Abstract

We present a nonlinear joint transform processor that can perform image enhancement. Image enhancement results are obtained for different degrees of nonlinearity applied to the joint power spectrum. The first-order harmonic term at the output plane produces the enhanced image which has the exact Fourier phase of the input image and a Fourier magnitude of the input modified by the nonlinearity. For compression types of nonlinearity, the thresholding will redistribute the energy in the Fourier magnitude of the image by increasing the magnitude of the higher spatial frequencies. Thus, the fine details of the image that are contained in the high spatial frequencies of the joint power spectrum are enhanced. We investigate the effects of various types of nonlinearity on the enhanced images. Analytical expressions for the enhanced images obtained by the nonlinear technique will be provided. Computer simulations of the nonlinear processor for image enhancement are presented to study the performance of the system. We show that the nonlinear technique produces reasonably good results and that it provides much better light efficiency when compared with the block spatial filtering technique.

© 1990 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (MaGraw-Hill, New York, 1968).
  2. D. Casasent, Optical Data Processing Applications (Springer-Verlag, New York, 1978).
    [CrossRef]
  3. J. L. Horner, “Light Utilization in Optical Correlators,” Appl. Opt. 21, 4511–4514 (1982).
    [CrossRef] [PubMed]
  4. H. J. Caulfield, “Role of the Horner Efficiency in the Optimization of Spatial Filters for Optical Pattern Recognition,” Appl. Opt. 21, 4391–4392 (1982).
    [CrossRef] [PubMed]
  5. B. Javidi, “Nonlinear Joint Power Spectrum Based Optical Correlation,” Appl. Opt. 28, 2358–2367 (1989).
    [CrossRef] [PubMed]
  6. B. Javidi, “Synthetic Discriminant Function-Based Binary” Nonlinear Optical Correlator,” Appl. Opt. 28, 2490–2493 (1989).
    [CrossRef] [PubMed]
  7. B. Javidi, H. J. Caulfield, J. L. Horner, “Image Deconvolution by Nonlinear Signal Processing,” Appl. Opt. 28, 3106–3111 (1989).
    [CrossRef] [PubMed]
  8. B. Javidi, J. L. Horner, “Multifunction Nonlinear Processor,” Opt. Eng. 28, 837–843 (1989).
  9. C. S. Weaver, J. W. Goodman, “A Technique for Optically Convolving Two Functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  10. D. Middleton, Statistical Communication Theory (McGraw-Hill, New York, 1960).
  11. W. B. Davenport, J. W. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1960).
  12. L. Pugliese, G. M. Morris, “Bandpass Filtering in Barium Titanate,” Appl. Opt. 27, 4535–4539 (1988).
    [CrossRef] [PubMed]
  13. A. Tai, T. Cheng, F. T. S. Yu, “Optical Logarithmic Filtering Using Inherent Film Nonlinearity,” Appl. Opt. 16, 2559–2564 (1977).
    [CrossRef] [PubMed]
  14. A. Vander Lugt, F. B. Rotz, “The Use of Film Nonlinearities in Optical Spatial Filtering,” Appl. Opt. 9, 215–222 (1970).
    [CrossRef]
  15. H. Kato, J. W. Goodman, “Nonlinear Filtering in Coherent Optical Systems Through Halftone Screen Processes,” Appl. Opt. 14, 1813–1824 (1975).
    [CrossRef] [PubMed]
  16. B. E. Saleh, “Architectures for” Nonlinear Optical Image Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 1151, 320–331 (1989).

1989 (5)

1988 (1)

1982 (2)

1977 (1)

1975 (1)

1970 (1)

1966 (1)

Casasent, D.

D. Casasent, Optical Data Processing Applications (Springer-Verlag, New York, 1978).
[CrossRef]

Caulfield, H. J.

Cheng, T.

Davenport, W. B.

W. B. Davenport, J. W. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1960).

Goodman, J. W.

Horner, J. L.

Javidi, B.

Kato, H.

Middleton, D.

D. Middleton, Statistical Communication Theory (McGraw-Hill, New York, 1960).

Morris, G. M.

Pugliese, L.

Root, J. W.

W. B. Davenport, J. W. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1960).

Rotz, F. B.

Saleh, B. E.

B. E. Saleh, “Architectures for” Nonlinear Optical Image Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 1151, 320–331 (1989).

Tai, A.

Vander Lugt, A.

Weaver, C. S.

Yu, F. T. S.

Appl. Opt. (10)

Opt. Eng. (1)

B. Javidi, J. L. Horner, “Multifunction Nonlinear Processor,” Opt. Eng. 28, 837–843 (1989).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

B. E. Saleh, “Architectures for” Nonlinear Optical Image Processing,” Proc. Soc. Photo-Opt. Instrum. Eng. 1151, 320–331 (1989).

