Abstract

The analysis of polarized filtered images has been proven useful in image dehazing. However, the current polarization-based dehazing algorithms are based on the assumption that the polarization is only associated with the airlight. This assumption does not hold up well in practice since both object radiance and airlight contribute to the polarization. In this study, a new polarization hazy imaging model is presented, which considers the joint polarization effects of the airlight and the object radiance in the imaging process. In addition, an effective method to synthesize the optimal polarized-difference (PD) image is introduced. Then, a decorrelation-based scheme is proposed to estimate the degree of polarization for the object from the polarized image input. After that, the haze-free image can be recovered based on the new polarization hazy imaging model. The qualitative and quantitative experimental results verify the effectiveness of this new dehazing scheme. As a by-product, this scheme also provides additional polarization properties of the objects in the image, which can be used in extended applications, such as scene segmentation and object recognition.

© 2014 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]

2013 (2)

S. Pyatykh, J. Hesser, and L. Zheng, “Image noise level estimation by principal component analysis,” IEEE Trans. Image Process. 22(2), 687–699 (2013).
[CrossRef] [PubMed]

C. H. Yeh, L.-W. Kang, M.-S. Lee, and C.-Y. Lin, “Haze effect removal from image via haze density estimation in optical model,” Opt. Express 21(22), 27127–27141 (2013).
[CrossRef] [PubMed]

2012 (1)

A. Mittal, A. K. Moorthy, and A. C. Bovik, “No-reference image quality assessment in the spatial domain,” IEEE Trans. Image Process. 21(12), 4695–4708 (2012).
[CrossRef] [PubMed]

2010 (1)

K. M. He, J. Sun, and X. O. Tang, “Single image haze removal using dark channel prior,” IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2341–2353 (2010).
[PubMed]

2009 (1)

2008 (2)

R. Fattal, “Single image dehazing,” ACM Trans. Graph. 27(3), 988–992 (2008).
[CrossRef]

S. Tominaga and A. Kimachi, “Polarization imaging for material classification,” Opt. Eng. 47(12), 123201 (2008).
[CrossRef]

2006 (2)

2005 (2)

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

D. Hoiem, A. A. Efros, and M. Hebert, “Automatic photo pop-up,” ACM Trans. Graph. 24(3), 577–584 (2005).
[CrossRef]

2003 (2)

2002 (2)

2000 (1)

1998 (1)

1996 (2)

H. Chen and L. B. Wolff, “Polarization phase-based method for material classification and object recognition in computer vision,” Proc. SPIE 2599, 54–63 (1996).
[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(11), 1855–1870 (1996).
[CrossRef] [PubMed]

1990 (1)

L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell. 12(11), 1059–1071 (1990).
[CrossRef]

1973 (1)

R. M. Haralick, K. Shanmugam, and I. H. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern. 3(6), 610–621 (1973).
[CrossRef]

Bovik, A. C.

A. Mittal, A. K. Moorthy, and A. C. Bovik, “No-reference image quality assessment in the spatial domain,” IEEE Trans. Image Process. 21(12), 4695–4708 (2012).
[CrossRef] [PubMed]

Chen, H.

H. Chen and L. B. Wolff, “Polarization phase-based method for material classification and object recognition in computer vision,” Proc. SPIE 2599, 54–63 (1996).
[CrossRef]

Chitwood, D.

Dinstein, I. H.

R. M. Haralick, K. Shanmugam, and I. H. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern. 3(6), 610–621 (1973).
[CrossRef]

Efros, A. A.

D. Hoiem, A. A. Efros, and M. Hebert, “Automatic photo pop-up,” ACM Trans. Graph. 24(3), 577–584 (2005).
[CrossRef]

Engheta, N.

Fattal, R.

R. Fattal, “Single image dehazing,” ACM Trans. Graph. 27(3), 988–992 (2008).
[CrossRef]

Haralick, R. M.

R. M. Haralick, K. Shanmugam, and I. H. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern. 3(6), 610–621 (1973).
[CrossRef]

He, K. M.

K. M. He, J. Sun, and X. O. Tang, “Single image haze removal using dark channel prior,” IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2341–2353 (2010).
[PubMed]

Hebert, M.

D. Hoiem, A. A. Efros, and M. Hebert, “Automatic photo pop-up,” ACM Trans. Graph. 24(3), 577–584 (2005).
[CrossRef]

Henry, R. C.

Hesser, J.

S. Pyatykh, J. Hesser, and L. Zheng, “Image noise level estimation by principal component analysis,” IEEE Trans. Image Process. 22(2), 687–699 (2013).
[CrossRef] [PubMed]

Hoiem, D.

D. Hoiem, A. A. Efros, and M. Hebert, “Automatic photo pop-up,” ACM Trans. Graph. 24(3), 577–584 (2005).
[CrossRef]

Kang, L.-W.

