Abstract

We present an approach for easily removing the effects of haze from passively acquired images. Our approach is based on the fact that usually the natural illuminating light scattered by atmospheric particles (airlight) is partially polarized. Optical filtering alone cannot remove the haze effects, except in restricted situations. Our method, however, stems from physics-based analysis that works under a wide range of atmospheric and viewing conditions, even if the polarization is low. The approach does not rely on specific scattering models such as Rayleigh scattering and does not rely on the knowledge of illumination directions. It can be used with as few as two images taken through a polarizer at different orientations. As a byproduct, the method yields a range map of the scene, which enables scene rendering as if imaged from different viewpoints. It also yields information about the atmospheric particles. We present experimental results of complete dehazing of outdoor scenes, in far-from-ideal conditions for polarization filtering. We obtain a great improvement of scene contrast and correction of color.

© 2003 Optical Society of America

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  49. For the calculation of the path radiance integral, we assume κ to be distance invariant. This is because typically most of the light in the scene comes from the Sun and sky and thus does not change much along the line of sight. Moreover, we assume that multiple scattering (which effects the angular scattering distribution) is dominated by single scattering.

2001 (1)

2000 (3)

1999 (4)

1998 (2)

J. P. Oakley, B. L. Satherley, “Improving image quality in poor visibility conditions using a physical model for contrast degradation,” IEEE Trans. Imag. Proc. 7, 167–179 (1998).
[CrossRef]

R. L. Lee, “Digital imaging of clear-sky polarization,” Appl. Opt. 37, 1465–1476 (1998).
[CrossRef]

1997 (3)

M. S. Quinby-Hunt, L. L. Erskine, A. J. Hunt, “Polarized light scattering by aerosols in the marine atmospheric boundary layer,” Appl. Opt. 36, 5168–5184 (1997).
[CrossRef] [PubMed]

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vision Comput. 15, 81–93 (1997).
[CrossRef]

S. K. Nayar, X. S. Fang, T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

1996 (2)

1995 (1)

1994 (2)

1993 (1)

A. M. Shutov, “Videopolarimeters,” Sov. J. Opt. Technol. 60, 295–301 (1993).

1991 (3)

1986 (1)

C. F. Bohren, A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54, 222–227 (1986).
[CrossRef]

1983 (1)

1981 (1)

1976 (1)

Adelson, E. H.

Ballard, S. S.

W. A. Shurcliff, S. S. Ballard, Polarized Light (Van Nostrand, Princeton, N.J., 1964), pp. 98–103.

Ben-Ezra, M.

M. Ben-Ezra, “Segmentation with invisible keying signal,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 2000), Vol. 1, pp. 32–37.

Bohren, C. F.

C. F. Bohren, A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54, 222–227 (1986).
[CrossRef]

Boult, T.

S. K. Nayar, X. S. Fang, T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

Bretenaker, F.

Brooks, R. R.

L. Grewe, R. R. Brooks, “Atmospheric attenuation reduction through multi-sensor fusion,” in Sensor Fusion: Architectures, Algorithms, and Applications II, B. V. Dasarathy, ed., Proc. SPIE3376, 102–109 (1998).
[CrossRef]

Cairns, B.

B. Cairns, B. E. Carlson, A. A. Lacis, E. E. Russell, “An analysis of ground-based polarimetric sky radiance measurements,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 382–393 (1997).
[CrossRef]

Cameron, B. D.

Canterakis, N.

S. Rahmann, N. Canterakis, “Reconstruction of specular surfaces using polarization imaging,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 2001), Vol. 1, pp. 149–155.

Carlson, B. E.

B. Cairns, B. E. Carlson, A. A. Lacis, E. E. Russell, “An analysis of ground-based polarimetric sky radiance measurements,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 382–393 (1997).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), pp. 24–37, 280–284.

Chang, P. C. Y.

Chenault, D. B.

