Abstract

Outdoor imaging in haze is plagued by poor visibility. A major problem is spatially-varying reduction of contrast by airlight, which is scattered by the haze particles towards the camera. However, images can be compensated for haze, and even yield a depth map of the scene. A key step in such scene recovery is subtraction of the airlight. In particular, this can be achieved by analyzing polarization-filtered images. This analysis requires parameters of the airlight, particularly its degree of polarization (DOP). These parameters were estimated in past studies by measuring pixels in sky areas. However, the sky is often unseen in the field of view. This paper derives several methods for estimating these parameters, when the sky is not in view. The methods are based on minor prior knowledge about a couple of scene points. Moreover, we propose blind estimation of the DOP, based on the image data. This estimation is based on independent component analysis (ICA). The methods were demonstrated in field experiments.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. S. Kopeika, A System Engineering Approach to Imaging, SPIE Press, Bellingham (1998).
  2. R. T. Tan, N. Pettersson, and L. Petersson, “Visibility enhancement for roads with foggy or hazy scenes,” In Proc. IEEE Intelligent Vehicles Symposium 19–24 (2007).
  3. R. C. Henry, S. Mahadev, S. Urquijo, and D. Chitwood “Color perception through atmospheric haze,” J. Opt. Soc. Am. A 17, 831–835 (2000).
    [Crossref]
  4. J. S. Jaffe, “Computer modelling and the design of optimal underwater imaging systems,” IEEE J. Oceanic Eng. 15, 101–111 (1990).
    [Crossref]
  5. D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” MTS Journal 42, 52–67 (2008).
  6. Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30, 570–587 (2005).
    [Crossref]
  7. P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. L. Jordan, and J. G. Walker, “Improving visibility depth in passive underwater imaging by use of polarization,” Appl. Opt. 42, 2794–2803 (2003).
    [Crossref] [PubMed]
  8. D. B. Chenault and J. L. Pezzaniti, “Polarization imaging through scattering media,” In Proc. SPIE  4133, 124–133 (2000).
  9. S. G. Demos and R. R. Alfano, “Optical polarization imaging,” Appl. Opt. 36, 150–155 (1997).
    [Crossref] [PubMed]
  10. X. Gan, S. P. Schilders, and M. Gu, “Image enhancement through turbid media under a microscope by use of polarization gating method,” J. Opt. Soc. Am. A 16, 2177–2184 (1999).
    [Crossref]
  11. S. Harsdorf, R. Reuter, and S. Tönebön, “Contrast-enhanced optical imaging of submersible targets,” In Proc. SPIE  3821, 378–383 (1999).
  12. M. J. Raković, G. W. Kattawar, M. Mehrübeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: theory and experiment,” Appl. Opt. 38, 3399–3408 (1999).
    [Crossref]
  13. S. P. Schilders, X. S. Gan, and M. Gu, “Resolution improvement in microscopic imaging through turbid media based on differential polarization gating,” Appl. Opt. 37, 4300–4302 (1998).
    [Crossref]
  14. J. S. Tyo, M. P. Rowe, E. N. Pugh, and N. Engheta, “Target detection in optically scattering media by polarization-difference imaging,” Appl. Opt. 35, 1855–1870 (1996).
    [Crossref] [PubMed]
  15. J. S. Tyo, “Enhancement of the point-spread function for imaging in scattering media by use of polarization-difference imaging,” J. Opt. Soc. Am. A 17, 1–10 (2000).
    [Crossref]
  16. K. M. Yemelyanov, S. S. Lin, E. N. Pugh, and N. Engheta, “Adaptive algorithms for two-channel polarization sensing under various polarization statistics with nonuniform distributions,” Appl. Opt. 45, 5504–5520 (2006).
    [Crossref] [PubMed]
  17. G. Horváth and D. Varjù, Polarized Light in Animal Vision, Springer-Verlag, Berlin (2004).
  18. N. Shashar, S. Sabbah, and T. W. Cronin, “Transmission of linearly polarized light in seawater: implications for polarization signaling,” J. Exper. Biology,  207, 3619–3628 (2004).
    [Crossref]
  19. R. Wehner, “Polarization vision a uniform sensory capacity?,” J. Exper. Biology 204, 2589–2596 (2001).
  20. F. Cozman and E. Kroktov, “Depth from scattering,” In Proc. IEEE CVPR, 801–806 (1997).
  21. K. Tan and J. P. Oakley, “Physics-based approach to color image enhancement in poor visibility conditions,” J. Opt. Soc. Am. A 18, 2460–2467 (2001).
    [Crossref]
  22. E. Namer and Y. Y. Schechner, “Advanced visibility improvement based on polarization filtered images,” In Proc. SPIE  5888, 36–45 (2005).
  23. Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Polarization-based vision through haze,” Appl. Opt. 42, 511–525 (2003).
    [Crossref] [PubMed]
  24. D. Miyazaki, M. Saito, Y. Sato, and K. Ikeuchi,“Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths,” J. Opt. Soc. Am. A 19, 687–694 (2002).
    [Crossref]
  25. V. Gruev, A. Ortu, N. Lazarus, J. V. der Spiegel, and N. Engheta, “Fabrication of a dual-tier thin film micropolarization array,” Opt. Express 15, 4994–5007 (2007).
