Abstract

Fringe orientation represents an important property of fringes. The estimation of orientation from a poor quality fringe image is still a challenging problem faced in this area. This paper introduces a new approach for estimating optical fringe orientation with a poor quality image. This approach is based on the power spectrum analysis of the Fourier transform. We evaluate the performance of this algorithm via application to a variety of test cases and comparison with the widely used gradient-based method and accumulate-differences method. The experimental results show that our method is capable of calculating fringe orientation robustly even when the quality of fringe images is considerably low because of high or low density, high noise, and low contrast. Under the same conditions, our accuracy is even better than that obtained with the gradient-based and accumulate-differences methods, especially for fringe images with poor quality.

© 2010 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. M. F. Augusteijn, L. E. Clemens, and K. A. Shaw, “Performance evaluation of texture measures for ground cover identification in satellite images by means of a neural network classifier,” IEEE Trans. Geosci. Remote Sensing 33, 616-626(1995).
    [CrossRef]
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    [CrossRef]
  13. A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, 1989).

2009 (1)

2008 (1)

2007 (4)

C. Tang, W. Wang, H. Yan, and X. Gu, “Tangent least-squares fitting filtering method for electrical speckle pattern interferometry phase fringe,” Appl. Opt. 46, 2907-2913 (2007).
[CrossRef] [PubMed]

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 method for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60-66(2007).
[CrossRef]

S. Chikkerur, A. N. Cartwright, and V. Govindaraju, “Fingerprint enhancement using STFT analysis,” Pattern Recogn. 40, 198-211 (2007).
[CrossRef]

2005 (1)

2002 (1)

2000 (1)

A. Dobroiu, A. Alexandrescu, D. Apostol, V. Nascov, and V. Damian, “Centering and profiling algorithm for processing Newton's rings fringe patterns,” Opt. Eng. 39, 3201-3206 (2000).
[CrossRef]

1999 (1)

1998 (1)

L. Hong, Y. Wan, and A. Jain, “Fingerprint image enhancement: algorithm and performance evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 777-789 (1998).
[CrossRef]

1995 (1)

M. F. Augusteijn, L. E. Clemens, and K. A. Shaw, “Performance evaluation of texture measures for ground cover identification in satellite images by means of a neural network classifier,” IEEE Trans. Geosci. Remote Sensing 33, 616-626(1995).
[CrossRef]

Alexandrescu, A.

A. Dobroiu, A. Alexandrescu, D. Apostol, V. Nascov, and V. Damian, “Centering and profiling algorithm for processing Newton's rings fringe patterns,” Opt. Eng. 39, 3201-3206 (2000).
[CrossRef]

Apostol, D.

A. Dobroiu, A. Alexandrescu, D. Apostol, V. Nascov, and V. Damian, “Centering and profiling algorithm for processing Newton's rings fringe patterns,” Opt. Eng. 39, 3201-3206 (2000).
[CrossRef]

Arnold, J. F.

Augusteijn, M. F.

M. F. Augusteijn, L. E. Clemens, and K. A. Shaw, “Performance evaluation of texture measures for ground cover identification in satellite images by means of a neural network classifier,” IEEE Trans. Geosci. Remote Sensing 33, 616-626(1995).
[CrossRef]

Baird, J. P.

Cartwright, A. N.

S. Chikkerur, A. N. Cartwright, and V. Govindaraju, “Fingerprint enhancement using STFT analysis,” Pattern Recogn. 40, 198-211 (2007).
[CrossRef]

Chang, Y.

Chikkerur, S.

S. Chikkerur, A. N. Cartwright, and V. Govindaraju, “Fingerprint enhancement using STFT analysis,” Pattern Recogn. 40, 198-211 (2007).
[CrossRef]

Clemens, L. E.

M. F. Augusteijn, L. E. Clemens, and K. A. Shaw, “Performance evaluation of texture measures for ground cover identification in satellite images by means of a neural network classifier,” IEEE Trans. Geosci. Remote Sensing 33, 616-626(1995).
[CrossRef]

Cui, X.

Damian, V.

A. Dobroiu, A. Alexandrescu, D. Apostol, V. Nascov, and V. Damian, “Centering and profiling algorithm for processing Newton's rings fringe patterns,” Opt. Eng. 39, 3201-3206 (2000).
[CrossRef]

de la Rosa, I.

Dobroiu, A.

