Abstract

Polarization-encoded imaging consists of the distributed measurements of polarization parameters for each pixel of an image. We address clustering of multidimensional polarization-encoded images. The spatial coherence of polarization information is considered. Two methods of analysis are proposed: polarization contrast enhancement and a more-sophisticated image-processing algorithm based on a Markovian model. The proposed algorithms are applied and validated with two different Mueller images acquired by a fully polarimetric imaging system.

© 2004 Optical Society of America

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    [CrossRef]
  31. N. Giordana, W. Pieczynski, “Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 465–475 (1997).
    [CrossRef]
  32. M. Mignotte, C. Collet, P. Pérez, P. Bouthemy, “Three-class Markovian segmentation of high resolution sonar images,” J. Computer Vision Image Underst. 76, 191–204 (1999).
    [CrossRef]
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    [CrossRef]
  34. W. Pieczynski, “Statistical image segmentation,” Mach. Graph. Vision 1, 261–268 (1992).
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  36. J.-M. Laferté, P. Pérez, F. Heitz, “Discrete Markov image modeling and inference on the quad-tree,” IEEE Trans. Image Process. 9, 390–404 (2000).
    [CrossRef]
  37. P. Rostaing, P. Pérez, J.-N. Provost, C. Collet, P. Bouthemy, “Multispectral spot images analysis using generalized Gaussian modeling: application to water depth mapping,” Comput. Vis. Image Underst. (to be published).
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    [CrossRef]

2001 (1)

F. Goudail, P. Réfrégier, “Statistical algorithms for processing polarimetric images in coherent light,” Trait. Signal 18(5–6), 297–319 (2001).

2000 (2)

P. Pérez, A. Chardin, J.-M. Laferté, “Noniterative manipulation of discrete energy-based models for image analysis,” Pattern Recogn. 33, 573–586 (2000).
[CrossRef]

J.-M. Laferté, P. Pérez, F. Heitz, “Discrete Markov image modeling and inference on the quad-tree,” IEEE Trans. Image Process. 9, 390–404 (2000).
[CrossRef]

1999 (5)

1998 (2)

1997 (1)

N. Giordana, W. Pieczynski, “Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 465–475 (1997).
[CrossRef]

1996 (3)

P. Pérez, F. Heitz, “Restriction of a Markov random field on a graph and multiresolution statistical image modeling,” IEEE Trans. Inf. Theory 42, 180–190 (1996).
[CrossRef]

Z. Kato, M. Berthod, J. Zérubia, “A hierarchical Markov random field model and multitemperature annealing for parallel image classification,” Graph. Models Image Process. 58, 18–37 (1996).
[CrossRef]

S.-Y. Lu, R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
[CrossRef]

1994 (3)

R. Sridhar, R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41, 1903–1915 (1994).
[CrossRef]

D. G. M. Anderson, R. Barakat, “Necessary and sufficient conditions for a Mueller matrix to be derivable from a Jones matrix,” J. Opt. Soc. Am. A 11, 2305–2319 (1994).
[CrossRef]

C. A. Bouman, M. Shapiro, “A multiscale random field model for Bayesian image segmentation,” IEEE Trans. Image Process. 3, 162–177 (1994).
[CrossRef] [PubMed]

1993 (4)

M. R. Luettgen, W. C. Karl, A. S. Willsky, R. Tenney, “Multiscale representation of Markov random fields,” IEEE Trans. Signal Process. 41, 3377–3395 (1993).
[CrossRef]

C. R. Givens, A. B. Kostinski, “A simple necessary and sufficient condition on physically realizable Mueller matrices,” J. Mod. Opt. 40, 471–481 (1993).
[CrossRef]

C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072–5088 (1993).
[CrossRef]

A. B. Kostinski, C. R. Givens, J. M. Kwiatkowski, “Constraints on Mueller matrices of polarization optics,” Appl. Opt. 32, 1646–1651 (1993).
[CrossRef] [PubMed]

1992 (4)

Z.-F. Xing, “On the deterministic and non-deterministic Mueller matrix,” J. Mod. Opt. 39, 461–484 (1992).
[CrossRef]

C. V. M. van der Mee, J. W. Hovenier, “Structure of matrices transforming Stokes parameters,” J. Math. Phys. 33, 3574–3584 (1992).
[CrossRef]

M. S. Kumar, R. Simon, “Characterization of Mueller matrices in polarization optics,” Opt. Commun. 88, 464–470 (1992).
[CrossRef]

W. Pieczynski, “Statistical image segmentation,” Mach. Graph. Vision 1, 261–268 (1992).

1986 (1)

S. R. Cloude, “Group theory and polarisation algebra,” Optik (Stuttgart) 75, 26–36 (1986).

1984 (1)

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 721–741 (1984).
[CrossRef]

1981 (1)

1979 (1)

1978 (1)

Anderson, D. G. M.