    [Crossref] [PubMed]
  26. N. Gupta, L. J. Denes, M. Gottlieb, D. R. Suhre, B. Kaminsky, and P. Metes, “Object detection with a field-portable spectropolarimetric imager,” Appl. Opt. 40, 6626–6632 (2001).
    [Crossref]
  27. C. K. Harnett and H. G. Craighead, “Liquid-crystal micropolarizer array for polarization-difference imaging,” Appl. Opt. 41, 1291–1296 (2002).
    [Crossref] [PubMed]
  28. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
    [Crossref] [PubMed]
  29. J. S. Tyo and H. Wei, “Optimizing imaging polarimeters constructed with imperfect optics,” Appl. Opt. 45, 5497–5503 (2006).
    [Crossref] [PubMed]
  30. J. Wolfe and R. Chipman, “High speed imaging polarimeter,” In Proc. SPIE  5158, 24–32 (2003).
  31. L. B. Wolff, “Polarization camera for computer vision with a beam splitter,”J. Opt. Soc. Am. A 11, 2935–2945 (1994).
    [Crossref]
  32. C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?,” American Journal of Physics 54, 222–227 (1986).
    [Crossref]
  33. D. K. Lynch, “Step brightness changes of distant mountain ridges and their perception,” Appl. Opt. 30, 3508–3513 (1991).
    [Crossref] [PubMed]
  34. E. J. McCartney, Optics of the Atmosphere: Scattering by Molecules and Particles, John Willey & Sons (1975).
  35. S. K. Nayar and S. G. Narasimhan, “Vision in bad weather,” Proc. IEEE ICCV, 820–827 (1999).
  36. For clarity of display, the images shown in this paper have undergone the same standard contrast stretch. This operation was done only towards the display. The algorithms described in the paper were run on raw, unstretched data. The data had been acquired using a Nikon D-100 camera, which has a linear radiometric response. The mounted zoom lens used with the camera was set to focal length of ≈ 200mm, except for Fig. 9 in which it was ≈ 85mm. The camera was pointed at or slightly below the horizon.
  37. H. Farid and E. H. Adelson, “Separating reflections from images by use of independent component analysis,” J. Opt. Soc. Amer A 16, 2136–2145 (1999).
    [Crossref]
  38. S. Shwartz, M. Zibulevsky, and Y. Y. Schechner, “Fast kernel entropy estimation and optimization,” Signal Processing 85, 1045–1058 (2005).
    [Crossref]
  39. S. Umeyama and G. Godin, “Separation of diffuse and specular components of surface reflection by use of polarization and statistical analysis of images,” IEEE Trans. PAMI 26, 639–647 (2004).
    [Crossref]
  40. D. Nuzilland, S. Curila, and M. Curila, “Blind separation in low frequencies using wavelet analysis, application to artificial vision,” In Proc. ICA, 77–82 (2003).
  41. S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind haze separation,” In Proc. IEEE CVPR  2, 1984–1991 (2006).
  42. E. H. Adelson, “Lightness perception and lightness illusions,” in The New Cognitive Neuroscience, 2nd ed. ch. 24 339–351, MIT Preess, Cambridge (2000).
  43. R. A. Chipman, “Depolarization index and the average degree of polarization,” Appl. Opt. 44, 2490–2495 (2005).
    [Crossref] [PubMed]
  44. S. J. Bell and T. J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Computation 7, 1129–1159 (1995).
    [Crossref] [PubMed]
  45. J.-F. Cardoso, “Blind signal separation: statistical principles,” Proc. IEEE 86, 2009–2025 (1998).
    [Crossref]
  46. A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, John Wiley and Sons, New York (2001).
    [Crossref]
  47. D. T. Pham and P. Garrat, “Blind separation of a mixture of independent sources through a quasi-maximum likelihood approach,” IEEE Trans. Signal Processing,  45, 1712–1725 (1997).
    [Crossref]
  48. P. Kisilev, M. Zibulevsky, and Y. Y. Zeevi, “Multiscale framework for blind source separation,” J. Machine Learning Research 4, 1339–1364 (2004).
  49. E. P. Simoncelli, “Statistical models for images: Compression, restoration and synthesis,” In Proc. Conf. Sig. Sys. and Computers, 673–678 (1997).
  50. An additional ICA ambiguity is permutation, which refers to mutual ordering of sources. This ambiguity does not concern us at all. The reason is that our physics-based formulation dictates a special form for the matrix W, and thus its rows are not mutually interchangeable.
  51. T. M. Cover and J. A. Thomas, Elements of Information Theory, John Wiley and Sons, New York (1991).
    [Crossref]
  52. T. Treibitz and Y. Y. Schechner, “Instant 3Descatter,” In Proc. IEEE CVPR 1861–1868 (2006).
  53. P. Bofill and M. Zibulevsky, “Underdetermined blind source separation using sparse representations,” Signal Processing 81, 2353–2362 (2001).
    [Crossref]
  54. M. Zibulevsky and B. A. Pearlmutter, “Blind source separation by sparse decomposition in a signal dictionary,” Neural Computation archive 13, 863–882 (2001).
    [Crossref]
  55. Y. Li, A. Cichocki, and S. Amari, “Analysis of sparse representation and blind source separation,” Neural Computation 16, 1193–1234 (2004).
    [Crossref] [PubMed]