D. B. Chenault, J. L. Pezzaniti, “Polarization imaging through scattering media,” in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Guggin, W. G. Egan, D. H. Goldstein, eds., Proc. SPIE4133, 124–133 (2000).
[CrossRef]

Chitwood, D.

Cho, Y.

H. Horinaka, K. Hashimoto, K. Wada, T. Umeda, Y. Cho, “Optical CT imaging in highly scattering media by extraction of photons preserving initial polarization,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 54–57 (1996).
[CrossRef]

Coté, G. L.

Coulson, K. L.

K. L. Coulson, “Polarization of light in the natural environment,” in Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 2–10 (1989).
[CrossRef]

Cozman, F.

F. Cozman, E. Krotkov, “Depth from scattering,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 801–806.
[CrossRef]

Denes, L. J.

L. J. Denes, M. Gottlieb, B. Kaminsky, P. Metes, “AOTF polarization difference imaging,” in 27th AIPR Workshop: Advances in Computer-Assisted Recognition, R. J. Mericsko, ed., Proc. SPIE3584, 106–115 (1998).
[CrossRef]

Emile, O.

Engheta, N.

Erskine, L. L.

Fang, X. S.

S. K. Nayar, X. S. Fang, T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

Farid, H.

Fraser, A. B.

C. F. Bohren, A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54, 222–227 (1986).
[CrossRef]

Gan, X.

Gedzelman, S. D.

Glassner, A. S.

A. S. Glassner, Principles of Digital Image Synthesis (Morgan Kaufmann, San Francisco, Calif., 1995), Appen. G.4.

Gottlieb, M.

L. J. Denes, M. Gottlieb, B. Kaminsky, P. Metes, “AOTF polarization difference imaging,” in 27th AIPR Workshop: Advances in Computer-Assisted Recognition, R. J. Mericsko, ed., Proc. SPIE3584, 106–115 (1998).
[CrossRef]

Grewe, L.

L. Grewe, R. R. Brooks, “Atmospheric attenuation reduction through multi-sensor fusion,” in Sensor Fusion: Architectures, Algorithms, and Applications II, B. V. Dasarathy, ed., Proc. SPIE3376, 102–109 (1998).
[CrossRef]

Gu, Min

Hashimoto, K.

H. Horinaka, K. Hashimoto, K. Wada, T. Umeda, Y. Cho, “Optical CT imaging in highly scattering media by extraction of photons preserving initial polarization,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 54–57 (1996).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 3rd ed. (Addison-Wesley, New York, 1998), pp. 340–342.

Hennings, D.

Henry, R. C.

Hitzfelder, S. J.

Hopcraft, K. I.

Horinaka, H.

H. Horinaka, K. Hashimoto, K. Wada, T. Umeda, Y. Cho, “Optical CT imaging in highly scattering media by extraction of photons preserving initial polarization,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 54–57 (1996).
[CrossRef]

Hunt, A. J.

Ikeuchi, K.

Kaminsky, B.

L. J. Denes, M. Gottlieb, B. Kaminsky, P. Metes, “AOTF polarization difference imaging,” in 27th AIPR Workshop: Advances in Computer-Assisted Recognition, R. J. Mericsko, ed., Proc. SPIE3584, 106–115 (1998).
[CrossRef]

Kashiwagi, H.

Kattawar, G. W.

Kiryati, N.

Können, G. P.

G. P. Können, Polarized Light in Nature (Cambridge University, Cambridge, UK, 1985), pp. 1–10, 29–54, 60–62, 131–137, 144–145.

Kopeika, N. S.

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE, Bellingham, Wash., 1998), pp. 446–452.

Krotkov, E.

F. Cozman, E. Krotkov, “Depth from scattering,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 801–806.
[CrossRef]

Lacis, A. A.

B. Cairns, B. E. Carlson, A. A. Lacis, E. E. Russell, “An analysis of ground-based polarimetric sky radiance measurements,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 382–393 (1997).
[CrossRef]

Le Floch, A.

Lee, R. L.

Lynch, D. K.

Mahadev, S.

