Abstract

The polarization of light carries much useful information about the environment. Biological studies have shown that some animal species use polarization information for navigation and other purposes. It has been previously shown that a bioinspired polarization-difference imaging (PDI) technique can facilitate detection and feature extraction of targets in scattering media. It has also been established [J. Opt. Soc. Am. A 15, 359 (1998)] that polarization sum and polarization difference are the optimum pair of linear combinations of images taken through two orthogonally oriented linear polarizers of a scene having a uniform distribution of polarization directions. However, in many real environments the scene has a nonuniform distribution of polarization directions. Using principal component analysis of the polarization statistics of the scene, we develop a method to determine the two optimum information channels with unequal weighting coefficients that can be formed as linear combinations of the images of a scene taken through a pair of linear polarizers not constrained to the horizontal and vertical directions of the scene. We determine the optimal orientations of linear polarization filters that enhance separation of a target from the background, where the target is defined as an area with distinct polarization characteristics as compared to the background. Experimental results confirm that in most situations adaptive PDI outperforms conventional PDI with fixed channels.

© 2006 Optical Society of America

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    [PubMed]
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  57. S.-S. Lin, K. M. Yemelyanov, E. N. Pugh, Jr., and N. Engheta, "Polarization enhanced visual surveillance techniques," in Proceedings of IEEE International Conference on Networking, Sensing, and Control (IEEE, 2004), pp. 216-221.

2005

Y. Y. Schechner and N. Karpel, "Recovery of underwater visibility and structure by polarization analysis," IEEE J. Ocean. Eng. 30, 570-587 (2005).
[CrossRef]

R. Nothdurft and G. Yao, "Expression of target optical properties in subsurface polarization-gated imaging," Opt. Express 13, 4185-4195 (2005).
[CrossRef] [PubMed]

2004

2003

2002

G. Horváth, J. Gál, T. Labhart, and R. Wehner, "Does reflection polarization by plants influence colour perception in insects? Polarimetric measurements applied to a polarization-sensitive model retina of Papilio butterflies," J. Exp. Biol. 205, 3281-3298 (2002).
[PubMed]

C. K. Hamett and H. G. Craighead, "Liquid-crystal micropolarizer array for polarization-difference imaging," Appl. Opt. 41, 1291-1296 (2002).
[CrossRef]

2001

I. Pomozi, G. Horváth, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

T. W. Cronin and N. Shashar, "The linearly polarized light field in clear, tropical marine waters: spatial and temporal variation of light intensity, degree of polarization and e-vector angle," J. Exp. Biol. 204, 2461-2467 (2001).
[PubMed]

A. M. Wallace, B. Liang, E. Trucco, and J. Clark, "Improving depth acquisition using polarized light," Int. J. Comput. Vis. 32, 87-109 (2001).
[CrossRef]

F. Goudail and P. Réfrégier, "Statistical techniques for target detection in polarization diversity images," Opt. Lett. 26, 644-646 (2001).
[CrossRef]

F. Goudail and P. Réfrégier, "Statistical algorithms for target detection in coherent active polarimetric images," J. Opt. Soc. Am. A 18, 3049-3060 (2001).
[CrossRef]

2000

J. G. Walker, P. C. Y. Chang, and K. I. Hopcraft, "Visibility depth improvement in active polarization imaging in scattering media," Appl. Opt. 39, 4933-4941 (2000).
[CrossRef]

C. W. Hawryshyn, "Ultraviolet polarization vision in fishes: possible mechanisms for coding e-vector," Philos. Trans. R. Soc. London , Ser. B 355, 1187-1190 (2000).
[CrossRef]

1999

1998

1997

W. B. Wang, S. G. Demos, J. Ali, and R. R. Alfano, "Imaging fluorescent objects embedded inside animal tissues using polarization-difference technique," Optics Commun. 142, 161-166 (1997).
[CrossRef]

S. Demos and R. Alfano, "Optical polarization imaging," Appl. Opt. 36, 150-155 (1997).
[CrossRef] [PubMed]

L. B. Wolff, T. A. Mancini, P. Pouliquen, and A. G. Andreou, "Liquid crystal polarization camera," IEEE Trans. Rob. Autom. 13, 195-203 (1997).
[CrossRef]

1996

N. Shashar and T. W. Cronin, "Polarization contrast vision in octopus," J. Exp. Biol. 199, 999-1004 (1996).
[PubMed]

N. Shashar, P. S. Rutledge, and T. W. Cronin, "Polarization vision in cuttlefish: a concealed communication channel?" J. Exp. Biol. 199, 2077-2084 (1996).
[PubMed]

J. S. Tyo, M. P. Rowe, E. N. Pugh, Jr., and N. Engheta, "Target detection in optically scattered media by polarization-difference imaging," Appl. Opt. 35, 1855-1870 (1996).
[CrossRef] [PubMed]

T. Labhart, "How polarization-sensitive interneurons perform at low degrees of polarization," J. Exp. Biol. 199, 1467-1475 (1996).
[PubMed]

1995

1994

1993

R. Wehner and G. D. Bernard, "Photoreceptor twist: a solution to the false colour problem," in Proceedings of the National Academy of Sciences of the United States of America, 90, 4132-4135 (1993).