2008 (1)

D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” MTS Journal 42, 52–67 (2008).

2007 (1)

2006 (4)

2005 (4)

E. Namer and Y. Y. Schechner, “Advanced visibility improvement based on polarization filtered images,” In Proc. SPIE  5888, 36–45 (2005).

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30, 570–587 (2005).
[Crossref]

R. A. Chipman, “Depolarization index and the average degree of polarization,” Appl. Opt. 44, 2490–2495 (2005).
[Crossref] [PubMed]

S. Shwartz, M. Zibulevsky, and Y. Y. Schechner, “Fast kernel entropy estimation and optimization,” Signal Processing 85, 1045–1058 (2005).
[Crossref]

2004 (4)

S. Umeyama and G. Godin, “Separation of diffuse and specular components of surface reflection by use of polarization and statistical analysis of images,” IEEE Trans. PAMI 26, 639–647 (2004).
[Crossref]

N. Shashar, S. Sabbah, and T. W. Cronin, “Transmission of linearly polarized light in seawater: implications for polarization signaling,” J. Exper. Biology,  207, 3619–3628 (2004).
[Crossref]

P. Kisilev, M. Zibulevsky, and Y. Y. Zeevi, “Multiscale framework for blind source separation,” J. Machine Learning Research 4, 1339–1364 (2004).

Y. Li, A. Cichocki, and S. Amari, “Analysis of sparse representation and blind source separation,” Neural Computation 16, 1193–1234 (2004).
[Crossref] [PubMed]

2003 (3)

2002 (2)

2001 (5)

R. Wehner, “Polarization vision a uniform sensory capacity?,” J. Exper. Biology 204, 2589–2596 (2001).

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

N. Gupta, L. J. Denes, M. Gottlieb, D. R. Suhre, B. Kaminsky, and P. Metes, “Object detection with a field-portable spectropolarimetric imager,” Appl. Opt. 40, 6626–6632 (2001).
[Crossref]

P. Bofill and M. Zibulevsky, “Underdetermined blind source separation using sparse representations,” Signal Processing 81, 2353–2362 (2001).
[Crossref]

M. Zibulevsky and B. A. Pearlmutter, “Blind source separation by sparse decomposition in a signal dictionary,” Neural Computation archive 13, 863–882 (2001).
[Crossref]

2000 (3)

1999 (5)

X. Gan, S. P. Schilders, and M. Gu, “Image enhancement through turbid media under a microscope by use of polarization gating method,” J. Opt. Soc. Am. A 16, 2177–2184 (1999).
[Crossref]

S. Harsdorf, R. Reuter, and S. Tönebön, “Contrast-enhanced optical imaging of submersible targets,” In Proc. SPIE  3821, 378–383 (1999).

M. J. Raković, G. W. Kattawar, M. Mehrübeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: theory and experiment,” Appl. Opt. 38, 3399–3408 (1999).
[Crossref]

S. K. Nayar and S. G. Narasimhan, “Vision in bad weather,” Proc. IEEE ICCV, 820–827 (1999).

H. Farid and E. H. Adelson, “Separating reflections from images by use of independent component analysis,” J. Opt. Soc. Amer A 16, 2136–2145 (1999).
[Crossref]

1998 (2)

1997 (2)

S. G. Demos and R. R. Alfano, “Optical polarization imaging,” Appl. Opt. 36, 150–155 (1997).
[Crossref] [PubMed]

D. T. Pham and P. Garrat, “Blind separation of a mixture of independent sources through a quasi-maximum likelihood approach,” IEEE Trans. Signal Processing,  45, 1712–1725 (1997).
[Crossref]

1996 (1)

1995 (1)

S. J. Bell and T. J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Computation 7, 1129–1159 (1995).
[Crossref] [PubMed]

1994 (1)

1991 (1)

1990 (1)

J. S. Jaffe, “Computer modelling and the design of optimal underwater imaging systems,” IEEE J. Oceanic Eng. 15, 101–111 (1990).
[Crossref]

1986 (1)

C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?,” American Journal of Physics 54, 222–227 (1986).
[Crossref]

Adelson, E. H.

H. Farid and E. H. Adelson, “Separating reflections from images by use of independent component analysis,” J. Opt. Soc. Amer A 16, 2136–2145 (1999).
[Crossref]

E. H. Adelson, “Lightness perception and lightness illusions,” in The New Cognitive Neuroscience, 2nd ed. ch. 24 339–351, MIT Preess, Cambridge (2000).

Alfano, R. R.

Amari, S.

Y. Li, A. Cichocki, and S. Amari, “Analysis of sparse representation and blind source separation,” Neural Computation 16, 1193–1234 (2004).
[Crossref] [PubMed]

Bell, S. J.

S. J. Bell and T. J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Computation 7, 1129–1159 (1995).
[Crossref] [PubMed]

Bofill, P.

P. Bofill and M. Zibulevsky, “Underdetermined blind source separation using sparse representations,” Signal Processing 81, 2353–2362 (2001).
[Crossref]

Bohren, C. F.

C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?,” American Journal of Physics 54, 222–227 (1986).
[Crossref]

Caimi, F. M.

D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” MTS Journal 42, 52–67 (2008).

Cameron, B. D.

Cardoso, J.-F.

J.-F. Cardoso, “Blind signal separation: statistical principles,” Proc. IEEE 86, 2009–2025 (1998).
[Crossref]

Chang, P. C. Y.

Chenault, D. B.

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
[Crossref] [PubMed]

D. B. Chenault and J. L. Pezzaniti, “Polarization imaging through scattering media,” In Proc. SPIE  4133, 124–133 (2000).

Chipman, R.

J. Wolfe and R. Chipman, “High speed imaging polarimeter,” In Proc. SPIE  5158, 24–32 (2003).

Chipman, R. A.

