Abstract

The use of polarization-sensitive sensors is being explored in a variety of applications. Polarization diversity has been shown to improve the performance of the automatic target detection and recognition in a significant way. However, it also brings out the problems associated with processing and storing more data and the problem of polarization distortion during transmission. We present a technique for extracting attributes that are invariant under polarization transformations. The polarimetric signatures are represented in terms of the components of the Stokes vectors. Invariant algebra is then used to extract a set of signature-related attributes that are invariant under linear transformation of the Stokes vectors. Experimental results using polarimetric infrared signatures of a number of manmade and natural objects undergoing systematic linear transformations support the invariancy of these attributes.

© 2007 Optical Society of America

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References

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  1. L. B. Wolff and T. E. B. Boult, "Constraining object features using a polarization reflectance model," IEEE Trans. Pattern Anal. Mach. Intell. 13, 635-657 (1991).
    [CrossRef]
  2. M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).
  3. F. A. Sadjadi and C. S. Chun, "Passive polarimetric IR target classification," IEEE Trans. Aerosp. Electron. Syst. 37, 740-751 (2001).
    [CrossRef]
  4. F. A. Sadjadi, "Improved target classification using optimum polarimetric SAR signatures," IEEE Trans. Aerosp. Electron. Syst. 38, 38-49 (2002).
    [CrossRef]
  5. F. A. Sadjadi and C. L. Chun, "Automatic detection of small objects from their infrared state-of-polarization vectors," Opt. Lett. 28, 531-533 (2003).
    [CrossRef] [PubMed]
  6. F. A. Sadjadi and C. S. Chun, "Remote sensing using passive infrared stokes parameters," Opt. Eng. J. 43, 2283-2291 (2004).
    [CrossRef]
  7. F. A. Sadjadi and A. Mahalanobis, "Target adaptive polarimetric SAR target discrimination using maximum average correlation height filters," Appl. Opt. 45, 3063-3070 (2006).
    [CrossRef] [PubMed]
  8. F. A. Sadjadi, "Adaptive polarimetric sensing for optimum radar signature classification using a genetic search algorithm," Appl. Opt. 45, 5677-5685 (2006).
    [CrossRef] [PubMed]
  9. H. Mott, Antennas for Radar and Communications: A Polarimetric Approach (Wiley, 1992).
  10. S. Huard, Polarization of Light (Wiley, 1996).
  11. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, 1991).
  12. W. Shurcliff, Polarized Light (Harvard U. Press, 1960).
  13. H. Van De Hulst, Light Scattering by Small Particles (Wiley, 1957).
  14. E. Collett, Polarized Light: Fundamentals and Applications (Dekker, 1993).
  15. O. Matoba and B. Javidi, "Three-dimensional polarimetric integral imaging," Opt. Lett. 29, 2375-2377 (2004).
    [CrossRef] [PubMed]
  16. C. S. Chun and F. A. Sadjadi, "Polarimetric laser radar target classification," Opt. Lett. 30, 1806-1808 (2005).
    [CrossRef] [PubMed]
  17. F. A. Sadjadi and E. L. Hall, "Three-dimensional moment invariants," IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 127-136 (1980).
    [PubMed]
  18. B. Sturmfels, Algorithms in Invariant Theory (Springer-Verlag, 1993).

2006 (2)

2005 (1)

2004 (2)

O. Matoba and B. Javidi, "Three-dimensional polarimetric integral imaging," Opt. Lett. 29, 2375-2377 (2004).
[CrossRef] [PubMed]

F. A. Sadjadi and C. S. Chun, "Remote sensing using passive infrared stokes parameters," Opt. Eng. J. 43, 2283-2291 (2004).
[CrossRef]

2003 (1)

2002 (1)

F. A. Sadjadi, "Improved target classification using optimum polarimetric SAR signatures," IEEE Trans. Aerosp. Electron. Syst. 38, 38-49 (2002).
[CrossRef]

2001 (1)

F. A. Sadjadi and C. S. Chun, "Passive polarimetric IR target classification," IEEE Trans. Aerosp. Electron. Syst. 37, 740-751 (2001).
[CrossRef]

1991 (1)

L. B. Wolff and T. E. B. Boult, "Constraining object features using a polarization reflectance model," IEEE Trans. Pattern Anal. Mach. Intell. 13, 635-657 (1991).
[CrossRef]

1980 (1)

F. A. Sadjadi and E. L. Hall, "Three-dimensional moment invariants," IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 127-136 (1980).
[PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Boult, T. E. B.

L. B. Wolff and T. E. B. Boult, "Constraining object features using a polarization reflectance model," IEEE Trans. Pattern Anal. Mach. Intell. 13, 635-657 (1991).
[CrossRef]

Chun, C. L.

Chun, C. S.

