Abstract

We address the problem of target detection in active polarimetric images. This technique, which has the appealing feature of revealing contrasts that do not appear in conventional intensity images, provides several images of the same scene. However, because of the presence of nonhomogeneity in the reflected intensity, it is preferable to perform target detection on the orthogonal-state contrast image, which is a measure of the degree of polarization of the reflected light when the coherency matrix is diagonal. We show that one can determine a simple nonlinear transformation of this orthogonal-state contrast image that leads to additive noise, and we then propose a simple and efficient technique for detecting targets in these images.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Goodman, Optics (Wiley, New York, 1985), pp. 347–356.
  2. R. A. Chipman, Proc. SPIE 3170, 68 (1997).
    [CrossRef]
  3. S. Breugnot and Ph. Clémenceau, Proc. SPIE 3707, 449 (1999).
    [CrossRef]
  4. J. S. Tyo, J. Opt. Soc. Am. A 15, 359 (1998).
    [CrossRef]
  5. M. P. Rowe, E. N. Pugh, J. S. Tyo, and N. Engheta, Opt. Lett. 20, 608 (1995).
    [CrossRef] [PubMed]
  6. H. V. Poor, An Introduction to Signal Detection and Estimation, (Springer-Verlag, Berlin, 1994), pp. 5–39.
    [CrossRef]
  7. P. Pagé, F. Goudail, and Ph. Réfrégier, Opt. Lett. 24, 1383 (1999).
    [CrossRef]
  8. T. S. Ferguson, Mathematical Statistics: A Decision Theoretic Approach (Academic, New York, 1967), pp. 125–132.

1999 (2)

S. Breugnot and Ph. Clémenceau, Proc. SPIE 3707, 449 (1999).
[CrossRef]

P. Pagé, F. Goudail, and Ph. Réfrégier, Opt. Lett. 24, 1383 (1999).
[CrossRef]

1998 (1)

1997 (1)

R. A. Chipman, Proc. SPIE 3170, 68 (1997).
[CrossRef]

1995 (1)

Breugnot, S.

S. Breugnot and Ph. Clémenceau, Proc. SPIE 3707, 449 (1999).
[CrossRef]

Chipman, R. A.

R. A. Chipman, Proc. SPIE 3170, 68 (1997).
[CrossRef]

Clémenceau, Ph.

S. Breugnot and Ph. Clémenceau, Proc. SPIE 3707, 449 (1999).
[CrossRef]

Engheta, N.

Ferguson, T. S.

T. S. Ferguson, Mathematical Statistics: A Decision Theoretic Approach (Academic, New York, 1967), pp. 125–132.

Goodman, J. W.

J. W. Goodman, Optics (Wiley, New York, 1985), pp. 347–356.

Goudail, F.

Pagé, P.

Poor, H. V.

H. V. Poor, An Introduction to Signal Detection and Estimation, (Springer-Verlag, Berlin, 1994), pp. 5–39.
[CrossRef]

Pugh, E. N.

Réfrégier, Ph.

Rowe, M. P.

Tyo, J. S.

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

Opt. Lett. (2)

Proc. SPIE (2)

R. A. Chipman, Proc. SPIE 3170, 68 (1997).
[CrossRef]

S. Breugnot and Ph. Clémenceau, Proc. SPIE 3707, 449 (1999).
[CrossRef]

Other (3)

H. V. Poor, An Introduction to Signal Detection and Estimation, (Springer-Verlag, Berlin, 1994), pp. 5–39.
[CrossRef]

T. S. Ferguson, Mathematical Statistics: A Decision Theoretic Approach (Academic, New York, 1967), pp. 125–132.

J. W. Goodman, Optics (Wiley, New York, 1985), pp. 347–356.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Real polarimetric image with channels s1 and s2 and the corresponding OSCI.

Fig. 2
Fig. 2

ROCs of different types of detection test:  diamonds, L; pluses, R; squares, N. The PDFs of channels s1 and s2 are gamma laws of order L=50 with means μ1a=7.25, μ1a=1.1, μ2b=5, and μ2b=1. Inset, gamma laws of order L=1 with means μ1a=60, μ2a=3, μ1b=5, and μ2b=1. The target size is 9 pixels, and the scanning window size is 25 pixels. The curves have been estimated with Monte Carlo simulations with 106 realizations.

Equations (6)

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

ρi,j=s1i,j-s2i,js1i,j+s2i,j.
Puρρ=1-u21-uρ2Ψηρ-u1-uρ.
Puρρ=2L-1!22L-1L-1!21-u2L1-ρ2L-11-uρ2L.
L=(i,jWlogPuaρρi,j)+(i,jW¯logPubρρi,j)-(i,jFlogPubρρi,j).
Pνββ=1-tanh2β-νΨηtanhβ-ν.
R=AIW-IW¯2,

Metrics