Kimachi, A.

S. Tominaga and A. Kimachi, “Polarization imaging for material classification,” Opt. Eng. 47(12), 123201 (2008).
[CrossRef]

Lee, M.-S.

Lin, C.-Y.

Lin, S. S.

Lo, M.

Mahadev, S.

Mittal, A.

A. Mittal, A. K. Moorthy, and A. C. Bovik, “No-reference image quality assessment in the spatial domain,” IEEE Trans. Image Process. 21(12), 4695–4708 (2012).
[CrossRef] [PubMed]

Moorthy, A. K.

A. Mittal, A. K. Moorthy, and A. C. Bovik, “No-reference image quality assessment in the spatial domain,” IEEE Trans. Image Process. 21(12), 4695–4708 (2012).
[CrossRef] [PubMed]

Namer, E.

E. Namer, S. Shwartz, and Y. Y. Schechner, “Skyless polarimetric calibration and visibility enhancement,” Opt. Express 17(2), 472–493 (2009).
[CrossRef] [PubMed]

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

Narasimhan, S. G.

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Polarization-based vision through haze,” Appl. Opt. 42(3), 511–525 (2003).
[CrossRef] [PubMed]

S. G. Narasimhan and S. K. Nayar, “Vision and the atmosphere,” Int. J. Comput. Vis. 48(3), 233–254 (2002).
[CrossRef]

Nayar, S. K.

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Polarization-based vision through haze,” Appl. Opt. 42(3), 511–525 (2003).
[CrossRef] [PubMed]

S. G. Narasimhan and S. K. Nayar, “Vision and the atmosphere,” Int. J. Comput. Vis. 48(3), 233–254 (2002).
[CrossRef]

Pugh, E.

Pugh, E. N.

Pyatykh, S.

S. Pyatykh, J. Hesser, and L. Zheng, “Image noise level estimation by principal component analysis,” IEEE Trans. Image Process. 22(2), 687–699 (2013).
[CrossRef] [PubMed]

Rowe, M. P.

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(11), 1855–1870 (1996).
[CrossRef] [PubMed]

Schechner, Y. Y.

Shanmugam, K.

R. M. Haralick, K. Shanmugam, and I. H. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern. 3(6), 610–621 (1973).
[CrossRef]

Shwartz, S.

Sun, J.

K. M. He, J. Sun, and X. O. Tang, “Single image haze removal using dark channel prior,” IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2341–2353 (2010).
[PubMed]

Tang, X. O.

K. M. He, J. Sun, and X. O. Tang, “Single image haze removal using dark channel prior,” IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2341–2353 (2010).
[PubMed]

Tominaga, S.

S. Tominaga and A. Kimachi, “Polarization imaging for material classification,” Opt. Eng. 47(12), 123201 (2008).
[CrossRef]

Tyo, J. S.

Urquijo, S.

Wolff, L. B.

H. Chen and L. B. Wolff, “Polarization phase-based method for material classification and object recognition in computer vision,” Proc. SPIE 2599, 54–63 (1996).
[CrossRef]

L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell. 12(11), 1059–1071 (1990).
[CrossRef]

Yeh, C. H.

Yemelyanov, K.

Yemelyanov, K. M.

Zheng, L.

S. Pyatykh, J. Hesser, and L. Zheng, “Image noise level estimation by principal component analysis,” IEEE Trans. Image Process. 22(2), 687–699 (2013).
[CrossRef] [PubMed]

ACM Trans. Graph. (2)

R. Fattal, “Single image dehazing,” ACM Trans. Graph. 27(3), 988–992 (2008).
[CrossRef]

D. Hoiem, A. A. Efros, and M. Hebert, “Automatic photo pop-up,” ACM Trans. Graph. 24(3), 577–584 (2005).
[CrossRef]

Appl. Opt. (1)

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(11), 1855–1870 (1996).
[CrossRef] [PubMed]

Appl. Opt. (3)

IEEE Trans. Image Process. (1)

S. Pyatykh, J. Hesser, and L. Zheng, “Image noise level estimation by principal component analysis,” IEEE Trans. Image Process. 22(2), 687–699 (2013).
[CrossRef] [PubMed]

IEEE Trans. Image Process. (1)

A. Mittal, A. K. Moorthy, and A. C. Bovik, “No-reference image quality assessment in the spatial domain,” IEEE Trans. Image Process. 21(12), 4695–4708 (2012).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

L. B. Wolff, “Polarization-based material classification from specular reflection,” IEEE Trans. Pattern Anal. Mach. Intell. 12(11), 1059–1071 (1990).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

K. M. He, J. Sun, and X. O. Tang, “Single image haze removal using dark channel prior,” IEEE Trans. Pattern Anal. Mach. Intell. 33(12), 2341–2353 (2010).
[PubMed]

