Abstract

Many applications use an active coherent illumination and analyze the variation of the polarization state of optical signals. However, as a result of the use of coherent light, these signals are generally strongly perturbed with speckle noise. This is the case, for example, for active polarimetric imaging systems that are useful for enhancing contrast between different elements in a scene. We propose a rigorous definition of the minimal set of parameters that characterize the difference between two coherent and partially polarized states. Indeed, two states of partially polarized light are a priori defined by eight parameters, for example, their two Stokes vectors. We demonstrate that the processing performance for such signal processing tasks as detection, localization, or segmentation of spatial or temporal polarization variations is uniquely determined by two scalar functions of these eight parameters. These two scalar functions are the invariant parameters that define the polarimetric contrast between two polarized states of coherent light. Different polarization configurations with the same invariant contrast parameters will necessarily lead to the same performance for a given task, which is a desirable quality for a rigorous contrast measure. The definition of these polarimetric contrast parameters simplifies the analysis and the specification of processing techniques for coherent polarimetric signals.

© 2002 Optical Society of America

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  3. R. A. Chipman, “Polarization diversity active imaging,” in Image Reconstruction and Restoration II, T. J. Schulz, ed., Proc. SPIE3170, 68–73 (1997).
    [CrossRef]
  4. S. G. Demos, R. R. Alfano, “Optical polarization imaging,” Appl. Opt. 36, 150–155 (1997).
    [CrossRef] [PubMed]
  5. M. Floc’h, G. Le Brun, C. Kieleck, J. Cariou, J. Lotrian, “Polarimetric considerations to optimize lidar detection of immersed targets,” Pure Appl. Opt. 7, 1327–1340 (1998).
    [CrossRef]
  6. P. Clémenceau, S. Breugnot, L. Collot, “Polarization diversity imaging,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 284–291 (1998).
  7. S. Breugnot, Ph. Clémenceau, “Modeling and performances of a polarization active imager at lambda= 806 nm,” in Laser Radar Technology and Applications IV, G. W. Kamerman, C. Werner, ed., Proc. SPIE3707, 449–460 (1999).
    [CrossRef]
  8. B. Johnson, R. Joseph, M. L. Nischan, A. Newbury, J. P. Kerekes, H. T. Barclay, B. C. Willard, J. J. Zayhowski, “Compact active hyperspectral imaging system for the detection of concealed targets,” in Detection and Remediation Technologies for Mines and Minelike Targets IV, A. C. Dubey, J. F. Harvey, J. T. Broach, R. E. Dugan, eds., Proc. SPIE3710, 144–153 (1999).
    [CrossRef]
  9. A. Gleckler, A. Gelbart, “Multiple-slit streak tube imaging lidar (MS-STIL) applications,” in Laser Radar Technology and Applications V, G. W. Kamerman, U. N. Singh, C. H. Werner, V. V. Molebny, eds., Proc. SPIE4035, 266–278 (2000).
    [CrossRef]
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    [CrossRef]
  11. J. E. Solomon, “Polarization imaging,” Appl. Opt. 20, 1537–1544 (1981).
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  12. R. Walraven, “Polarization imagery,” Opt. Eng. 20, 14–18 (1981).
    [CrossRef]
  13. L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 1059–1071 (1990).
    [CrossRef]
  14. W. G. Egan, W. R. Johnson, V. S. Whitehead, “Terrestrial polarization imagery obtained from the space shuttle: characterization and interpretation,” Appl. Opt. 30, 435–442 (1991).
    [CrossRef] [PubMed]
  15. L. B. Wolff, “Polarization camera for computer vision with a beam splitter,” J. Opt. Soc. Am. A 11, 2935–2945 (1994).
    [CrossRef]
  16. J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
    [CrossRef]
  17. L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vision Comput. 15, 81–93 (1997).
    [CrossRef]
  18. S. Lin, S. W. Lee, “Detection of specularity using stereo in color and polarization space,” Comput. Vision Image Understand. 65, 336–346 (1997).
    [CrossRef]
  19. S. K. Nayar, X. S. Fang, T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
    [CrossRef]
  20. M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis and Remote Sensing II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (1999).
    [CrossRef]
  21. J. Q. Peterson, G. L. Jensen, M. E. Greenman, J. Kristl, “Calibration of the hyperspectral imaging polarimeter,” in Polarization: Measurement, Analysis and Remote Sensing II, D. H. Goldstein, D. B. Chenault, ed., Proc. SPIE3754, 296–307 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. T. S. Ferguson, Mathematical Statistics, a Decision Theoretic Approach (Academic, New York, 1967).
  25. C. G. Giri, Group Invariance in Statistical Inference (World Scientific, Singapore, 1996).
  26. A. O. Hero, C. Guillouet, “Robust detection of SAR/IR targets via invariance,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 472–475.
  27. D. P. Huttenlocher, W. J. Rucklidge, “A multi-resolution technique for comparing images using the Hausdorff dis- tance,” (Department of Computer Science, Cornell University, Ithaca, N.Y., 1992).
  28. J. W. Goodman, “The speckle effect in coherent imaging,” in Statistical Optics (Wiley, New York, 1985), pp. 347–356.
  29. S. Huard, “Polarized optical wave,” in Polarization of Light (Wiley, Masson, Paris, 1997), pp. 1–35.
  30. P. Pellat-Finet, “Geometrical approach to polarization optics—I: Geometrical structure of polarized light,” Optik (Stuttgart) 87, 27–33 (1991).
  31. P. Pellat-Finet, “Geometrical approach to polarization optics—II: Quaternionic representation of polarized light,” Optik (Stuttgart) 87, 68–76 (1991).
  32. S. Huard, “Propagation of states of polarization in optical devices,” in Polarization of Light (Wiley, Paris, 1997), pp. 86–130.

