Abstract

A two-step algorithm for reliable recognition of a target imbedded into a two-dimensional nonuniformly illuminated and noisy scene is presented. The input scene is preprocessed with a space-domain pointwise procedure followed by an optimum correlation. The preprocessing is based on an estimate of the source illumination function, whereas the correlation filter is optimized with respect to the mean-squared-error criterion for detecting a target in the preprocessed scene. Computer simulations are provided and compared with those of various common techniques in terms of recognition performance and tolerance to nonuniform illumination as well as to additive noise. Experimental optodigital results are also provided and discussed.

© 2009 Optical Society of America

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  1. A. Vanderlugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139-145 (1964).
  2. C. S. Weaver and J. L. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248-1249 (1966).
    [CrossRef] [PubMed]
  3. V. H. Diaz-Ramirez and V. Kober, “Adaptive phase-input joint transform correlator,” Appl. Opt. 46, 6543-6551 (2007).
    [CrossRef] [PubMed]
  4. B. Javidi and J. Wang, “Design of filters to detect a noisy target in nonoverlapping background noise,” J. Opt. Soc. Am. A 11, 2604-2612 (1994).
    [CrossRef]
  5. B. Javidi and J. Wang, “Optimum filter for detecting a target in multiplicative noise and additive noise,” J. Opt. Soc. Am. A 14, 836-844 (1997).
    [CrossRef]
  6. P. Refregier, B. Javidi, and G. Zhang, “Minimum mean-square-error filter for pattern recognition with spatially disjoint signal and scene noise,” Opt. Lett. 18, 1453-1455 (1993).
    [CrossRef] [PubMed]
  7. E. M. Ramos-Michel and V. Kober, “Design of correlation filters for recognition of linearly distorted objects in linearly degraded scenes,” J. Opt. Soc. Am. A 24, 3403-3417 (2007).
    [CrossRef]
  8. H. H. Arsenault and D. Lefebvre, “Homomorphic cameo filter for pattern recognition,” Opt. Lett. 25, 1567-1569 (2000).
    [CrossRef]
  9. D. Lefebvre, H. H. Arsenault, P. Garcia-Martinez, and C. Ferreira, “Recognition of unsegmented targets invariant under transformations of intensity,” Appl. Opt. 41, 6135-6142(2002).
    [CrossRef] [PubMed]
  10. P. Garcia-Martinez, M. Tejera, C. Ferreira, D. Lefebvre, and H. H. Arsenault, “Optical implementation of the weighted sliced orthogonal nonlinear generalized correlation for nonuniform illumination conditions,” Appl. Opt. 41, 6867-6874(2002).
    [CrossRef] [PubMed]
  11. S. Zhang and M. A. Karim, “Normalized joint transform correlator for target recognition,” Opt. Eng. 39, 1184-1189(2000).
    [CrossRef]
  12. C. F. Hester and D. Casasent, “Multivariant technique for multiclass pattern recognition,” Appl. Opt. 19, 1758-1761(1980).
    [CrossRef] [PubMed]
  13. J. A. Gonzalez-Fraga, V. Kober, and J. Alvarez-Borrego, “Adaptive synthetic discriminant function filters for pattern recognition,” Opt. Eng 45, 057051 (2006).
  14. J. J. Valles, J. Garcia, P. Garcia-Martinez, and H. H. Arsenault, “Three-dimensional object detection under arbitrary lighting conditions,” Appl. Opt. 45, 5237-5247 (2006).
    [CrossRef] [PubMed]
  15. B. K. Horn, Robot Vision (MIT, 1986).
  16. Q. Zheng and R. Chellappa, “Estimation of illuminant direction, albedo, and shape from shading,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 680-702 (1991).
    [CrossRef]
  17. A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, 1988).
  18. J. P. Fitch, E. J. Coyle, and N. C. Gallagher, “Median filtering by threshold decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183-1188 (1984).
    [CrossRef]
  19. B. V. K. Vijaya-Kumar and L. Hassebrook, “Performance measures of correlation filters,” Appl. Opt. 29, 2997-3006 (1990).
    [CrossRef]
  20. B. K. P. Horn, “Understanding image intensities,” Aritf. Intell. 8, 201-231 (1977).
    [CrossRef]
  21. K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. A 57, 1105-1114 (1967).
    [CrossRef]
  22. B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311-317 (1975).
    [CrossRef]
  23. R. Cook and K. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7-24 (1982).
    [CrossRef]
  24. S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflections: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611-634 (1991).
    [CrossRef]
  25. R. Zhang, P. Tsai, J. E. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690-706 (1999).
    [CrossRef]
  26. W. K. Pratt, Digital Image Processing (Wiley-Interscience Publication, 1991).
  27. L. P. Yaroslavsky and M. Eden, Fundamentals of Digital Optics, (Birkhäuser Boston, 1996).
  28. V. H. Diaz-Ramirez, V. Kober, and J. Alvarez-Borrego, “Pattern recognition with an adaptive joint transform correlator,” Appl. Opt. 45, 5929-5941 (2006).
    [CrossRef] [PubMed]

