Abstract

A new binary classification method for Mueller matrix images is presented which optimizes the polarization state analyzer (PSA) and the polarization state generator (PSG) using a statistical divergence between pixel values in two regions of an image. This optimization generalizes to multiple PSA/PSG pairs so that the classification performance as a function of number of polarimetric measurements can be considered. Optimizing PSA/PSG pairs gives insight into which polarimetric measurements are most useful for the binary classification. For example, in scenes with strong diattenuation, retardance, or depolarization certain PSA/PSG pairs would make two regions in an image look very similar and other pairs would make the regions look very different. The method presented in this paper provides a quantitative method for ensuring the images acquired can be classified optimally.

© 2017 Optical Society of America

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References

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2016 (1)

J. Rehbinder, H. Haddad, S. Deby, B. Teig, A. Nazac, T. Novikova, A. Pierangelo, and F. Moreau, “Ex vivo Mueller polarimetric imaging of the uterine cervix: a first statistical evaluation,” J. Biomed. Opt. 21, 071113 (2016).
[Crossref]

2015 (1)

2014 (1)

2012 (3)

2011 (3)

2009 (4)

2007 (1)

2006 (1)

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

2004 (1)

1996 (2)

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

F. Le Roy-Bréhonnet, B. Le Jeune, P. Elies, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D 29, 34–38 (1996).
[Crossref]

Aïnouz, S.

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

Anna, G.

Barrett, H.

H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2013).

Bénière, A.

Bertaux, N.

Boffety, M.

Cariou, J.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Elies, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D 29, 34–38 (1996).
[Crossref]

Chipman, R. A.

Clarkson, E.

Collet, C.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).

DasGupta, A.

A. DasGupta, Asymptotic Theory of Statistics and Probability (Springer, 2008).

De Martino, A.

Deby, S.

J. Rehbinder, H. Haddad, S. Deby, B. Teig, A. Nazac, T. Novikova, A. Pierangelo, and F. Moreau, “Ex vivo Mueller polarimetric imaging of the uterine cervix: a first statistical evaluation,” J. Biomed. Opt. 21, 071113 (2016).
[Crossref]

Dolfi, D.

Elies, P.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Elies, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D 29, 34–38 (1996).
[Crossref]

Galland, F.

Goudail, F.

Haddad, H.

J. Rehbinder, H. Haddad, S. Deby, B. Teig, A. Nazac, T. Novikova, A. Pierangelo, and F. Moreau, “Ex vivo Mueller polarimetric imaging of the uterine cervix: a first statistical evaluation,” J. Biomed. Opt. 21, 071113 (2016).
[Crossref]

Hoover, B. G.

I. J. Vaughn, B. G. Hoover, and J. S. Tyo, “Classification using active polarimetry,” Proc SPIE 8364, 83640S (2012).

B. G. Hoover and J. S. Tyo, “Polarization components analysis for invariant discrimination,” Appl. Opt. 46, 8364–8373 (2007).
[Crossref]

Hu, H.

Kupinski, M. K.

Le Jeune, B.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Elies, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D 29, 34–38 (1996).
[Crossref]

Le Roy-Bréhonnet, F.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Elies, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D 29, 34–38 (1996).
[Crossref]

Lotrian, J.

F. Le Roy-Bréhonnet, B. Le Jeune, P. Elies, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D 29, 34–38 (1996).
[Crossref]

Lu, S.-Y.

Moreau, F.

J. Rehbinder, H. Haddad, S. Deby, B. Teig, A. Nazac, T. Novikova, A. Pierangelo, and F. Moreau, “Ex vivo Mueller polarimetric imaging of the uterine cervix: a first statistical evaluation,” J. Biomed. Opt. 21, 071113 (2016).
[Crossref]

Myers, K.

H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2013).

Nazac, A.

J. Rehbinder, H. Haddad, S. Deby, B. Teig, A. Nazac, T. Novikova, A. Pierangelo, and F. Moreau, “Ex vivo Mueller polarimetric imaging of the uterine cervix: a first statistical evaluation,” J. Biomed. Opt. 21, 071113 (2016).
[Crossref]

Novikova, T.

J. Rehbinder, H. Haddad, S. Deby, B. Teig, A. Nazac, T. Novikova, A. Pierangelo, and F. Moreau, “Ex vivo Mueller polarimetric imaging of the uterine cervix: a first statistical evaluation,” J. Biomed. Opt. 21, 071113 (2016).
[Crossref]

Orlik, X.

Pierangelo, A.

J. Rehbinder, H. Haddad, S. Deby, B. Teig, A. Nazac, T. Novikova, A. Pierangelo, and F. Moreau, “Ex vivo Mueller polarimetric imaging of the uterine cervix: a first statistical evaluation,” J. Biomed. Opt. 21, 071113 (2016).
[Crossref]

Rehbinder, J.

J. Rehbinder, H. Haddad, S. Deby, B. Teig, A. Nazac, T. Novikova, A. Pierangelo, and F. Moreau, “Ex vivo Mueller polarimetric imaging of the uterine cervix: a first statistical evaluation,” J. Biomed. Opt. 21, 071113 (2016).
[Crossref]

Richert, M.

Sauer, H.

Stoll, M. P.

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

Takakura, Y.

Teig, B.

J. Rehbinder, H. Haddad, S. Deby, B. Teig, A. Nazac, T. Novikova, A. Pierangelo, and F. Moreau, “Ex vivo Mueller polarimetric imaging of the uterine cervix: a first statistical evaluation,” J. Biomed. Opt. 21, 071113 (2016).
[Crossref]

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).