2001 (1)

2000 (1)

1998 (1)

M. Floc’h, G. Le Brun, C. Kieleck, J. Cariou, J. Lotrian, “Polarimetric considerations to optimize lidar detection of immersed targets,” Pure Appl. Opt. 7, 1327–1340 (1998).
[CrossRef]

1997 (4)

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vision Comput. 15, 81–93 (1997).
[CrossRef]

S. Lin, S. W. Lee, “Detection of specularity using stereo in color and polarization space,” Comput. Vision Image Understand. 65, 336–346 (1997).
[CrossRef]

S. K. Nayar, X. S. Fang, T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

S. G. Demos, R. R. Alfano, “Optical polarization imaging,” Appl. Opt. 36, 150–155 (1997).
[CrossRef] [PubMed]

1996 (1)

1995 (2)

1994 (1)

1991 (3)

W. G. Egan, W. R. Johnson, V. S. Whitehead, “Terrestrial polarization imagery obtained from the space shuttle: characterization and interpretation,” Appl. Opt. 30, 435–442 (1991).
[CrossRef] [PubMed]

P. Pellat-Finet, “Geometrical approach to polarization optics—I: Geometrical structure of polarized light,” Optik (Stuttgart) 87, 27–33 (1991).

P. Pellat-Finet, “Geometrical approach to polarization optics—II: Quaternionic representation of polarized light,” Optik (Stuttgart) 87, 68–76 (1991).

1990 (1)

L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 1059–1071 (1990).
[CrossRef]

1981 (2)

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 14–18 (1981).
[CrossRef]

J. E. Solomon, “Polarization imaging,” Appl. Opt. 20, 1537–1544 (1981).
[CrossRef] [PubMed]

Alfano, R. R.

Ax, G. R.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis and Remote Sensing II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (1999).
[CrossRef]

Barclay, H. T.

B. Johnson, R. Joseph, M. L. Nischan, A. Newbury, J. P. Kerekes, H. T. Barclay, B. C. Willard, J. J. Zayhowski, “Compact active hyperspectral imaging system for the detection of concealed targets,” in Detection and Remediation Technologies for Mines and Minelike Targets IV, A. C. Dubey, J. F. Harvey, J. T. Broach, R. E. Dugan, eds., Proc. SPIE3710, 144–153 (1999).
[CrossRef]

Boult, T.

S. K. Nayar, X. S. Fang, T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

Breugnot, S.