2007 (2)

2006 (3)

2002 (2)

2000 (2)

S. Zhang and M. A. Karim, “Normalized joint transform correlator for target recognition,” Opt. Eng. 39, 1184-1189(2000).
[CrossRef]

H. H. Arsenault and D. Lefebvre, “Homomorphic cameo filter for pattern recognition,” Opt. Lett. 25, 1567-1569 (2000).
[CrossRef]

1999 (1)

R. Zhang, P. Tsai, J. E. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690-706 (1999).
[CrossRef]

1997 (1)

1994 (1)

1993 (1)

1991 (2)

S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflections: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611-634 (1991).
[CrossRef]

Q. Zheng and R. Chellappa, “Estimation of illuminant direction, albedo, and shape from shading,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 680-702 (1991).
[CrossRef]

1990 (1)

1984 (1)

J. P. Fitch, E. J. Coyle, and N. C. Gallagher, “Median filtering by threshold decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183-1188 (1984).
[CrossRef]

1982 (1)

R. Cook and K. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7-24 (1982).
[CrossRef]

1980 (1)

1977 (1)

B. K. P. Horn, “Understanding image intensities,” Aritf. Intell. 8, 201-231 (1977).
[CrossRef]

1975 (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311-317 (1975).
[CrossRef]

1967 (1)

K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. A 57, 1105-1114 (1967).
[CrossRef]

1966 (1)

1964 (1)

A. Vanderlugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139-145 (1964).

Alvarez-Borrego, J.

V. H. Diaz-Ramirez, V. Kober, and J. Alvarez-Borrego, “Pattern recognition with an adaptive joint transform correlator,” Appl. Opt. 45, 5929-5941 (2006).
[CrossRef] [PubMed]

J. A. Gonzalez-Fraga, V. Kober, and J. Alvarez-Borrego, “Adaptive synthetic discriminant function filters for pattern recognition,” Opt. Eng 45, 057051 (2006).

Arsenault, H. H.

Casasent, D.

Chellappa, R.

Q. Zheng and R. Chellappa, “Estimation of illuminant direction, albedo, and shape from shading,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 680-702 (1991).
[CrossRef]

Cook, R.

R. Cook and K. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7-24 (1982).
[CrossRef]

Coyle, E. J.

J. P. Fitch, E. J. Coyle, and N. C. Gallagher, “Median filtering by threshold decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183-1188 (1984).
[CrossRef]

Cryer, J. E.

R. Zhang, P. Tsai, J. E. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690-706 (1999).
[CrossRef]

Diaz-Ramirez, V. H.

Eden, M.

L. P. Yaroslavsky and M. Eden, Fundamentals of Digital Optics, (Birkhäuser Boston, 1996).

Ferreira, C.

Fitch, J. P.

J. P. Fitch, E. J. Coyle, and N. C. Gallagher, “Median filtering by threshold decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183-1188 (1984).
[CrossRef]

Gallagher, N. C.