IEEE Trans. Syst. Man Cybern. (1)

R. M. Haralick, K. Shanmugam, and I. H. Dinstein, “Textural features for image classification,” IEEE Trans. Syst. Man Cybern. 3(6), 610–621 (1973).
[CrossRef]

Int. J. Comput. Vis. (1)

S. G. Narasimhan and S. K. Nayar, “Vision and the atmosphere,” Int. J. Comput. Vis. 48(3), 233–254 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

S. Tominaga and A. Kimachi, “Polarization imaging for material classification,” Opt. Eng. 47(12), 123201 (2008).
[CrossRef]

Opt. Express (4)

Proc. SPIE (2)

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

H. Chen and L. B. Wolff, “Polarization phase-based method for material classification and object recognition in computer vision,” Proc. SPIE 2599, 54–63 (1996).
[CrossRef]

Other (12)

J. P. Tarel and N. Hautiere, “Fast visibility restoration from a single color or gray level image,” in Proceedings of IEEE International Conference on Computer Vision and Pattern Recognition (IEEE, 2009), pp. 2201–2208.
[CrossRef]

R. T. Tan, “Visibility in bad weather from a single image,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–8.
[CrossRef]

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Instant dehazing of images using polarization,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2001), pp. 325–332.
[CrossRef]

S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind haze separation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006), pp. 1984–1991.
[CrossRef]

M. Saito, Y. Sato, K. Ikeuchi, and H. Kashiwagi, “Measurement of surface orientations of transparent objects using polarization in highlight,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1999), pp. 381–386.
[CrossRef]

M. Bass, Devices, Measurements, and Properties, Vol. 2 of Handbook of Optics (McGraw-Hill, 1995), Chap. 22.

M. W. Hyde, S. C. Cain, J. D. Schmidt, and M. J. Havrilla, “Material classification of an unknown object using turbulence-degraded polarimetric imagery,” in Proceedings of IEEE Transactions on Geoscience and Remote Sensing (IEEE, 2010), pp. 264–276.
[CrossRef]

L. B. Wolff, “Using polarization to separate reflection components,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 363–369.
[CrossRef]

M. Ben-Ezra, “Segmentation with invisible keying signal,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2000), pp. 32–37.
[CrossRef]

K.M. Yemelyanov, S.S. Lin, E.N. Pugh, Jr., and N. Engheta, “Polarization-based segmentation for enhancement of target detection in adaptive polarization-difference imaging,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2005), paper JWA51.

A. Mittal, R. Soundararajan, and A. C. Bovik, “Making a completely blind image quality analyzer,” in Proceedings of IEEE Conference on Signal Processing Letters (IEEE, 2013), pp. 209–212.

K. M. He, J. Sun, and X. Tang, “Guided image filtering,” in Proceedings of European Conference on Computer Vision, K. Daniilidis, P. Maragos, N. Paragios, eds. (Berlin, 2010), pp. 1–14.

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Figures (10)

Fig. 1
Fig. 1

The components of a hazy image. (a) components of intensity. (b) Schechner et al.’s view of polarization’s components. (c) the proposed view of polarization’s components.

Fig. 2
Fig. 2

The description of the observed scene. (a) an observed scene. (b) the underlying topography of the light path. (c) the scene segmentation results.

Fig. 3
Fig. 3

The statistical results for mean of DoLP of each region. Each dot represents the DoLP of the corresponding region and each line corresponds to a polarized image group.

Fig. 4
Fig. 4

Flowchart of our proposed method.

Fig. 5
Fig. 5

Experimental images.

Fig. 6
Fig. 6

Key parameter estimation and dehazing results for Scene 1. (a) synthesizing image I max . (b) synthesizing image I min . (c) polarized-difference (PD) image. (d) estimated rough DoLP map ρ D . (e) Estimated rough transmission map t of R-channel. (f) refined transmission map t ^ of R-channel. (g) final DoLP map ρ ^ D . (h) sky region detection. (i) dehazing results with rough ρ D .(j) dehazing results with refined ρ ^ D .

Fig. 7
Fig. 7

Experimental results for Scenes 5 and 6. (a) dehazing result of Scene 5. (b) dehazing result of Scene 6.

Fig. 8
Fig. 8

Comparision experiment with and without ρ D for Scene 2. (a) dehazed image considering only the polarization of airlight. (b) dehazed images. (c) magnified region on the red rectangle in (a). (d) magnified region on the red rectangle in (b).

Fig. 9
Fig. 9

Dehazing results for Scenes 3 and 4. (a) and (c) are the dehazed image without considering the DoLP of object. (b) and (d) are our dehazed images.