A. Dobroiu, A. Alexandrescu, D. Apostol, V. Nascov, and V. Damian, “Centering and profiling algorithm for processing Newton's rings fringe patterns,” Opt. Eng. 39, 3201-3206 (2000).
[CrossRef]

Fu, S.

X. Yang, Q. Yu, and S. Fu, “A combined method 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]

Govindaraju, V.

S. Chikkerur, A. N. Cartwright, and V. Govindaraju, “Fingerprint enhancement using STFT analysis,” Pattern Recogn. 40, 198-211 (2007).
[CrossRef]

Gu, X.

Han, L.

Hong, L.

L. Hong, Y. Wan, and A. Jain, “Fingerprint image enhancement: algorithm and performance evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 777-789 (1998).
[CrossRef]

Jain, A.

L. Hong, Y. Wan, and A. Jain, “Fingerprint image enhancement: algorithm and performance evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 777-789 (1998).
[CrossRef]

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, 1989).

Larkin, K. G.

Liu, X.

Nascov, V.

A. Dobroiu, A. Alexandrescu, D. Apostol, V. Nascov, and V. Damian, “Centering and profiling algorithm for processing Newton's rings fringe patterns,” Opt. Eng. 39, 3201-3206 (2000).
[CrossRef]

Qiu, Z.

Quiroga, J. A.

Ren, H.

Shaw, K. A.

M. F. Augusteijn, L. E. Clemens, and K. A. Shaw, “Performance evaluation of texture measures for ground cover identification in satellite images by means of a neural network classifier,” IEEE Trans. Geosci. Remote Sensing 33, 616-626(1995).
[CrossRef]

Sun, X.

Tang, C.

Villa, J.

Wan, Y.

L. Hong, Y. Wan, and A. Jain, “Fingerprint image enhancement: algorithm and performance evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 777-789 (1998).
[CrossRef]

Wang, W.

Wang, X.

Yan, H.

Yang, X.

X. Yang, Q. Yu, and S. Fu, “A combined method 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]

Yu, Q.

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 method for obtaining fringe orientations of ESPI,” Opt. Commun. 273, 60-66(2007).
[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]

Zhou, D.

Zhou, X.

Appl. Opt. (3)

IEEE Trans. Geosci. Remote Sensing (1)

M. F. Augusteijn, L. E. Clemens, and K. A. Shaw, “Performance evaluation of texture measures for ground cover identification in satellite images by means of a neural network classifier,” IEEE Trans. Geosci. Remote Sensing 33, 616-626(1995).
[CrossRef]

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

L. Hong, Y. Wan, and A. Jain, “Fingerprint image enhancement: algorithm and performance evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 777-789 (1998).
[CrossRef]

Opt. Commun. (2)

X. Yang, Q. Yu, and S. Fu, “A combined method 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]

Opt. Eng. (1)

A. Dobroiu, A. Alexandrescu, D. Apostol, V. Nascov, and V. Damian, “Centering and profiling algorithm for processing Newton's rings fringe patterns,” Opt. Eng. 39, 3201-3206 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Pattern Recogn. (1)

S. Chikkerur, A. N. Cartwright, and V. Govindaraju, “Fingerprint enhancement using STFT analysis,” Pattern Recogn. 40, 198-211 (2007).
[CrossRef]

Other (1)

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, 1989).

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Figures (6)

Fig. 1
Fig. 1

Collection of the tested images: (a) computer-simulated dense and noisy interferogram based on Eq. (21), (b) experimentally obtained interferometric fringe image using a Michelson interferometer, (c) experimentally obtained original ESPI fringe, (d) another experimentally obtained original ESPI fringe.

Fig. 2
Fig. 2

Estimated orientation by the gradient-based method of (a) Fig. 1a, (b) Fig. 1b, (c) Fig. 1c, and (d) Fig. 1d.

Fig. 3
Fig. 3

Estimated orientation by the accumulate-differences method of (a) Fig. 1a, (b) Fig. 1b, (c) Fig. 1c, (d) Fig. 1d.

Fig. 4
Fig. 4

Estimated orientation by our proposed method of (a) Fig. 1a, (b) Fig. 1b, (c) Fig. 1c, (d) Fig. 1d.

Fig. 5
Fig. 5

Filtered images where the fringe orientation is calculated by the gradient-based method: (a) filtered image of Fig. 1c, (b) filtered image of Fig. 1d.

Fig. 6
Fig. 6

Filtered images where the fringe orientation is calculated by our method: (a) filtered image of Fig. 1c, (b) filtered image of Fig. 1d.