S. Breugnot, Ph. Clémenceau, “Modeling and performances of a polarization active imager at lambda= 806 nm,” in Laser Radar Technology and Applications IV, G. W. Kamerman, C. Werner, ed., Proc. SPIE3707, 449–460 (1999).
[CrossRef]

P. Clémenceau, S. Breugnot, L. Collot, “Polarization diversity imaging,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 284–291 (1998).

Cariou, J.

M. Floc’h, G. Le Brun, C. Kieleck, J. Cariou, J. Lotrian, “Polarimetric considerations to optimize lidar detection of immersed targets,” Pure Appl. Opt. 7, 1327–1340 (1998).
[CrossRef]

Chipman, R. A.

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

R. A. Chipman, “Polarization diversity active imaging,” in Image Reconstruction and Restoration II, T. J. Schulz, ed., Proc. SPIE3170, 68–73 (1997).
[CrossRef]

Clémenceau, P.

P. Clémenceau, S. Breugnot, L. Collot, “Polarization diversity imaging,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 284–291 (1998).

Clémenceau, Ph.

S. Breugnot, Ph. Clémenceau, “Modeling and performances of a polarization active imager at lambda= 806 nm,” in Laser Radar Technology and Applications IV, G. W. Kamerman, C. Werner, ed., Proc. SPIE3707, 449–460 (1999).
[CrossRef]

Collot, L.

P. Clémenceau, S. Breugnot, L. Collot, “Polarization diversity imaging,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 284–291 (1998).

Demos, S. G.

Egan, W. G.

Engheta, N.

Fang, X. S.

S. K. Nayar, X. S. Fang, T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

Ferguson, T. S.

T. S. Ferguson, Mathematical Statistics, a Decision Theoretic Approach (Academic, New York, 1967).

Floc’h, M.

M. Floc’h, G. Le Brun, C. Kieleck, J. Cariou, J. Lotrian, “Polarimetric considerations to optimize lidar detection of immersed targets,” Pure Appl. Opt. 7, 1327–1340 (1998).
[CrossRef]

Gelbart, A.

A. Gleckler, A. Gelbart, “Multiple-slit streak tube imaging lidar (MS-STIL) applications,” in Laser Radar Technology and Applications V, G. W. Kamerman, U. N. Singh, C. H. Werner, V. V. Molebny, eds., Proc. SPIE4035, 266–278 (2000).
[CrossRef]

Giri, C. G.

C. G. Giri, Group Invariance in Statistical Inference (World Scientific, Singapore, 1996).

Gleckler, A.

A. Gleckler, A. Gelbart, “Multiple-slit streak tube imaging lidar (MS-STIL) applications,” in Laser Radar Technology and Applications V, G. W. Kamerman, U. N. Singh, C. H. Werner, V. V. Molebny, eds., Proc. SPIE4035, 266–278 (2000).
[CrossRef]

Goodman, J. W.

J. W. Goodman, “The speckle effect in coherent imaging,” in Statistical Optics (Wiley, New York, 1985), pp. 347–356.

J. W. Goodman, “Laser speckle and related phenomena,” in Statistical Properties of Laser Speckle Patterns, Vol. 9 of Topics in Applied Physics (Springer-Verlag, Heidelberg, 1975), pp. 9–75.
[CrossRef]

Goudail, F.

Greenman, M. E.

J. Q. Peterson, G. L. Jensen, M. E. Greenman, J. Kristl, “Calibration of the hyperspectral imaging polarimeter,” in Polarization: Measurement, Analysis and Remote Sensing II, D. H. Goldstein, D. B. Chenault, ed., Proc. SPIE3754, 296–307 (1999).
[CrossRef]

Guillouet, C.

A. O. Hero, C. Guillouet, “Robust detection of SAR/IR targets via invariance,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 472–475.

Hero, A. O.

A. O. Hero, C. Guillouet, “Robust detection of SAR/IR targets via invariance,” in Proceedings of the IEEE International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997), Vol. 3, pp. 472–475.

Howe, J. D.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis and Remote Sensing II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (1999).
[CrossRef]

Huard, S.

S. Huard, “Polarized optical wave,” in Polarization of Light (Wiley, Masson, Paris, 1997), pp. 1–35.

S. Huard, “Propagation of states of polarization in optical devices,” in Polarization of Light (Wiley, Paris, 1997), pp. 86–130.

Huttenlocher, D. P.

