yu, Q.

Zhang, F.

Zhou, P.

P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC),” Opt. Eng. 40(8), 1613–1620 (2001).
[CrossRef]

Appl. Opt. (3)

Chin. Opt. Lett. (1)

Comput. Vis. Image Underst. (1)

Y. Chen, C. A. Z. Barcelos, and B. A. Mair, “Smoothing and edge detection by time-varying coupled nonlinear diffusion equations,” Comput. Vis. Image Underst. 82(2), 85–100 (2001).
[CrossRef]

IEEE T. Syst Man Cy. (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE T. Syst Man Cy. 9(1), 62–66 (1979).
[CrossRef]

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

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990).
[CrossRef]

J. Comput. Phys. (1)

B. Merriman, J. Bence, and S. Osher, “Motion of multiple junctions: A level set approach,” J. Comput. Phys. 112(2), 334–363 (1994).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

C. Tang, F. Zhang, H. Yan, and Z. Chen, “Denoising in electronic speckle pattern interferometry fringes by the filtering method based on partial differential equations,” Opt. Commun. 260(1), 91–96 (2006).
[CrossRef]

Opt. Eng. (2)

P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC),” Opt. Eng. 40(8), 1613–1620 (2001).
[CrossRef]

A. Dávila, G. H. Kaufmann, and D. Kerr, “Scale-space filter for smoothing electronic speckle pattern interferometry fringes,” Opt. Eng. 35(12), 3549–3554 (1996).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (3)

K. Genovese, L. Lamberti, and C. Pappalettere, “A comprehensive ESPI based system for combined measurement of shape and deformation of electronic components,” Opt. Lasers Eng. 42(5), 543–562 (2004).
[CrossRef]

G. Rajshekhar and P. Rastogi, “Editorial, “Fringe analysis: Premise and perspectives,” Opt. Lasers Eng. 50(8), iii–x (2012).
[CrossRef]

C. Tang, L. Wang, H. Yan, and C. Li, “Comparison on performance of some representative and recent filtering methods in electronic speckle pattern interferometry,” Opt. Lasers Eng. 50(8), 1036–1051 (2012).
[CrossRef]

Opt. Lett. (2)

SIAM J. Numer. Anal. (2)

F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29(1), 182–193 (1992).
[CrossRef]

L. Alvarez, P.-L. Lions, and J.-M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM J. Numer. Anal. 29(3), 845–866 (1992).
[CrossRef]

Other (2)

A. P. Witkin, “Scale-space filtering,” Proc. IJCAI, 1019–1021 (Karlsruhe, 1983).

http://cgm.cs.mcgill.ca/~godfried/teaching/projects97/azar/skeleton.html .

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Figures (4)

Fig. 1
Fig. 1

The computer-simulated fringe patterns and their filtered images. (a-1) Initial image with the speckle size of one pixel. (a-2) SAD filtered result of Fig. 1(a-1), (a-3) ACD filtered result of Fig. 1(a-1), (b-1) Initial image with the speckle size of two pixels. (b-2) SAD filtered result of Fig. 1 (b-1), (b-3) ACD filtered result of Fig. 1 (b-1).

Fig. 2
Fig. 2

An experimentally obtained fringe pattern and its filtered images. (a) Initial image. (b) SAD filtered result of Fig. 2(a), (c) ACD filtered result of Fig. 2(a).

Fig. 3
Fig. 3

Binarization results of Fig. 1 and their centerline images. (a) OTSU binarization result of Fig. 1(b-3). (b) MBO binarization result of Fig. 1(b-1). (c) ACD binarization result of Fig. 1(b-1). (d) Centerline of Fig. 3(a). (e) Centerline of Fig. 3(b). (f) Centerline of Fig. 3(c).

Fig. 4
Fig. 4

Binarization results of Fig. 2 and their centerline images. (a) OTSU binarization result of Fig. 2(c). (b) MBO binarization result of Fig. 2(a). (c) ACD binarization result of Fig. 2(a). (d) Centerline of Fig. 4(a). (e) Centerline of Fig. 4(b). (f) Centerline of Fig. 4(c).

