Abstract

The concept of a statistical filter for objects that comprise several regions is introduced. The process is optimal in the presence of nonoverlapping noise for the target and may perform independently of variations in the mean value in every region. The basic performance of the filter is described, and a comparison with other types of processing is made.

© 2001 Optical Society of America

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References

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  1. G. L. Turin, IRE Trans. Inf. Theory IT-6, 311 (1960).
    [CrossRef]
  2. A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 145 (1964).
  3. P. Garcia-Martinez, H. H. Arsenault, and S. Roy, Opt. Commun. 173, 185 (2000).
    [CrossRef]
  4. B. Javidi and J. Wang, J. Opt. Soc. Am. A 11, 2604 (1994).
    [CrossRef]
  5. R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Wiley, New York, 1973).
  6. F. Goudail and P. Réfrégier, Opt. Lett. 21, 495 (1996).
    [CrossRef] [PubMed]
  7. B. Javidi, P. Réfrégier, and P. Willet, Opt. Lett. 18, 1660 (1993).
    [CrossRef] [PubMed]
  8. F. Guérault and P. Réfrégier, Opt. Commun. 142, 197 (1997).
    [CrossRef]
  9. P. H. Garthwaite, I. T. Jolliffe, and B. Jones, Statistical Inference (Prentice-Hall, London, 1995).
  10. V. Pagé, F. Goudail, and P. Réfrégier, Opt. Lett. 24, 1383 (1999).
    [CrossRef]
  11. C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images (Artech House, Norwood, Mass., 1998).

2000

P. Garcia-Martinez, H. H. Arsenault, and S. Roy, Opt. Commun. 173, 185 (2000).
[CrossRef]

1999

1997

F. Guérault and P. Réfrégier, Opt. Commun. 142, 197 (1997).
[CrossRef]

1996

1994

1993

1964

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 145 (1964).

1960

G. L. Turin, IRE Trans. Inf. Theory IT-6, 311 (1960).
[CrossRef]

Arsenault, H. H.

P. Garcia-Martinez, H. H. Arsenault, and S. Roy, Opt. Commun. 173, 185 (2000).
[CrossRef]

Duda, R. O.

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

Garcia-Martinez, P.

P. Garcia-Martinez, H. H. Arsenault, and S. Roy, Opt. Commun. 173, 185 (2000).
[CrossRef]

Garthwaite, P. H.

P. H. Garthwaite, I. T. Jolliffe, and B. Jones, Statistical Inference (Prentice-Hall, London, 1995).

Goudail, F.

Guérault, F.

F. Guérault and P. Réfrégier, Opt. Commun. 142, 197 (1997).
[CrossRef]

Hart, P. E.

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

Javidi, B.

Jolliffe, I. T.

P. H. Garthwaite, I. T. Jolliffe, and B. Jones, Statistical Inference (Prentice-Hall, London, 1995).

Jones, B.

P. H. Garthwaite, I. T. Jolliffe, and B. Jones, Statistical Inference (Prentice-Hall, London, 1995).

Oliver, C.

C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images (Artech House, Norwood, Mass., 1998).

Pagé, V.

Quegan, S.

C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images (Artech House, Norwood, Mass., 1998).

Réfrégier, P.

Roy, S.

P. Garcia-Martinez, H. H. Arsenault, and S. Roy, Opt. Commun. 173, 185 (2000).
[CrossRef]

Turin, G. L.

G. L. Turin, IRE Trans. Inf. Theory IT-6, 311 (1960).
[CrossRef]

VanderLugt, A.

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 145 (1964).

Wang, J.

Willet, P.

IEEE Trans. Inf. Theory

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 145 (1964).

IRE Trans. Inf. Theory

G. L. Turin, IRE Trans. Inf. Theory IT-6, 311 (1960).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

P. Garcia-Martinez, H. H. Arsenault, and S. Roy, Opt. Commun. 173, 185 (2000).
[CrossRef]

F. Guérault and P. Réfrégier, Opt. Commun. 142, 197 (1997).
[CrossRef]

Opt. Lett.

Other

P. H. Garthwaite, I. T. Jolliffe, and B. Jones, Statistical Inference (Prentice-Hall, London, 1995).

C. Oliver and S. Quegan, Understanding Synthetic Aperture Radar Images (Artech House, Norwood, Mass., 1998).

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

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Figures (4)

Fig. 1
Fig. 1

Input image used for the experiments: a, noise-free image; b, image corrupted with exponential noise.

Fig. 2
Fig. 2

Normalized profiles of the output plane for a, a single-region MLRT with an unknown mean; b, a four-region MLRT with known mean values; and c, a four-region MLRT with unknown mean values. Vertical lines indicate the target locations.

Fig. 3
Fig. 3

a, Images from a CCD camera at low light levels, showing five cases of a three-dimensional object under different illumination conditions. b, Description of the object’s regions, indicated with gray levels.

Fig. 4
Fig. 4

a, Output for the one-region MLRT, b, output for the five-region MLRT.

Equations (5)

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

r=logPθw,s+logPθb,s-logPθF,s,
rknownL=k=0L-1iwklogPθwk,si+iblogPθb,si-iFlogPθF,si,
rknownL=k=0L-1Nklogθwk-Nblogθb+NFlogθF-k=0L-1Nkθ^wkθwk-Nbθ^bθb+NFθ^FθF,
runknownL=-k=0L-1Nklogθ^wk-Nblogθ^b+NFlogθ^F.
runknown=k=0L-1Nkθ^wklogθ^wk+Nbθ^blogθ^b-NFθ^Flogθ^F.

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