D. P. Huttenlocher, W. J. Rucklidge, “A multi-resolution technique for comparing images using the Hausdorff dis- tance,” (Department of Computer Science, Cornell University, Ithaca, N.Y., 1992).

Jensen, G. L.

J. Q. Peterson, G. L. Jensen, M. E. Greenman, J. Kristl, “Calibration of the hyperspectral imaging polarimeter,” in Polarization: Measurement, Analysis and Remote Sensing II, D. H. Goldstein, D. B. Chenault, ed., Proc. SPIE3754, 296–307 (1999).
[CrossRef]

Johnson, B.

B. Johnson, R. Joseph, M. L. Nischan, A. Newbury, J. P. Kerekes, H. T. Barclay, B. C. Willard, J. J. Zayhowski, “Compact active hyperspectral imaging system for the detection of concealed targets,” in Detection and Remediation Technologies for Mines and Minelike Targets IV, A. C. Dubey, J. F. Harvey, J. T. Broach, R. E. Dugan, eds., Proc. SPIE3710, 144–153 (1999).
[CrossRef]

Johnson, W. R.

Joseph, R.

B. Johnson, R. Joseph, M. L. Nischan, A. Newbury, J. P. Kerekes, H. T. Barclay, B. C. Willard, J. J. Zayhowski, “Compact active hyperspectral imaging system for the detection of concealed targets,” in Detection and Remediation Technologies for Mines and Minelike Targets IV, A. C. Dubey, J. F. Harvey, J. T. Broach, R. E. Dugan, eds., Proc. SPIE3710, 144–153 (1999).
[CrossRef]

Kerekes, J. P.

B. Johnson, R. Joseph, M. L. Nischan, A. Newbury, J. P. Kerekes, H. T. Barclay, B. C. Willard, J. J. Zayhowski, “Compact active hyperspectral imaging system for the detection of concealed targets,” in Detection and Remediation Technologies for Mines and Minelike Targets IV, A. C. Dubey, J. F. Harvey, J. T. Broach, R. E. Dugan, eds., Proc. SPIE3710, 144–153 (1999).
[CrossRef]

Kieleck, C.

M. Floc’h, G. Le Brun, C. Kieleck, J. Cariou, J. Lotrian, “Polarimetric considerations to optimize lidar detection of immersed targets,” Pure Appl. Opt. 7, 1327–1340 (1998).
[CrossRef]

Kiryati, N.

Kristl, J.

J. Q. Peterson, G. L. Jensen, M. E. Greenman, J. Kristl, “Calibration of the hyperspectral imaging polarimeter,” in Polarization: Measurement, Analysis and Remote Sensing II, D. H. Goldstein, D. B. Chenault, ed., Proc. SPIE3754, 296–307 (1999).
[CrossRef]

Le Brun, G.

M. Floc’h, G. Le Brun, C. Kieleck, J. Cariou, J. Lotrian, “Polarimetric considerations to optimize lidar detection of immersed targets,” Pure Appl. Opt. 7, 1327–1340 (1998).
[CrossRef]

Lee, S. W.

S. Lin, S. W. Lee, “Detection of specularity using stereo in color and polarization space,” Comput. Vision Image Understand. 65, 336–346 (1997).
[CrossRef]

Lin, S.

S. Lin, S. W. Lee, “Detection of specularity using stereo in color and polarization space,” Comput. Vision Image Understand. 65, 336–346 (1997).
[CrossRef]

Lotrian, J.

M. Floc’h, G. Le Brun, C. Kieleck, J. Cariou, J. Lotrian, “Polarimetric considerations to optimize lidar detection of immersed targets,” Pure Appl. Opt. 7, 1327–1340 (1998).
[CrossRef]

Miller, M. A.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis and Remote Sensing II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (1999).
[CrossRef]

Nayar, S. K.

S. K. Nayar, X. S. Fang, T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

Newbury, A.

B. Johnson, R. Joseph, M. L. Nischan, A. Newbury, J. P. Kerekes, H. T. Barclay, B. C. Willard, J. J. Zayhowski, “Compact active hyperspectral imaging system for the detection of concealed targets,” in Detection and Remediation Technologies for Mines and Minelike Targets IV, A. C. Dubey, J. F. Harvey, J. T. Broach, R. E. Dugan, eds., Proc. SPIE3710, 144–153 (1999).
[CrossRef]

Nischan, M. L.