Chitwood, D.

Cichocki, A.

Y. Li, A. Cichocki, and S. Amari, “Analysis of sparse representation and blind source separation,” Neural Computation 16, 1193–1234 (2004).
[Crossref] [PubMed]

Coté, G. L.

Cover, T. M.

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

Cozman, F.

F. Cozman and E. Kroktov, “Depth from scattering,” In Proc. IEEE CVPR, 801–806 (1997).

Craighead, H. G.

Cronin, T. W.

N. Shashar, S. Sabbah, and T. W. Cronin, “Transmission of linearly polarized light in seawater: implications for polarization signaling,” J. Exper. Biology,  207, 3619–3628 (2004).
[Crossref]

Curila, M.

D. Nuzilland, S. Curila, and M. Curila, “Blind separation in low frequencies using wavelet analysis, application to artificial vision,” In Proc. ICA, 77–82 (2003).

Curila, S.

D. Nuzilland, S. Curila, and M. Curila, “Blind separation in low frequencies using wavelet analysis, application to artificial vision,” In Proc. ICA, 77–82 (2003).

Dalgleish, F. R.

D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” MTS Journal 42, 52–67 (2008).

Demos, S. G.

Denes, L. J.

der Spiegel, J. V.

Engheta, N.

Farid, H.

H. Farid and E. H. Adelson, “Separating reflections from images by use of independent component analysis,” J. Opt. Soc. Amer A 16, 2136–2145 (1999).
[Crossref]

Flitton, J. C.

Fraser, A. B.

C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?,” American Journal of Physics 54, 222–227 (1986).
[Crossref]

Gan, X.

Gan, X. S.

Garrat, P.

D. T. Pham and P. Garrat, “Blind separation of a mixture of independent sources through a quasi-maximum likelihood approach,” IEEE Trans. Signal Processing,  45, 1712–1725 (1997).
[Crossref]

Godin, G.

S. Umeyama and G. Godin, “Separation of diffuse and specular components of surface reflection by use of polarization and statistical analysis of images,” IEEE Trans. PAMI 26, 639–647 (2004).
[Crossref]

Goldstein, D. L.

Gottlieb, M.

Gruev, V.

Gu, M.

Gupta, N.

Harnett, C. K.

Harsdorf, S.

S. Harsdorf, R. Reuter, and S. Tönebön, “Contrast-enhanced optical imaging of submersible targets,” In Proc. SPIE  3821, 378–383 (1999).

Henry, R. C.

Hopcraft, K. I.

Horváth, G.

G. Horváth and D. Varjù, Polarized Light in Animal Vision, Springer-Verlag, Berlin (2004).

Hyvärinen, A.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, John Wiley and Sons, New York (2001).
[Crossref]

Ikeuchi, K.

Jaffe, J. S.

J. S. Jaffe, “Computer modelling and the design of optimal underwater imaging systems,” IEEE J. Oceanic Eng. 15, 101–111 (1990).
[Crossref]

Jakeman, E.

Jordan, D. L.

Kaminsky, B.

Karhunen, J.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, John Wiley and Sons, New York (2001).
[Crossref]

Karpel, N.

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30, 570–587 (2005).
[Crossref]

Kattawar, G. W.

Kisilev, P.

P. Kisilev, M. Zibulevsky, and Y. Y. Zeevi, “Multiscale framework for blind source separation,” J. Machine Learning Research 4, 1339–1364 (2004).

Kocak, D. M.

D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” MTS Journal 42, 52–67 (2008).

Kopeika, N. S.

N. S. Kopeika, A System Engineering Approach to Imaging, SPIE Press, Bellingham (1998).

Kroktov, E.

F. Cozman and E. Kroktov, “Depth from scattering,” In Proc. IEEE CVPR, 801–806 (1997).

Lazarus, N.

Li, Y.

Y. Li, A. Cichocki, and S. Amari, “Analysis of sparse representation and blind source separation,” Neural Computation 16, 1193–1234 (2004).
[Crossref] [PubMed]

Lin, S. S.

Lynch, D. K.

Mahadev, S.

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere: Scattering by Molecules and Particles, John Willey & Sons (1975).

Mehrübeoglu, M.

Metes, P.

Miyazaki, D.

Namer, E.

S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind haze separation,” In Proc. IEEE CVPR  2, 1984–1991 (2006).

E. Namer and Y. Y. Schechner, “Advanced visibility improvement based on polarization filtered images,” In Proc. SPIE  5888, 36–45 (2005).

Narasimhan, S. G.

Nayar, S. K.

Nuzilland, D.

D. Nuzilland, S. Curila, and M. Curila, “Blind separation in low frequencies using wavelet analysis, application to artificial vision,” In Proc. ICA, 77–82 (2003).

Oakley, J. P.

Oja, E.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, John Wiley and Sons, New York (2001).
[Crossref]

Ortu, A.

Pearlmutter, B. A.

M. Zibulevsky and B. A. Pearlmutter, “Blind source separation by sparse decomposition in a signal dictionary,” Neural Computation archive 13, 863–882 (2001).
[Crossref]

Petersson, L.

R. T. Tan, N. Pettersson, and L. Petersson, “Visibility enhancement for roads with foggy or hazy scenes,” In Proc. IEEE Intelligent Vehicles Symposium 19–24 (2007).

Pettersson, N.

