Abstract

We propose a new algorithm for estimating the location of an object in multichannel images when the noise is spatially disjointed from (nonoverlapping with) the target. This algorithm is optimal for nonoverlapping noise and for multichannel images in the maximum-likelihood sense. We consider the case in which the statistical parameters of the input scene are unknown and are estimated by observation. We assess the results for simulated images with white and Gaussian background, for a large scale of variances of the background noise, and different values of the contrast in the scene. We compare the results of this algorithm with the results obtained with two other algorithms, the optimal algorithm for monochannel nonoverlapping noise and the optimal algorithm for multichannel additive noise, and we show that in both cases improvement can be obtained. We show the efficiency of the estimation for real input scenes when the background noise is correlated clutter noise. This algorithm has the same complexity as correlation, and the improvement is obtained with no more calculation cost than with classic methods.

© 2000 Optical Society of America

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  1. C. Warde, H. J. Caulfield, F. T. S. Yu, J. E. Ludman, Opt. Commun. 49, 241–244 (1984).
    [CrossRef]
  2. F. T. S. Yu, B. Javidi, “Experiments on real time polychromatic signal detection by matched spatial filtering,” Opt. Commun. 56, 384–388 (1986).
    [CrossRef]
  3. H. J. Caulfield, I. Moreno, J. Campos, M. J. Yzuel, “Coherent recognition of colored patterns,” Opt. Commun. 133, 77–81 (1997).
    [CrossRef]
  4. E. Badiqué, Y. Komiya, N. Ohyama, J. Tsujichy, T. Honda, “Colour image correlation,” Opt. Commun. 61, 181–186 (1987).
    [CrossRef]
  5. C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel filtering,” Opt. Eng. 31, 2231–2238 (1992).
    [CrossRef]
  6. M. S. Millan, J. Campos, C. Fereirra, M. J. Yzuel, “Matched filter and phase only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
    [CrossRef]
  7. Z. Gu, S. H. Lee, Y. Fainman, “Statistical recognition of color images,” Appl. Opt. 26, 3145–3152 (1992).
    [CrossRef]
  8. M. S. Millan, M. J. Yzuel, J. Campos, C. Ferreira, “Different strategies in optical recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
    [CrossRef] [PubMed]
  9. J. Campos, M. Montes-Usategui, I. Juvells, M. J. Yzuel, “On the necessity of multiple filters in optical pattern recognition,” in Euro-American Workshop on Optical Pattern Recognition, Ph. Réfrégier, B. Javidi, eds. (SPIE Press, Bellingham, Washington, 1994), pp. 137–166.
  10. L. P. Yaroslavsky, “The theory of optimal methods for localization of objects in images,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1993), Vol. XXXII, pp. 145–201 (1993).
  11. M. Guillaume, Ph. Réfrégier, J. Campos, V. Lashin, “Detection theory approach to multichannel pattern location,” Opt. Lett. 22, 1887–1889 (1997).
    [CrossRef]
  12. M. Guillaume, J. Campos, V. Lashin, “Pattern location estimation for multichannel images,” Opt. Commun. 165, 107–117 (1999).
    [CrossRef]
  13. B. Javidi, J. Wang, “Limitation of the classic definition of the correlation signal-to-noise ratio in optical pattern recogition with disjoint signal and scene noise,” Appl. Opt. 31, 6826–6829 (1992).
    [CrossRef] [PubMed]
  14. Ph. Réfrégier, Théorie du Signal. Signal Information Fluctuations (Masson, Paris, 1993).
  15. B. Javidi, Ph. Réfrégier, P. Willet, “Optimum receiver design for pattern recognition with nonoverlapping target and scene noise,” Opt. Lett. 18, 1660–1662 (1993).
    [CrossRef] [PubMed]
  16. F. Goudail, Ph. Réfrégier, “Optimal detection of a target with random gray levels on a spatially disjoint noise,” Opt. Lett. 21, 495–497 (1996).
    [CrossRef] [PubMed]
  17. V. Kober, J. Campos, “Accuracy of location measurements of a noisy target in nonoverlapping background,” J. Opt. Soc. Am. A 13, 1653–1666 (1996).
    [CrossRef]
  18. F. Goudail, V. Laude, Ph. Réfrégier, “Influence of non-overlapping noise on regularized linear filters for pattern recognition,” Opt. Lett. 20, 2237–2239 (1995).
    [CrossRef]
  19. F. Goudail, Ph. Réfrégier, “Optimal and suboptimal detection of a target with random gray levels imbedded in non-overlapping noise,” Opt. Commun. 125, 211–216 (1996).
    [CrossRef]