J. P. Fitch, E. J. Coyle, and N. C. Gallagher, “Median filtering by threshold decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183-1188 (1984).
[CrossRef]

Garcia, J.

Garcia-Martinez, P.

Gonzalez-Fraga, J. A.

J. A. Gonzalez-Fraga, V. Kober, and J. Alvarez-Borrego, “Adaptive synthetic discriminant function filters for pattern recognition,” Opt. Eng 45, 057051 (2006).

Goodman, J. L.

Hassebrook, L.

Hester, C. F.

Horn, B. K.

B. K. Horn, Robot Vision (MIT, 1986).

Horn, B. K. P.

B. K. P. Horn, “Understanding image intensities,” Aritf. Intell. 8, 201-231 (1977).
[CrossRef]

Ikeuchi, K.

S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflections: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611-634 (1991).
[CrossRef]

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, 1988).

Javidi, B.

Kanade, T.

S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflections: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611-634 (1991).
[CrossRef]

Karim, M. A.

S. Zhang and M. A. Karim, “Normalized joint transform correlator for target recognition,” Opt. Eng. 39, 1184-1189(2000).
[CrossRef]

Kober, V.

Lefebvre, D.

Nayar, S. K.

S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflections: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611-634 (1991).
[CrossRef]

Phong, B. T.

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311-317 (1975).
[CrossRef]

Pratt, W. K.

W. K. Pratt, Digital Image Processing (Wiley-Interscience Publication, 1991).

Ramos-Michel, E. M.

Refregier, P.

Shah, M.

R. Zhang, P. Tsai, J. E. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690-706 (1999).
[CrossRef]

Sparrow, E. M.

K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. A 57, 1105-1114 (1967).
[CrossRef]

Tejera, M.

Torrance, K.

R. Cook and K. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7-24 (1982).
[CrossRef]

Torrance, K. E.

K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. A 57, 1105-1114 (1967).
[CrossRef]

Tsai, P.

R. Zhang, P. Tsai, J. E. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690-706 (1999).
[CrossRef]

Valles, J. J.

Vanderlugt, A.

A. Vanderlugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139-145 (1964).

Vijaya-Kumar, B. V. K.

Wang, J.

Weaver, C. S.

Yaroslavsky, L. P.

L. P. Yaroslavsky and M. Eden, Fundamentals of Digital Optics, (Birkhäuser Boston, 1996).

Zhang, G.

Zhang, R.

R. Zhang, P. Tsai, J. E. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690-706 (1999).
[CrossRef]

Zhang, S.

S. Zhang and M. A. Karim, “Normalized joint transform correlator for target recognition,” Opt. Eng. 39, 1184-1189(2000).
[CrossRef]

Zheng, Q.

Q. Zheng and R. Chellappa, “Estimation of illuminant direction, albedo, and shape from shading,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 680-702 (1991).
[CrossRef]

ACM Trans. Graph. (1)

R. Cook and K. Torrance, “A reflectance model for computer graphics,” ACM Trans. Graph. 1, 7-24 (1982).
[CrossRef]

Appl. Opt. (8)

Aritf. Intell. (1)

B. K. P. Horn, “Understanding image intensities,” Aritf. Intell. 8, 201-231 (1977).
[CrossRef]

Commun. ACM (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311-317 (1975).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (1)

J. P. Fitch, E. J. Coyle, and N. C. Gallagher, “Median filtering by threshold decomposition,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 1183-1188 (1984).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. Vanderlugt, “Signal detection by complex filtering,” IEEE Trans. Inf. Theory IT-10, 139-145 (1964).

