Abstract

Images taken in noncooperative environments do not always have targets under the same illumination conditions. There is a need for methods to detect targets independently of the illumination. We propose a technique that yields correlation peaks that are invariant under a linear intensity transformation of object intensity. The new locally adaptive contrast-invariant filter accomplishes this by combining three correlations in a nonlinear way. This method is not only intensity invariant but also has good discrimination and resistance to noise. We present simulation results for various intensity transformations with and without random and correlated noise. When the noise is high enough to threaten errors, the method trades off intensity invariance in order to achieve the optimum signal to noise ratio, and the peak to sidelobe ratio in the presence of clutter is always greater than one. In the presence of random disjoint noise, the signal to noise ratio is independent of the target contrast and of the level of the noise.

© 2002 Optical Society of America

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References

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  1. F. M. Dickey, L. A. Romero, “Normalized correlation for pattern recognition,” Opt. Lett. 16, 1186–1188 (1991).
    [CrossRef] [PubMed]
  2. B. A. Kast, F. M. Dickey, “Normalization of correlators,” in Optical information processing systems and architectures III, B. Javidi, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.1564, 34–42 (1991).
    [CrossRef]
  3. R. Kotynski, K. Chalasinska-Macukow, “Normalization of correlation filter based on the Hölder’s inequality,” in Optics in Computing ’98, P. H. Chavel, D. A. Miller, H. Thienpont, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.3490, 195–198 (1998).
    [CrossRef]
  4. R. Kotynski, K. Chalasinska-Macukow, “Multi-object intensity-invariant pattern recognition with an optimum processor for correlated noise,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.3749, 316–317 (1999).
    [CrossRef]
  5. H. H. Arsenault, Y. Sheng, J. Bulabois, “Modified composite filter for pattern recognition in presence of noise with a non-zero mean,” Opt. Commun. 63, 15–20 (1987).
    [CrossRef]
  6. H. J. Caulfield, W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 19, 2354–2356 (1969).
    [CrossRef]
  7. C. F. Hester, D. Casasent, “Multivariate technique for multiclass pattern recognition,” Appl. Opt. 19, 1758–1761 (1980).
    [CrossRef] [PubMed]
  8. H. H. Arsenault, C. Belisle, “Contrast-invariant pattern recognition using circular harmonic component,” Appl. Opt. 24, 2072–2075 (1985).
    [CrossRef]
  9. Y.-H. Hsu, H. H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
    [CrossRef] [PubMed]
  10. P. Garcia-Martinez, H. H. Arsenault, C. Ferreira, “Binary image decomposition for intensity-invariant optical nonlinear correlation,” in Optics in Computing 2000, R. A. Lessard, T. V. Galstian, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.4089, 433–438 (2000).
    [CrossRef]
  11. P. Garcia-Martinez, H. H. Arsenault, “A correlation matrix representation using sliced orthogonal nonlinear generalized decomposition,” Opt. Commun. 172, 181–192 (1999).
    [CrossRef]
  12. P. Garcia-Martinez, H. H. Arsenault, S. E. Roy, “Optical implementation of the sliced orthogonal nonlinear generalized correlation for image degraded by nonoverlapping noise,” Opt. Commun. 173, 185–193 (2000).
    [CrossRef]
  13. H. H. Arsenault, D. Lefebvre, “Homomorphic cameo filter for pattern recognition that is invariant with change of illumination,” Opt. Lett. 25, 1567–1569 (2000).
    [CrossRef]
  14. S. Zhang, M. A. Karim, “Illumination invariant pattern recognition with joint-transform-correlator-based morphological correlation,” Appl. Opt. 38, 7228–7237 (1999).
    [CrossRef]
  15. K. Chalasinska-Macukow, E. Baranska, “Discrimination of characters using phase information only,” J. Opt. Soc. A 21, 261–266 (1990).
  16. K. Chalasinska-Macukow, F. Turon, M. J. Yzuel, J. Campos, “Contrast performance of pure phase correlation,” J. Opt. Soc. A 24, 71–75 (1993).
  17. M. Rahmati, L. G. Hassebrook, B. V. K. Vijaya Kumar, “Automatic target recognition with intensity- and distortion-invariant hybrid composite filters,” in Optical Pattern Recognition IV, D. P. Casasent, ed.Proc. SPIE1959, 133–145 (1993).
    [CrossRef]
  18. J. T. Tippett, L. C. Clapp, eds. Optical and Electro-Optical Information Processing, (MIT Press, Cambridge, Mass., 1965), pp. 130–133.
  19. A. Papoulis, Probability, Random Processes and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984), p. 241.
  20. J. L. Horner, P. Gianino, “Phase-only matched filtering,” App. Opt. 23, 812–816 (1984).
    [CrossRef]
  21. A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory. 10, 139–145 (1964).
    [CrossRef]

