Abstract

In this paper, we extend to the Mueller imaging framework a formerly introduced Bayesian approach dealing with polarimetric data reduction and robust clustering of polarization encoded images in the piecewise constant case. The extension was made possible thanks to a suitable writing of the observation model in the Mueller context that relies on the system�??s coherency matrix and Cholesky decomposition such that the admissibility constraints are easily captured. This generalization comes at the cost of nonlinearity with respect to the parameters that have to be estimated. This estimation-clustering problem is tackled in a Bayesian framework where a hierarchical stochastic model based on a Markov random field proposed by Potts is used. This fully unsupervised approach is extensively tested over synthetic data as well as real Mueller images.

© 2008 Optical Society of America

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  1. J. Zallat, and Ch. Heinrich, "Polarimetric data reduction: a Bayesian approach," Opt. Express 15, 83-96 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-1-83.
    [CrossRef]
  2. J. Zallat, S. A¨ınouz, and M.-P. Stoll, "Optimal configurations for imaging polarimeters: impact of image noise and systematic errors," J. Opt. A: Pure Appl. Opt. 8, 807-814 (2006).
    [CrossRef]
  3. S. Cloude, and E. Pottier, "Concept of polarization entropy in optical scattering: polarization analysis and measurement," Opt. Eng. 34, 1599-1610 (1995).
    [CrossRef]
  4. G. Golub, and C. Van Loan, Matrix computation (The Johns Hopkins U. Press, Third edition, 1996).
  5. G. Winkler, Image analysis, random fields and Markov chain Monte Carlo methods: a mathematical introduction (Springer, Second edition, 2006).
  6. P. Green, and S. Richardson, "Hidden Markov models and disease mapping," J. Am. Stat. Assoc. 97, 1055-1070 (2002).
    [CrossRef]
  7. S.-Y. Lu, and R. Chipman, "Interpretation of Mueller matrices based on polar decomposition," J. Opt. Soc. Am. A 13, 1106-1113 (1996).

2007

2006

J. Zallat, S. A¨ınouz, and M.-P. Stoll, "Optimal configurations for imaging polarimeters: impact of image noise and systematic errors," J. Opt. A: Pure Appl. Opt. 8, 807-814 (2006).
[CrossRef]

2002

P. Green, and S. Richardson, "Hidden Markov models and disease mapping," J. Am. Stat. Assoc. 97, 1055-1070 (2002).
[CrossRef]

1996

1995

S. Cloude, and E. Pottier, "Concept of polarization entropy in optical scattering: polarization analysis and measurement," Opt. Eng. 34, 1599-1610 (1995).
[CrossRef]

A¨inouz, S.

J. Zallat, S. A¨ınouz, and M.-P. Stoll, "Optimal configurations for imaging polarimeters: impact of image noise and systematic errors," J. Opt. A: Pure Appl. Opt. 8, 807-814 (2006).
[CrossRef]

Chipman, R.

Cloude, S.

S. Cloude, and E. Pottier, "Concept of polarization entropy in optical scattering: polarization analysis and measurement," Opt. Eng. 34, 1599-1610 (1995).
[CrossRef]

Green, P.

P. Green, and S. Richardson, "Hidden Markov models and disease mapping," J. Am. Stat. Assoc. 97, 1055-1070 (2002).
[CrossRef]

Heinrich, Ch.

Lu, S.-Y.

Pottier, E.

S. Cloude, and E. Pottier, "Concept of polarization entropy in optical scattering: polarization analysis and measurement," Opt. Eng. 34, 1599-1610 (1995).
[CrossRef]

Richardson, S.

P. Green, and S. Richardson, "Hidden Markov models and disease mapping," J. Am. Stat. Assoc. 97, 1055-1070 (2002).
[CrossRef]

Stoll, M.-P.

J. Zallat, S. A¨ınouz, and M.-P. Stoll, "Optimal configurations for imaging polarimeters: impact of image noise and systematic errors," J. Opt. A: Pure Appl. Opt. 8, 807-814 (2006).
[CrossRef]

Zallat, J.

J. Zallat, and Ch. Heinrich, "Polarimetric data reduction: a Bayesian approach," Opt. Express 15, 83-96 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-1-83.
[CrossRef]

J. Zallat, S. A¨ınouz, and M.-P. Stoll, "Optimal configurations for imaging polarimeters: impact of image noise and systematic errors," J. Opt. A: Pure Appl. Opt. 8, 807-814 (2006).
[CrossRef]

J. Am. Stat. Assoc.

P. Green, and S. Richardson, "Hidden Markov models and disease mapping," J. Am. Stat. Assoc. 97, 1055-1070 (2002).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

J. Zallat, S. A¨ınouz, and M.-P. Stoll, "Optimal configurations for imaging polarimeters: impact of image noise and systematic errors," J. Opt. A: Pure Appl. Opt. 8, 807-814 (2006).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

S. Cloude, and E. Pottier, "Concept of polarization entropy in optical scattering: polarization analysis and measurement," Opt. Eng. 34, 1599-1610 (1995).
[CrossRef]

Opt. Express

Other

G. Golub, and C. Van Loan, Matrix computation (The Johns Hopkins U. Press, Third edition, 1996).

G. Winkler, Image analysis, random fields and Markov chain Monte Carlo methods: a mathematical introduction (Springer, Second edition, 2006).

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