Abstract

We present an effective way to solve the denoising problem of fringe patterns in optics interferometry. The proposed method is based on the topological analysis of an appropriate cost function. To overcome the blurring drawback of the linear diffusion approach, the linear diffusion coefficient at each edge is perturbed successively. The total variation of a discrete cost function can be taken as an indicator function to pick out the most suitable edges of pixels at which the diffusion coefficients are to be perturbed. Then, a filtered image can be obtained by using selected diffusion coefficients associated to the edges. We demonstrate the performance of the proposed method via application to numerically simulated and experimentally obtained fringe patterns.

© 2010 Optical Society of America

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2010 (3)

2009 (3)

D. Auroux and M. Masmoudi, J. Math. Imaging Vision 33, 122 (2009).
[CrossRef]

D. Auroux, Math. Comput. Model. 49, 2191 (2009).
[CrossRef]

W. J. Zhang and W. B. Zhang, in Fifth International Conference on Information Assurance and Security (IEEE, 2009).

2008 (4)

I. Larrabide, R. A. Feijóo, A. A. Novotny, and E. A. Taroco, Comput. Struct. 86, 1386 (2008).
[CrossRef]

K. M. Qian, H. X. Wang, and W. J. Gao, Appl. Opt. 47, 5408 (2008).
[CrossRef]

C. Tang, L. Han, H. W. Ren, D. J. Zhou, Y. M. Chang, X. H. Wang, and X. L. Cui, Opt. Lett. 33, 2179 (2008).
[CrossRef] [PubMed]

P. Gao, B. L. Yao, and J. H. Han, J. Mod. Opt. 55, 2233 (2008).
[CrossRef]

2007 (2)

2006 (1)

L. J. Belaid, M. Jaoua, M. Masmoudi, and L. Siala, C. R. Math 342, 313 (2006).
[CrossRef]

2005 (1)

S. Amstutz, I. Horchani, and M. Masmoudi, Control Cybern. 34, 81 (2005).

2003 (1)

B. Samet, C. R. Math 336, 1033 (2003).
[CrossRef]

1996 (1)

1985 (1)

1983 (1)

Amstutz, S.

S. Amstutz, I. Horchani, and M. Masmoudi, Control Cybern. 34, 81 (2005).

Auroux, D.

D. Auroux and M. Masmoudi, J. Math. Imaging Vision 33, 122 (2009).
[CrossRef]

D. Auroux, Math. Comput. Model. 49, 2191 (2009).
[CrossRef]

Belaid, L. J.

L. J. Belaid, M. Jaoua, M. Masmoudi, and L. Siala, C. R. Math 342, 313 (2006).
[CrossRef]

Chang, Y. M.

Cui, X. L.

Feijóo, R. A.

I. Larrabide, R. A. Feijóo, A. A. Novotny, and E. A. Taroco, Comput. Struct. 86, 1386 (2008).
[CrossRef]

Gao, P.

Gao, T.

Gao, W. J.

Gu, X. H.

Han, J. H.

P. Gao, B. L. Yao, and J. H. Han, J. Mod. Opt. 55, 2233 (2008).
[CrossRef]

Han, L.

Harder, I.

Horchani, I.

S. Amstutz, I. Horchani, and M. Masmoudi, Control Cybern. 34, 81 (2005).

Jaoua, M.

L. J. Belaid, M. Jaoua, M. Masmoudi, and L. Siala, C. R. Math 342, 313 (2006).
[CrossRef]

Larrabide, I.

I. Larrabide, R. A. Feijóo, A. A. Novotny, and E. A. Taroco, Comput. Struct. 86, 1386 (2008).
[CrossRef]

Macy, W. W.

Mantel, K.

Masmoudi, M.

D. Auroux and M. Masmoudi, J. Math. Imaging Vision 33, 122 (2009).
[CrossRef]

L. J. Belaid, M. Jaoua, M. Masmoudi, and L. Siala, C. R. Math 342, 313 (2006).
[CrossRef]

S. Amstutz, I. Horchani, and M. Masmoudi, Control Cybern. 34, 81 (2005).

Nercissian, V.

Novotny, A. A.

I. Larrabide, R. A. Feijóo, A. A. Novotny, and E. A. Taroco, Comput. Struct. 86, 1386 (2008).
[CrossRef]

Nugent, K. A.

Qian, K. M.

