Abstract

We present a method for orientation-selective edge detection and enhancement based on the irradiance transport equation. The proposed technique distinguishes the sign of the derivative of the intensity pattern along an arbitrarily selected direction. The method is based on the capacity of liquid-crystal displays to generate simultaneously a contrast reverted replica of the image displayed on it. When both images (the original one and its replica) are imagined across a slightly defocused plane, one obtains an image with enhanced first derivatives. Unlike most Fourier methods, the proposed technique works well with a low-coherence light source, and it does not require precise alignment. The proposed method does not involve numerical processing, and thus it could be potentially useful for processing large images in real-time applications. Validation experiments are presented.

© 2010 Optical Society of America

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  1. M. Fak-aim, A. Seanton, and S. Kaitwanidvilai, “Automatic visual inspection of bump in flip chip using edge detection with genetic algorithm,” Proceedings of the International Multiconference of Engineers and Computer Scientists 2008 (International Association of Engineers, 2008), Vol I, pp. 19-21.
  2. B.-L. Liang, Z.-Q. Wang, G.-G. Mu, J.-H. Guan, H.-L. Liu, and C. M. Cartwright, “Real-time edge-enhanced optical correlation with a cerium-doped potassium sodium strontium barium niobate photorefractive crystal,” Appl. Opt. 39, 2925-2930 (2000).
    [CrossRef]
  3. C. S. Yelleswarapu, S.-R. Kothapalli, and D. V. G. L. N. Rao, “Optical Fourier techniques for medical image processing and phase contrast imaging,” Opt. Commun. 281, 1876-1888(2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. R. C. Gonzalez and P. Wintz, Digital Image Processing (Addison-Wesley, 1977).
  7. J. A. Ferrari, J. L. Flores, C. D. Perciante, and E. Frins, “Edge enhancement and image equalization by unsharp masking using self-adaptive photochromic filters,” Appl. Opt. 48, 3570-3579 (2009).
    [CrossRef] [PubMed]
  8. X. Lin, J. Ohtsubo, and T. Takemori, “Real-time optical image subtraction and edge enhancement using ferroelectric liquid-crystal devices based on speckle modulation,” Appl. Opt. 35, 3148-3155 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  11. J. A. Davis, D. E. McNamara, and D. M. Cottrell, “Image processing with the radial Hilbert transform: theory and experiments,” Opt. Lett. 25, 99-101 (2000).
    [CrossRef]
  12. H. Kasprzak, “Differentiation of a noninteger order and its optical implementation,” Appl. Opt. 21, 3287-3291 (1982).
    [CrossRef] [PubMed]
  13. J. A. Davis, D. A. Smith, D. E. McNamara, D. M. Cottrell, and J. Campos, “Fractional derivatives--analysis and experimental implementation,” Appl. Opt. 40, 5943-5948 (2001).
    [CrossRef]
  14. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13, 689-694 (2005).
    [CrossRef] [PubMed]
  15. J. Mazzaferri and S. Ledesma, “Rotation invariant real-time optical edge detector,” Opt. Commun. 272, 367-376 (2007).
    [CrossRef]
  16. J. A. Davis and M. D. Nowak, “Selective edge enhancement of images with an acousto-optic light modulator,” Appl. Opt. 41, 4835-4839 (2002).
    [CrossRef] [PubMed]
  17. D. Cao, P. P. Banerjee, and T.-C. Poon, “Image edge enhancement with two cascaded acousto-optic cells with contra propagating sound,” Appl. Opt. 37, 3007-3014 (1998).
    [CrossRef]
  18. G. Situ, G. Pedrini, and W. Osten, “Spiral phase filtering and orientation-selective edge detection/enhancement,” J. Opt. Soc. Am. A 26, 1788-1797 (2009).
    [CrossRef]
  19. N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6-10 (1984).
    [CrossRef]
  20. M. R. Teague, “Deterministic phase retrieval: a Green's function solution,” J. Opt. Soc. Am. 73, 1434-1441 (1983).
    [CrossRef]
  21. F. Roddier, “Wavefront sensing and the irradiance transport equation,” Appl. Opt. 29, 1402-1403 (1990).
    [CrossRef] [PubMed]
  22. C. D. Perciante, J. A. Ferrari, and A. Dubra, “Visualization of phase objects using incoherent illumination,” Opt. Commun. 183, 15-18 (2000).
    [CrossRef]
  23. C. D. Perciante and J. A. Ferrari, “Visualization of two-dimensional phase gradients by subtraction of a reference periodic pattern,” Appl. Opt. 39, 2081-2083 (2000).
    [CrossRef]

