Abstract

Until now, most studies about polarimetric contrast optimization have focused on the discrimination of two regions (a target and a background). In this paper, we propose a methodology to determine the set of polarimetric measurements that optimize discrimination of an arbitrary number of regions with different polarimetric properties. We show on real world examples that in some situations, a few number of optimized polarimetric measurements can overcome the performance of full Mueller matrix imaging.

© 2011 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (1)

2010 (2)

2009 (3)

2007 (2)

2006 (1)

J. Zallat, S. Ainouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters : impact of image noise and systematic errors.” J. Opt. A 8, 807–814 (2006).
[CrossRef]

2005 (1)

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21–28 (2005).
[CrossRef]

2004 (1)

2003 (1)

2002 (3)

J. S. Tyo, “Design of optimal polarimeters : maximization of the signal-to-noise ratio and minimization of systematic error,” Appl. Opt. 41, 619–630 (2002).
[CrossRef] [PubMed]

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[CrossRef] [PubMed]

A. Jain, P. Moulin, M. I. Miller, and K. Ramchandran, “Information-theoretic bounds on target recognition performance based on degraded image data,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 1153–1166 (2002).
[CrossRef]

2000 (2)

S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at λ = 806 nm,” Opt. Eng. 39, 2681–2688 (2000).
[CrossRef]

J. Yang and et al., “Numerical methods for solving the optimal problem of contrast enhancement,” IEEE transactions on geoscience and remote sensing 38, 965–971 (2000).
[CrossRef]

1998 (1)

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

1996 (1)

1993 (1)

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

1988 (1)

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

1981 (1)

Abdelali, B.

Ahmad, J.

J. Ahmad and Y. Takakura, “Improving segmentation maps using polarization imaging,” in “IEEE International Conference on Image Processing,” (2007).
[CrossRef]

Ainouz, S.

J. Zallat, S. Ainouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters : impact of image noise and systematic errors.” J. Opt. A 8, 807–814 (2006).
[CrossRef]

S. Ainouz, O. Morel, and F. Meriaudeau, “Geometric-based segmentation of polarization-encoded images,” in “IEEE International Conference on Signal Image Technology and Internet Based System,” (2008).
[CrossRef]

Antonelli, M.-R.

Bénière, A.

Boulbry, B.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21–28 (2005).
[CrossRef]

Boulvert, F.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21–28 (2005).
[CrossRef]

Breugnot, S.

S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at λ = 806 nm,” Opt. Eng. 39, 2681–2688 (2000).
[CrossRef]

Bueno, J. M.

Campbell, M.

Cariou, J.

M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Snapshot mueller matrix polarimeter by wavelength polarization coding,” Opt. Express 15, 13660–13668 (2007).
[CrossRef] [PubMed]

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21–28 (2005).
[CrossRef]

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

Clémenceau, P.

S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at λ = 806 nm,” Opt. Eng. 39, 2681–2688 (2000).
[CrossRef]

Cookson, C.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory (John Wiley and Sons, New York, 1991).
[CrossRef]

De Martino, A.

Delyon, G.

Duan, Q. Y.

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

Dubreuil, M.

Engheta, N.

Floc’h, M.

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

Fukunaga, K.

K. Fukunaga, Introduction to statistical pattern recognition (Academic Press, San Diego, 1990).

Gayet, B.

Goudail, F.

Gupta, V. K.

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

Hoover, B. G.

Hunter, J.

Jacques, S. L.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[CrossRef] [PubMed]

Jain, A.

A. Jain, P. Moulin, M. I. Miller, and K. Ramchandran, “Information-theoretic bounds on target recognition performance based on degraded image data,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 1153–1166 (2002).
[CrossRef]

Johnson, S. J.

Kieleck, C.

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

Kisilak, M.

Kong, J. A.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

Le Brun, G.

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21–28 (2005).
[CrossRef]

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

Le Jeune, B.

M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Snapshot mueller matrix polarimeter by wavelength polarization coding,” Opt. Express 15, 13660–13668 (2007).
[CrossRef] [PubMed]

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21–28 (2005).
[CrossRef]

Lee, K.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[CrossRef] [PubMed]

Lotrian, J.

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

Meriaudeau, F.