B. Johnson, R. Joseph, M. L. Nischan, A. Newbury, J. P. Kerekes, H. T. Barclay, B. C. Willard, J. J. Zayhowski, “Compact active hyperspectral imaging system for the detection of concealed targets,” in Detection and Remediation Technologies for Mines and Minelike Targets IV, A. C. Dubey, J. F. Harvey, J. T. Broach, R. E. Dugan, eds., Proc. SPIE3710, 144–153 (1999).
[CrossRef]

Pellat-Finet, P.

P. Pellat-Finet, “Geometrical approach to polarization optics—I: Geometrical structure of polarized light,” Optik (Stuttgart) 87, 27–33 (1991).

P. Pellat-Finet, “Geometrical approach to polarization optics—II: Quaternionic representation of polarized light,” Optik (Stuttgart) 87, 68–76 (1991).

Peterson, J. Q.

J. Q. Peterson, G. L. Jensen, M. E. Greenman, J. Kristl, “Calibration of the hyperspectral imaging polarimeter,” in Polarization: Measurement, Analysis and Remote Sensing II, D. H. Goldstein, D. B. Chenault, ed., Proc. SPIE3754, 296–307 (1999).
[CrossRef]

Pezzaniti, J. L.

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

Pugh, E. N.

Réfrégier, Ph.

Rowe, M. P.

Rucklidge, W. J.

D. P. Huttenlocher, W. J. Rucklidge, “A multi-resolution technique for comparing images using the Hausdorff dis- tance,” (Department of Computer Science, Cornell University, Ithaca, N.Y., 1992).

Schechner, Y. Y.

Shamir, J.

Smith, M. H.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis and Remote Sensing II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (1999).
[CrossRef]

Solomon, J. E.

Tyo, J. S.

Walraven, R.

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 14–18 (1981).
[CrossRef]

Whitehead, V. S.

Willard, B. C.

B. Johnson, R. Joseph, M. L. Nischan, A. Newbury, J. P. Kerekes, H. T. Barclay, B. C. Willard, J. J. Zayhowski, “Compact active hyperspectral imaging system for the detection of concealed targets,” in Detection and Remediation Technologies for Mines and Minelike Targets IV, A. C. Dubey, J. F. Harvey, J. T. Broach, R. E. Dugan, eds., Proc. SPIE3710, 144–153 (1999).
[CrossRef]

Wolff, L. B.

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vision Comput. 15, 81–93 (1997).
[CrossRef]

L. B. Wolff, “Polarization camera for computer vision with a beam splitter,” J. Opt. Soc. Am. A 11, 2935–2945 (1994).
[CrossRef]

L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 1059–1071 (1990).
[CrossRef]

Woodruff, J. B.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis and Remote Sensing II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (1999).
[CrossRef]

Zayhowski, J. J.

B. Johnson, R. Joseph, M. L. Nischan, A. Newbury, J. P. Kerekes, H. T. Barclay, B. C. Willard, J. J. Zayhowski, “Compact active hyperspectral imaging system for the detection of concealed targets,” in Detection and Remediation Technologies for Mines and Minelike Targets IV, A. C. Dubey, J. F. Harvey, J. T. Broach, R. E. Dugan, eds., Proc. SPIE3710, 144–153 (1999).
[CrossRef]

Appl. Opt. (4)

Comput. Vision Image Understand. (1)

S. Lin, S. W. Lee, “Detection of specularity using stereo in color and polarization space,” Comput. Vision Image Understand. 65, 336–346 (1997).
[CrossRef]

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

L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 1059–1071 (1990).
[CrossRef]

Image Vision Comput. (1)

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vision Comput. 15, 81–93 (1997).
[CrossRef]

Int. J. Comput. Vision (1)

S. K. Nayar, X. S. Fang, T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (2)

J. L. Pezzaniti, R. A. Chipman, “Mueller matrix imaging polarimetry,” Opt. Eng. 34, 1558–1568 (1995).
[CrossRef]

R. Walraven, “Polarization imagery,” Opt. Eng. 20, 14–18 (1981).
[CrossRef]

Opt. Lett. (2)

Optik (Stuttgart) (2)

P. Pellat-Finet, “Geometrical approach to polarization optics—I: Geometrical structure of polarized light,” Optik (Stuttgart) 87, 27–33 (1991).

