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

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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 (3)

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]

S. Shwartz, M. Zibulevsky, and Y. Y. Schechner, "Fast kernel entropy estimation and optimization," Signal Processing 85, 1045-1058 (2005).
[CrossRef]

R. A. Chipman, "Depolarization index and the average degree of polarization," Appl. Opt. 44, 2490-2495 (2005).
[CrossRef] [PubMed]

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 fieldportable 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]

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.

Chipman, R.

J. Wolfe, 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.

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]

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.

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.

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).

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.

Mehrübeoglu, M.

Metes, P.

Miyazaki, D.

Namer, E.

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.

Oakley, J. P.

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]

Pezzaniti, J. L.

D. B. Chenault, 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).

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]

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, M. Zibulevsky, and Y. Y. Schechner, "Fast kernel entropy estimation and optimization," Signal Processing 85, 1045-1058 (2005).
[CrossRef]

Suhre, D. R.

Tan, K.

Tönebön, S.

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

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.

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, 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]

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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)

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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.

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