IEEE Trans. Pattern Anal. Mach. Intell. (3)

Q. Zheng and R. Chellappa, “Estimation of illuminant direction, albedo, and shape from shading,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 680-702 (1991).
[CrossRef]

S. K. Nayar, K. Ikeuchi, and T. Kanade, “Surface reflections: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611-634 (1991).
[CrossRef]

R. Zhang, P. Tsai, J. E. Cryer, and M. Shah, “Shape from shading: a survey,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 690-706 (1999).
[CrossRef]

J. Opt. Soc. Am. A (4)

Opt. Eng (1)

J. A. Gonzalez-Fraga, V. Kober, and J. Alvarez-Borrego, “Adaptive synthetic discriminant function filters for pattern recognition,” Opt. Eng 45, 057051 (2006).

Opt. Eng. (1)

S. Zhang and M. A. Karim, “Normalized joint transform correlator for target recognition,” Opt. Eng. 39, 1184-1189(2000).
[CrossRef]

Opt. Lett. (2)

Other (4)

B. K. Horn, Robot Vision (MIT, 1986).

A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, 1988).

W. K. Pratt, Digital Image Processing (Wiley-Interscience Publication, 1991).

L. P. Yaroslavsky and M. Eden, Fundamentals of Digital Optics, (Birkhäuser Boston, 1996).

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Figures (14)

Fig. 1
Fig. 1

Illumination model geometry.

Fig. 2
Fig. 2

Block diagram of the proposed method.

Fig. 3
Fig. 3

(a) Input scene. (b) Illumination function. (c) Observed scene.

Fig. 4
Fig. 4

Correlation intensity planes obtained with: (a) HCF, (b) WSONG, (c) HMSE, (d) OF.

Fig. 5
Fig. 5

Preprocessed scene obtained with the proposed method.

Fig. 6
Fig. 6

Correlation intensity plane obtained with the proposed method.

Fig. 7
Fig. 7

Observed scenes with different levels of nonuniform illumination degradation: (a) low severity, (b) medium severity, (c) hard severity. Illumination functions used in observed scenes with: (d) low severity, (e) medium severity, (f) hard severity.

Fig. 8
Fig. 8

Recognition performance of tested filters: (a) HMSE, (b) OF, (c) proposed method. Corresponding standard deviations obtained with: (d) HMSE, (e) OF, (f) proposed method.

Fig. 9
Fig. 9

Nonuniformly illuminated scene containing: (a) small target, (c) enlarged target. (b) Correlation plane profile obtained from (a). (d) Correlation plane profile obtained from (c).

Fig. 10
Fig. 10

Optical setup used for generation of observed scene with nonuniform illumination.

Fig. 11
Fig. 11

(a) Experimental observed scene. (b) Estimated illumination function. (c) Preprocessed image.

Fig. 12
Fig. 12

Optical setup of joint transform correlator.

Fig. 13
Fig. 13

Joint input images for real experiments: (a) positive part of the reference image, (b) negative part of the reference image.

Fig. 14
Fig. 14

Experimental intensity correlation plane obtained with the proposed method.

Tables (1)

Tables Icon

Table 1 DC Obtained with Different Illuminant Parameters Versus Real Parameters “ u org a

Equations (29)