P. Pellat-Finet, “Geometrical approach to polarization optics—II: Quaternionic representation of polarized light,” Optik (Stuttgart) 87, 68–76 (1991).

Pure Appl. Opt. (1)

M. Floc’h, G. Le Brun, C. Kieleck, J. Cariou, J. Lotrian, “Polarimetric considerations to optimize lidar detection of immersed targets,” Pure Appl. Opt. 7, 1327–1340 (1998).
[CrossRef]

Other (15)

P. Clémenceau, S. Breugnot, L. Collot, “Polarization diversity imaging,” in Laser Radar Technology and Applications III, G. W. Kamerman, ed., Proc. SPIE3380, 284–291 (1998).

S. Breugnot, Ph. Clémenceau, “Modeling and performances of a polarization active imager at lambda= 806 nm,” in Laser Radar Technology and Applications IV, G. W. Kamerman, C. Werner, ed., Proc. SPIE3707, 449–460 (1999).
[CrossRef]

B. Johnson, R. Joseph, M. L. Nischan, A. Newbury, J. P. Kerekes, H. T. Barclay, B. C. Willard, J. J. Zayhowski, “Compact active hyperspectral imaging system for the detection of concealed targets,” in Detection and Remediation Technologies for Mines and Minelike Targets IV, A. C. Dubey, J. F. Harvey, J. T. Broach, R. E. Dugan, eds., Proc. SPIE3710, 144–153 (1999).
[CrossRef]

A. Gleckler, A. Gelbart, “Multiple-slit streak tube imaging lidar (MS-STIL) applications,” in Laser Radar Technology and Applications V, G. W. Kamerman, U. N. Singh, C. H. Werner, V. V. Molebny, eds., Proc. SPIE4035, 266–278 (2000).
[CrossRef]

R. A. Chipman, “Polarization diversity active imaging,” in Image Reconstruction and Restoration II, T. J. Schulz, ed., Proc. SPIE3170, 68–73 (1997).
[CrossRef]

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis and Remote Sensing II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 137–143 (1999).
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Figures (4)

Fig. 1
Fig. 1

(a) Ideal image model, composed of a target zone of intensity Ia and a background zone of intensity Ib, (b) image (a) perturbed with additive Gaussian noise, (c) image (a) perturbed with multiplicative exponential noise.

Fig. 2
Fig. 2

Illustration of the invariant subsets HG(u) for two values u0 and u1 of the parameter set u in the case where the dimension of the parameter set of the pdf is d=1, that is, u0=(p0(a), p0(b)) and u1=(p1(a), p1(b)). The two subsets correspond to two different values of the performance measure.

Fig. 3
Fig. 3

Principle of the derivation of the polarimetric contrast parameters. In the top pair, the two polarimetric states Γa and Γb are represented. The lengths of the axes of the ellipses are the eigenvalues of the matrices, and the angles illustrate the principal polarization states U and V. This is a symbolic representation, since the principal states are, in fact, represented by two parameters (θ, ϕ). The middle pair represent the result of applying the whitening transform Γa-1/2 to both states. The bottom pair represent the result of applying the matrix X, with the consequence that the matrix XΓbX is diagonal.

Fig. 4
Fig. 4

Definition of the angle Ω between two polarization states in the Poincaré sphere.