Ren, H. W.

Samet, B.

B. Samet, C. R. Math 336, 1033 (2003).
[CrossRef]

Seah, H. S.

Siala, L.

L. J. Belaid, M. Jaoua, M. Masmoudi, and L. Siala, C. R. Math 342, 313 (2006).
[CrossRef]

Surrel, Y.

Tang, C.

Taroco, E. A.

I. Larrabide, R. A. Feijóo, A. A. Novotny, and E. A. Taroco, Comput. Struct. 86, 1386 (2008).
[CrossRef]

Wang, H. X.

Wang, L. L.

Wang, W. P.

Wang, X. H.

Wu, J.

Yan, H. Q.

Yan, S.

Yao, B. L.

Zhang, W. B.

W. J. Zhang and W. B. Zhang, in Fifth International Conference on Information Assurance and Security (IEEE, 2009).

Zhang, W. J.

W. J. Zhang and W. B. Zhang, in Fifth International Conference on Information Assurance and Security (IEEE, 2009).

Zhou, D. J.

Appl. Opt. (6)

C. R. Math (2)

L. J. Belaid, M. Jaoua, M. Masmoudi, and L. Siala, C. R. Math 342, 313 (2006).
[CrossRef]

B. Samet, C. R. Math 336, 1033 (2003).
[CrossRef]

Comput. Struct. (1)

I. Larrabide, R. A. Feijóo, A. A. Novotny, and E. A. Taroco, Comput. Struct. 86, 1386 (2008).
[CrossRef]

Control Cybern. (1)

S. Amstutz, I. Horchani, and M. Masmoudi, Control Cybern. 34, 81 (2005).

J. Math. Imaging Vision (1)

D. Auroux and M. Masmoudi, J. Math. Imaging Vision 33, 122 (2009).
[CrossRef]

J. Mod. Opt. (1)

P. Gao, B. L. Yao, and J. H. Han, J. Mod. Opt. 55, 2233 (2008).
[CrossRef]

Math. Comput. Model. (1)

D. Auroux, Math. Comput. Model. 49, 2191 (2009).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Other (1)

W. J. Zhang and W. B. Zhang, in Fifth International Conference on Information Assurance and Security (IEEE, 2009).

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Figures (3)

Fig. 1
Fig. 1

(a) Pixel m neighborhood and diffusion coefficient k m , p . (b) Example of the index of the edges in computation.

Fig. 2
Fig. 2

(a) Simulated image with noise. (b) Result obtained using the proposed method. (c) Result obtained using the method of Tang et al. (six iterations). (d) Result obtained using the WFT method [6].

Fig. 3
Fig. 3

(a) Experimentally obtained fringe pattern. (b) Result obtained using the proposed method. (c) Best result obtained using the WFT method.

Equations (11)

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u m ( t 2 ) u m ( t 1 ) = p n m t 1 t 2 k m , p u m , p ( t ) d t .
u t m = u t 1 m + Δ t p n m k m , p u t 1 m , p ,
E ( u ) = 1 / 2 Ω ( v u ) 2 d Ω + μ Ω k | u | 2 d Ω ,
E d ( u t ) = 1 / 2 m ( v m u t m ) 2 + μ m p n m k m , p · u t m , p · u t m , p .
E d [ u t ( k ε l ) ] = E d [ u t ( k 0 ) ] + D T d ( k ε l ) ,
D T d ( k ε l ) D d [ u t ( k 0 ) ] , [ u t ( k ε l ) u t ( k 0 ) ] ,
D ( u ) = ( v u ) + 2 μ k 0 Δ u .
D T d ( k ε l ) [ v m 1 u t m 1 ( k 0 ) + 2 μ k 0 Δ u t m 1 ( k 0 ) ] [ u t m 1 ( k ε l ) u t m 1 ( k 0 ) ] + [ v m 2 u t m 2 ( k 0 ) + 2 μ k 0 Δ u t m 2 ( k 0 ) ] [ u t m 2 ( k ε l ) u t m 2 ( k 0 ) ] ,
k 1 l = { k ε if D T d ( k ε l ) U α , k 0 else ;
U α := { D T d ( k ε l ) : D T d ( k ε l ) < 0 and D T d ( k ε l ) is in the α % most negative values of D T d } .
f = 1 ( I 0 I ) 2 / I 0 2 ,

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