1999 (1)

M. Guillaume, J. Campos, V. Lashin, “Pattern location estimation for multichannel images,” Opt. Commun. 165, 107–117 (1999).
[CrossRef]

1997 (2)

M. Guillaume, Ph. Réfrégier, J. Campos, V. Lashin, “Detection theory approach to multichannel pattern location,” Opt. Lett. 22, 1887–1889 (1997).
[CrossRef]

H. J. Caulfield, I. Moreno, J. Campos, M. J. Yzuel, “Coherent recognition of colored patterns,” Opt. Commun. 133, 77–81 (1997).
[CrossRef]

1996 (3)

1995 (1)

1993 (1)

1992 (4)

1989 (1)

M. S. Millan, J. Campos, C. Fereirra, M. J. Yzuel, “Matched filter and phase only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
[CrossRef]

1987 (1)

E. Badiqué, Y. Komiya, N. Ohyama, J. Tsujichy, T. Honda, “Colour image correlation,” Opt. Commun. 61, 181–186 (1987).
[CrossRef]

1986 (1)

F. T. S. Yu, B. Javidi, “Experiments on real time polychromatic signal detection by matched spatial filtering,” Opt. Commun. 56, 384–388 (1986).
[CrossRef]

1984 (1)

C. Warde, H. J. Caulfield, F. T. S. Yu, J. E. Ludman, Opt. Commun. 49, 241–244 (1984).
[CrossRef]

Badiqué, E.

E. Badiqué, Y. Komiya, N. Ohyama, J. Tsujichy, T. Honda, “Colour image correlation,” Opt. Commun. 61, 181–186 (1987).
[CrossRef]

Campos, J.

M. Guillaume, J. Campos, V. Lashin, “Pattern location estimation for multichannel images,” Opt. Commun. 165, 107–117 (1999).
[CrossRef]

M. Guillaume, Ph. Réfrégier, J. Campos, V. Lashin, “Detection theory approach to multichannel pattern location,” Opt. Lett. 22, 1887–1889 (1997).
[CrossRef]

H. J. Caulfield, I. Moreno, J. Campos, M. J. Yzuel, “Coherent recognition of colored patterns,” Opt. Commun. 133, 77–81 (1997).
[CrossRef]

V. Kober, J. Campos, “Accuracy of location measurements of a noisy target in nonoverlapping background,” J. Opt. Soc. Am. A 13, 1653–1666 (1996).
[CrossRef]

C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel filtering,” Opt. Eng. 31, 2231–2238 (1992).
[CrossRef]

M. S. Millan, M. J. Yzuel, J. Campos, C. Ferreira, “Different strategies in optical recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
[CrossRef] [PubMed]

M. S. Millan, J. Campos, C. Fereirra, M. J. Yzuel, “Matched filter and phase only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
[CrossRef]

J. Campos, M. Montes-Usategui, I. Juvells, M. J. Yzuel, “On the necessity of multiple filters in optical pattern recognition,” in Euro-American Workshop on Optical Pattern Recognition, Ph. Réfrégier, B. Javidi, eds. (SPIE Press, Bellingham, Washington, 1994), pp. 137–166.

Caulfield, H. J.

H. J. Caulfield, I. Moreno, J. Campos, M. J. Yzuel, “Coherent recognition of colored patterns,” Opt. Commun. 133, 77–81 (1997).
[CrossRef]

C. Warde, H. J. Caulfield, F. T. S. Yu, J. E. Ludman, Opt. Commun. 49, 241–244 (1984).
[CrossRef]

Fainman, Y.

Fereirra, C.

M. S. Millan, J. Campos, C. Fereirra, M. J. Yzuel, “Matched filter and phase only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
[CrossRef]

Ferreira, C.

M. S. Millan, M. J. Yzuel, J. Campos, C. Ferreira, “Different strategies in optical recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
[CrossRef] [PubMed]

C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel filtering,” Opt. Eng. 31, 2231–2238 (1992).
[CrossRef]

Goudail, F.

Gu, Z.

Guillaume, M.

M. Guillaume, J. Campos, V. Lashin, “Pattern location estimation for multichannel images,” Opt. Commun. 165, 107–117 (1999).
[CrossRef]

M. Guillaume, Ph. Réfrégier, J. Campos, V. Lashin, “Detection theory approach to multichannel pattern location,” Opt. Lett. 22, 1887–1889 (1997).
[CrossRef]

Honda, T.