1992

C. W. Hawryshyn, "Polarization vision in fish," Am. Sci. 80, 164-175, 1992.

1991

1990

L. B. Wolff, "Polarization-based material classification from specular reflection," IEEE Trans. Pattern Anal. Mach. Intell. 12, 1059-1071 (1990).
[CrossRef]

1989

R. Wehner, "Neurobiology of polarization vision," Trends Neurosci. 12, 353-359 (1989).
[CrossRef] [PubMed]

1988

T. Labhart, "Polarization opponent interneurones in the insect visual system," Nature 331, 435-437 (1988).
[CrossRef]

1987

R. Wehner, "'Matched filters': neural models of the external world," J. Comp. Physiol. A 161, 511-531 (1987).
[CrossRef]

1983

G. Buchsbaum and A. Gottschalk, "Trichromacy, opponent colors coding and optimum color information transmission in the retina," Proc. R. Soc. London , Ser. B 220, 89-113 (1983).
[CrossRef]

1981

1976

R. Wehner, "Polarized-light navigation by insects," Sci. Am. 235, 106-114 (1976).
[CrossRef] [PubMed]

1949

K. von Frisch, "Die polarisation des himmelslichtes als orientierender faktor bei den tanzen der biener," Experimentia 5, 142-148 (1949).
[CrossRef]

Alfano, R.

Alfano, R. R.

S. G. Demos, W. B. Wang, and R. R. Alfano, "Imaging objects hidden in scattering media with fluorescence polarization preservation of contrast agents," Appl. Opt. 37, 792-797 (1998).
[CrossRef]

W. B. Wang, S. G. Demos, J. Ali, and R. R. Alfano, "Imaging fluorescent objects embedded inside animal tissues using polarization-difference technique," Optics Commun. 142, 161-166 (1997).
[CrossRef]

Ali, J.

W. B. Wang, S. G. Demos, J. Ali, and R. R. Alfano, "Imaging fluorescent objects embedded inside animal tissues using polarization-difference technique," Optics Commun. 142, 161-166 (1997).
[CrossRef]

Andreou, A. G.

L. B. Wolff, T. A. Mancini, P. Pouliquen, and A. G. Andreou, "Liquid crystal polarization camera," IEEE Trans. Rob. Autom. 13, 195-203 (1997).
[CrossRef]

L. B. Wolff and A. G. Andreou, "Polarization camera sensors," Image Vis. Comput. 13, 497-510 (1995).
[CrossRef]

Bernard, G. D.

R. Wehner and G. D. Bernard, "Photoreceptor twist: a solution to the false colour problem," in Proceedings of the National Academy of Sciences of the United States of America, 90, 4132-4135 (1993).

Bigue, L.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 2002).

Buchsbaum, G.

G. Buchsbaum and A. Gottschalk, "Trichromacy, opponent colors coding and optimum color information transmission in the retina," Proc. R. Soc. London , Ser. B 220, 89-113 (1983).
[CrossRef]

Caldwell, R. L.

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T.-H. Chiou, "Polarization vision and its role in biological signaling," Integr. Comp. Biol. 43, 549-558 (2003).
[CrossRef] [PubMed]

Chang, P. C. Y.

Chen, H.

H. Chen and L. B. Wolff, "Polarization phase-based method for material classification and object recognition in computer vision," in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1996), pp. 128-135.

Cheroske, A. G.

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T.-H. Chiou, "Polarization vision and its role in biological signaling," Integr. Comp. Biol. 43, 549-558 (2003).
[CrossRef] [PubMed]

Chiou, T.-H.

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T.-H. Chiou, "Polarization vision and its role in biological signaling," Integr. Comp. Biol. 43, 549-558 (2003).
[CrossRef] [PubMed]

Clark, J.

A. M. Wallace, B. Liang, E. Trucco, and J. Clark, "Improving depth acquisition using polarized light," Int. J. Comput. Vis. 32, 87-109 (2001).
[CrossRef]

Craighead, H. G.