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere: Scattering by Molecules and Particles (Wiley, New York, 1976).

Mehrübeoglu, M.

Metes, P.

L. J. Denes, M. Gottlieb, B. Kaminsky, P. Metes, “AOTF polarization difference imaging,” in 27th AIPR Workshop: Advances in Computer-Assisted Recognition, R. J. Mericsko, ed., Proc. SPIE3584, 106–115 (1998).
[CrossRef]

Narasimhan, S. G.

S. G. Narasimhan, S. K. Nayar, “Removing weather effects from monochrome images,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 2001), Vol. II, pp. 186–193.

S. K. Nayar, S. G. Narasimhan, “Vision in bad weather,” in Proceedings of the IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 820–827.
[CrossRef]

S. G. Narasimhan, S. K. Nayar, “Chromatic framework for vision in bad weather,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 2000), Vol. I, pp. 598–605.

Y. Y. Schechner, S. G. Narasimhan, S. K. Nayar, “Instant dehazing of images using polarization,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 2001), Vol. 1, pp. 325–332.

Nayar, S. K.

S. K. Nayar, X. S. Fang, T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

Y. Y. Schechner, S. G. Narasimhan, S. K. Nayar, “Instant dehazing of images using polarization,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 2001), Vol. 1, pp. 325–332.

S. G. Narasimhan, S. K. Nayar, “Chromatic framework for vision in bad weather,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 2000), Vol. I, pp. 598–605.

S. G. Narasimhan, S. K. Nayar, “Removing weather effects from monochrome images,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 2001), Vol. II, pp. 186–193.

S. K. Nayar, S. G. Narasimhan, “Vision in bad weather,” in Proceedings of the IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, New York, 1999), pp. 820–827.
[CrossRef]

Oakley, J. P.

K. Tan, J. P. Oakley, “Physics-based approach to color image enhancement in poor visibility conditions,” J. Opt. Soc. Am. A 18, 2460–2467 (2001).
[CrossRef]

J. P. Oakley, B. L. Satherley, “Improving image quality in poor visibility conditions using a physical model for contrast degradation,” IEEE Trans. Imag. Proc. 7, 167–179 (1998).
[CrossRef]

Pencikowski, P. S.

P. S. Pencikowski, “Low-cost vehicle-mounted enhanced vision system comprised of a laser illuminator and range-gated camera,” in Enhanced and Synthetic Vision, J. G. Verly, ed., Proc. SPIE2736, 222–227 (1996).

Pezzaniti, J. L.

D. B. Chenault, J. L. Pezzaniti, “Polarization imaging through scattering media,” in Polarization Analysis, Measurement, and Remote Sensing III, D. B. Chenault, M. J. Guggin, W. G. Egan, D. H. Goldstein, eds., Proc. SPIE4133, 124–133 (2000).
[CrossRef]

Plass, G. N.

Prosch, T.

Pugh, E. N.

Quinby-Hunt, M. S.

Rahmann, S.

S. Rahmann, N. Canterakis, “Reconstruction of specular surfaces using polarization imaging,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 2001), Vol. 1, pp. 149–155.

Rakovic, M. J.

Raschke, E.

Rastegar, S.

Rowe, M. P.

Russell, E. E.

B. Cairns, B. E. Carlson, A. A. Lacis, E. E. Russell, “An analysis of ground-based polarimetric sky radiance measurements,” in Polarization: Measurement, Analysis, and Remote Sensing, D. H. Goldstein, R. A. Chipman, eds., Proc. SPIE3121, 382–393 (1997).
[CrossRef]

Saito, M.

Satherley, B. L.

J. P. Oakley, B. L. Satherley, “Improving image quality in poor visibility conditions using a physical model for contrast degradation,” IEEE Trans. Imag. Proc. 7, 167–179 (1998).
[CrossRef]

Sato, Y.

Schechner, Y. Y.