S. Ainouz, O. Morel, and F. Meriaudeau, “Geometric-based segmentation of polarization-encoded images,” in “IEEE International Conference on Signal Image Technology and Internet Based System,” (2008).
[CrossRef]

Miller, M. I.

A. Jain, P. Moulin, M. I. Miller, and K. Ramchandran, “Information-theoretic bounds on target recognition performance based on degraded image data,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 1153–1166 (2002).
[CrossRef]

Morel, O.

S. Ainouz, O. Morel, and F. Meriaudeau, “Geometric-based segmentation of polarization-encoded images,” in “IEEE International Conference on Signal Image Technology and Internet Based System,” (2008).
[CrossRef]

Moulin, P.

A. Jain, P. Moulin, M. I. Miller, and K. Ramchandran, “Information-theoretic bounds on target recognition performance based on degraded image data,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 1153–1166 (2002).
[CrossRef]

Narasimhan, S. G.

Nayar, S. K.

Novak, L. M.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

Novikova, T.

Pierangelo, A.

Pugh, E. N.

Ramchandran, K.

A. Jain, P. Moulin, M. I. Miller, and K. Ramchandran, “Information-theoretic bounds on target recognition performance based on degraded image data,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 1153–1166 (2002).
[CrossRef]

Ramella-Roman, J. C.

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[CrossRef] [PubMed]

Réfrégier, P.

Rivet, S.

M. Dubreuil, S. Rivet, B. Le Jeune, and J. Cariou, “Snapshot mueller matrix polarimeter by wavelength polarization coding,” Opt. Express 15, 13660–13668 (2007).
[CrossRef] [PubMed]

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21–28 (2005).
[CrossRef]

Rowe, M. P.

Schechner, Y. Y.

Shin, R. T.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

Solomon, J. E.

Sorooshian, S.

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

Stoll, M. P.

J. Zallat, S. Ainouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters : impact of image noise and systematic errors.” J. Opt. A 8, 807–814 (2006).
[CrossRef]

Swartz, A. A.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

Takakura, Y.

J. Ahmad and Y. Takakura, “Improving segmentation maps using polarization imaging,” in “IEEE International Conference on Image Processing,” (2007).
[CrossRef]

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory (John Wiley and Sons, New York, 1991).
[CrossRef]

Tyo, J. S.

Validire, P.

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation and Modulation Theory (John Wiley and Sons, Inc., New York, 1968).

Wang, Z.

Yang, J.

J. Yang and et al., “Numerical methods for solving the optimal problem of contrast enhancement,” IEEE transactions on geoscience and remote sensing 38, 965–971 (2000).
[CrossRef]

Yueh, H. A.

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

Zallat, J.

J. Zallat, S. Ainouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters : impact of image noise and systematic errors.” J. Opt. A 8, 807–814 (2006).
[CrossRef]

Appl. Opt. (5)

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

A. Jain, P. Moulin, M. I. Miller, and K. Ramchandran, “Information-theoretic bounds on target recognition performance based on degraded image data,” IEEE Trans. Pattern Anal. Mach. Intell. 24, 1153–1166 (2002).
[CrossRef]

IEEE transactions on geoscience and remote sensing (1)

J. Yang and et al., “Numerical methods for solving the optimal problem of contrast enhancement,” IEEE transactions on geoscience and remote sensing 38, 965–971 (2000).
[CrossRef]

J. Biomed. Opt. (1)

S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002).
[CrossRef] [PubMed]

J. Geophys. Res. (1)

A. A. Swartz, H. A. Yueh, J. A. Kong, L. M. Novak, and R. T. Shin, “Optimal polarizations for achieving maximal constrast in radar images,” J. Geophys. Res. 93, 15252–15260 (1988).
[CrossRef]

J. Opt. A (1)

J. Zallat, S. Ainouz, and M. P. Stoll, “Optimal configurations for imaging polarimeters : impact of image noise and systematic errors.” J. Opt. A 8, 807–814 (2006).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

F. Boulvert, B. Boulbry, G. Le Brun, B. Le Jeune, S. Rivet, and J. Cariou, “Analysis of the depolarizing properties of irradiated pig skin,” J. Opt. A Pure Appl. Opt. 7, 21–28 (2005).
[CrossRef]