E. Badiqué, Y. Komiya, N. Ohyama, J. Tsujichy, T. Honda, “Colour image correlation,” Opt. Commun. 61, 181–186 (1987).
[CrossRef]

Javidi, B.

Juvells, I.

J. Campos, M. Montes-Usategui, I. Juvells, M. J. Yzuel, “On the necessity of multiple filters in optical pattern recognition,” in Euro-American Workshop on Optical Pattern Recognition, Ph. Réfrégier, B. Javidi, eds. (SPIE Press, Bellingham, Washington, 1994), pp. 137–166.

Kober, V.

Komiya, Y.

E. Badiqué, Y. Komiya, N. Ohyama, J. Tsujichy, T. Honda, “Colour image correlation,” Opt. Commun. 61, 181–186 (1987).
[CrossRef]

Lashin, V.

M. Guillaume, J. Campos, V. Lashin, “Pattern location estimation for multichannel images,” Opt. Commun. 165, 107–117 (1999).
[CrossRef]

M. Guillaume, Ph. Réfrégier, J. Campos, V. Lashin, “Detection theory approach to multichannel pattern location,” Opt. Lett. 22, 1887–1889 (1997).
[CrossRef]

Laude, V.

Lee, S. H.

Ludman, J. E.

C. Warde, H. J. Caulfield, F. T. S. Yu, J. E. Ludman, Opt. Commun. 49, 241–244 (1984).
[CrossRef]

Millan, M. S.

C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel filtering,” Opt. Eng. 31, 2231–2238 (1992).
[CrossRef]

M. S. Millan, M. J. Yzuel, J. Campos, C. Ferreira, “Different strategies in optical recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
[CrossRef] [PubMed]

M. S. Millan, J. Campos, C. Fereirra, M. J. Yzuel, “Matched filter and phase only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
[CrossRef]

Montes-Usategui, M.

J. Campos, M. Montes-Usategui, I. Juvells, M. J. Yzuel, “On the necessity of multiple filters in optical pattern recognition,” in Euro-American Workshop on Optical Pattern Recognition, Ph. Réfrégier, B. Javidi, eds. (SPIE Press, Bellingham, Washington, 1994), pp. 137–166.

Moreno, I.

H. J. Caulfield, I. Moreno, J. Campos, M. J. Yzuel, “Coherent recognition of colored patterns,” Opt. Commun. 133, 77–81 (1997).
[CrossRef]

Ohyama, N.

E. Badiqué, Y. Komiya, N. Ohyama, J. Tsujichy, T. Honda, “Colour image correlation,” Opt. Commun. 61, 181–186 (1987).
[CrossRef]

Réfrégier, Ph.

Tsujichy, J.

E. Badiqué, Y. Komiya, N. Ohyama, J. Tsujichy, T. Honda, “Colour image correlation,” Opt. Commun. 61, 181–186 (1987).
[CrossRef]

Wang, J.

Warde, C.

C. Warde, H. J. Caulfield, F. T. S. Yu, J. E. Ludman, Opt. Commun. 49, 241–244 (1984).
[CrossRef]

Willet, P.

Yaroslavsky, L. P.

L. P. Yaroslavsky, “The theory of optimal methods for localization of objects in images,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1993), Vol. XXXII, pp. 145–201 (1993).

Yu, F. T. S.

F. T. S. Yu, B. Javidi, “Experiments on real time polychromatic signal detection by matched spatial filtering,” Opt. Commun. 56, 384–388 (1986).
[CrossRef]

C. Warde, H. J. Caulfield, F. T. S. Yu, J. E. Ludman, Opt. Commun. 49, 241–244 (1984).
[CrossRef]

Yzuel, M. J.

H. J. Caulfield, I. Moreno, J. Campos, M. J. Yzuel, “Coherent recognition of colored patterns,” Opt. Commun. 133, 77–81 (1997).
[CrossRef]

C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel filtering,” Opt. Eng. 31, 2231–2238 (1992).
[CrossRef]

M. S. Millan, M. J. Yzuel, J. Campos, C. Ferreira, “Different strategies in optical recognition of polychromatic images,” Appl. Opt. 31, 2560–2567 (1992).
[CrossRef] [PubMed]

M. S. Millan, J. Campos, C. Fereirra, M. J. Yzuel, “Matched filter and phase only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
[CrossRef]

J. Campos, M. Montes-Usategui, I. Juvells, M. J. Yzuel, “On the necessity of multiple filters in optical pattern recognition,” in Euro-American Workshop on Optical Pattern Recognition, Ph. Réfrégier, B. Javidi, eds. (SPIE Press, Bellingham, Washington, 1994), pp. 137–166.