Creelman, C. D.

N. A. Macmillan and C. D. Creelman, Detection Theory: A User's Guide (Cambridge U. Press, 1991).

Cronin, T. W.

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T.-H. Chiou, "Polarization vision and its role in biological signaling," Integr. Comp. Biol. 43, 549-558 (2003).
[CrossRef] [PubMed]

T. W. Cronin and N. Shashar, "The linearly polarized light field in clear, tropical marine waters: spatial and temporal variation of light intensity, degree of polarization and e-vector angle," J. Exp. Biol. 204, 2461-2467 (2001).
[PubMed]

N. Shashar and T. W. Cronin, "Polarization contrast vision in octopus," J. Exp. Biol. 199, 999-1004 (1996).
[PubMed]

N. Shashar, P. S. Rutledge, and T. W. Cronin, "Polarization vision in cuttlefish: a concealed communication channel?" J. Exp. Biol. 199, 2077-2084 (1996).
[PubMed]

Demos, S.

Demos, S. G.

S. G. Demos, W. B. Wang, and R. R. Alfano, "Imaging objects hidden in scattering media with fluorescence polarization preservation of contrast agents," Appl. Opt. 37, 792-797 (1998).
[CrossRef]

W. B. Wang, S. G. Demos, J. Ali, and R. R. Alfano, "Imaging fluorescent objects embedded inside animal tissues using polarization-difference technique," Optics Commun. 142, 161-166 (1997).
[CrossRef]

DeVlaminck, V.

Egan, W. G.

Engheta, N.

Flitton, J. C.

Gál, J.

G. Horváth, J. Gál, T. Labhart, and R. Wehner, "Does reflection polarization by plants influence colour perception in insects? Polarimetric measurements applied to a polarization-sensitive model retina of Papilio butterflies," J. Exp. Biol. 205, 3281-3298 (2002).
[PubMed]

Galland, F.

Gan, X. S.

Goldstein, D.

D. Goldstein, Polarized Light (Dekker, 2003).
[CrossRef]

Gottschalk, A.

G. Buchsbaum and A. Gottschalk, "Trichromacy, opponent colors coding and optimum color information transmission in the retina," Proc. R. Soc. London , Ser. B 220, 89-113 (1983).
[CrossRef]

Goudail, F.

Gu, M.

Hamett, C. K.

Hawryshyn, C. W.

C. W. Hawryshyn, "Ultraviolet polarization vision in fishes: possible mechanisms for coding e-vector," Philos. Trans. R. Soc. London , Ser. B 355, 1187-1190 (2000).
[CrossRef]

C. W. Hawryshyn, "Polarization vision in fish," Am. Sci. 80, 164-175, 1992.

Hopcraft, K. I.

Horváth, G.

G. Horváth, J. Gál, T. Labhart, and R. Wehner, "Does reflection polarization by plants influence colour perception in insects? Polarimetric measurements applied to a polarization-sensitive model retina of Papilio butterflies," J. Exp. Biol. 205, 3281-3298 (2002).
[PubMed]

I. Pomozi, G. Horváth, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

Jakeman, E.

Johnson, W. R.

Jolliffe, I. T.

I. T. Jolliffe, Principal Component Analysis (Springer-Verlag, 1986).

Jordan, D. L.

Karpel, N.

Y. Y. Schechner and N. Karpel, "Recovery of underwater visibility and structure by polarization analysis," IEEE J. Ocean. Eng. 30, 570-587 (2005).
[CrossRef]

Y. Y. Schechner and N. Karpel, "Clear underwater vision," in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2004), pp. 536-543.

Kiang, Y.

Kiryati, N.

Labhart, T.

G. Horváth, J. Gál, T. Labhart, and R. Wehner, "Does reflection polarization by plants influence colour perception in insects? Polarimetric measurements applied to a polarization-sensitive model retina of Papilio butterflies," J. Exp. Biol. 205, 3281-3298 (2002).
[PubMed]

T. Labhart, "How polarization-sensitive interneurons perform at low degrees of polarization," J. Exp. Biol. 199, 1467-1475 (1996).
[PubMed]

T. Labhart, "Polarization opponent interneurones in the insect visual system," Nature 331, 435-437 (1988).
[CrossRef]

T. Labhart and E. P. Meyer, Neural mechanisms in insect navigation: polarization compass and odometer, Curr. Opin. Neurobiol. 12, 707-714 (2002).

Liang, B.

A. M. Wallace, B. Liang, E. Trucco, and J. Clark, "Improving depth acquisition using polarized light," Int. J. Comput. Vis. 32, 87-109 (2001).
[CrossRef]

Lin, S.-S.