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

J. Optim. Theory Appl. (1)

Q. Y. Duan, V. K. Gupta, and S. Sorooshian, “A shuffled complex evolution approach for effective and efficient global minimization,” J. Optim. Theory Appl. 76, 501–521 (1993).
[CrossRef]

Opt. Eng. (1)

S. Breugnot and P. Clémenceau, “Modeling and performances of a polarization active imager at λ = 806 nm,” Opt. Eng. 39, 2681–2688 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Pure Appl. Opt. (1)

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

Other (5)

S. Ainouz, O. Morel, and F. Meriaudeau, “Geometric-based segmentation of polarization-encoded images,” in “IEEE International Conference on Signal Image Technology and Internet Based System,” (2008).
[CrossRef]

J. Ahmad and Y. Takakura, “Improving segmentation maps using polarization imaging,” in “IEEE International Conference on Image Processing,” (2007).
[CrossRef]

K. Fukunaga, Introduction to statistical pattern recognition (Academic Press, San Diego, 1990).

H. L. Van Trees, Detection, Estimation and Modulation Theory (John Wiley and Sons, Inc., New York, 1968).

T. M. Cover and J. A. Thomas, Elements of Information Theory (John Wiley and Sons, New York, 1991).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Polarimetric imaging setup

Fig. 2
Fig. 2

(a) Scheme of the scene. (b) Intensity Image

Fig. 3
Fig. 3

(a) Mueller image of the scene with an integration time of t0/16 ∼ 5ms. (b) Results of the classification.

Fig. 4
Fig. 4

Optimal sets of N = 1, 2 and 3 projections maximizing the separability of the objects in the scene. Last column: results of classification using a ML classifier. Last row : classification results obtained with full Mueller matrix data. The polarization states in illumination and analysis are represented by their azimuth (α) and ellipticity (ɛ): (αS,ɛS)(αT ,ɛT).

Fig. 5
Fig. 5

Estimated PDF of the four classes in the scene (estimated on sample of around 300 pixels in each class). This projection corresponds to the results in the first row of the figure 4.

Fig. 6
Fig. 6

Representation of pixels of the four classes in the 2-dimensional space defined by the two images presented in the second row of the Fig. 4.

Fig. 7
Fig. 7

Representation of pixels of the four classes in the 3-dimensional space defined by the three images presented in the third row of the Fig. 4.

Fig. 8
Fig. 8

Evolution of the contrast criterion in function of the number of optimal images acquired. The integration for one set of images is keeping constant and equal to t0 ∼ 80ms.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

i = η I 0 2 T T M S
x p = [ i 1 p i 2 p i N p ] where i n p = η I 0 2 T n T M p S n
P k ( x ) = 1 2 π det ( Γ k ) exp [ 1 2 ( x x ¯ k ) T Γ k 1 ( x x ¯ k ) ]
L k = log [ P k ( x ) ] = 1 2 log [ 2 π det ( Γ k ) ] 1 2 ( x x ¯ k ) T Γ k 1 ( x x ¯ k )
k ^ = arg max k [ 1 , K ] [ L k ]
x ¯ ^ k = 1 P k p Ω k x k p
Γ ^ k = 1 P k p Ω k ( x k p x ¯ k ) ( x k p x ¯ k ) T
i = η I 0 2 q T m
[ M 00 M 01 M 02 M 03 M 10 M 11 M 12 M 13 M 20 M 21 M 22 M 23 M 30 M 31 M 32 M 33 ]
m = [ M 00 M 01 M 02 M 33 ]
( 𝒮 ^ , 𝒯 ^ ) = arg max 𝒮 , 𝒯 [ C ( 𝒮 , 𝒯 ) ]
B k , l = ln [ 𝒟 [ P k ( x ) P l ( x ) ] 1 / 2 d x ]
B k , l ( 𝒮 , 𝒯 ) = 1 8 ( x ¯ k x ¯ l ) T [ Γ k + Γ l 2 ] 1 ( x ¯ k x ¯ l ) + 1 2 log [ det ( Γ k + Γ l 2 ) det ( Γ k ) det ( Γ l ) ]
C ( 𝒮 , 𝒯 ) = min ( k , l ) , k l [ B k , l ( 𝒮 , 𝒯 ) ]

Metrics