Abstract

We describe a pattern recognition processor based on a new optimal χ2 filtering method that is designed to localize a target with unknown gray levels appearing on a random background. This processor consists of preprocessing of the analyzed image followed by correlations with binary masks.

© 1997 Optical Society of America

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References

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  1. A. VanderLugt, IEEE Trans. Inform. Theory IT-10, 139 (1964).
  2. B. Javidi and J. Wang, Appl. Opt. 31, 6826 (1992).
    [CrossRef] [PubMed]
  3. F. Goudail, V. Laude, and Ph. Réfrégier, Opt. Lett. 20, 2237 (1995).
    [CrossRef]
  4. Ph. Réfrégier, B. Javidi, and G. Zhang, Opt. Lett. 18, 1453 (1993).
    [CrossRef]
  5. B. Javidi, Ph. Réfrégier, and P. Willet, Opt. Lett. 18, 1660 (1993).
    [CrossRef] [PubMed]
  6. R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973), pp. 10–35.
  7. F. Goudail and Ph. Réfrégier, Opt. Lett. 21, 495 (1996).
    [CrossRef] [PubMed]
  8. F. Goudail and Ph. Réfrégier, Opt. Commun. 125, 211 (1996).
    [CrossRef]
  9. Ph. Réfrégier, F. Goudail, and Th. Gaidon, Opt. Commun. 128, 211 (1996).
    [CrossRef]
  10. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1960), pp. 243–248.
  11. Ph. Réfrégier, B. Javidi, and V. Laude, Opt. Lett. 19, 405 (1994).

1996 (3)

F. Goudail and Ph. Réfrégier, Opt. Commun. 125, 211 (1996).
[CrossRef]

Ph. Réfrégier, F. Goudail, and Th. Gaidon, Opt. Commun. 128, 211 (1996).
[CrossRef]

F. Goudail and Ph. Réfrégier, Opt. Lett. 21, 495 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

1993 (2)

1992 (1)

1964 (1)

A. VanderLugt, IEEE Trans. Inform. Theory IT-10, 139 (1964).

Duda, R. O.

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973), pp. 10–35.

Feller, W.

W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1960), pp. 243–248.

Gaidon, Th.

Ph. Réfrégier, F. Goudail, and Th. Gaidon, Opt. Commun. 128, 211 (1996).
[CrossRef]

Goudail, F.

Ph. Réfrégier, F. Goudail, and Th. Gaidon, Opt. Commun. 128, 211 (1996).
[CrossRef]

F. Goudail and Ph. Réfrégier, Opt. Commun. 125, 211 (1996).
[CrossRef]

F. Goudail and Ph. Réfrégier, Opt. Lett. 21, 495 (1996).
[CrossRef] [PubMed]

F. Goudail, V. Laude, and Ph. Réfrégier, Opt. Lett. 20, 2237 (1995).
[CrossRef]

Hart, P. E.

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973), pp. 10–35.

Javidi, B.

Laude, V.

Réfrégier, Ph.

VanderLugt, A.

A. VanderLugt, IEEE Trans. Inform. Theory IT-10, 139 (1964).

Wang, J.

Willet, P.

Zhang, G.

Appl. Opt. (1)

IEEE Trans. Inform. Theory (1)

A. VanderLugt, IEEE Trans. Inform. Theory IT-10, 139 (1964).

Opt. Commun. (2)

F. Goudail and Ph. Réfrégier, Opt. Commun. 125, 211 (1996).
[CrossRef]

Ph. Réfrégier, F. Goudail, and Th. Gaidon, Opt. Commun. 128, 211 (1996).
[CrossRef]

Opt. Lett. (5)

Other (2)

R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973), pp. 10–35.

W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1960), pp. 243–248.

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Figures (3)

Fig. 1
Fig. 1

(a) Example of a scene used in the simulations. (b) Binary support of the reference. (c) Result of the processing of (a) with the optimal χ2 filtering method. (d) Result of the processing of (a) with the optimal filter for white Gaussian pdf’s. Note: (c) and (d) are plots of the maximum of each line of the output plane of the considered method.

Fig. 2
Fig. 2

Probabilities of detection obtained with the optimal filter for white Gaussian pdf’s (curve  a) and with the optimal χ2 filtering method (curve  b). The pdf parameters of the background are mb=0 and σb=1. The pdf parameters of the target are ma=δ and σa=1+δ. The correlation lengths l are equal to 1 in the target and in the background.

Fig. 3
Fig. 3

(a) Scene used in the test. (b) Gray-level reference object. (c) Result of the processing of (a) with the optimal χ2 filtering method. (d) Result of the processing of (a) with the optimal nonlinear joint-transform correlator filter. Note: (c) and (d) are plots of the maximum of each line of the output plane of the considered method.

Equations (8)

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si=aiwi-j+bi1-wi-j,
yi=jViμjsj,
yi=giinwi-jin+gioutwi-jout+gifrwi-jfr.
Pχ2zi=122πziμexp-zi2µ.
P[z|Hj, μin, μout, μfr]=A exp-12μini=1Nziwi-jin-12μouti=1Nziwi-jout-12μfri=1Nziwi-jfr,
A-1=8πN/2μinNin/2μoutNout/2μfrNfr/2i=1Nzi.
μˆαj=1Nα{i|wi-jα=1}zi=1Nαzwαj,
Fj=-Nin logμ^inj-Nout logμ^outj-Nfr logμ^frj.

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