S.-S. Lin, K. M. Yemelyanov, E. N. Pugh, Jr., and N. Engheta, "Polarization enhanced visual surveillance techniques," in Proceedings of IEEE International Conference on Networking, Sensing, and Control (IEEE, 2004), pp. 216-221.

K. M. Yemelyanov, S.-S. Lin, W. Q. Luis, E. N. Pugh, Jr., and N. Engheta, "Bio-inspired display of polarization information using selected visual cues," in Polarization Science and Remote Sensing, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5158, 71-84 (2003).

Lo, M. A.

Luis, W. Q.

K. M. Yemelyanov, S.-S. Lin, W. Q. Luis, E. N. Pugh, Jr., and N. Engheta, "Bio-inspired display of polarization information using selected visual cues," in Polarization Science and Remote Sensing, J. A. Shaw and J. S. Tyo, eds., Proc. SPIE 5158, 71-84 (2003).

Macmillan, N. A.

N. A. Macmillan and C. D. Creelman, Detection Theory: A User's Guide (Cambridge U. Press, 1991).

Mancini, T. A.

L. B. Wolff, T. A. Mancini, P. Pouliquen, and A. G. Andreou, "Liquid crystal polarization camera," IEEE Trans. Rob. Autom. 13, 195-203 (1997).
[CrossRef]

Marshall, J.

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T.-H. Chiou, "Polarization vision and its role in biological signaling," Integr. Comp. Biol. 43, 549-558 (2003).
[CrossRef] [PubMed]

Meyer, E. P.

T. Labhart and E. P. Meyer, Neural mechanisms in insect navigation: polarization compass and odometer, Curr. Opin. Neurobiol. 12, 707-714 (2002).

Narasimhan, S. G.

Nayar, S. K.

Nothdurft, R.

Pomozi, I.

I. Pomozi, G. Horváth, and R. Wehner, "How the clear-sky angle of polarization pattern continues underneath clouds: full-sky measurements and implications for animal orientation," J. Exp. Biol. 204, 2933-2942 (2001).
[PubMed]

Pouliquen, P.

L. B. Wolff, T. A. Mancini, P. Pouliquen, and A. G. Andreou, "Liquid crystal polarization camera," IEEE Trans. Rob. Autom. 13, 195-203 (1997).
[CrossRef]

Pugh, E. N.

Réfrégier, P.

Rowe, M. P.

Rutledge, P. S.

N. Shashar, P. S. Rutledge, and T. W. Cronin, "Polarization vision in cuttlefish: a concealed communication channel?" J. Exp. Biol. 199, 2077-2084 (1996).
[PubMed]

Schechner, Y. Y.

Y. Y. Schechner and N. Karpel, "Recovery of underwater visibility and structure by polarization analysis," IEEE J. Ocean. Eng. 30, 570-587 (2005).
[CrossRef]

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, "Polarization-based vision through haze," Appl. Opt. 42, 511-525 (2003).
[CrossRef] [PubMed]

Y. Y. Schechner, J. Shamir, and N. Kiryati, "Vision through semireflecting media: polarization analysis," Opt. Lett. 24, 1088-1090 (1999).
[CrossRef]

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[CrossRef]

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[CrossRef] [PubMed]

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[CrossRef]

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[PubMed]

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[PubMed]

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R. Wehner and G. D. Bernard, "Photoreceptor twist: a solution to the false colour problem," in Proceedings of the National Academy of Sciences of the United States of America, 90, 4132-4135 (1993).

Y. Y. Schechner and N. Karpel, "Clear underwater vision," in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2004), pp. 536-543.

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Figures (12)

Fig. 1
Fig. 1

(Color online) Layout of the experimental setup: (a) photograph of the setup, (b) 7-patch target together with a U.S. dime (10-cent coin).

Fig. 2
Fig. 2

(Color online) Normalized histograms of polarization parameters of the background: (a) half of total pixel intensity I U ; (b) degree of linear polarization p; (c) angle of polarization θ. Total number of pixels in the image was 800 × 600 . Images of I U and p in the top row are stretched to cover an 8-bit gray-scale range. The reason we have systematic variations in the images of I U and p is that the light comes from the one side (top left corner).

Fig. 3
Fig. 3

Normalized histogram of the (a) dark noise of the camera compared to the normalized histogram (b) of the background image.