Artal, P.

Ax, G. R.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis, and Remote Sensing, D. B. Chenault, M. J. Duggin, W. G. Egan, D. H. Goldstein, eds., Proc. SPIE3754, 137–143.

Azzam, R. M. A.

Barakat, R.

Berthod, M.

Z. Kato, M. Berthod, J. Zérubia, “A hierarchical Markov random field model and multitemperature annealing for parallel image classification,” Graph. Models Image Process. 58, 18–37 (1996).
[CrossRef]

Bouman, C. A.

C. A. Bouman, M. Shapiro, “A multiscale random field model for Bayesian image segmentation,” IEEE Trans. Image Process. 3, 162–177 (1994).
[CrossRef] [PubMed]

Bouthemy, P.

M. Mignotte, C. Collet, P. Pérez, P. Bouthemy, “Three-class Markovian segmentation of high resolution sonar images,” J. Computer Vision Image Underst. 76, 191–204 (1999).
[CrossRef]

P. Rostaing, P. Pérez, J.-N. Provost, C. Collet, P. Bouthemy, “Multispectral spot images analysis using generalized Gaussian modeling: application to water depth mapping,” Comput. Vis. Image Underst. (to be published).

Bueno, J. M.

Chardin, A.

P. Pérez, A. Chardin, J.-M. Laferté, “Noniterative manipulation of discrete energy-based models for image analysis,” Pattern Recogn. 33, 573–586 (2000).
[CrossRef]

Chipman, R. A.

P. Y. Gerligand, M. H. Smith, R. A. Chipman, “Polarimetric images of a cone,” Opt. Express 4, 420–430 (1999), http://www.opticsexpress.org .
[CrossRef] [PubMed]

S.-Y. Lu, R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998).
[CrossRef]

S.-Y. Lu, R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
[CrossRef]

R. A. Chipman, “Polarimetry,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1993), pp. 22.1–22.33.

Cloude, S. R.

S. R. Cloude, “Group theory and polarisation algebra,” Optik (Stuttgart) 75, 26–36 (1986).

Collet, C.

M. Mignotte, C. Collet, P. Pérez, P. Bouthemy, “Three-class Markovian segmentation of high resolution sonar images,” J. Computer Vision Image Underst. 76, 191–204 (1999).
[CrossRef]

P. Rostaing, J.-N. Provost, C. Collet, “Unsupervised multispectral image segmentation using generalized Gaussian noise model,” in Proceedings of the International Workshop EMMCVPR’99, Vol. 1654 of Springer Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1999), pp. 141–156.

P. Rostaing, P. Pérez, J.-N. Provost, C. Collet, P. Bouthemy, “Multispectral spot images analysis using generalized Gaussian modeling: application to water depth mapping,” Comput. Vis. Image Underst. (to be published).

del Toro Iniesta, J. C.

Duda, R. O.

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley Interscience, New York, 1973).

Fry, E. S.

Geman, D.

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 721–741 (1984).
[CrossRef]

Geman, S.

S. Geman, D. Geman, “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6, 721–741 (1984).
[CrossRef]

Gerligand, P. Y.

Giordana, N.

N. Giordana, W. Pieczynski, “Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 465–475 (1997).
[CrossRef]

Givens, C. R.

C. R. Givens, A. B. Kostinski, “A simple necessary and sufficient condition on physically realizable Mueller matrices,” J. Mod. Opt. 40, 471–481 (1993).
[CrossRef]

A. B. Kostinski, C. R. Givens, J. M. Kwiatkowski, “Constraints on Mueller matrices of polarization optics,” Appl. Opt. 32, 1646–1651 (1993).
[CrossRef] [PubMed]

Goudail, F.