2009 (2)

2008 (1)

C. S. Yelleswarapu, S.-R. Kothapalli, and D. V. G. L. N. Rao, “Optical Fourier techniques for medical image processing and phase contrast imaging,” Opt. Commun. 281, 1876-1888(2008).
[CrossRef] [PubMed]

2007 (1)

J. Mazzaferri and S. Ledesma, “Rotation invariant real-time optical edge detector,” Opt. Commun. 272, 367-376 (2007).
[CrossRef]

2005 (1)

2002 (1)

2001 (2)

2000 (4)

1998 (2)

1996 (1)

1991 (1)

P. G. Tahoces, J. Correa, M. Souto, C. Gonzalez, L. Gomez, and J. J. Vidal, “Enhancement of chest and breast radiographs by automatic spatial filtering,” IEEE Trans. Med. Imaging 10, 330-335 (1991).
[CrossRef] [PubMed]

1990 (1)

1987 (1)

J. A. Sorenson and C. R. Mitchell, “Evaluation of optical unsharp masking and contrast enhancement of low-scatter chest radiographs,” Am. J. Roentgenol. 149, 275-281 (1987).

1984 (1)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6-10 (1984).
[CrossRef]

1983 (1)

1982 (1)

Banerjee, P. P.

Bernet, S.

Campos, J.

Cao, D.

Cartwright, C. M.

Correa, J.

P. G. Tahoces, J. Correa, M. Souto, C. Gonzalez, L. Gomez, and J. J. Vidal, “Enhancement of chest and breast radiographs by automatic spatial filtering,” IEEE Trans. Med. Imaging 10, 330-335 (1991).
[CrossRef] [PubMed]

Cotrell, D. M.

Cottrell, D. M.

Davis, J. A.

Dubra, A.

C. D. Perciante, J. A. Ferrari, and A. Dubra, “Visualization of phase objects using incoherent illumination,” Opt. Commun. 183, 15-18 (2000).
[CrossRef]

Fak-aim, M.

M. Fak-aim, A. Seanton, and S. Kaitwanidvilai, “Automatic visual inspection of bump in flip chip using edge detection with genetic algorithm,” Proceedings of the International Multiconference of Engineers and Computer Scientists 2008 (International Association of Engineers, 2008), Vol I, pp. 19-21.

Ferrari, J. A.

Flores, J. L.

Frins, E.

Fürhapter, S.

Gomez, L.

P. G. Tahoces, J. Correa, M. Souto, C. Gonzalez, L. Gomez, and J. J. Vidal, “Enhancement of chest and breast radiographs by automatic spatial filtering,” IEEE Trans. Med. Imaging 10, 330-335 (1991).
[CrossRef] [PubMed]

Gonzalez, C.

P. G. Tahoces, J. Correa, M. Souto, C. Gonzalez, L. Gomez, and J. J. Vidal, “Enhancement of chest and breast radiographs by automatic spatial filtering,” IEEE Trans. Med. Imaging 10, 330-335 (1991).
[CrossRef] [PubMed]

Gonzalez, R. C.

R. C. Gonzalez and P. Wintz, Digital Image Processing (Addison-Wesley, 1977).

Guan, J.-H.

Jesacher, A.

Kaitwanidvilai, S.

M. Fak-aim, A. Seanton, and S. Kaitwanidvilai, “Automatic visual inspection of bump in flip chip using edge detection with genetic algorithm,” Proceedings of the International Multiconference of Engineers and Computer Scientists 2008 (International Association of Engineers, 2008), Vol I, pp. 19-21.