Other (4)

D. Middleton, Statistical Communication Theory (McGraw-Hill, New York, 1960).

W. B. Davenport, J. W. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1960).

J. W. Goodman, Introduction to Fourier Optics (MaGraw-Hill, New York, 1968).

D. Casasent, Optical Data Processing Applications (Springer-Verlag, New York, 1978).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Joint transform processor for image enhancement: (a) implementation using an optically addressed SLM and (b) implementation using an electrically addressed SLM.

Fig. 2
Fig. 2

Input image used in the nonlinear image enhancement tests.

Fig. 3
Fig. 3

(a) Block diagram of the computer simulation and (b) arrangement of the input image and the point source function.

Fig. 4
Fig. 4

Enhanced images for various degrees of nonlinearity: (a) k = 0.8; (b) k = 0.5; (c) k = 0.3; and (d) k = 0.

Tables (1)

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Table I Light Efficiency Comparison of Techniques for Edge Enhancementa

Equations (18)

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s ( x , y ) = d ( x , y - y o ) + t ( x , y + y o ) .
S ( ω x , ω y ) = T ( ω x , ω y ) exp [ j ϕ T ( ω x , ω y ) ] exp [ - j y o ω y ] + D ( ω x , ω y ) exp [ j ϕ D ( ω x , ω y ) ] exp [ j y o ω y ] ,
E ( ω x , ω y ) = S ( ω x , ω y ) 2 = T 2 ( ω x , ω y ) + A 2 + A T ( ω x , ω y ) exp [ j ϕ T ( ω x , ω y ) ] exp [ - j 2 y o ω y ] + A T ( ω x , ω y ) exp [ - j ϕ T ( ω x , ω y ) ] exp [ j 2 y o ω y ] .
G ( ω ) = - g ( E ) exp ( - j ω E ) d E .
g ( E ) = 1 2 π - G ( ω ) exp ( j ω E ) d ω .
g ( E ) = 1 2 π - G ( ω ) exp { j 2 ω [ T 2 ( ω x , ω y ) + A 2 ] } × exp { j 2 ω A T ( ω x , ω y ) cos [ 2 y o ω y + ϕ T ( ω x , ω y ) ] } d ω .
exp { j 2 ω A T ( ω x , ω y ) cos [ 2 y o ω y + ϕ T ( ω x , ω y ) ] } = v = 0 v ( j ) v J v [ 2 ω A T ( ω x , ω y ) ] cos [ 2 v y o ω y + v ϕ T ( ω x , ω y ) ] ,
v = { 1 , v = 0 , 2 , v > 0 ,
g ( E ) = v = 0 v 2 π ( j ) v - G ( ω ) exp { j 2 ω [ A 2 + T 2 ( ω x , ω y ) ] } × J v [ 2 ω A T ( ω x , ω y ) ] cos [ 2 v y o ω y + v ϕ T ( ω x , ω y ) ] d ω .
g ( E ) = v = 0 H v [ T ( ω x , ω y ) ] cos [ 2 v y o ω y + v ϕ T ( ω x , ω y ) ] ,
H v [ T ( ω x , ω y ) ] = v 2 π ( j ) ν - G ( ω ) exp { j 2 ω [ A 2 + T 2 ( ω x , ω y ) ] } × J v [ 2 ω A T ( ω x , ω y ) ] d ω .
y = { x k , x 0 , - x k , x < 0.
G ( ω ) = 2 ( j ω ) k + 1 Γ ( k + 1 ) ,
H v [ T ( ω x , ω y ) ] = Γ ( k + 1 ) v π ( j ) v - k - 1 - 1 ω k + 1 J v [ 2 ω A T ( ω x , ω y ) ] d ω .
H v [ T ( ω x , ω y ) ] = A k Γ ( k + 1 ) v [ T ( ω x , ω y ) ] k Γ ( 1 - v - k 2 ) Γ ( 1 + v + k 2 ) ,
g k ( E ) = v = 1 ( v odd ) v A k Γ ( k + 1 ) [ T ( ω x , ω y ) ] k Γ ( 1 - v - k 2 ) Γ ( 1 + v + k 2 ) × cos [ 2 v y o ω y + v ϕ T ( ω x , ω y ) ] .
g 1 k ( E ) = 2 Γ ( k + 1 ) A k [ T ( ω x , ω y ) ] k Γ ( 1 - 1 - k 2 ) Γ ( 1 + 1 + k 2 ) cos [ 2 y o ω y + ϕ T ( ω x , ω y ) ] .
I ( x , y ) = 1 N 1 N 2 i = 1 N 1 j = 1 N 2 f ( x i , y j ) 2 ,

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