2000

P. Garcia-Martinez, H. H. Arsenault, S. E. Roy, “Optical implementation of the sliced orthogonal nonlinear generalized correlation for image degraded by nonoverlapping noise,” Opt. Commun. 173, 185–193 (2000).
[CrossRef]

H. H. Arsenault, D. Lefebvre, “Homomorphic cameo filter for pattern recognition that is invariant with change of illumination,” Opt. Lett. 25, 1567–1569 (2000).
[CrossRef]

1999

P. Garcia-Martinez, H. H. Arsenault, “A correlation matrix representation using sliced orthogonal nonlinear generalized decomposition,” Opt. Commun. 172, 181–192 (1999).
[CrossRef]

S. Zhang, M. A. Karim, “Illumination invariant pattern recognition with joint-transform-correlator-based morphological correlation,” Appl. Opt. 38, 7228–7237 (1999).
[CrossRef]

1993

K. Chalasinska-Macukow, F. Turon, M. J. Yzuel, J. Campos, “Contrast performance of pure phase correlation,” J. Opt. Soc. A 24, 71–75 (1993).

1991

1990

K. Chalasinska-Macukow, E. Baranska, “Discrimination of characters using phase information only,” J. Opt. Soc. A 21, 261–266 (1990).

1987

H. H. Arsenault, Y. Sheng, J. Bulabois, “Modified composite filter for pattern recognition in presence of noise with a non-zero mean,” Opt. Commun. 63, 15–20 (1987).
[CrossRef]

1985

1984

J. L. Horner, P. Gianino, “Phase-only matched filtering,” App. Opt. 23, 812–816 (1984).
[CrossRef]

1982

1980

1969

H. J. Caulfield, W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 19, 2354–2356 (1969).
[CrossRef]

1964

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory. 10, 139–145 (1964).
[CrossRef]

Arsenault, H. H.

P. Garcia-Martinez, H. H. Arsenault, S. E. Roy, “Optical implementation of the sliced orthogonal nonlinear generalized correlation for image degraded by nonoverlapping noise,” Opt. Commun. 173, 185–193 (2000).
[CrossRef]

H. H. Arsenault, D. Lefebvre, “Homomorphic cameo filter for pattern recognition that is invariant with change of illumination,” Opt. Lett. 25, 1567–1569 (2000).
[CrossRef]

P. Garcia-Martinez, H. H. Arsenault, “A correlation matrix representation using sliced orthogonal nonlinear generalized decomposition,” Opt. Commun. 172, 181–192 (1999).
[CrossRef]

H. H. Arsenault, Y. Sheng, J. Bulabois, “Modified composite filter for pattern recognition in presence of noise with a non-zero mean,” Opt. Commun. 63, 15–20 (1987).
[CrossRef]

H. H. Arsenault, C. Belisle, “Contrast-invariant pattern recognition using circular harmonic component,” Appl. Opt. 24, 2072–2075 (1985).
[CrossRef]

Y.-H. Hsu, H. H. Arsenault, “Optical pattern recognition using circular harmonic expansion,” Appl. Opt. 21, 4016–4019 (1982).
[CrossRef] [PubMed]

P. Garcia-Martinez, H. H. Arsenault, C. Ferreira, “Binary image decomposition for intensity-invariant optical nonlinear correlation,” in Optics in Computing 2000, R. A. Lessard, T. V. Galstian, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.4089, 433–438 (2000).
[CrossRef]

Baranska, E.