Kasprzak, H.

Khoo, I. C.

Kothapalli, S.-R.

C. S. Yelleswarapu, S.-R. Kothapalli, and D. V. G. L. N. Rao, “Optical Fourier techniques for medical image processing and phase contrast imaging,” Opt. Commun. 281, 1876-1888(2008).
[CrossRef] [PubMed]

L. N. Rao, D. V. G.

C. S. Yelleswarapu, S.-R. Kothapalli, and D. V. G. L. N. Rao, “Optical Fourier techniques for medical image processing and phase contrast imaging,” Opt. Commun. 281, 1876-1888(2008).
[CrossRef] [PubMed]

Ledesma, S.

J. Mazzaferri and S. Ledesma, “Rotation invariant real-time optical edge detector,” Opt. Commun. 272, 367-376 (2007).
[CrossRef]

Liang, B.-L.

Lin, X.

Liu, H.-L.

Mazzaferri, J.

J. Mazzaferri and S. Ledesma, “Rotation invariant real-time optical edge detector,” Opt. Commun. 272, 367-376 (2007).
[CrossRef]

McNamara, D. E.

Mitchell, C. R.

J. A. Sorenson and C. R. Mitchell, “Evaluation of optical unsharp masking and contrast enhancement of low-scatter chest radiographs,” Am. J. Roentgenol. 149, 275-281 (1987).

Mu, G.-G.

Nowak, M. D.

Ohtsubo, J.

Osten, W.

Pedrini, G.

Perciante, C. D.

Poon, T.-C.

Ritsch-Marte, M.

Roddier, F.

Seanton, A.

M. Fak-aim, A. Seanton, and S. Kaitwanidvilai, “Automatic visual inspection of bump in flip chip using edge detection with genetic algorithm,” Proceedings of the International Multiconference of Engineers and Computer Scientists 2008 (International Association of Engineers, 2008), Vol I, pp. 19-21.

Shih, M. Y.

Shishido, A.

Situ, G.

Smith, D. A.

Sorenson, J. A.

J. A. Sorenson and C. R. Mitchell, “Evaluation of optical unsharp masking and contrast enhancement of low-scatter chest radiographs,” Am. J. Roentgenol. 149, 275-281 (1987).

Souto, M.

P. G. Tahoces, J. Correa, M. Souto, C. Gonzalez, L. Gomez, and J. J. Vidal, “Enhancement of chest and breast radiographs by automatic spatial filtering,” IEEE Trans. Med. Imaging 10, 330-335 (1991).
[CrossRef] [PubMed]

Streibl, N.

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6-10 (1984).
[CrossRef]

Tahoces, P. G.

P. G. Tahoces, J. Correa, M. Souto, C. Gonzalez, L. Gomez, and J. J. Vidal, “Enhancement of chest and breast radiographs by automatic spatial filtering,” IEEE Trans. Med. Imaging 10, 330-335 (1991).
[CrossRef] [PubMed]

Takemori, T.

Teague, M. R.

Vidal, J. J.

P. G. Tahoces, J. Correa, M. Souto, C. Gonzalez, L. Gomez, and J. J. Vidal, “Enhancement of chest and breast radiographs by automatic spatial filtering,” IEEE Trans. Med. Imaging 10, 330-335 (1991).
[CrossRef] [PubMed]

Wang, Z.-Q.

Wintz, P.

R. C. Gonzalez and P. Wintz, Digital Image Processing (Addison-Wesley, 1977).

Yelleswarapu, C. S.

C. S. Yelleswarapu, S.-R. Kothapalli, and D. V. G. L. N. Rao, “Optical Fourier techniques for medical image processing and phase contrast imaging,” Opt. Commun. 281, 1876-1888(2008).
[CrossRef] [PubMed]

Am. J. Roentgenol. (1)

J. A. Sorenson and C. R. Mitchell, “Evaluation of optical unsharp masking and contrast enhancement of low-scatter chest radiographs,” Am. J. Roentgenol. 149, 275-281 (1987).