Appl. Opt. (3)

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

Opt. Commun. (7)

M. S. Millan, J. Campos, C. Fereirra, M. J. Yzuel, “Matched filter and phase only filter performance in colour image recognition,” Opt. Commun. 73, 277–284 (1989).
[CrossRef]

C. Warde, H. J. Caulfield, F. T. S. Yu, J. E. Ludman, Opt. Commun. 49, 241–244 (1984).
[CrossRef]

F. T. S. Yu, B. Javidi, “Experiments on real time polychromatic signal detection by matched spatial filtering,” Opt. Commun. 56, 384–388 (1986).
[CrossRef]

H. J. Caulfield, I. Moreno, J. Campos, M. J. Yzuel, “Coherent recognition of colored patterns,” Opt. Commun. 133, 77–81 (1997).
[CrossRef]

E. Badiqué, Y. Komiya, N. Ohyama, J. Tsujichy, T. Honda, “Colour image correlation,” Opt. Commun. 61, 181–186 (1987).
[CrossRef]

M. Guillaume, J. Campos, V. Lashin, “Pattern location estimation for multichannel images,” Opt. Commun. 165, 107–117 (1999).
[CrossRef]

F. Goudail, Ph. Réfrégier, “Optimal and suboptimal detection of a target with random gray levels imbedded in non-overlapping noise,” Opt. Commun. 125, 211–216 (1996).
[CrossRef]

Opt. Eng. (1)

C. Ferreira, M. S. Millan, M. J. Yzuel, J. Campos, “Experimental results in color pattern recognition by multichannel filtering,” Opt. Eng. 31, 2231–2238 (1992).
[CrossRef]

Opt. Lett. (4)

Other (3)

Ph. Réfrégier, Théorie du Signal. Signal Information Fluctuations (Masson, Paris, 1993).

J. Campos, M. Montes-Usategui, I. Juvells, M. J. Yzuel, “On the necessity of multiple filters in optical pattern recognition,” in Euro-American Workshop on Optical Pattern Recognition, Ph. Réfrégier, B. Javidi, eds. (SPIE Press, Bellingham, Washington, 1994), pp. 137–166.

L. P. Yaroslavsky, “The theory of optimal methods for localization of objects in images,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1993), Vol. XXXII, pp. 145–201 (1993).

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Figures (9)

Fig. 1
Fig. 1

R, G, B channels of the image of a butterfly that we used to perform the simulations. R+G+B, addition of the three channels; R+nb, R channel with a nonoverlapping background; R+nb+n, red channel with a nonoverlapping background and additive noise.

Fig. 2
Fig. 2

Probabilities of good location as a function of additive-noise variance for the simulated images: α¯=(1, 1, 1), σ¯b2=(100, 100, 100). The background mean is the same in each channel (except for mb¯=mr¯), and takes the following values: ○, mb(l)=0; △, mb(l)=100; ◇, mb(l)=mb(l)=mr(l); □, mb(l)=150; +, mb(l)=225.

Fig. 3
Fig. 3

Probabilities of good location as a function of the additive-noise variance for the simulated images: α¯=(1, 1, 1); the background mean, mb¯=mr¯=(117, 97, 72). The background variance has the same value, [σb(l)2], in each channel and takes the following values: + indicates [σr(l)]2, ◇ indicates 105, ● indicates 5×105, △ indicates 106, and □ indicates 107.

Fig. 4
Fig. 4

Probabilities of good location as a function of additive-noise variance for the simulated images, for the following values of α¯: ○, α¯=(1, 1, 1); +, α¯=(1, 1, 2); △, α¯=(2, 2, 2); ◇, α¯=(1, 1, 10).

Fig. 5
Fig. 5

Comparison of the probabilities of good location for ◇, proposed NOMC model; △, NOBW model; ○, MCAN model. The variance of the background is σ¯b2¯=(100, 100, 100), and the mean value of the background is (a) mb(l)=0, (b) mb(l)=mr(l), and (c) mb(l)=255.

