Abstract

In this paper, we introduce a general Bayesian approach to estimate polarization parameters in the Stokes imaging framework. We demonstrate that this new approach yields a neat solution to the polarimetric data reduction problem that preserves the physical admissibility constraints and provides a robust clustering of Stokes images in regard to image noises. The proposed approach is extensively evaluated by using synthetic simulated data and applied to cluster and retrieves the Stokes image issuing from a set of real measurements.

© 2007 Optical Society of America

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  1. D. Miyazaki, M. Saito, Y. Sato, and K. Ikeuchi, "Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths," J. Opt. Soc. Am. A 19, 687-694 (2002).
  2. D. Miyazaki, M. Kagesawa, and K. Ikeuchi, "Transparent surface modeling from a pair of polarization images," IEEE Trans. PAMI 26,920-932 (2004).
  3. J. M. Bueno and P. Artal, "Double-pass imaging polarimetry in the human eye," Opt. Letters. 2464-66 (1999).
  4. S. D. Giattina,  et al., "Assessment of coronary plaque collagen with polarization sensitive optical coherence tomography (PS-OCT)," Int. J. Cardiol. 107, 400-409 (2006).
    [CrossRef]
  5. D. H. Goldstein, D. B. Chenault, and Society of Photo-optical Instrumentation Engineers, Polarization: measurement, analysis, and remote sensing II, 19-21 July, 1999, Denver, Colorado. 1999, Bellingham, Washington: SPIE. ix, 426 p.
  6. M. H. Smith, "Optimizing a dual-rotating-retarder Mueller matrix polarimeter," in Polarization Analysis and Measurements IV, SPIE (2001).
  7. J. S. Tyo, "Design of optimal polarimeters: maximization of signal-to-noise ratio and minimization of systematic error," Appl. Opt. 41619-630 (2002).
  8. S. Ainouz, J. Zallat, A. de Martino, and C. Collet., "Physical interpretation of polarization-encoded images by color preview," Opt. Express 14, 5916-5927 (2006).
    [CrossRef]
  9. S. N. Savenkov, "Optimization and structuring of the instrument matrix for polarimetric measurements," Opt. Eng. 41, 965-972 (2002).
    [CrossRef]
  10. J. Bernardo and A. Smith, Bayesian Theory, (Wiley, 2000).
  11. A. Gelman, J. Carlin, H. Stern, and D. Rubin, Bayesian data analysis, Second ed., (CRC Press, 2003).
  12. S. Z. Li, Markov random field modeling in image analysis, Second ed., (Springer, 2001).
  13. A. Gray, J. Kay, and D. Titterington, "An empirical study of the simulation of various models used for images," IEEE Trans. PAMI,  16, 507-513 (1994).
  14. A. Dunmur and D. Titterington, "Computational Bayesian analysis of hidden Markov mesh models," IEEE PAMI. 19, 1296-1300 (1997).
  15. S. Richardson and P. Green, "On Bayesian analysis of mixtures with an unknown number of components (with discussion)," J. R. Stat. Soc. Ser. B. 59, 731-792 (1997).
    [CrossRef]
  16. J. Besag, "On the statistical analysis of dirty pictures (with discussion)," J. R. Stat. Soc. B 48, 259-302 (1986).

2006

S. D. Giattina,  et al., "Assessment of coronary plaque collagen with polarization sensitive optical coherence tomography (PS-OCT)," Int. J. Cardiol. 107, 400-409 (2006).
[CrossRef]

S. Ainouz, J. Zallat, A. de Martino, and C. Collet., "Physical interpretation of polarization-encoded images by color preview," Opt. Express 14, 5916-5927 (2006).
[CrossRef]

2004

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, "Transparent surface modeling from a pair of polarization images," IEEE Trans. PAMI 26,920-932 (2004).

2002

1999

J. M. Bueno and P. Artal, "Double-pass imaging polarimetry in the human eye," Opt. Letters. 2464-66 (1999).

1997

A. Dunmur and D. Titterington, "Computational Bayesian analysis of hidden Markov mesh models," IEEE PAMI. 19, 1296-1300 (1997).

S. Richardson and P. Green, "On Bayesian analysis of mixtures with an unknown number of components (with discussion)," J. R. Stat. Soc. Ser. B. 59, 731-792 (1997).
[CrossRef]

1994

A. Gray, J. Kay, and D. Titterington, "An empirical study of the simulation of various models used for images," IEEE Trans. PAMI,  16, 507-513 (1994).

1986

J. Besag, "On the statistical analysis of dirty pictures (with discussion)," J. R. Stat. Soc. B 48, 259-302 (1986).

Ainouz, S.

Artal, P.

J. M. Bueno and P. Artal, "Double-pass imaging polarimetry in the human eye," Opt. Letters. 2464-66 (1999).

Besag, J.

J. Besag, "On the statistical analysis of dirty pictures (with discussion)," J. R. Stat. Soc. B 48, 259-302 (1986).

Bueno, J. M.