F. Goudail, P. Réfrégier, “Statistical algorithms for processing polarimetric images in coherent light,” Trait. Signal 18(5–6), 297–319 (2001).

Graffigne, C.

C. Graffigne, F. Heitz, Pérez, F. Prêteux, M. Sigelle, J. Zerubia, “Hierarchical Markov random field models applied to image analysis: a review,” in Neural, Morphological, and Stochastic Methods in Image and Signal Processing, E. R. Dougherty, F. J. Preteux, S. S. Shen, eds., Proc. SPIE2568, 2–17 (1995).

Hart, P. E.

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley Interscience, New York, 1973).

Heitz, F.

J.-M. Laferté, P. Pérez, F. Heitz, “Discrete Markov image modeling and inference on the quad-tree,” IEEE Trans. Image Process. 9, 390–404 (2000).
[CrossRef]

P. Pérez, F. Heitz, “Restriction of a Markov random field on a graph and multiresolution statistical image modeling,” IEEE Trans. Inf. Theory 42, 180–190 (1996).
[CrossRef]

C. Graffigne, F. Heitz, Pérez, F. Prêteux, M. Sigelle, J. Zerubia, “Hierarchical Markov random field models applied to image analysis: a review,” in Neural, Morphological, and Stochastic Methods in Image and Signal Processing, E. R. Dougherty, F. J. Preteux, S. S. Shen, eds., Proc. SPIE2568, 2–17 (1995).

Hovenier, J. W.

C. V. M. van der Mee, J. W. Hovenier, “Structure of matrices transforming Stokes parameters,” J. Math. Phys. 33, 3574–3584 (1992).
[CrossRef]

Howe, J. D.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis, and Remote Sensing, D. B. Chenault, M. J. Duggin, W. G. Egan, D. H. Goldstein, eds., Proc. SPIE3754, 137–143.

Howell, B. J.

Jordan, D. L.

Karl, W. C.

M. R. Luettgen, W. C. Karl, A. S. Willsky, R. Tenney, “Multiscale representation of Markov random fields,” IEEE Trans. Signal Process. 41, 3377–3395 (1993).
[CrossRef]

Kato, Z.

Z. Kato, M. Berthod, J. Zérubia, “A hierarchical Markov random field model and multitemperature annealing for parallel image classification,” Graph. Models Image Process. 58, 18–37 (1996).
[CrossRef]

Kattawar, G. W.

Kostinski, A. B.

A. B. Kostinski, C. R. Givens, J. M. Kwiatkowski, “Constraints on Mueller matrices of polarization optics,” Appl. Opt. 32, 1646–1651 (1993).
[CrossRef] [PubMed]

C. R. Givens, A. B. Kostinski, “A simple necessary and sufficient condition on physically realizable Mueller matrices,” J. Mod. Opt. 40, 471–481 (1993).
[CrossRef]

Kumar, M. S.

M. S. Kumar, R. Simon, “Characterization of Mueller matrices in polarization optics,” Opt. Commun. 88, 464–470 (1992).
[CrossRef]

Kwiatkowski, J. M.

Laferté, J.-M.

J.-M. Laferté, P. Pérez, F. Heitz, “Discrete Markov image modeling and inference on the quad-tree,” IEEE Trans. Image Process. 9, 390–404 (2000).
[CrossRef]

P. Pérez, A. Chardin, J.-M. Laferté, “Noniterative manipulation of discrete energy-based models for image analysis,” Pattern Recogn. 33, 573–586 (2000).
[CrossRef]

Landi degl’ Innocenti, E.

Lewis, G. D.

Lu, S.-Y.

S.-Y. Lu, R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998).
[CrossRef]

S.-Y. Lu, R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
[CrossRef]

Luettgen, M. R.

M. R. Luettgen, W. C. Karl, A. S. Willsky, R. Tenney, “Multiscale representation of Markov random fields,” IEEE Trans. Signal Process. 41, 3377–3395 (1993).
[CrossRef]

Mignotte, M.

M. Mignotte, C. Collet, P. Pérez, P. Bouthemy, “Three-class Markovian segmentation of high resolution sonar images,” J. Computer Vision Image Underst. 76, 191–204 (1999).
[CrossRef]

Miller, M. A.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis, and Remote Sensing, D. B. Chenault, M. J. Duggin, W. G. Egan, D. H. Goldstein, eds., Proc. SPIE3754, 137–143.