Tyo, J. S.

Vaughn, I. J.

I. J. Vaughn, B. G. Hoover, and J. S. Tyo, “Classification using active polarimetry,” Proc SPIE 8364, 83640S (2012).

Zallat, J.

J. Zallat, S. Aïnouz, 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. Zallat, C. Collet, and Y. Takakura, “Clustering of polarization-encoded images,” Appl. Opt. 43, 283–292 (2004).
[Crossref]

Appl. Opt. (3)

J. Biomed. Opt. (1)

J. Rehbinder, H. Haddad, S. Deby, B. Teig, A. Nazac, T. Novikova, A. Pierangelo, and F. Moreau, “Ex vivo Mueller polarimetric imaging of the uterine cervix: a first statistical evaluation,” J. Biomed. Opt. 21, 071113 (2016).
[Crossref]

J. Opt. A (1)

J. Zallat, S. Aïnouz, 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. Soc. Am. A (3)

J. Phys. D (1)

F. Le Roy-Bréhonnet, B. Le Jeune, P. Elies, J. Cariou, and J. Lotrian, “Optical media and target characterization by Mueller matrix decomposition,” J. Phys. D 29, 34–38 (1996).
[Crossref]

Opt. Express (2)

Opt. Lett. (6)

Proc SPIE (1)

I. J. Vaughn, B. G. Hoover, and J. S. Tyo, “Classification using active polarimetry,” Proc SPIE 8364, 83640S (2012).

Other (3)

T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, 1991).

H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2013).

A. DasGupta, Asymptotic Theory of Statistics and Probability (Springer, 2008).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Normalized Mueller matrix measurement of orthogonal polarizers, (b) a randomly selected PSA/PSG pair, and (c) J-CQO PSA/PSG pair. The visual contrast of the log-likelihood images is similar in (b) and (c) but the value of J is about 2 orders of magnitude more in (c).

Fig. 2.
Fig. 2.

(a) Normalized Mueller matrix measurement of two retarders, (b) a randomly selected PSA/PSG pair, and (c) J-CQO PSA/PSG pair. The visual contrast of the log-likelihood images is greater in (c) than (b) and in particular the spatial variance in each region is reduced. The value of J is many orders of magnitude greater in (c) than (b).

Fig. 3.
Fig. 3.

(a) Normalized Mueller matrix measurement of two pieces of sandpaper: 400 and 800 grit, (b) a randomly selected PSA/PSG pair, and (c) J-CQO PSA/PSG pair. The visual contrast in the log-likelihood image is much greater in (c) than (b). The value of J is an order of magnitude greater in (c) than (b).

Fig. 4.
Fig. 4.

(a) Normalized Mueller matrix measurement of two pieces of transparent tape at 40° from each other, (b) a randomly selected PSA/PSG pair, and (c) J-CQO PSA/PSG pair. The visual contrast in the log-likelihood image is much greater in (c) than (b). The region were the tape overlaps becomes evident in (c). The value of J increases from 0 in (b) to 24 in (c).

Fig. 5.
Fig. 5.

(a) Normalized Mueller matrix measurement of two pieces of transparent tape at 8° from each other, (b) a randomly selected PSA/PSG pair, and (c) J-CQO PSA/PSG pair. Visual discrimination is possible in the log-likelihood image of (c) but not in (b). For the J-CQO solution J = 3 indicating a difficult discrimination task. The log-likelihood histogram in (c) is not bi-modal but the regions can be distinguished when the log-likelihood is viewed as an image due to spatial correlations.

Equations (21)

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

i = a t Mg .
g = M 1 1 M 2 g ,
g = M 1 1 RM 2 g .
d = a g ,
A B = ( a 11 B a 1 n B a m 1 B a m n B ) .
i = d t m ,
λ ( m ) = ln [ p r 1 ( m ) ] ln [ p r 2 ( m ) ]
F KL ( p r 1 | | p r 2 ) = λ ( i ) 1 ,
F KL ( p r 2 | | p r 1 ) = λ ( i ) 2 ,
f ( x ) n = R L f ( x ) p r n ( x ) d L x .
J ( d ) = λ ( i ) 1 λ ( i ) 2 .
2 J ( d ) = 2 + σ 2 2 + Δ i 2 σ 1 2 + σ 1 2 + Δ i 2 σ 2 2 ,
D = ( a 1 g 1 a 2 g 2 a L g L ) .
2 J ( D ) = 2 L + tr [ C 2 1 C 1 ] + Δ i t C 2 1 Δ i + tr [ C 1 1 C 2 ] + Δ i t C 1 1 Δ i ,
d J = d t ( K 2 + Δ m Δ m t ) [ I dd t K 1 σ 1 2 ] σ 1 2 + d t ( K 1 + Δ m Δ m t ) [ I dd t K 2 σ 2 2 ] σ 2 2 ,
a i J ( d ) = [ d J ] t d a i = [ d J ] t ( e i g ) .
a J = i 4 [ d J ] t [ e i g ] e i .
g J = i 4 [ d J ] t [ a e i t ] e i .
θ n a J ( d ) = [ a J ] t a θ n a = i 4 [ e i g t ] t [ d J ] a i θ n a ,
θ n g J ( d ) = [ g J ] t g θ n g = i 4 [ a e i t ] t [ d J ] g i θ n g .
D J = C 1 1 D t ( K 2 + Δ m Δ m t ) [ I DC 1 1 D t K 1 ] + C 2 1 D t ( K 1 + Δ m Δ m t ) [ I DC 2 1 D t K 2 ] .

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