Appl. Opt. (10)

B.-L. Liang, Z.-Q. Wang, G.-G. Mu, J.-H. Guan, H.-L. Liu, and C. M. Cartwright, “Real-time edge-enhanced optical correlation with a cerium-doped potassium sodium strontium barium niobate photorefractive crystal,” Appl. Opt. 39, 2925-2930 (2000).
[CrossRef]

J. A. Ferrari, J. L. Flores, C. D. Perciante, and E. Frins, “Edge enhancement and image equalization by unsharp masking using self-adaptive photochromic filters,” Appl. Opt. 48, 3570-3579 (2009).
[CrossRef] [PubMed]

X. Lin, J. Ohtsubo, and T. Takemori, “Real-time optical image subtraction and edge enhancement using ferroelectric liquid-crystal devices based on speckle modulation,” Appl. Opt. 35, 3148-3155 (1996).
[CrossRef] [PubMed]

J. A. Davis, D. E. McNamara, and D. M. Cotrell, “Analysis of the fractional Hilbert transform,” Appl. Opt. 37, 6911-6913(1998).
[CrossRef]

H. Kasprzak, “Differentiation of a noninteger order and its optical implementation,” Appl. Opt. 21, 3287-3291 (1982).
[CrossRef] [PubMed]

J. A. Davis, D. A. Smith, D. E. McNamara, D. M. Cottrell, and J. Campos, “Fractional derivatives--analysis and experimental implementation,” Appl. Opt. 40, 5943-5948 (2001).
[CrossRef]

J. A. Davis and M. D. Nowak, “Selective edge enhancement of images with an acousto-optic light modulator,” Appl. Opt. 41, 4835-4839 (2002).
[CrossRef] [PubMed]

D. Cao, P. P. Banerjee, and T.-C. Poon, “Image edge enhancement with two cascaded acousto-optic cells with contra propagating sound,” Appl. Opt. 37, 3007-3014 (1998).
[CrossRef]

F. Roddier, “Wavefront sensing and the irradiance transport equation,” Appl. Opt. 29, 1402-1403 (1990).
[CrossRef] [PubMed]

C. D. Perciante and J. A. Ferrari, “Visualization of two-dimensional phase gradients by subtraction of a reference periodic pattern,” Appl. Opt. 39, 2081-2083 (2000).
[CrossRef]

IEEE Trans. Med. Imaging (1)

P. G. Tahoces, J. Correa, M. Souto, C. Gonzalez, L. Gomez, and J. J. Vidal, “Enhancement of chest and breast radiographs by automatic spatial filtering,” IEEE Trans. Med. Imaging 10, 330-335 (1991).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

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

Opt. Commun. (4)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6-10 (1984).
[CrossRef]

J. Mazzaferri and S. Ledesma, “Rotation invariant real-time optical edge detector,” Opt. Commun. 272, 367-376 (2007).
[CrossRef]

C. S. Yelleswarapu, S.-R. Kothapalli, and D. V. G. L. N. Rao, “Optical Fourier techniques for medical image processing and phase contrast imaging,” Opt. Commun. 281, 1876-1888(2008).
[CrossRef] [PubMed]

C. D. Perciante, J. A. Ferrari, and A. Dubra, “Visualization of phase objects using incoherent illumination,” Opt. Commun. 183, 15-18 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (2)

R. C. Gonzalez and P. Wintz, Digital Image Processing (Addison-Wesley, 1977).

M. Fak-aim, A. Seanton, and S. Kaitwanidvilai, “Automatic visual inspection of bump in flip chip using edge detection with genetic algorithm,” Proceedings of the International Multiconference of Engineers and Computer Scientists 2008 (International Association of Engineers, 2008), Vol I, pp. 19-21.

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Figures (4)

Fig. 1
Fig. 1

Afocal optical imaging system using oblique illumination, i.e., the object is illuminated with an off-axis plane wave.

Fig. 2
Fig. 2

Experimental setup: P, polarizer; LCD, liquid-crystal- display; L 0 , 1 , 2 , lenses; M, mask; and A 1 , 2 , orthogonal analyzers.