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t ˜ ( x x 0 ) = b t ( x x 0 ) ,
log [ f ( x ) ] = log [ t ( x x 0 ) ] + log [ b ] .
h cm ( x ) = a 1 log [ t ( x ) ] + a 2 log [ w t ( x ) ] ,
a ( x ) = i = 0 N 1 i BIN i [ a ( x ) ] ,
BIN i [ a ( x ) ] = { 1 ; a ( x ) = i 0 ; a ( x ) i .
f ( x ) g ( x ) = i = 0 N 1 j = 1 N 1 i j BIN i [ f ( x ) ] BIN j [ g ( x ) ] .
Ω f , g ( x ) = i = 0 N 1 j = 1 N 1 W i j BIN i [ f ( x ) ] BIN j [ g ( x ) ] ,
f ( x ) = u ( x ) [ t ( x x 0 ) + w t ^ ( x x 0 ) b ( x ) ] + n ( x ) ,
H of ( ω ) = μ m [ T ( ω ) + μ b W t ^ ( ω ) ] * 1 2 π N m ( ω ) [ | T ( ω ) + μ b W t ^ ( ω ) | 2 + 1 2 π N b 0 ( ω ) | W t ^ ( ω ) | 2 + N ( ω ) ] ,
I ( x 0 , y 0 ) = cos ( θ ) = cos ( π 2 β ) ,
β = arctan [ S z [ ( S x x 0 ) 2 + ( S y y 0 ) 2 ] 1 / 2 ] = arctan [ r cos ( τ ) [ ( r tan τ cos α x 0 ) 2 + ( r tan τ sin α y 0 ) 2 ] 1 / 2 ] .
I ( x 0 , y 0 ) = cos { π 2 arctan [ r cos ( τ ) [ ( r tan τ cos α x 0 ) 2 + ( r tan τ sin α y 0 ) 2 ] 1 / 2 ] } .
α = arctan ( E { x ˜ L / x L 2 ˜ + y L 2 ˜ } E { y ˜ L / x L 2 ˜ + y L 2 ˜ } ) ; [ x ˜ L y ˜ L ] = ( B t B ) 1 B t [ δ I 1 δ I 2 δ I N ] ,
E { I } E { I 2 } = 0.5577 + 0.6240 cos τ + 0.1882 cos 2 τ 0.6514 cos 3 τ 0.5350 cos 4 τ + 0.9282 cos 5 τ + 0.3476 cos 6 τ 0.4984 cos 7 τ .
ρ = E { I } f 1 ( τ ) + ( E { I 2 } f 2 ( τ ) ) 1 / 2 f 1 2 ( τ ) + f 2 ( τ ) ,
f ( x ) = t ˜ ( x , x 0 ) u ( x ) + n ˜ ( x , x 0 ) ,
t ˜ ( x , x 0 ) = t ( x x 0 ) + μ b w t ^ ( x x 0 ) ,
n ˜ ( x , x 0 ) = n ( x ) + b 0 ( x ) w t ^ ( x x 0 ) u ( x ) .
F ( ω ) = 1 2 π T ˜ ( ω ) U ( ω ) + N ˜ ( ω ) ,
f ˜ ( x ) t ˜ ( x , x 0 ) + n ˜ ( x , x 0 ) h r ( x ) ,
h r ( x ) = u * ( x ) P t ˜ ( x ) P t ˜ ( x ) | u ( x ) | 2 + P n ˜ ( x ) = 1 u ( x ) | u ( x ) | 2 | u ( x ) | 2 + Λ ( x ) ,
MSE = E { | y d ( x ) y a ( x ) | 2 } d x = h c ( μ ) h c ( ν ) C t ˜ ( ν μ ) d μ d ν 2 h c ( μ ) t ˜ ( μ ) d μ + h c ( μ ) h c ( ν ) C h r ( ν μ ) C n ˜ ( ν μ ) d μ d ν + δ 2 ( x x 0 ) d x ,
MSE = 1 2 π | H c ( ω ) | 2 S t ( ω ) d ω + 1 2 π | H c ( ω ) | 2 S n ( ω ) d ω 1 π H c ( ω ) T ( ω ) d ω + c ,
H c ( ω ) = [ T ( ω ) + μ b W ^ ( ω ) ] * | T ( ω ) + μ b W ^ ( ω ) | 2 + 1 2 π B 0 ( ω ) | W ^ ( ω ) | 2 + 1 2 π N ( ω ) | H r ( ω ) | 2 ,
DC = 1 | C B ( 0 ) | 2 | C T ( 0 ) | 2 ,
f ( x ) = [ t ( x x 0 ) + w t ^ ( x x 0 ) b ( x ) ] u ( x ) .
f log ( x ) = log [ t ( x x 0 ) + b ( x ) w t ^ ( x x 0 ) ] + log u ( x ) .
f log ( x ) = log [ t ( x x 0 ) ] + log [ b ( x ) w t ^ ( x x 0 ) u ( x ) ] = t log ( x ; x 0 ) + n log ( x ) ,
H hmse ( ω ) = T log * ( ω ) | T log ( ω ) | 2 + S N log ( ω ) ,

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