Y. Y. Schechner, J. Shamir, N. Kiryati, “Polarization and statistical analysis of scenes containing a semireflector,” J. Opt. Soc. Am. A 17, 276–284 (2000).
[CrossRef]

Y. Y. Schechner, S. G. Narasimhan, S. K. Nayar, “Instant dehazing of images using polarization,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 2001), Vol. 1, pp. 325–332.

Schilders, S. P.

Schwartz, P.

Shamir, J.

Shurcliff, W. A.

W. A. Shurcliff, S. S. Ballard, Polarized Light (Van Nostrand, Princeton, N.J., 1964), pp. 98–103.

Shutov, A. M.

A. M. Shutov, “Videopolarimeters,” Sov. J. Opt. Technol. 60, 295–301 (1993).

Solomon, J. E.

Sweet, B. T.

B. T. Sweet, C. L. Tiana, “Image processing and fusion for landing guidance,” in Enhanced and Synthetic Vision, J. G. Verly, ed., Proc. SPIE2736, 84–95 (1996).

Tan, K.

Tiana, C. L.

B. T. Sweet, C. L. Tiana, “Image processing and fusion for landing guidance,” in Enhanced and Synthetic Vision, J. G. Verly, ed., Proc. SPIE2736, 84–95 (1996).

Tyo, J. S.

Umeda, T.

H. Horinaka, K. Hashimoto, K. Wada, T. Umeda, Y. Cho, “Optical CT imaging in highly scattering media by extraction of photons preserving initial polarization,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 54–57 (1996).
[CrossRef]

Urquijo, S.

Wada, K.

H. Horinaka, K. Hashimoto, K. Wada, T. Umeda, Y. Cho, “Optical CT imaging in highly scattering media by extraction of photons preserving initial polarization,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 54–57 (1996).
[CrossRef]

Walker, J. G.

Wang, L. V.

Wolff, L. B.

L. B. Wolff, “Polarization vision: a new sensory approach to image understanding,” Image Vision Comput. 15, 81–93 (1997).
[CrossRef]

L. B. Wolff, “Polarization camera for computer vision with a beam splitter,” J. Opt. Soc. Am. A 11, 2935–2945 (1994).
[CrossRef]

Am. J. Phys. (1)

C. F. Bohren, A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54, 222–227 (1986).
[CrossRef]

Appl. Opt. (12)

T. Prosch, D. Hennings, E. Raschke, “Video polarimetry: a new imaging technique in atmospheric science,” Appl. Opt. 22, 1360–1363 (1983).
[CrossRef] [PubMed]

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

R. L. Lee, “Digital imaging of clear-sky polarization,” Appl. Opt. 37, 1465–1476 (1998).
[CrossRef]

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For the calculation of the path radiance integral, we assume κ to be distance invariant. This is because typically most of the light in the scene comes from the Sun and sky and thus does not change much along the line of sight. Moreover, we assume that multiple scattering (which effects the angular scattering distribution) is dominated by single scattering.

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Figures (7)

Fig. 1
Fig. 1

(Dashed rays) Light coming from the illuminant (e.g., Sun) and scattered toward the camera by atmospheric particles is the airlight (path radiance) A. The airlight increases with the distance z of the object. (Solid ray) The light emanating from the object is attenuated along the line of sight as z increases, leading to the direct transmission D. Without scattering, object radiance would have been L object. The scene is imaged through a polarizing filter at angle α. The polarization component parallel to the plane of incidence is best transmitted through the filter at α = θ.

Fig. 2
Fig. 2

At each point the minimum measured image irradiance as a function of α is I . The maximum is I . The difference between these measurements is due to the difference between the airlight components A , A . This difference is related to the unknown airlight A by the parameter p, which is the airlight degree of polarization. Without a polarizer the image irradiance is I total, which is proportional to the sum of airlight and the unknown direct transmission.

Fig. 3
Fig. 3

Images of the polarization components corresponding to the minimal and the maximal radiances. Note that I (the image of irradiance) has the best image contrast that optics alone can yield, and yet there is no significant improvement over the image of the worst polarization state.