K. Chalasinska-Macukow, E. Baranska, “Discrimination of characters using phase information only,” J. Opt. Soc. A 21, 261–266 (1990).

Belisle, C.

Bulabois, J.

H. H. Arsenault, Y. Sheng, J. Bulabois, “Modified composite filter for pattern recognition in presence of noise with a non-zero mean,” Opt. Commun. 63, 15–20 (1987).
[CrossRef]

Campos, J.

K. Chalasinska-Macukow, F. Turon, M. J. Yzuel, J. Campos, “Contrast performance of pure phase correlation,” J. Opt. Soc. A 24, 71–75 (1993).

Casasent, D.

Caulfield, H. J.

H. J. Caulfield, W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 19, 2354–2356 (1969).
[CrossRef]

Chalasinska-Macukow, K.

K. Chalasinska-Macukow, F. Turon, M. J. Yzuel, J. Campos, “Contrast performance of pure phase correlation,” J. Opt. Soc. A 24, 71–75 (1993).

K. Chalasinska-Macukow, E. Baranska, “Discrimination of characters using phase information only,” J. Opt. Soc. A 21, 261–266 (1990).

R. Kotynski, K. Chalasinska-Macukow, “Multi-object intensity-invariant pattern recognition with an optimum processor for correlated noise,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.3749, 316–317 (1999).
[CrossRef]

R. Kotynski, K. Chalasinska-Macukow, “Normalization of correlation filter based on the Hölder’s inequality,” in Optics in Computing ’98, P. H. Chavel, D. A. Miller, H. Thienpont, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.3490, 195–198 (1998).
[CrossRef]

Dickey, F. M.

F. M. Dickey, L. A. Romero, “Normalized correlation for pattern recognition,” Opt. Lett. 16, 1186–1188 (1991).
[CrossRef] [PubMed]

B. A. Kast, F. M. Dickey, “Normalization of correlators,” in Optical information processing systems and architectures III, B. Javidi, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.1564, 34–42 (1991).
[CrossRef]

Ferreira, C.

P. Garcia-Martinez, H. H. Arsenault, C. Ferreira, “Binary image decomposition for intensity-invariant optical nonlinear correlation,” in Optics in Computing 2000, R. A. Lessard, T. V. Galstian, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.4089, 433–438 (2000).
[CrossRef]

Garcia-Martinez, P.

P. Garcia-Martinez, H. H. Arsenault, S. E. Roy, “Optical implementation of the sliced orthogonal nonlinear generalized correlation for image degraded by nonoverlapping noise,” Opt. Commun. 173, 185–193 (2000).
[CrossRef]

P. Garcia-Martinez, H. H. Arsenault, “A correlation matrix representation using sliced orthogonal nonlinear generalized decomposition,” Opt. Commun. 172, 181–192 (1999).
[CrossRef]

P. Garcia-Martinez, H. H. Arsenault, C. Ferreira, “Binary image decomposition for intensity-invariant optical nonlinear correlation,” in Optics in Computing 2000, R. A. Lessard, T. V. Galstian, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.4089, 433–438 (2000).
[CrossRef]

Gianino, P.

J. L. Horner, P. Gianino, “Phase-only matched filtering,” App. Opt. 23, 812–816 (1984).
[CrossRef]

Hassebrook, L. G.

M. Rahmati, L. G. Hassebrook, B. V. K. Vijaya Kumar, “Automatic target recognition with intensity- and distortion-invariant hybrid composite filters,” in Optical Pattern Recognition IV, D. P. Casasent, ed.Proc. SPIE1959, 133–145 (1993).
[CrossRef]

Hester, C. F.

Horner, J. L.

J. L. Horner, P. Gianino, “Phase-only matched filtering,” App. Opt. 23, 812–816 (1984).
[CrossRef]

Hsu, Y.-H.

Karim, M. A.

Kast, B. A.

B. A. Kast, F. M. Dickey, “Normalization of correlators,” in Optical information processing systems and architectures III, B. Javidi, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.1564, 34–42 (1991).
[CrossRef]

Kotynski, R.