Equations (61)

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A:χRA[χ].
PΓ(A)=12πdet(Γ)exp-12AΓ-1A.
Γa=Ia(1)ρaρa*Ia(2),Γb=Ib(1)ρbρb*Ib(2).
Γa=UMaU,
Γb=VMbV,
U=u1-u2*u2u1*,V=v1-v2*v2v1*
Ma=μ1a00μ2a,Mb=μ1b00μ2b,
Γa-1/2=UMa-1/2U.
Γb=Γa-1/2ΓbΓa-1/2=UMa-1/2UVMbVUMa-1/2U=UMa-1/2TMbTMa-1/2U.
T=t1-t2*t2t1*.
Γb=Xλ100λ2X
Z=XΓa-1/2,
det(Γa-1/2ΓbΓa-1/2),
tr(Γa-1/2ΓaΓa-1/2),
α=det(Γa-1/2ΓbΓa-1/2)=λ1λ2,
β=tr(Γa-1/2ΓbΓa-1/2)2[det(Γa-1/2ΓbΓa-1/2)]1/2=λ1+λ22λ1λ2.
Iw=μ1w+μ2w,Pw=μ1w-μ2wμ1w+μ2w,(ψw, χw),
α=IbIa21-Pb21-Pa2,
β=1-PaPbcos Ω1-Pa21-Pb2,
Qw=Iw2(1-Pw2),
α=QbQa,
β=Qa+b-Qa-Qb2QaQb.
Pu[χ]=Pp(a)(x1)  Pp(a)(xN1)Pp(b)(xN1+1)  Pp(b)(xN),
χ()dχ
=[x1]1[xN]D()d[x1]1d[x1]2d[x1]3  d[xN]D-1d[xN]D,
Mu(A)=χC[RA[χ],R0]Pu[χ]dχ.
AuM=argminA Mu(A),
Muopt=Mu(AuM).
Pv[χ]dχ=Pu[Y]dY,
Mv(A)=χC[RA[χ],R0]Pv[χ]dχ,
Mv(A)=YC[RA[g(Y)],R0]Pu[Y]dY,
Mv(A)=YC[RAg[Y],R0]Pu[Y]dY,
Mv(A)=Mu(Ag).
argminA Mv(A)=argminA Mu(Ag)=argminA Mu(A),
Mvopt=Muopt,
det[Γb]=μ1bμ2bμ1aμ2a.
Iw=μ1w+μ2w,
Pw=μ1w-μ2wμ1w+μ2w,
det(Γb)=IbIa21-Pb21-Pa2.
tr(QQ)=i=12j=12|qij|2.
Ma-1/2TMb1/2=(μ1b/μ1a)1/2t1-(μ2b/μ1a)1/2t2*(μ1b/μ2a)1/2t2(μ2b/μ2a)1/2t1*.
tr(Γb)=μ1bμ1a+μ2bμ2a|t1|2+μ1bμ2a+μ2bμ1a|t2|2.
tr(Γb)=μ1bμ1a+μ2bμ2a+(μ1b-μ2b)(μ1a-μ2a)μ1aμ2a|t2|2.
|t2|2 = |u1|2|v2|2+|u2|2|v1|2-2 Re(u1v2u2*v1*).
u=cos θasin θaexp(iϕa),v=cos θbsin θbexp(iϕb).
|t2|2 =cos2 θasin2 θb+cos2 θbsin2 θa-2 cos θacos θbsin θasin θbcos(ϕb-ϕa)=sin2(θb-θa)+12 (sin 2 θasin 2 θb)[1-cos(ϕb-ϕa)],
sin(θb-θa)=sin θbcos θa-sin θacos θb,
2 sin θacos θa=sin 2 θa.
1-cos(θb-ϕa)=2 sin2[(ϕb-ϕa)/2],
|t2|2 =sin2(θb-θa)+sin 2 θasin 2 θbsin2[(ϕb-ϕa)/2].
|t2|2 =sin2Ω2.
tr(Γb)=μ1bμ1a+μ2bμ2a+(μ1b-μ2b)(μ1a-μ2a)μ1aμ2asin2Ω2.
tr(Γb)=2 IbIa11-Pa21-PaPb+2PaPbsin2Ω2.
α=det(Γb)=IbIa21-Pb21-Pa2,
β=tr(Γb)2det(Γb)=1-PaPbcos Ω1-Pa21-Pb2.
α=QbQa.
Γa+b=Γa+Γb=Γa1/2(Id+Γa-1/2ΓbΓa-1/2)Γa1/2,
=Γa1/2X(Id+D)XΓa1/2,
Qa+b=det(Γa+b)=Qa(1+λ1+λ2+λ1λ2)=Qa(1+2βα+α),
Qa+b=Qa+2βQaQb+Qb,
β=Qa+b-Qa-Qb2QaQb.

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