Pérez,

C. Graffigne, F. Heitz, Pérez, F. Prêteux, M. Sigelle, J. Zerubia, “Hierarchical Markov random field models applied to image analysis: a review,” in Neural, Morphological, and Stochastic Methods in Image and Signal Processing, E. R. Dougherty, F. J. Preteux, S. S. Shen, eds., Proc. SPIE2568, 2–17 (1995).

Pérez, P.

J.-M. Laferté, P. Pérez, F. Heitz, “Discrete Markov image modeling and inference on the quad-tree,” IEEE Trans. Image Process. 9, 390–404 (2000).
[CrossRef]

P. Pérez, A. Chardin, J.-M. Laferté, “Noniterative manipulation of discrete energy-based models for image analysis,” Pattern Recogn. 33, 573–586 (2000).
[CrossRef]

M. Mignotte, C. Collet, P. Pérez, P. Bouthemy, “Three-class Markovian segmentation of high resolution sonar images,” J. Computer Vision Image Underst. 76, 191–204 (1999).
[CrossRef]

P. Pérez, F. Heitz, “Restriction of a Markov random field on a graph and multiresolution statistical image modeling,” IEEE Trans. Inf. Theory 42, 180–190 (1996).
[CrossRef]

P. Rostaing, P. Pérez, J.-N. Provost, C. Collet, P. Bouthemy, “Multispectral spot images analysis using generalized Gaussian modeling: application to water depth mapping,” Comput. Vis. Image Underst. (to be published).

Petty, T. E.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis, and Remote Sensing, D. B. Chenault, M. J. Duggin, W. G. Egan, D. H. Goldstein, eds., Proc. SPIE3754, 137–143.

Pieczynski, W.

N. Giordana, W. Pieczynski, “Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 465–475 (1997).
[CrossRef]

W. Pieczynski, “Statistical image segmentation,” Mach. Graph. Vision 1, 261–268 (1992).

Prêteux, F.

C. Graffigne, F. Heitz, Pérez, F. Prêteux, M. Sigelle, J. Zerubia, “Hierarchical Markov random field models applied to image analysis: a review,” in Neural, Morphological, and Stochastic Methods in Image and Signal Processing, E. R. Dougherty, F. J. Preteux, S. S. Shen, eds., Proc. SPIE2568, 2–17 (1995).

Provost, J.-N.

P. Rostaing, P. Pérez, J.-N. Provost, C. Collet, P. Bouthemy, “Multispectral spot images analysis using generalized Gaussian modeling: application to water depth mapping,” Comput. Vis. Image Underst. (to be published).

P. Rostaing, J.-N. Provost, C. Collet, “Unsupervised multispectral image segmentation using generalized Gaussian noise model,” in Proceedings of the International Workshop EMMCVPR’99, Vol. 1654 of Springer Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1999), pp. 141–156.

Rahmann, S.

S. Rahmann, “Polarization images: a geometric interpretation for shape analysis,” in 15th International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), Vol. 3, pp. 542–546.

Rakovic, M. J.

Réfrégier, P.

F. Goudail, P. Réfrégier, “Statistical algorithms for processing polarimetric images in coherent light,” Trait. Signal 18(5–6), 297–319 (2001).

Roberts, P. J.

Rostaing, P.

P. Rostaing, P. Pérez, J.-N. Provost, C. Collet, P. Bouthemy, “Multispectral spot images analysis using generalized Gaussian modeling: application to water depth mapping,” Comput. Vis. Image Underst. (to be published).

P. Rostaing, J.-N. Provost, C. Collet, “Unsupervised multispectral image segmentation using generalized Gaussian noise model,” in Proceedings of the International Workshop EMMCVPR’99, Vol. 1654 of Springer Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1999), pp. 141–156.

Shapiro, M.

C. A. Bouman, M. Shapiro, “A multiscale random field model for Bayesian image segmentation,” IEEE Trans. Image Process. 3, 162–177 (1994).
[CrossRef] [PubMed]

Sigelle, M.