Fig. 3
Fig. 3

(a) Image displayed on the LCD; the x coordinate is horizontal and the y coordinate is vertical. Images (b) and (c) were obtained with ξ in the x direction for Δ z = 1.00 ( ± 0.05 ) mm and Δ z = 1.00 ( ± 0.05 ) mm , respectively. Finally, images (d) and (e) were obtained with ξ in the y direction for Δ z = 1.00 ( ± 0.05 ) mm and Δ z = 1.00 ( ± 0.05 ) mm , respectively. The subfigures in the upper-right corners show the cross sections of the arrow and the output patterns.

Fig. 4
Fig. 4

(a) Lena picture displayed on the LCD. Images (b) and (c) show optically processed images obtained at the plane Σ, with ξ in the x direction for Δ z = ± 0.50 ( ± 0.05 ) mm , respectively.

Equations (21)

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E ( x , y , z ) = I ( x , y , z ) exp [ i ϕ ( x , y , z ) ] ,
2 π λ I z = I · ϕ I 2 ϕ ,
I ( x , y , z + Δ z ) I ( x , y , z ) λ Δ z 2 π ( I · ϕ + I 2 ϕ ) ,
ϕ ( x , y , z ) = 2 π r · e ^ / λ = 2 π ( sin ( α ) ξ + cos ( α ) z ) / λ ,
I ( x , y , z + Δ z ) I ( x , y , z ) ( I · e ^ ) Δ z .
I n ( x , y , z ) 1 I p ( x , y ) ,
I p ( x , y , z + Δ z ) + I n ( x , y , z + Δ z ) I p ( x , y , z ) + I n ( x , y , z ) [ ( I p I n ) · e ^ ) ] Δ z .
I p ( x , y , z + Δ z ) + I n ( x , y , z + Δ z ) 1 2 ( I p · e ^ ) Δ z 1 2 I ξ sin ( α ) Δ z .
I p ( x , y , z ) = cos 2 ( θ ( x , y ) ) .
I n ( x , y , z ) = sin 2 ( θ ( x , y ) ) = 1 I p ( x , y , z ) .
E ( x , y , z ) = E ˜ ( k x , k y , 0 ) exp [ i ( k x x + k y y ) ] exp [ i k z 1 k x 2 + k y 2 k 2 ] d k x d k y ,
k z 1 ( k x 2 + k y 2 ) k 2 k z [ 1 ( k x 2 + k y 2 ) 2 k 2 ( k x 4 + k y 4 ) 8 k 4 + ]
E ( x , y , z ) = exp ( i k z ) A ( x , y , z ) ,
A ( x , y , z ) E ˜ ( k x , k y , 0 ) exp [ i ( k x x + k y y ) ] exp [ i ( k x 2 + k y 2 ) z 2 k ] d k x d k y .
2 k i A z + 2 A = 0 ,
A ( x , y , z + Δ z ) E ˜ ( k x , k y , 0 ) exp [ i ( k x x + k y y ) ] exp [ i ( k x 2 + k y 2 ) ( z + Δ z ) 2 k ] d k x d k y A ( x , y , z ) i Δ z 2 k E ˜ ( k x , k y , 0 ) exp [ i ( k x x + k y y ) ] ( k x 2 + k y 2 ) d k x d k y A ( x , y , z ) + i Δ z 2 k 2 A ( x , y , z ) .
I ( x , y , z + Δ z ) = I ( x , y , z ) + 2 Re [ i Δ z 2 k A * ( x , y , z ) 2 A ( x , y , x ) ] ,
2 A = ( 2 | A | ) exp ( i ϕ ) + 2 i ( ϕ · | A | ) exp ( i ϕ ) + i | A | ( 2 ϕ ) exp ( i ϕ ) | A | | ϕ | 2 exp ( i ϕ ) .
Re [ i A * 2 A ] = 2 | A | ( ϕ · | A | ) | A | 2 2 ϕ = I · ϕ I 2 ϕ .
I ( x , y , z + Δ z ) = I ( x , y , z ) Δ z k [ I · ϕ + I 2 ϕ ] ,
k I z + I · ϕ + I 2 ϕ = 0 ,

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