Fig. 10
Fig. 10

Comparison with Schechner’s dehazing results. (a) the two-group input polarized images. Each group has a worst-polarized image and a best-polarized image. (b) Schechner’s results. (c) our dehazed images.

Tables (2)

Tables Icon

Table 1 The noise level comparison of dehazing images with and without considering ρ D

Tables Icon

Table 2 The six scene dehazed result’s image quality

Equations (23)

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

S ( x , y ) = ( S 0 ( x , y ) S 1 ( x , y ) S 2 ( x , y ) S 3 ( x , y ) ) = ( I ( x , y , 0 0 ) + I ( x , y , 9 0 0 ) I ( x , y , 0 0 ) - I ( x , y , 9 0 0 ) I ( x , y , 45 0 ) - I ( x , y , 45 0 ) I L ( x , y ) - I R ( x , y ) ) .
ρ λ = ( S 1 λ ) 2 + ( S 2 λ ) 2 S 0 λ .
α λ = 1 2 arc tan ( S 2 λ S 1 λ ) .
I λ ( x , y , θ ) = 1 2 S 0 λ ( x , y ) + 1 2 S 1 λ ( x , y ) cos 2 θ + 1 2 S 2 λ ( x , y ) sin 2 θ .
S 0 ( x , y ) = S 0 D ( x , y ) + S 0 A ( x , y ) .
S 0 D ( x , y ) = J ( x , y ) t ( x , y ) .
S 0 A ( x , y ) = A ( 1 - t ( x , y ) ) .
t ( x , y ) = exp ( β d ( x , y ) ) .
ρ ( x , y ) = I max ( x , y , θ max ) I min ( x , y , θ min ) I max ( x , y , θ max ) + I min ( x , y , θ min ) = Δ I ( x , y ) S 0 ( x , y ) .
ρ D ( x , y ) = I max D ( x , y , θ max ) I min D ( x , y , θ min ) I max D ( x , y , θ max ) + I min D ( x , y , θ min ) = Δ D ( x , y ) S 0 D ( x , y ) .
ρ A ( x , y ) = I max A ( x , y , θ max ) I min A ( x , y , θ min ) I max A ( x , y , θ max ) + I min A ( x , y , θ min ) = Δ A ( x , y ) S 0 A ( x , y ) .
ρ ( x , y ) S 0 ( x , y ) = ρ D ( x , y ) S 0 D ( x , y ) + ρ A ( x , y ) S 0 A ( x , y ) .
t ( x , y ) = 1 Δ I ( x , y ) ρ D ( x , y ) S 0 ( x , y ) A ( ρ A ( x , y ) ρ D ( x , y ) ) .
J ( x , y ) = Δ I ( x , y ) ρ A ( x , y ) S 0 ( x , y ) ρ D ( x , y ) ( 1 S 0 ( x , y ) / A ) + Δ I ( x , y ) / A ρ A ( x , y ) .
I λ ( x , y , θ ) = 1 2 ( 1 ρ λ ( x , y ) ) S 0 λ ( x , y ) + ρ λ ( x , y ) S 0 λ ( x , y ) cos 2 ( α λ ( x , y ) θ ) .
I max ( x , y , θ max ) = 1 2 ( 1 + ρ ( x , y ) ) S 0 ( x , y ) . I min ( x , y , θ min ) = 1 2 ( 1 ρ ( x , y ) ) S 0 ( x , y ) .
A = 1 | Ω | ( x , y ) Ω ( I max ( x , y , θ max ) + I min ( x , y , θ min ) ) . ρ A = 1 | Ω | ( x , y ) Ω ( I max ( x , y , θ max ) I min ( x , y , θ min ) I max ( x , y , θ max ) + I min ( x , y , θ min ) ) .
ρ D ( x , y ) = arg min ρ D ( x , y ) | C o v ω ( x , y ) ( t ( x , y ) , J 1 ( x , y ) ) | .
E ( ρ D ) = C o v { ρ D S 0 ( x , y ) Δ I ( x , y ) , ρ D S 0 ( x , y ) Δ I ( x , y ) A ( ρ D ρ A ) Δ I ( x , y ) ρ A S 0 ( x , y ) } ( ρ D ρ A ) A 2 .
t ^ i = j W i j ( I ) t j .
W i j ( I ) = 1 | ω k | 2 k : ( i , j ) ω k ( 1 + ( I i μ k ) ( I j μ k ) σ k 2 + ε ) .
J ( x , y ) = Δ I ( x , y ) ρ A ( x , y ) S 0 ( x , y ) Δ I ( x , y ) / A ρ A ( x , y ) .
D ( ν 1 , ν 2 , Σ 1 , Σ 2 ) = ( ν 1 ν 2 ) T ( Σ 1 + Σ 2 2 ) 1 ( ν 1 ν 2 ) .

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