R. Kotynski, K. Chalasinska-Macukow, “Normalization of correlation filter based on the Hölder’s inequality,” in Optics in Computing ’98, P. H. Chavel, D. A. Miller, H. Thienpont, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.3490, 195–198 (1998).
[CrossRef]

R. Kotynski, K. Chalasinska-Macukow, “Multi-object intensity-invariant pattern recognition with an optimum processor for correlated noise,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.3749, 316–317 (1999).
[CrossRef]

Lefebvre, D.

Maloney, W. T.

H. J. Caulfield, W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 19, 2354–2356 (1969).
[CrossRef]

Papoulis, A.

A. Papoulis, Probability, Random Processes and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984), p. 241.

Rahmati, M.

M. Rahmati, L. G. Hassebrook, B. V. K. Vijaya Kumar, “Automatic target recognition with intensity- and distortion-invariant hybrid composite filters,” in Optical Pattern Recognition IV, D. P. Casasent, ed.Proc. SPIE1959, 133–145 (1993).
[CrossRef]

Romero, L. A.

Roy, S. E.

P. Garcia-Martinez, H. H. Arsenault, S. E. Roy, “Optical implementation of the sliced orthogonal nonlinear generalized correlation for image degraded by nonoverlapping noise,” Opt. Commun. 173, 185–193 (2000).
[CrossRef]

Sheng, Y.

H. H. Arsenault, Y. Sheng, J. Bulabois, “Modified composite filter for pattern recognition in presence of noise with a non-zero mean,” Opt. Commun. 63, 15–20 (1987).
[CrossRef]

Turon, F.

K. Chalasinska-Macukow, F. Turon, M. J. Yzuel, J. Campos, “Contrast performance of pure phase correlation,” J. Opt. Soc. A 24, 71–75 (1993).

Vander Lugt, A.

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory. 10, 139–145 (1964).
[CrossRef]

Vijaya Kumar, B. V. K.

M. Rahmati, L. G. Hassebrook, B. V. K. Vijaya Kumar, “Automatic target recognition with intensity- and distortion-invariant hybrid composite filters,” in Optical Pattern Recognition IV, D. P. Casasent, ed.Proc. SPIE1959, 133–145 (1993).
[CrossRef]

Yzuel, M. J.

K. Chalasinska-Macukow, F. Turon, M. J. Yzuel, J. Campos, “Contrast performance of pure phase correlation,” J. Opt. Soc. A 24, 71–75 (1993).

Zhang, S.

App. Opt.

J. L. Horner, P. Gianino, “Phase-only matched filtering,” App. Opt. 23, 812–816 (1984).
[CrossRef]

Appl. Opt.

IEEE Trans. Inf. Theory.

A. Vander Lugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory. 10, 139–145 (1964).
[CrossRef]

J. Opt. Soc. A

K. Chalasinska-Macukow, E. Baranska, “Discrimination of characters using phase information only,” J. Opt. Soc. A 21, 261–266 (1990).

K. Chalasinska-Macukow, F. Turon, M. J. Yzuel, J. Campos, “Contrast performance of pure phase correlation,” J. Opt. Soc. A 24, 71–75 (1993).

Opt. Commun.

P. Garcia-Martinez, H. H. Arsenault, “A correlation matrix representation using sliced orthogonal nonlinear generalized decomposition,” Opt. Commun. 172, 181–192 (1999).
[CrossRef]

P. Garcia-Martinez, H. H. Arsenault, S. E. Roy, “Optical implementation of the sliced orthogonal nonlinear generalized correlation for image degraded by nonoverlapping noise,” Opt. Commun. 173, 185–193 (2000).
[CrossRef]

H. H. Arsenault, Y. Sheng, J. Bulabois, “Modified composite filter for pattern recognition in presence of noise with a non-zero mean,” Opt. Commun. 63, 15–20 (1987).
[CrossRef]

Opt. Lett.