C. Graffigne, F. Heitz, Pérez, F. Prêteux, M. Sigelle, J. Zerubia, “Hierarchical Markov random field models applied to image analysis: a review,” in Neural, Morphological, and Stochastic Methods in Image and Signal Processing, E. R. Dougherty, F. J. Preteux, S. S. Shen, eds., Proc. SPIE2568, 2–17 (1995).

Simon, R.

R. Sridhar, R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41, 1903–1915 (1994).
[CrossRef]

M. S. Kumar, R. Simon, “Characterization of Mueller matrices in polarization optics,” Opt. Commun. 88, 464–470 (1992).
[CrossRef]

Smith, M. H.

P. Y. Gerligand, M. H. Smith, R. A. Chipman, “Polarimetric images of a cone,” Opt. Express 4, 420–430 (1999), http://www.opticsexpress.org .
[CrossRef] [PubMed]

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis, and Remote Sensing, D. B. Chenault, M. J. Duggin, W. G. Egan, D. H. Goldstein, eds., Proc. SPIE3754, 137–143.

M. H. Smith, “Interpreting Mueller matrix images of tissues,” in Laser-Tissue Interaction XII: Photochemical, Photothermal, and Photomechanical, D. D. Duncan, S. L. Jacques, P. C. Johnson, eds., Proc. SPIE4257, 82–89 (2001).

Sornsin, E. A.

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis, and Remote Sensing, D. B. Chenault, M. J. Duggin, W. G. Egan, D. H. Goldstein, eds., Proc. SPIE3754, 137–143.

Sridhar, R.

R. Sridhar, R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41, 1903–1915 (1994).
[CrossRef]

Tenney, R.

M. R. Luettgen, W. C. Karl, A. S. Willsky, R. Tenney, “Multiscale representation of Markov random fields,” IEEE Trans. Signal Process. 41, 3377–3395 (1993).
[CrossRef]

van der Mee, C. V. M.

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C. V. M. van der Mee, J. W. Hovenier, “Structure of matrices transforming Stokes parameters,” J. Math. Phys. 33, 3574–3584 (1992).
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M. R. Luettgen, W. C. Karl, A. S. Willsky, R. Tenney, “Multiscale representation of Markov random fields,” IEEE Trans. Signal Process. 41, 3377–3395 (1993).
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M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis, and Remote Sensing, D. B. Chenault, M. J. Duggin, W. G. Egan, D. H. Goldstein, eds., Proc. SPIE3754, 137–143.

Xing, Z.-F.

Z.-F. Xing, “On the deterministic and non-deterministic Mueller matrix,” J. Mod. Opt. 39, 461–484 (1992).
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Zerubia, J.

C. Graffigne, F. Heitz, Pérez, F. Prêteux, M. Sigelle, J. Zerubia, “Hierarchical Markov random field models applied to image analysis: a review,” in Neural, Morphological, and Stochastic Methods in Image and Signal Processing, E. R. Dougherty, F. J. Preteux, S. S. Shen, eds., Proc. SPIE2568, 2–17 (1995).

Zérubia, J.

Z. Kato, M. Berthod, J. Zérubia, “A hierarchical Markov random field model and multitemperature annealing for parallel image classification,” Graph. Models Image Process. 58, 18–37 (1996).
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Appl. Opt. (5)

Graph. Models Image Process. (1)

Z. Kato, M. Berthod, J. Zérubia, “A hierarchical Markov random field model and multitemperature annealing for parallel image classification,” Graph. Models Image Process. 58, 18–37 (1996).
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IEEE Trans. Image Process. (2)

J.-M. Laferté, P. Pérez, F. Heitz, “Discrete Markov image modeling and inference on the quad-tree,” IEEE Trans. Image Process. 9, 390–404 (2000).
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C. A. Bouman, M. Shapiro, “A multiscale random field model for Bayesian image segmentation,” IEEE Trans. Image Process. 3, 162–177 (1994).
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IEEE Trans. Inf. Theory (1)

P. Pérez, F. Heitz, “Restriction of a Markov random field on a graph and multiresolution statistical image modeling,” IEEE Trans. Inf. Theory 42, 180–190 (1996).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

N. Giordana, W. Pieczynski, “Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation,” IEEE Trans. Pattern Anal. Mach. Intell. 19, 465–475 (1997).
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IEEE Trans. Signal Process. (1)