R. T. Tan, N. Pettersson, and L. Petersson, “Visibility enhancement for roads with foggy or hazy scenes,” In Proc. IEEE Intelligent Vehicles Symposium 19–24 (2007).

Pezzaniti, J. L.

D. B. Chenault and J. L. Pezzaniti, “Polarization imaging through scattering media,” In Proc. SPIE  4133, 124–133 (2000).

Pham, D. T.

D. T. Pham and P. Garrat, “Blind separation of a mixture of independent sources through a quasi-maximum likelihood approach,” IEEE Trans. Signal Processing,  45, 1712–1725 (1997).
[Crossref]

Pugh, E. N.

Rakovic, M. J.

Rastegar, S.

Reuter, R.

S. Harsdorf, R. Reuter, and S. Tönebön, “Contrast-enhanced optical imaging of submersible targets,” In Proc. SPIE  3821, 378–383 (1999).

Rowe, M. P.

Sabbah, S.

N. Shashar, S. Sabbah, and T. W. Cronin, “Transmission of linearly polarized light in seawater: implications for polarization signaling,” J. Exper. Biology,  207, 3619–3628 (2004).
[Crossref]

Saito, M.

Sato, Y.

Schechner, Y. Y.

D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” MTS Journal 42, 52–67 (2008).

S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind haze separation,” In Proc. IEEE CVPR  2, 1984–1991 (2006).

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30, 570–587 (2005).
[Crossref]

E. Namer and Y. Y. Schechner, “Advanced visibility improvement based on polarization filtered images,” In Proc. SPIE  5888, 36–45 (2005).

S. Shwartz, M. Zibulevsky, and Y. Y. Schechner, “Fast kernel entropy estimation and optimization,” Signal Processing 85, 1045–1058 (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]

T. Treibitz and Y. Y. Schechner, “Instant 3Descatter,” In Proc. IEEE CVPR 1861–1868 (2006).

Schilders, S. P.

Sejnowski, T. J.

S. J. Bell and T. J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Computation 7, 1129–1159 (1995).
[Crossref] [PubMed]

Shashar, N.

N. Shashar, S. Sabbah, and T. W. Cronin, “Transmission of linearly polarized light in seawater: implications for polarization signaling,” J. Exper. Biology,  207, 3619–3628 (2004).
[Crossref]

Shaw, J. A.

Shwartz, S.

S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind haze separation,” In Proc. IEEE CVPR  2, 1984–1991 (2006).

S. Shwartz, M. Zibulevsky, and Y. Y. Schechner, “Fast kernel entropy estimation and optimization,” Signal Processing 85, 1045–1058 (2005).
[Crossref]

Simoncelli, E. P.

E. P. Simoncelli, “Statistical models for images: Compression, restoration and synthesis,” In Proc. Conf. Sig. Sys. and Computers, 673–678 (1997).

Suhre, D. R.

Tan, K.

Tan, R. T.

R. T. Tan, N. Pettersson, and L. Petersson, “Visibility enhancement for roads with foggy or hazy scenes,” In Proc. IEEE Intelligent Vehicles Symposium 19–24 (2007).

Thomas, J. A.

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

Tönebön, S.

S. Harsdorf, R. Reuter, and S. Tönebön, “Contrast-enhanced optical imaging of submersible targets,” In Proc. SPIE  3821, 378–383 (1999).

Treibitz, T.

T. Treibitz and Y. Y. Schechner, “Instant 3Descatter,” In Proc. IEEE CVPR 1861–1868 (2006).

Tyo, J. S.

Umeyama, S.

S. Umeyama and G. Godin, “Separation of diffuse and specular components of surface reflection by use of polarization and statistical analysis of images,” IEEE Trans. PAMI 26, 639–647 (2004).
[Crossref]

Urquijo, S.

Varjù, D.

G. Horváth and D. Varjù, Polarized Light in Animal Vision, Springer-Verlag, Berlin (2004).

Walker, J. G.

Wang, L. V.

Wehner, R.

R. Wehner, “Polarization vision a uniform sensory capacity?,” J. Exper. Biology 204, 2589–2596 (2001).

Wei, H.

Wolfe, J.

J. Wolfe and R. Chipman, “High speed imaging polarimeter,” In Proc. SPIE  5158, 24–32 (2003).

Wolff, L. B.

Yemelyanov, K. M.

Zeevi, Y. Y.

P. Kisilev, M. Zibulevsky, and Y. Y. Zeevi, “Multiscale framework for blind source separation,” J. Machine Learning Research 4, 1339–1364 (2004).

Zibulevsky, M.

S. Shwartz, M. Zibulevsky, and Y. Y. Schechner, “Fast kernel entropy estimation and optimization,” Signal Processing 85, 1045–1058 (2005).
[Crossref]

P. Kisilev, M. Zibulevsky, and Y. Y. Zeevi, “Multiscale framework for blind source separation,” J. Machine Learning Research 4, 1339–1364 (2004).