Fig. 6
Fig. 6

Comparison of the probabilities of good location versus variance of the additive noise in the B and G channels for the three algorithms: ◇, NOMC; △, NOBW; ○ MCAN. The variance of the background is 100 in the three channels, and the mean value of the background is (a) mb¯=(0, 0, 0), (b) mb¯=mr¯, (c) mb¯=(255,255,255). The additive noise variance σn2¯ is proportional to (10-2, 1, 1), respectively, in the R, G, B channels.

Fig. 7
Fig. 7

Comparison of the results for the three algorithms: ◇, NOMC; △, NOBW; ○, MCAN. The mean value of the background is mb¯=mr¯, and (a) α¯=(1, 1, 2) and σb2¯=(100, 100, 100), (b) α¯=(1, 1, 1), and σb2¯=(102, 102, 106).

Fig. 8
Fig. 8

R, G, B channels of the input scene with a real background.

Fig. 9
Fig. 9

Probabilities of good detection for real input scenes when (a) C=1.3, and (b) C=3 for ◇, the NOMC and △ the NOBW algorithms.

Equations (22)

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

si(l)=α(l)ri-j(l)Wi-j(l)+bi(l)[1-Wi-j(l)]+ni(l).
l=log L(j, α¯, σ¯n, m¯b, σ¯b)=l=1P-log((2π)N/2[σn(l)]Na(l){[σn(l)]2+[σb(l)]2}Nb(l)/2)-l=1P12[σn(l)]2i=1N[si(l)-α(l)ri-j(l)]2Wi-j(l)-l=1P12{[σn(l)]2+[σb(l)]2}×i=1N[si(l)-mb(l)]2[1-Wi-j(l)],
jML=arg maxj[log L(j, α¯, σ¯n, m¯b, σ¯b)]
jML=arg maxjl=1P-log((2π)N/2[σn(l)]Na(l)×{[σn(l)]2+[σb(l)]2}Nb(l)/2)-l=1P12[σn(l)]2×{CW,s2(l)(j)-2α(l)Cr,s(l)(j)+[α(l)]2Cr,r(l)(0)}-l=1P12×{[σn(l)]2+[σb(l)]2}×{Cs,s(l)(0)-CW,s2(l)(j)-2mb(l)C1,s(l)(0)+2mb(l)CW,s(l)(j)+Nb(l)[mb(l)]2},
 log L(j, α¯, σ¯n, m¯b, σ¯b)α(l)=0,
 log L(j, α¯, σ¯n, m¯b, σ¯b)σn(l)=0,
 log L(j, α¯, σ¯n, m¯b, σ¯b)mb(l)=0,
 log L(j, α¯, σ¯n, m¯b, σ¯b)σb(l)=0.
αML(l)(j)=Cr,s(l)(j)Cr,r(0),
mbML(l)(j)=1Nb(l)[C1,s(l)(0)-CW,s(l)(j)],
[σnML(l)(j)]2=A(l)(j)Na(l),
[σbML(l)(j)]2=B(l)(j)Nb(l)-A(l)(j)Na(l),
B(l)(j)=C(1-W),s2(l)(j)-1Nb(l)[C(1-W),s(l)(j)]2,
A(l)(j)=CW,s2(l)(j)-[Cr,s(l)(j)]2Cr,r(l)(0).
jML=arg maxjl=1p-Na(l) log[A(l)(j)]-Nb(l) log[B(l)(j)],
jML=arg minjl=1PNa(l) log{[σnML(l)(j)]2}+Nb(l) log{[σnML(l)(j)]2+[σbML(l)(j)]2}.
B(j)=C(1-W),s2(j)-1Nb[C(1-W),s(j)]2,
A(j)=CW,s2(j)-Cr,s2(j)Cr,r(0),
jML=arg maxj{-Na log[A(j)]-Nb log[B(j)]}.
jML=arg maxj l=1P logCs,s(l)(0)-Cr,sl2(j)Cr,r(l)(0).
jML=arg maxj l=1PCr,s(l)(j)α(l)2{[σn(l)]2+[σb(l)]2}-l=1PCW,s(l)×(j)mb(l)[σn(l)]2+[σb(l)2]-l=1PCW,s2(l)(j)×σbl22[σn(l)2]{[σn(l)]2+[σb(l)]2}.
σb(l)22[σn(l)2]{[σn(l)]2+[σn(l)]2}=β(l)(1+β(l))[σn(l)2], β(l)=σb(l)2/σn(l)2.

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