C. S. Chun and F. A. Sadjadi, "Polarimetric laser radar target classification," Opt. Lett. 30, 1806-1808 (2005).
[CrossRef] [PubMed]

F. A. Sadjadi and C. S. Chun, "Remote sensing using passive infrared stokes parameters," Opt. Eng. J. 43, 2283-2291 (2004).
[CrossRef]

F. A. Sadjadi and C. S. Chun, "Passive polarimetric IR target classification," IEEE Trans. Aerosp. Electron. Syst. 37, 740-751 (2001).
[CrossRef]

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications (Dekker, 1993).

Hall, E. L.

F. A. Sadjadi and E. L. Hall, "Three-dimensional moment invariants," IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 127-136 (1980).
[PubMed]

Huard, S.

S. Huard, Polarization of Light (Wiley, 1996).

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, 1991).

Javidi, B.

Mahalanobis, A.

Matoba, O.

Mott, H.

H. Mott, Antennas for Radar and Communications: A Polarimetric Approach (Wiley, 1992).

Sadjadi, F. A.

F. A. Sadjadi, "Adaptive polarimetric sensing for optimum radar signature classification using a genetic search algorithm," Appl. Opt. 45, 5677-5685 (2006).
[CrossRef] [PubMed]

F. A. Sadjadi and A. Mahalanobis, "Target adaptive polarimetric SAR target discrimination using maximum average correlation height filters," Appl. Opt. 45, 3063-3070 (2006).
[CrossRef] [PubMed]

C. S. Chun and F. A. Sadjadi, "Polarimetric laser radar target classification," Opt. Lett. 30, 1806-1808 (2005).
[CrossRef] [PubMed]

F. A. Sadjadi and C. S. Chun, "Remote sensing using passive infrared stokes parameters," Opt. Eng. J. 43, 2283-2291 (2004).
[CrossRef]

F. A. Sadjadi and C. L. Chun, "Automatic detection of small objects from their infrared state-of-polarization vectors," Opt. Lett. 28, 531-533 (2003).
[CrossRef] [PubMed]

F. A. Sadjadi, "Improved target classification using optimum polarimetric SAR signatures," IEEE Trans. Aerosp. Electron. Syst. 38, 38-49 (2002).
[CrossRef]

F. A. Sadjadi and C. S. Chun, "Passive polarimetric IR target classification," IEEE Trans. Aerosp. Electron. Syst. 37, 740-751 (2001).
[CrossRef]

F. A. Sadjadi and E. L. Hall, "Three-dimensional moment invariants," IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 127-136 (1980).
[PubMed]

Shurcliff, W.

W. Shurcliff, Polarized Light (Harvard U. Press, 1960).

Sturmfels, B.

B. Sturmfels, Algorithms in Invariant Theory (Springer-Verlag, 1993).

Van De Hulst, H.

H. Van De Hulst, Light Scattering by Small Particles (Wiley, 1957).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

Wolff, L. B.

L. B. Wolff and T. E. B. Boult, "Constraining object features using a polarization reflectance model," IEEE Trans. Pattern Anal. Mach. Intell. 13, 635-657 (1991).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Aerosp. Electron. Syst. (2)

F. A. Sadjadi and C. S. Chun, "Passive polarimetric IR target classification," IEEE Trans. Aerosp. Electron. Syst. 37, 740-751 (2001).
[CrossRef]

F. A. Sadjadi, "Improved target classification using optimum polarimetric SAR signatures," IEEE Trans. Aerosp. Electron. Syst. 38, 38-49 (2002).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

L. B. Wolff and T. E. B. Boult, "Constraining object features using a polarization reflectance model," IEEE Trans. Pattern Anal. Mach. Intell. 13, 635-657 (1991).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, (1)

F. A. Sadjadi and E. L. Hall, "Three-dimensional moment invariants," IEEE Trans. Pattern Anal. Mach. Intell. PAMI-2, 127-136 (1980).
[PubMed]

Opt. Eng. J. (1)

F. A. Sadjadi and C. S. Chun, "Remote sensing using passive infrared stokes parameters," Opt. Eng. J. 43, 2283-2291 (2004).
[CrossRef]

Opt. Lett. (3)

Other (8)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1959).

B. Sturmfels, Algorithms in Invariant Theory (Springer-Verlag, 1993).

H. Mott, Antennas for Radar and Communications: A Polarimetric Approach (Wiley, 1992).

S. Huard, Polarization of Light (Wiley, 1996).

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, 1991).

W. Shurcliff, Polarized Light (Harvard U. Press, 1960).

H. Van De Hulst, Light Scattering by Small Particles (Wiley, 1957).

E. Collett, Polarized Light: Fundamentals and Applications (Dekker, 1993).

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Figures (20)

Fig. 1
Fig. 1

Polarimetric imagery of a scene showing an M35 truck at α = 0 ° .

Fig. 2
Fig. 2

Polarimetric imagery of a scene showing an M35 truck at α = 45 ° .