P. Bofill and M. Zibulevsky, “Underdetermined blind source separation using sparse representations,” Signal Processing 81, 2353–2362 (2001).
[Crossref]

M. Zibulevsky and B. A. Pearlmutter, “Blind source separation by sparse decomposition in a signal dictionary,” Neural Computation archive 13, 863–882 (2001).
[Crossref]

American Journal of Physics (1)

C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?,” American Journal of Physics 54, 222–227 (1986).
[Crossref]

Appl. Opt. (13)

D. K. Lynch, “Step brightness changes of distant mountain ridges and their perception,” Appl. Opt. 30, 3508–3513 (1991).
[Crossref] [PubMed]

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

N. Gupta, L. J. Denes, M. Gottlieb, D. R. Suhre, B. Kaminsky, and P. Metes, “Object detection with a field-portable spectropolarimetric imager,” Appl. Opt. 40, 6626–6632 (2001).
[Crossref]

C. K. Harnett and H. G. Craighead, “Liquid-crystal micropolarizer array for polarization-difference imaging,” Appl. Opt. 41, 1291–1296 (2002).
[Crossref] [PubMed]

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
[Crossref] [PubMed]

J. S. Tyo and H. Wei, “Optimizing imaging polarimeters constructed with imperfect optics,” Appl. Opt. 45, 5497–5503 (2006).
[Crossref] [PubMed]

P. C. Y. Chang, J. C. Flitton, K. I. Hopcraft, E. Jakeman, D. L. Jordan, and J. G. Walker, “Improving visibility depth in passive underwater imaging by use of polarization,” Appl. Opt. 42, 2794–2803 (2003).
[Crossref] [PubMed]

M. J. Raković, G. W. Kattawar, M. Mehrübeoğlu, B. D. Cameron, L. V. Wang, S. Rastegar, and G. L. Coté, “Light backscattering polarization patterns from turbid media: theory and experiment,” Appl. Opt. 38, 3399–3408 (1999).
[Crossref]

S. P. Schilders, X. S. Gan, and M. Gu, “Resolution improvement in microscopic imaging through turbid media based on differential polarization gating,” Appl. Opt. 37, 4300–4302 (1998).
[Crossref]

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

S. G. Demos and R. R. Alfano, “Optical polarization imaging,” Appl. Opt. 36, 150–155 (1997).
[Crossref] [PubMed]

K. M. Yemelyanov, S. S. Lin, E. N. Pugh, and N. Engheta, “Adaptive algorithms for two-channel polarization sensing under various polarization statistics with nonuniform distributions,” Appl. Opt. 45, 5504–5520 (2006).
[Crossref] [PubMed]

R. A. Chipman, “Depolarization index and the average degree of polarization,” Appl. Opt. 44, 2490–2495 (2005).
[Crossref] [PubMed]

IEEE J. Oceanic Eng. (2)

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30, 570–587 (2005).
[Crossref]

J. S. Jaffe, “Computer modelling and the design of optimal underwater imaging systems,” IEEE J. Oceanic Eng. 15, 101–111 (1990).
[Crossref]

IEEE Trans. PAMI (1)

S. Umeyama and G. Godin, “Separation of diffuse and specular components of surface reflection by use of polarization and statistical analysis of images,” IEEE Trans. PAMI 26, 639–647 (2004).
[Crossref]

IEEE Trans. Signal Processing (1)

D. T. Pham and P. Garrat, “Blind separation of a mixture of independent sources through a quasi-maximum likelihood approach,” IEEE Trans. Signal Processing,  45, 1712–1725 (1997).
[Crossref]

J. Exper. Biology (2)

N. Shashar, S. Sabbah, and T. W. Cronin, “Transmission of linearly polarized light in seawater: implications for polarization signaling,” J. Exper. Biology,  207, 3619–3628 (2004).
[Crossref]

R. Wehner, “Polarization vision a uniform sensory capacity?,” J. Exper. Biology 204, 2589–2596 (2001).

J. Machine Learning Research (1)

P. Kisilev, M. Zibulevsky, and Y. Y. Zeevi, “Multiscale framework for blind source separation,” J. Machine Learning Research 4, 1339–1364 (2004).

J. Opt. Soc. Am. A (6)

J. Opt. Soc. Amer A (1)

H. Farid and E. H. Adelson, “Separating reflections from images by use of independent component analysis,” J. Opt. Soc. Amer A 16, 2136–2145 (1999).
[Crossref]

MTS Journal (1)

D. M. Kocak, F. R. Dalgleish, F. M. Caimi, and Y. Y. Schechner, “A focus on recent developments and trends in underwater imaging,” MTS Journal 42, 52–67 (2008).

Neural Computation (2)

Y. Li, A. Cichocki, and S. Amari, “Analysis of sparse representation and blind source separation,” Neural Computation 16, 1193–1234 (2004).
[Crossref] [PubMed]

S. J. Bell and T. J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Computation 7, 1129–1159 (1995).
[Crossref] [PubMed]

Neural Computation archive (1)

M. Zibulevsky and B. A. Pearlmutter, “Blind source separation by sparse decomposition in a signal dictionary,” Neural Computation archive 13, 863–882 (2001).
[Crossref]

Opt. Express (1)

Proc. IEEE (1)

J.-F. Cardoso, “Blind signal separation: statistical principles,” Proc. IEEE 86, 2009–2025 (1998).
[Crossref]

Proc. IEEE ICCV (1)

S. K. Nayar and S. G. Narasimhan, “Vision in bad weather,” Proc. IEEE ICCV, 820–827 (1999).

Signal Processing (2)

S. Shwartz, M. Zibulevsky, and Y. Y. Schechner, “Fast kernel entropy estimation and optimization,” Signal Processing 85, 1045–1058 (2005).
[Crossref]

P. Bofill and M. Zibulevsky, “Underdetermined blind source separation using sparse representations,” Signal Processing 81, 2353–2362 (2001).
[Crossref]

Other (18)

E. P. Simoncelli, “Statistical models for images: Compression, restoration and synthesis,” In Proc. Conf. Sig. Sys. and Computers, 673–678 (1997).