Fig. 4
Fig. 4

(Color online) Distribution of the polarization parameters characterizing the standard background scene. Each panel presents a pseudocolor representation of the distribution of one of the parameters: (a) α ( φ 1 , φ 2 ) , (b) β ( φ 1 , φ 2 ) , (c) λ 1 ( φ 1 , φ 2 ) , (d) λ 2 ( φ 1 , φ 2 ) . The scales for each parameter are provided to the right of each panel.

Fig. 5
Fig. 5

Principal components of the scene corresponding to three cases of interest. Left column shows PC 1 , and right column PC 2 images, respectively. Panels (a)–(c) correspond to cases 1–3, respectively. All the images are linearly rescaled to exploit the 8-bit displayable range. The size of the images was 800 × 600 pixels.

Fig. 6
Fig. 6

Normalized histograms of (a) PC 1 and (b) PC 2 for all the cases shown as images in Fig. 5. The standard deviations of PCs for all three cases considered are shown in the figures.

Fig. 7
Fig. 7

Scheme of the specially created target where regions used for the sensitivity index calculation are marked in black. Dashed lines identify the direction of scratches in the specific patch. The left region is referred to as region one and the right region is referred to as region two, respectively.

Fig. 8
Fig. 8

Polarization components for the nontarget and target scenes of the experiments under natural lighting. The left panel shows I U , p, and θ (top to bottom) images of the nontarget scene, and the right panel shows those for the target scene. The I U plots in both cases are linearly rescaled to use the full 8-bit gray-scale display range.

Fig. 9
Fig. 9

Comparison in target detection between images obtained by our new adaptive algorithm and by the conventional PDI algorithm. They are the principal component images obtained from the images shown in Fig. 8. Panels (a) and (b) are PC 1 and PC 2 for case 1. Panels (c) and (d) are conventional PS and PD images (case 3). Panels (e) and (f) are PC 1 and PC 2 for case 2. All images were linearly rescaled to cover an 8-bit gray-level display range.

Fig. 10
Fig. 10

(a) SNR for PC 1 and PC 2 . Here, the signal is the area of the aluminum disk, and the noise is the rest area of the corresponding PC. (b) Normalized histograms of the PC 2 images with a shift from the optimal (case 1) pair of angles. Increasing variance in the PC 2 image with rotation of the optimal pair of angles is shown.

Fig. 11
Fig. 11

SNRs for the PC 1 , PC 2 , PS, PD, and p with the presence of (a) artificially added Gaussian noise, and (b) white noise. Images of (c) PC 2 and (d) p for 5 % of added Gaussian noise. Individual features of the aluminum disk, such as the appearance of patches, is better visible in the PC2 image.

Fig. 12
Fig. 12

Stretched images of (a) PC2 and (b) p. (c) Normalized histograms of images shown in panels (a) and (b). Standard deviations for PC 2 and p are σ 2 = 0.0054 and σ 2 = 0.041 , respectively.

Tables (1)

Tables Icon

Table 1 Adaptive Parameters Corresponding to the Cases Considered for the Benchmark Target

Equations (10)

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

I ( x , y , φ ) = I U ( x , y ) ( 1 + p ( x , y ) cos { 2 [ θ ( x , y ) φ ] } ) ,
I U ( x , y ) = I 0 ( x , y ) + I 90 ( x , y ) 2 ,
p ( x , y ) = { [ 1 I 45 ( x , y ) I U ( x , y ) ] 2 + [ 1 I 90 ( x , y ) I U ( x , y ) ] 2 } 1 / 2 ,
θ ( x , y ) = 1 2 tan - 1 [ I U ( x , y ) - I 0 ( x , y ) I U ( x , y ) - I 45 ( x , y ) ] .
[ PS ( x , y ) PD ( x , y ) ] = [ 1 1 1 1 ] T [ I 90 ( x , y ) I 0 ( x , y ) ] ,
C ( φ 1 , φ 2 ) = [ E ( I 1 I 1 ) E 2 ( I 1 ) E ( I 1 I 2 ) E ( I 1 ) E ( I 2 ) E ( I 1 I 2 ) E ( I 1 ) E ( I 2 ) E ( I 2 I 2 ) E 2 ( I 2 ) ] ,
T ( φ 1 , φ 2 ) = [ β ( φ 1 , φ 2 ) α ( φ 1 , φ 2 ) α ( φ 1 , φ 2 ) β ( φ 1 , φ 2 ) ] .
[ PC 1 ( φ 1 , φ 2 ) PC 2 ( φ 1 , φ 2 ) ] = T ( φ 1 , φ 2 ) [ I ( φ 1 ) I ( φ 2 ) ] .
d a = | μ T μ B ( σ T 2 + σ B 2 ) / 2 | ,
SNR = | μ D μ W σ W | ,

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