J. M. Bueno and P. Artal, "Double-pass imaging polarimetry in the human eye," Opt. Letters. 2464-66 (1999).

Collet, C.

de Martino, A.

Dunmur, A.

A. Dunmur and D. Titterington, "Computational Bayesian analysis of hidden Markov mesh models," IEEE PAMI. 19, 1296-1300 (1997).

Giattina, S. D.

S. D. Giattina,  et al., "Assessment of coronary plaque collagen with polarization sensitive optical coherence tomography (PS-OCT)," Int. J. Cardiol. 107, 400-409 (2006).
[CrossRef]

Gray, A.

A. Gray, J. Kay, and D. Titterington, "An empirical study of the simulation of various models used for images," IEEE Trans. PAMI,  16, 507-513 (1994).

Green, P.

S. Richardson and P. Green, "On Bayesian analysis of mixtures with an unknown number of components (with discussion)," J. R. Stat. Soc. Ser. B. 59, 731-792 (1997).
[CrossRef]

Ikeuchi, K.

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, "Transparent surface modeling from a pair of polarization images," IEEE Trans. PAMI 26,920-932 (2004).

D. Miyazaki, M. Saito, Y. Sato, and K. Ikeuchi, "Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths," J. Opt. Soc. Am. A 19, 687-694 (2002).

Kagesawa, M.

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, "Transparent surface modeling from a pair of polarization images," IEEE Trans. PAMI 26,920-932 (2004).

Kay, J.

A. Gray, J. Kay, and D. Titterington, "An empirical study of the simulation of various models used for images," IEEE Trans. PAMI,  16, 507-513 (1994).

Miyazaki, D.

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, "Transparent surface modeling from a pair of polarization images," IEEE Trans. PAMI 26,920-932 (2004).

D. Miyazaki, M. Saito, Y. Sato, and K. Ikeuchi, "Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths," J. Opt. Soc. Am. A 19, 687-694 (2002).

Richardson, S.

S. Richardson and P. Green, "On Bayesian analysis of mixtures with an unknown number of components (with discussion)," J. R. Stat. Soc. Ser. B. 59, 731-792 (1997).
[CrossRef]

Saito, M.

Sato, Y.

Savenkov, S. N.

S. N. Savenkov, "Optimization and structuring of the instrument matrix for polarimetric measurements," Opt. Eng. 41, 965-972 (2002).
[CrossRef]

Titterington, D.

A. Dunmur and D. Titterington, "Computational Bayesian analysis of hidden Markov mesh models," IEEE PAMI. 19, 1296-1300 (1997).

A. Gray, J. Kay, and D. Titterington, "An empirical study of the simulation of various models used for images," IEEE Trans. PAMI,  16, 507-513 (1994).

Tyo, J. S.

Zallat, J.

Appl. Opt.

IEEE PAMI.

A. Dunmur and D. Titterington, "Computational Bayesian analysis of hidden Markov mesh models," IEEE PAMI. 19, 1296-1300 (1997).

IEEE Trans. PAMI

A. Gray, J. Kay, and D. Titterington, "An empirical study of the simulation of various models used for images," IEEE Trans. PAMI,  16, 507-513 (1994).

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, "Transparent surface modeling from a pair of polarization images," IEEE Trans. PAMI 26,920-932 (2004).

Int. J. Cardiol.

S. D. Giattina,  et al., "Assessment of coronary plaque collagen with polarization sensitive optical coherence tomography (PS-OCT)," Int. J. Cardiol. 107, 400-409 (2006).
[CrossRef]

J. Opt. Soc. Am. A

J. R. Stat. Soc. B

J. Besag, "On the statistical analysis of dirty pictures (with discussion)," J. R. Stat. Soc. B 48, 259-302 (1986).

J. R. Stat. Soc. Ser. B.

S. Richardson and P. Green, "On Bayesian analysis of mixtures with an unknown number of components (with discussion)," J. R. Stat. Soc. Ser. B. 59, 731-792 (1997).
[CrossRef]

Opt. Eng.

S. N. Savenkov, "Optimization and structuring of the instrument matrix for polarimetric measurements," Opt. Eng. 41, 965-972 (2002).
[CrossRef]

Opt. Express

Opt. Letters.

J. M. Bueno and P. Artal, "Double-pass imaging polarimetry in the human eye," Opt. Letters. 2464-66 (1999).

Other

D. H. Goldstein, D. B. Chenault, and Society of Photo-optical Instrumentation Engineers, Polarization: measurement, analysis, and remote sensing II, 19-21 July, 1999, Denver, Colorado. 1999, Bellingham, Washington: SPIE. ix, 426 p.

M. H. Smith, "Optimizing a dual-rotating-retarder Mueller matrix polarimeter," in Polarization Analysis and Measurements IV, SPIE (2001).

J. Bernardo and A. Smith, Bayesian Theory, (Wiley, 2000).

A. Gelman, J. Carlin, H. Stern, and D. Rubin, Bayesian data analysis, Second ed., (CRC Press, 2003).

S. Z. Li, Markov random field modeling in image analysis, Second ed., (Springer, 2001).

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