An additional ICA ambiguity is permutation, which refers to mutual ordering of sources. This ambiguity does not concern us at all. The reason is that our physics-based formulation dictates a special form for the matrix W, and thus its rows are not mutually interchangeable.

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

T. Treibitz and Y. Y. Schechner, “Instant 3Descatter,” In Proc. IEEE CVPR 1861–1868 (2006).

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, John Wiley and Sons, New York (2001).
[Crossref]

D. Nuzilland, S. Curila, and M. Curila, “Blind separation in low frequencies using wavelet analysis, application to artificial vision,” In Proc. ICA, 77–82 (2003).

S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind haze separation,” In Proc. IEEE CVPR  2, 1984–1991 (2006).

E. H. Adelson, “Lightness perception and lightness illusions,” in The New Cognitive Neuroscience, 2nd ed. ch. 24 339–351, MIT Preess, Cambridge (2000).

For clarity of display, the images shown in this paper have undergone the same standard contrast stretch. This operation was done only towards the display. The algorithms described in the paper were run on raw, unstretched data. The data had been acquired using a Nikon D-100 camera, which has a linear radiometric response. The mounted zoom lens used with the camera was set to focal length of ≈ 200mm, except for Fig. 9 in which it was ≈ 85mm. The camera was pointed at or slightly below the horizon.

E. J. McCartney, Optics of the Atmosphere: Scattering by Molecules and Particles, John Willey & Sons (1975).

E. Namer and Y. Y. Schechner, “Advanced visibility improvement based on polarization filtered images,” In Proc. SPIE  5888, 36–45 (2005).

F. Cozman and E. Kroktov, “Depth from scattering,” In Proc. IEEE CVPR, 801–806 (1997).

J. Wolfe and R. Chipman, “High speed imaging polarimeter,” In Proc. SPIE  5158, 24–32 (2003).

N. S. Kopeika, A System Engineering Approach to Imaging, SPIE Press, Bellingham (1998).

R. T. Tan, N. Pettersson, and L. Petersson, “Visibility enhancement for roads with foggy or hazy scenes,” In Proc. IEEE Intelligent Vehicles Symposium 19–24 (2007).

D. B. Chenault and J. L. Pezzaniti, “Polarization imaging through scattering media,” In Proc. SPIE  4133, 124–133 (2000).

S. Harsdorf, R. Reuter, and S. Tönebön, “Contrast-enhanced optical imaging of submersible targets,” In Proc. SPIE  3821, 378–383 (1999).

G. Horváth and D. Varjù, Polarized Light in Animal Vision, Springer-Verlag, Berlin (2004).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1.
Fig. 1.

Dehazing of Scene 1 (distant up to 34 km). (a) The best polarized image. The two circles mark buildings. The rectangles mark arbitrary points at different distances. (b) The environmental parameters are estimated using the sky (sky-based dehazing). (c) Result of a feature-based method assisted by ICA (d) Result of a distance-based method assisted by ICA (e) Distance-based result.

Fig. 2.
Fig. 2.

[Dashed rays] Ambient light is scattered towards the camera by atmospheric particles, creating airlight A. It increases with object distance. [Solid ray] The light emanating from the object is attenuated as the distance increases, yielding the direct transmission D. Without scattering, the object radiance would have been L object.

Fig. 3.
Fig. 3.

The function G(V) at each color channel, corresponding to distances z 1 = 11km and z 2 = 23km in Scene 1. Note that G| V=0 > 0 and G| V=1 = 0. Since G(V) has a single minimum, it has only a single root in the domain V ∈ (0,1).

Fig. 4.
Fig. 4.

The airlight map  corresponding to Scene 1.

Fig. 5.
Fig. 5.

The function Gp (V) at each color channel, corresponding to distances z 1 = 11km and z 2 = 23km in Scene 1. Note that Gp | V=0 < 0 and Gp | V=1 =0. Since Gp (V) has a single maximum, it has only a single root in the domain V ∈ (0,1).

Fig. 6.
Fig. 6.

(a) A raw hazy image of Scene 2, whose distances are up to 22 km. (b) Sky-based dehazing. (c) Feature-based dehazing assisted by ICA. (d) Distance-based dehazing assisted by ICA. (e) Distance-based result.

Fig. 7.
Fig. 7.

The direct transmission D has a strong negative correlation to the airlight A. These images correspond to Scene 2. In a wavelet channel of these images, Ac,Dc have much less mutually dependency.

Fig. 8.
Fig. 8.

Histograms of across the wavelet channels, corresponding to Fig. 1. In each color channel, the most frequent value of was selected.

Fig. 9.
Fig. 9.

Dehazing of Scene 3, whose distances are up to 13.5 km. The scene contains smoke. (a) The best polarized raw image. (b) Sky-based dehazing. (c) Result of a feature-based method assisted by ICA (d) Result of a distance-based method assisted by ICA (e) Distance-based result.

Fig. 10.
Fig. 10.

Dehazing of Scene 4, whose distances are up to 31 km. (a) The best polarized image. (b) Sky-based dehazing. (c) Result of a feature-based method assisted by ICA (d) Result of a distance-based method assisted by ICA (e) Distance-based result.

Fig. 11.
Fig. 11.