Tables (2)

Tables Icon

Table 1 Global Orientation Errors, θ Error, Corresponding to Various Fringe Spacings and Variance of Gaussian Noise

Tables Icon

Table 2 Computational Times Corresponding to Various Window Sizes

Equations (25)

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F ( ω k , ω l ) = 1 w × w k = 0 w 1 l = 0 w 1 f ( k , l ) e i 2 π ( ω k k / w + ω l l / w ) ,
F ( ω k , ω l ) = | F ( ω k , ω l ) | exp ( i ϕ ( ω k , ω l ) ) ,
| F ( ω k , ω l ) | = R 2 ( ω k , ω l ) + I 2 ( ω k , ω l )
ϕ ( ω k , ω l ) = tan 1 [ I R ]
E ( ω k , ω l ) = | F ( ω k , ω l ) | 2 = R 2 ( ω k , ω l ) + I 2 ( ω k , ω l ) .
E ( r m , θ n ) = E ( ω k , ω l ) ,
p ( r m , θ n ) = p ( ω k , ω l ) = E ( ω k , ω l ) E sum ,
E sum = m n E ( r m , θ n ) = k l E ( ω k , ω l ) .
p ( θ n ) = m p ( r m , θ n ) .
O ( i , j ) = 1 2 tan 1 ( n p ( θ n ) sin ( 2 θ k , l ) n p ( θ n ) cos ( 2 θ k , l ) ) .
O ( i , j ) = 1 2 tan 1 ( n m p ( r m , θ n ) sin ( 2 θ k , l ) n m p ( r m , θ n ) cos ( 2 θ k , l ) ) = 1 2 tan 1 ( k l E ( ω k , ω l ) E sum sin ( 2 θ k , l ) k l E ( ω k , ω l ) E sum cos ( 2 θ k , l ) ) = 1 2 tan 1 ( k l E ( ω k , ω l ) sin ( 2 θ k , l ) k l E ( ω k , ω l ) cos ( 2 θ k , l ) ) .
θ k , l = tan 1 ( k , l ) .
G ( x , y ) = { μ d + σ d 2 · ( f ( x , y ) μ ) 2 σ 2 if   f ( x , y ) > μ μ d σ d 2 · ( f ( x , y ) μ ) 2 σ 2 otherwise ,
F e n ( ω k , ω l ) = F ( ω k , ω l ) | F ( ω k , ω l ) | n ,
Φ x ' ( x , y ) = k = w 2 1 2 w 2 1 2 l = w 2 1 2 w 2 1 2 F ( k , l ) Φ x ( x + k , y + l )
Φ y ' ( x , y ) = k = w 2 1 2 w 2 1 2 l = w 2 1 2 w 2 1 2 F ( k , l ) Φ y ( x + k , y + l ) ,
O ( i , j ) = 1 2 tan 1 k l 2 f x ( k , l ) f y ( k , l ) k l ( f x 2 ( k , l ) f y 2 ( k , l ) ) .
O ( i , j ) = 1 2 tan 1 ( D 0 ° D 90 ° D 45 ° D 135 ° ) ,
D angle ( i , j ) = ( k , l ) w × w d angle ( k , l ) ( angle = 0 ° , 45 ° , 90 ° , 135 ° ) ,
d 0 ( k , l ) = | f ( k 1 , l ) f ( k + 1 , l ) × 2 | , d 45 ( k , l ) = | f ( k 1 , l + 1 ) f ( k + 1 , l 1 ) | d 90 ( k , l ) = | f ( k , l 1 ) f ( k , l + 1 ) × 2 | d 135 ( k , l ) = | f ( k 1 , l 1 ) f ( k + 1 , l + 1 ) | .
I ( x , y ) = A ( x , y ) + B ( x , y ) cos ϕ ( x , y ) + N ( x , y ) ,
ϕ ( x , y ) = 2 π x 2 + y 2 P .
θ error = 1 M × N x = 1 M y = 1 N | sin ( O ( x , y ) O T ( x , y ) ) | ,
u ( x , y , t ) t = u x x cos 2 θ + u y y sin 2 θ + 2 u x y sin θ cos θ ,
u i , j n + 1 = u i , j n + Δ t [ ( u x x ) i , j n cos 2 ( θ i , j ) + ( u y y ) i , j n sin 2 ( θ i , j ) + 2 ( u x y ) i , j n cos ( θ i , j ) sin ( θ i , j ) ] ,

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