Other

M. Rahmati, L. G. Hassebrook, B. V. K. Vijaya Kumar, “Automatic target recognition with intensity- and distortion-invariant hybrid composite filters,” in Optical Pattern Recognition IV, D. P. Casasent, ed.Proc. SPIE1959, 133–145 (1993).
[CrossRef]

J. T. Tippett, L. C. Clapp, eds. Optical and Electro-Optical Information Processing, (MIT Press, Cambridge, Mass., 1965), pp. 130–133.

A. Papoulis, Probability, Random Processes and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984), p. 241.

P. Garcia-Martinez, H. H. Arsenault, C. Ferreira, “Binary image decomposition for intensity-invariant optical nonlinear correlation,” in Optics in Computing 2000, R. A. Lessard, T. V. Galstian, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.4089, 433–438 (2000).
[CrossRef]

B. A. Kast, F. M. Dickey, “Normalization of correlators,” in Optical information processing systems and architectures III, B. Javidi, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.1564, 34–42 (1991).
[CrossRef]

R. Kotynski, K. Chalasinska-Macukow, “Normalization of correlation filter based on the Hölder’s inequality,” in Optics in Computing ’98, P. H. Chavel, D. A. Miller, H. Thienpont, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.3490, 195–198 (1998).
[CrossRef]

R. Kotynski, K. Chalasinska-Macukow, “Multi-object intensity-invariant pattern recognition with an optimum processor for correlated noise,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, ed., Proc. Soc. Photo.-Opt. Instrum. Eng.3749, 316–317 (1999).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Target images: true and false targets.

Fig. 2
Fig. 2

Scene containing true (top) and false (bottom) targets. Objects in corresponding positions in the top and bottom halves have similar intensities.

Fig. 3
Fig. 3

Correlation results with only disjoint correlated noise: All of the true correlation peaks are equal.

Fig. 4
Fig. 4

Scene with additive Gaussian noise and disjoint correlated noise.

Fig. 5
Fig. 5

Correlation results for additive Gaussian noise.

Tables (2)

Tables Icon

Table 1 Intensity Transformation Parametersa

Tables Icon

Table 2 Comparative Performance in the Presence of Noise

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

fx=afx+bx,
hx=αfx+βx, fx * hxx=0=1, x * hxx=0=0,
α=RRffR-Rf2, β=-RfRffR-Rf2,
Rff=fx * fxx=0, R=x * xx=0, Rf=Rf=fx * xx=0.
hx=RRffR-Rf2fx-RfR x.
hx  fx-μfx=f0x,
s2x * xN-sx * x2N2.
C=1f0 * f0x=0×sx * f0x2s2x * x-1/Nsx * x2.
cos2 θ=g0x ° f0x2|g0x|2|f0x|2.
g2x ° x-1/Ngx ° x2.
cos2 θ=1f0x * f0xx=0×gx * f0x2g2x * x-1/Ngx * x2.
Ey2x=σ2E,
E=- |hx|2dx=Rf0f00
C0=σ2Rf0f0NRf0f0σ2=1N,
af+n * f02=aRf0f0+Rfn2.
σaf+n2=a2σf2+σn2,
Ca2Rf0f02NRf0f0a2σf02+σn2=N2a2σf04N2σf02a2σf02+σn2,
Ca2σf2a2σf2+σn2.
σn2  0
C  1,
σn2a2σf2  1, Ca2σf2σn2.
Cm=|afx+nx * f0x|2Rf0f02=aRf0f0+Rf0n2Rf0f02a2.
Cm=n * f2Rf0f02=Rf0n2Rf0f02,
SNRm=a2Rffσn2=a2Nσf2σn2,
SNR=a2Nσf2a2σf2+σn2.
R=SNRSNRm=σn2a2σf2+σn2=11+a2σf2σn2.
σn2  a2σf2 Rσn2a2σf2
Cg=g * f02NRffσg2=Rf0g2NRffσg2=Rf0g2RffRgg.
PSRf=CCg=RffRggRfg2,
Cmf=g * f02Rff2=Rfg2Rff2,
PSRm=a2Rff2Rfg2.
Q=PSRPSRm=Rgga2Rff.
Q1/a2.

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