Dehazing of Scene 5, whose distances are up to 30 km. (a) The best polarized image. (b) Sky-based dehazing. (c) Result of a feature-based method assisted by ICA (d) Result of a distance-based method assisted by ICA (e) Distance-based result.

Fig. 12.
Fig. 12.

A histogram of ρ, based on PDFs fitted to data of 5364 different images c (x,y), which were derived from various values of p, wavelet channels c and different raw images. In this histogram, ρ = 0.9±0.3.

Tables (3)

Tables Icon

Table 1. The requirements of prior knowledge in the different methods.

Tables Icon

Table 2. The [red green blue] values of the parameter given in percent, estimated using the methods described in Secs. 3.1 and 4. The results are compared to p sky, which is based on sky pixels. In Scene 4, there were no similar features residing at known distances, to be used in Sec. 3.1.

Tables Icon

Table 3. The [red green blue] values of the parameter Â, given in percents of the camera dynamic range. Estimations of  are based on various methods described in Secs. 3.1,3.2, and 3.3. The results are compared to A sky , which is based on sky pixels. In Scene 4, there were no similar features residing at known distances, to be used in Sec. 3.1.

Equations (68)

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

D=Lobjectt,
t=eβz
A=0za(z)dz=A(1t).
Itotal=D+A
A=Amin+Amax.
Imin=Amin+D/2,Imax=Amax+D/2.
p=(AmaxAmin) / A ,
0 p 1 .
Imin=A(1p) / 2 +D/2,Imax=A(1+p)/2+D/2.
Itotal=Imin+Imax.
Â=(ImaxImin) / p .
t̂=1Â/A.
L̂object=(ÎtotalÂ)/t̂ .
I1max=Lbuild2 eβz1 +Amax(1eβz1),
I1min=Lbuild2eβz1+Amin(1eβz1)
I1max=Lbuild2eβz2+Amax(1eβz2),
I1min=Lbuild2eβz2+Amin(1eβz2).
C1=I1maxI1min,C2=I2maxI2min .
C1(1Vz1)=AmaxAmin,
C2(1Vz2)=AmaxAmin,
Veβ.
G(V)=C1Vz2C2Vz1+(C2C1)=0.
(I1max+I1min)=LbuildVz1+(Amax+Amin)(1Vz1),
(I2max+I2min)=LbuildVz2+(Amax+Amin)(1Vz2).
Â(Amax+Amin)=(I2max+I2min)V0z1(I1max+I1min)V0z2V0z1V0z2.
ΔAAmaxAmin =I1maxI1min1V0z1 .
p̂=ΔAÂ.
GV=z2C1Vz21z1C2Vz11
V=(z1C2z2C1)1(z2z1).
V˜=Vz1=eβz1.
G˜ (V) C1V˜z˜C2V˜+(C2C1)=0.
Â=(I1max+I1min)V˜0(I1max+I1min)V˜0z˜V˜0V˜0z˜.
ΔA=I1maxI1min1V˜0.
eβz=1ÂA.
Vz1=1Â(x1,y1)A,Vz2=1Â(x2,y2)A,
A(Vz1Vz2)=Â(x2,y2)Â(x1,y1)
A(2Vz1Vz2)=Â(x2,y2)+Â(x1,y1).
Gp(V)(α1)Vz2+(α+1)Vz12α=0,
α=Â(x2,y2)Â(x1,y1)Â(x2,y2)+Â(x1,y1).
Â=Â(x1,y1)1V0z1.
G˜p(V)(α1)V˜z˜+(α+1)V˜2α=0,
Â=Â(x1,y1)1V˜0.
Îktotal=Lbuild+Sbuild  (xk,yk) ,
Sbuild(1Lbuild/A)
Â=L̂build/(1Sbuild).
L̂object=(11/p)Imaxxy+(1+1/p)Iminxy1[ImaxxyIminxy]/(Ap).
[ImaxImin]=M [AD] ,
M=[(1+p)/21/2(1p)/21/2].
[ÂD̂]=W [ImaxImin] ,
W=[1/p1/p(p1)/p(p+1)/p].
Dcxy=𝓦{Dxy}
[ ÂcD̂c ] = W [ IcmaxIcmin ] ,
𝓘(Âc,D̂c)=𝓗Âc+𝓗D̂c𝓗Âc,D̂c.
A˜c=IcmaxIcmin.
D˜c=w1Icmax+w2Icmin
w1(p1),w2(p+1).
W˜=[11w1w2].
𝓘 (D˜c,A˜c) = 𝓗D˜c + 𝓗D˜c 𝓗Âc,D̂c
𝓘(D˜c,A˜c)=𝓗D˜c+𝓗A˜clogdet(W˜)𝓗Icmax,Icmin.
{ŵ1,ŵ2}=argminw1,w2{𝓗D˜clogw2+w1},
p̂=ŵ1+ŵ2ŵ2ŵ1
PDF(D˜c)=μρσexp[(D˜c/σ)ρ] ,
PDF(D˜c)=μ(ρ)exp(D˜cρ) .
𝓗D˜c=𝓔 {log[PDF(D˜c)]} ,
𝓗̂D˜c=ν(ρ)+1Nx,yD˜cxyρ.
{ŵ1,ŵ2}=argminw1,w2{logw2+w1+1Nx,yD˜cxyρ}.
{ ŵ1 , ŵ2 } = minw1,w2{logw2+w1+1Nx,yD˜cxy} ,
where D˜c=w1Icmax +w2Icmin.

Metrics