Fig. 3
Fig. 3

Polarimetric imagery of a scene showing an M35 truck at α = 90 ° .

Fig. 4
Fig. 4

Polarimetric imagery of a scene showing a T72 tank at α = 0 ° .

Fig. 5
Fig. 5

Polarimetric imagery of a scene showing a T72 tank at α = 45 ° .

Fig. 6
Fig. 6

Polarimetric imagery of a scene showing a T72 tank at α = 90 ° .

Fig. 7
Fig. 7

(Color online) First invariant as a function of α for the scene shown in Fig. 1.

Fig. 8
Fig. 8

(Color online) Second invariant as a function of α for the scene shown in Fig. 1.

Fig. 9
Fig. 9

(Color online) Third invariant as a function of α for the scene shown in Fig. 1.

Fig. 10
Fig. 10

(Color online) Fourth invariant as a function of α for the scene shown in Fig. 1.

Fig. 11
Fig. 11

(Color online) Fifth invariant as a function of α for the scene shown in Fig. 1.

Fig. 12
Fig. 12

(Color online) Sixth invariant as a function of α for the scene shown in Fig. 1.

Fig. 13
Fig. 13

(Color online) Seventh invariant as a function of α for the scene shown in Fig. 1.

Fig. 14
Fig. 14

(Color online) First invariant as a function of α for the scene shown in Fig. 4.

Fig. 15
Fig. 15

(Color online) Second invariant as a function of α for the scene shown in Fig. 4.

Fig. 16
Fig. 16

(Color online) Third invariant as a function of α for the scene shown in Fig. 4.

Fig. 17
Fig. 17

(Color online) Fourth invariant as a function of α for the scene shown in Fig. 4.

Fig. 18
Fig. 18

(Color online) Fifth invariant as a function of α for the scene shown in Fig. 4.

Fig. 19
Fig. 19

(Color online) Sixth invariant as a function of α for the scene shown in Fig. 4.

Fig. 20
Fig. 20

(Color online) Seventh invariant as a function of α for the scene shown in Fig. 4.

Equations (20)

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S 1 = | E H | 2 + | E V | 2 ,
S 2 = | E H | 2 | E V | 2 ,
S 3 = 2 | E H | | E V | cos ( ψ ) ,
S 4 = 2 | E H | | E V | sin ( ψ ) ,
P L P = S 2 + S 3 S 1 ,
Ang L P = 1 2 arctan ( S 3 S 2 ) .
S′ = M i r S .
( S 1 S 2 S 3 S 4 ) = [ 1 0 0 0 0 a b 0 0 c d 0 0 0 0 1 ] ( S 1 S 2 S 3 S 4 ) .
m p q = S 2 p S 3 q P ( S 2 , S 3 ) d S 2 d S 3 .
M ( u 1 , u 2 ) = p = 0 1 p ! ( u 1 S 2 + u 2 S 3 ) p P ( S 2 , S 3 ) × d S 2 d S 3 .
μ p q ( P ) = S 2 S 3 ( S 2 S 2 ¯ ) p ( S 3 S 3 ¯ ) q P ( S 2 , S 3 ) ,
η p q ( P ) = μ p q μ 00 ( p + q ) / 2 + 1 .
ϕ 1 ( P ) = η 20 + η 02 ,
ϕ 2 ( P ) = ( η 20 η 02 ) 2 + 4 η 11 2 ,
ϕ 3 ( P ) = ( η 30 3 η 12 ) 2 + ( 3 η 21 η 03 ) 2 ,
ϕ 4 ( P ) = ( η 30 + η 12 ) 2 + ( η 21 + η 03 ) 2 ,
ϕ 5 ( P ) = ( η 30 3 η 12 ) ( η 30 + η 12 ) [ ( η 30 + η 12 ) 2 3 ( η 21 + η 03 ) 2 ] + ( 3 η 21 η 03 ) ( η 21 + η 03 ) × [ 3 ( η 30 + η 12 ) ( η 21 + η 03 ) 2 ] ,
ϕ 6 ( P ) = ( η 20 η 02 ) [ ( η 30 + η 12 ) 2 ( η 21 + η 03 ) 2 ] + 4 η 11 ( η 30 + η 12 ) ( η 21 + η 03 ) ,
ϕ 7 ( P ) = ( 3 η 21 η 03 ) ( η 30 + η 12 ) [ ( η 30 + η 12 ) 2 3 ( η 21 + η 03 ) 2 ] + ( 3 η 12 η 30 ) ( η 21 + η 03 ) × [ 3 ( η 30 + η 12 ) 2 ( η 21 + η 03 ) 2 ] .
M i r = [ 1 0 0 0 0 cos ( 2 α ) sin ( 2 α ) 0 0 sin ( 2 α ) cos ( 2 α ) 0 0 0 0 1 ] .

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