Tables (3)

Tables Icon

Table 1 Parameters Used in Figs. 1 and 2

Tables Icon

Table 2 Performance Evaluation for Each Filtered Image Shown in Figs. 1 and 2

Tables Icon

Table 3 Parameters Used in Figs. 3 and 4

Equations (28)

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

u t =F[ u(x,y,t) ],u( x,y,0 )=I( x,y )
u t =div( c( | u | )u ),u( x,y,0 )=I( x,y )
c k ( s )= [ 1+ ( s/k ) 2 ] 1
u t =div( c( | G σ *u | )u ),u( x,y,0 )=I( x,y )
u t = 2 u D 2 u( u,u ) | u | 2 ,u( x,y,0 )=I( x,y )
u t =| u |div( u | u | ),u( x,y,0 )=I( x,y )
u t =c( | v | )| u |div( u | u | ),v= G σ u,u( x,y,0 )=I( x,y )
v t =a( t )div( v | v | )b( vu )
{ u t =c( | v | )[ α| u |div( u | u | )+β D 2 u( u,u ) | u | 2 ][ 1c( | v | ) ]( uI ),u(x,y,0)=I(x,y) v t =a( t )div( v | v | )b( vu ),v(x,y,0)=I(x,y)
( u t ) i,j n = u i,j n+1 u i,j n Δt
( u x ) i,j n = ( u i+1,j n u i1,j n ) /2
( u y ) i,j n = ( u i,j+1 n u i,j1 n ) /2
( 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 |= ( [ ( u x ) i,j n ] 2 + [ ( u y ) i,j n ] 2 ) 1 2
| u i,j n |div( u i,j n | u i,j n | )= [ ( u y ) i,j n ] 2 ( u xx ) i,j n 2 ( u x ) i,j n ( u y ) i,j n ( u xy ) i,j n + [ ( u x ) i,j n ] 2 ( u yy ) i,j n [ ( u x ) i,j n ] 2 + [ ( u y ) i,j n ] 2
D 2 u i,j n ( u i,j n , u i,j n ) | u i,j n | 2 = [ ( u x ) i,j n ] 2 ( u xx ) i,j n +2 ( u x ) i,j n ( u y ) i,j n ( u xy ) i,j n + [ ( u y ) i,j n ] 2 ( u yy ) i,j n [ ( u x ) i,j n ] 2 + [ ( u y ) i,j n ] 2
div( v i,j n | v i,j n | )= [ ( v y ) i,j n ] 2 ( v xx ) i,j n 2 ( v x ) i,j n ( v y ) i,j n ( v xy ) i,j n + [ ( v x ) i,j n ] 2 ( v yy ) i,j n ( [ ( v x ) i,j n ] 2 + [ ( v y ) i,j n ] 2 ) 3 2
{ u i,j n+1 = u i,j n +Δt{ ξ i,j n [ α| u i,j n |div( u i,j n | u i,j n | )+β D 2 u i,j n ( u i,j n , u i,j n ) | u i,j n | 2 ]( 1 ξ i,j n )( u i,j n I i,j ) } v i,j n+1 = v i,j n + a n div( v i,j n | v i,j n | )b( v i,j n u i,j n )
I( x,y )=P( x,y )+Q( x,y ) N m ( x,y )cosφ( x,y )+ N A ( x,y )
ϕ(x,y)=20π[ ( xM/2 M ) 2 + ( y N ) 2 ],x=1,2,,M,y=1,2,,N
s= 1 M×N k=1 M l=1 N σ k,l I k,l
σ k,l = 1 8 i=1 1 j=1 1 ( I ki,lj I k,l ) 2
u t = 2 u,u(x,y,0)= χ D ( x,y )
u={ 1ifu>T 0otherwise
u i,j n+1 = u i,j n +Δt( u i+1,j n + u i1,j n + u i,j+1 n + u i,j1 n 4 u i,j n )
{ u t =c( | v | )[ α| u |div( u | u | )+β D 2 u( u,u ) | u | 2 ][ 1c( | v | ) ]( uI ),u(x,y,0)= χ D ( x,y ) v t =a( t )div( v | v | )b( vu ),v(x,y,0)= χ D ( x,y )

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