Fig. 4
Fig. 4

(a) The dehazed image has much better contrast and color than the optically filtered image, especially in the distant regions of the scene (compare with Fig. 3). (b) and (c), As described in Section 5, we estimate the range map of the scene. We use it to render the dehazed scene from different perspectives, as if the viewer descends. Note the occlusion of the background by the foreground tree on the right. Note also the distant mountains occluded by the closer ridge.

Fig. 5
Fig. 5

Photograph with the best contrast that optics alone can give (a) is almost as poor as the worst polarization state (b). The dehazed image (c) has much better contrast and color, especially in the distant regions of the scene (note the green forest and the red roofs).

Fig. 6
Fig. 6

Range map of the scene shown in Fig. 3, estimated as a byproduct of the dehazing algorithm. The farther the object, the darker the shading.

Fig. 7
Fig. 7

Range map of the scene shown in Fig. 5, estimated as a byproduct of the dehazing algorithm. Some surfaces of close objects are wrongly marked as distant ones as a result of their high degree of polarization.

Equations (63)

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A=A1-tz,
tz=exp-0z βzdz,
tz=exp-βz.
pA-A/A,
A=A+A
D=Lobjecttz,
Itotal=D+A,
I=D/2+A,
A=A1-p/2.
I=D/2+A,
A=A1+p/2.
Itotal=I+I.
Â=Î-Î/p,
Îtotal=Î+Î.
Dˆ=Îtotal-Â.
tˆ=1-Â/A.
Lˆobject=Îtotal-Âtˆ=Îtotal-Â1-Â/A.
βzˆ=-ln1-Âx, y/A.
βz¯x, yβrzˆx, y+βgzˆx, y+βbzˆx, y/3.
δz1βexpβz-b ln 21pA.
sr=x,y βrzˆx, yx,yβz¯x, y,
sg=x,y βgzˆx, yx,yβz¯x, y,
sb=x,y βbzˆx, yx,yβz¯x, y.
srsgsb=0.260.320.42,
Itotal=Lobjecttz+A1-tzA.
Pˆx, y=ΔIx, yItotalx, y,
ΔIx, yÎx, y-Îx, y.
Pˆx, yA-AA+A=p.
Â=Itotalsky, pˆ=ΔIskyItotalsky.
pˆrpˆgpˆb0.280.250.22.
pˆpˆ.
δLˆobjectsky=2σ1-1/-1,
Dˆx, y=Îtotalx, ypˆpˆ-Pˆx, y.
Îtotalx, y=Lobject+1p-LobjectpAΔIx, y.
C11p-L1objectpA
Îtotalk=L1object+C1ΔIk,
p=1C1-L1object/C11A.
p=1C2-L2object/C21A.
Aα=A1-p cos2α-θ/2,
I1=D/2+Aα1,
I2=D/2+Aα2.
AeffectiveAα1+Aα2,
peffectiveAα2-Aα1Aeffective,
IeffectivetotalI1+I2=D+Aeffective.
Aeffective=fA=fA1-tz=Aeffective1-tz,
f=1-p cosα1+α2-2θcosα1-α2.
Âeffective=I2-I1peffective.
Dˆ=Ieffectivetotal-Âeffective.
tˆ=1-ÂeffectiveAeffective.
Lˆobject=Ieffectivetotal-Âeffective1-Âeffective/Aeffective.
peffective=ApAeffectivesinα1+α2-2θsinα2-α1.
α1+α2/2=θ, θ+90°.
dDzD=-βzdz.
tz=exp-0z βzdz.
dAz=κβzdz exp-0z βzdz.
Az=0zdAz=-κexp-0z βzdz-10z=κ1-tz.
A=κ1-t.
A=A1-t1-tz.
A=A1-tz,
ΔIsky=Ap,
Itotalsky=Lobjectskyt+A.
Lˆobject=Dˆ/tˆ.
tˆ=1-ÂA1-t,

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