Abstract

Electronic speckle pattern interferometry is one of the methods measuring the displacement on object surfaces in which fringe patterns need to be evaluated. Noise is one of the key problems affecting further processing and reducing measurement quality. We propose an application of coherence-enhancing diffusion to fringe-pattern denoising. It smoothes a fringe pattern along directions both parallel and perpendicular to fringe orientation with suitable diffusion speeds to more effectively reduce noise and improve fringe-pattern quality. It is a generalized work of Tang et al.’s [Opt. Lett. 33, 2179 (2008) ] model that only smoothes a fringe pattern along fringe orientation. Since our model diffuses a fringe pattern with an additional direction, it is able to denoise low-density fringes as well as improve denoising effectiveness for high-density fringes. Theoretical analysis as well as simulation and experimental verifications are addressed.

© 2009 Optical Society of America

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References

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  1. R. Jones and C. Wykes (Cambridge U. Press, 1983).
  2. P. Perona and J. Malik, IEEE Trans. Pattern Anal. Mach. Intell. 12, 629 (1990).
    [CrossRef]
  3. F. Catte, T. Coll, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182 (1992).
  4. L. Alvarez, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 845 (1992).
  5. C. Tang, L. Han, H. Ren, D. Zhou, Y. Chang, X. Wang, and X. Cui, Opt. Lett. 33, 2179 (2008).
    [CrossRef] [PubMed]
  6. J. Weickert, Int. J. Comput. Vis. 31, 111 (1999).
    [CrossRef]
  7. J. Weickert, Computer Analysis of Images and Patterns, Lecture Notes in Comp. Science, V.Hlavac and R.Sara, eds. (Springer, 1995), p. 230.
  8. J. Weickert and H. Scharr, J. Visual Commun. Image Represent 13, 103 (2002).
    [CrossRef]

2008 (1)

2002 (1)

J. Weickert and H. Scharr, J. Visual Commun. Image Represent 13, 103 (2002).
[CrossRef]

1999 (1)

J. Weickert, Int. J. Comput. Vis. 31, 111 (1999).
[CrossRef]

1992 (2)

F. Catte, T. Coll, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182 (1992).

L. Alvarez, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 845 (1992).

1990 (1)

P. Perona and J. Malik, IEEE Trans. Pattern Anal. Mach. Intell. 12, 629 (1990).
[CrossRef]

Alvarez, L.

L. Alvarez, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 845 (1992).

Catte, F.

F. Catte, T. Coll, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182 (1992).

Chang, Y.

Coll, T.

F. Catte, T. Coll, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182 (1992).

Cui, X.

Han, L.

Jones, R.

R. Jones and C. Wykes (Cambridge U. Press, 1983).

Lions, P. L.

F. Catte, T. Coll, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182 (1992).

L. Alvarez, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 845 (1992).

Malik, J.

P. Perona and J. Malik, IEEE Trans. Pattern Anal. Mach. Intell. 12, 629 (1990).
[CrossRef]

Morel, J. M.

F. Catte, T. Coll, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182 (1992).

L. Alvarez, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 845 (1992).

Perona, P.

P. Perona and J. Malik, IEEE Trans. Pattern Anal. Mach. Intell. 12, 629 (1990).
[CrossRef]

Ren, H.

Scharr, H.

J. Weickert and H. Scharr, J. Visual Commun. Image Represent 13, 103 (2002).
[CrossRef]

Tang, C.

Wang, X.

Weickert, J.

J. Weickert and H. Scharr, J. Visual Commun. Image Represent 13, 103 (2002).
[CrossRef]

J. Weickert, Int. J. Comput. Vis. 31, 111 (1999).
[CrossRef]

J. Weickert, Computer Analysis of Images and Patterns, Lecture Notes in Comp. Science, V.Hlavac and R.Sara, eds. (Springer, 1995), p. 230.

Wykes, C.

R. Jones and C. Wykes (Cambridge U. Press, 1983).

Zhou, D.

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

P. Perona and J. Malik, IEEE Trans. Pattern Anal. Mach. Intell. 12, 629 (1990).
[CrossRef]

Int. J. Comput. Vis. (1)

J. Weickert, Int. J. Comput. Vis. 31, 111 (1999).
[CrossRef]

J. Visual Commun. Image Represent (1)

J. Weickert and H. Scharr, J. Visual Commun. Image Represent 13, 103 (2002).
[CrossRef]

Opt. Lett. (1)

SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. (2)

F. Catte, T. Coll, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 182 (1992).

L. Alvarez, P. L. Lions, and J. M. Morel, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 29, 845 (1992).

Other (2)

J. Weickert, Computer Analysis of Images and Patterns, Lecture Notes in Comp. Science, V.Hlavac and R.Sara, eds. (Springer, 1995), p. 230.

R. Jones and C. Wykes (Cambridge U. Press, 1983).

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Figures (4)

Fig. 1
Fig. 1

Distance map estimation.

Fig. 2
Fig. 2

Denoising results with a computer-simulated fringe pattern: (a) original image, (b) filtered image by model in Eq. (1), (c) distance map for model in Eq. (3), (d) filtered image by model in Eq. (3).

Fig. 3
Fig. 3

Plotting of the middle column of images 2b, 2d.

Fig. 4
Fig. 4

Denoising results with real fringe pattern: (a) original image, (b) filtered image by model in Eq. (1), (c) distance map for model in Eq. (3), (d) filtered image by model in Eq. (3).

Equations (11)

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u ( x , y , t ) t = g ( u ) ( u x x cos 2 θ + u y y sin 2 θ + 2 u x y sin θ cos θ ) , u ( x , y , 0 ) = u 0 ( x , y ) ,
θ i , j = 1 2 tan 1 k , l 2 u x ( k , l ) u y ( k , l ) k , l ( u x 2 ( k , l ) u y 2 ( k , l ) ) ,
u t = div ( D u ) , u ( 0 ) = u 0 ,
J ρ ( u σ ) = K ρ ( u σ u σ ) = ( 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 22 j 11 + ( 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 ) ,
μ 1 , 2 = ( ( j 11 + j 22 ) ± ( j 11 j 22 ) 2 + 4 j 12 2 ) 2 .
D ( J ρ ( u σ ) ) = ( ω 1 ω 2 ) ( λ 1 0 0 λ 2 ) ( ω 1 T ω 2 T ) .
J ρ = [ k , l u σ x 2 k , l u σ x u σ y k , l u σ x u σ y k , l u σ y 2 ] .
D = λ 2 ( cos 2 θ sin θ cos θ sin θ cos θ sin 2 θ ) .
u t = λ 2 ( x y ) ( cos 2 θ sin θ cos θ sin θ cos θ sin 2 θ ) ( u x u y ) = λ 2 ( cos 2 θ u x x + 2 sin θ cos θ u x y + sin 2 θ u y y ) ,
{ λ 1 = { α t N max ( α , ( d thr ) max ( d ) ) t > N } , λ 2 = 1 }

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