M. R. Luettgen, W. C. Karl, A. S. Willsky, R. Tenney, “Multiscale representation of Markov random fields,” IEEE Trans. Signal Process. 41, 3377–3395 (1993).
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J. Computer Vision Image Underst. (1)

M. Mignotte, C. Collet, P. Pérez, P. Bouthemy, “Three-class Markovian segmentation of high resolution sonar images,” J. Computer Vision Image Underst. 76, 191–204 (1999).
[CrossRef]

J. Math. Phys. (2)

C. V. M. van der Mee, “An eigenvalue criterion for matrices transforming Stokes parameters,” J. Math. Phys. 34, 5072–5088 (1993).
[CrossRef]

C. V. M. van der Mee, J. W. Hovenier, “Structure of matrices transforming Stokes parameters,” J. Math. Phys. 33, 3574–3584 (1992).
[CrossRef]

J. Mod. Opt. (3)

R. Sridhar, R. Simon, “Normal form for Mueller matrices in polarization optics,” J. Mod. Opt. 41, 1903–1915 (1994).
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Z.-F. Xing, “On the deterministic and non-deterministic Mueller matrix,” J. Mod. Opt. 39, 461–484 (1992).
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W. Pieczynski, “Statistical image segmentation,” Mach. Graph. Vision 1, 261–268 (1992).

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M. S. Kumar, R. Simon, “Characterization of Mueller matrices in polarization optics,” Opt. Commun. 88, 464–470 (1992).
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S.-Y. Lu, R. A. Chipman, “Mueller matrices and the degree of polarization,” Opt. Commun. 146, 11–14 (1998).
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Opt. Express (1)

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Optik (Stuttgart) (1)

S. R. Cloude, “Group theory and polarisation algebra,” Optik (Stuttgart) 75, 26–36 (1986).

Pattern Recogn. (1)

P. Pérez, A. Chardin, J.-M. Laferté, “Noniterative manipulation of discrete energy-based models for image analysis,” Pattern Recogn. 33, 573–586 (2000).
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Trait. Signal (1)

F. Goudail, P. Réfrégier, “Statistical algorithms for processing polarimetric images in coherent light,” Trait. Signal 18(5–6), 297–319 (2001).

Other (8)

M. H. Smith, J. D. Howe, J. B. Woodruff, M. A. Miller, G. R. Ax, T. E. Petty, E. A. Sornsin, “Multispectral infrared Stokes imaging polarimeter,” in Polarization: Measurement, Analysis, and Remote Sensing, D. B. Chenault, M. J. Duggin, W. G. Egan, D. H. Goldstein, eds., Proc. SPIE3754, 137–143.

M. H. Smith, “Interpreting Mueller matrix images of tissues,” in Laser-Tissue Interaction XII: Photochemical, Photothermal, and Photomechanical, D. D. Duncan, S. L. Jacques, P. C. Johnson, eds., Proc. SPIE4257, 82–89 (2001).

S. Rahmann, “Polarization images: a geometric interpretation for shape analysis,” in 15th International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2000), Vol. 3, pp. 542–546.

P. Rostaing, J.-N. Provost, C. Collet, “Unsupervised multispectral image segmentation using generalized Gaussian noise model,” in Proceedings of the International Workshop EMMCVPR’99, Vol. 1654 of Springer Lecture Notes in Computer Science (Springer-Verlag, Berlin, 1999), pp. 141–156.

P. Rostaing, P. Pérez, J.-N. Provost, C. Collet, P. Bouthemy, “Multispectral spot images analysis using generalized Gaussian modeling: application to water depth mapping,” Comput. Vis. Image Underst. (to be published).

R. A. Chipman, “Polarimetry,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1993), pp. 22.1–22.33.

R. O. Duda, P. E. Hart, Pattern Classification and Scene Analysis (Wiley Interscience, New York, 1973).

C. Graffigne, F. Heitz, Pérez, F. Prêteux, M. Sigelle, J. Zerubia, “Hierarchical Markov random field models applied to image analysis: a review,” in Neural, Morphological, and Stochastic Methods in Image and Signal Processing, E. R. Dougherty, F. J. Preteux, S. S. Shen, eds., Proc. SPIE2568, 2–17 (1995).

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