Abstract

Many dehazing methods have proven to be effective in removing haze out of the hazy image, but few of them are adaptive in handling the dense haze. In this paper, based on the angle of polarization (AOP) distribution analysis we propose a kind of polarimetric dehazing method, which is verified to be capable of enhancing the contrast and the range of visibility of images taken in dense haze substantially. It is found that the estimating precision of the intensity of airlight is a key factor which determines the dehazing quality, and fortunately our method involves a high precision estimation inherently. In the experiments a good dehazing performance is demonstrated, especially for dense haze removal. We find that the visibility can be enhanced at least 74%. Besides, the method can be used not only in dense haze but also in severe sea fog.

© 2015 Optical Society of America

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References

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  1. K. Garg and S. K. Nayar, “Vision and rain,” Int. J. Comput. Vis. 75(1), 3–27 (2007).
    [Crossref]
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    [Crossref]
  3. K. He, J. Sun, and X. Tang, “Single image haze removal using dark channel prior,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 2341–2353 (2010).
    [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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  7. T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
    [Crossref] [PubMed]
  8. J. Mudge and M. Virgen, “Real time polarimetric dehazing,” Appl. Opt. 52(9), 1932–1938 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  10. J. Fade, S. Panigrahi, A. Carré, L. Frein, C. Hamel, F. Bretenaker, H. Ramachandran, and M. Alouini, “Long-range polarimetric imaging through fog,” Appl. Opt. 53(18), 3854–3865 (2014).
    [Crossref] [PubMed]
  11. G. Woodell, D. J. Jobson, Z. Rahman, and G. Hines, “Enhancement of imagery in poor visibility conditions,” Sensors, and Command, Control, Communications, and Intelligence Technologies for Homeland Security and Homeland Defense 5778 (2005).
  12. L. Schaul, C. Fredembach, and S. Süsstrunk, “Color image dehazing using the near-infrared,” in 16th IEEE International Conference on Image Processing (ICIP, 2009), pp. 1629–1632.
    [Crossref]
  13. T. Treibitz and Y. Y. Schechner, “Polarization: Beneficial for visibility enhancement?” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2009), 525–532 (2009).
  14. J. Liang, L. Y. Ren, H. J. Ju, E. S. Qu, and Y. L. Wang, “Visibility enhancement of hazy images based on a universal polarimetric imaging method,” J. Appl. Phys. 116(17), 173107 (2014).
    [Crossref]
  15. C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54(3), 222–227 (1986).
    [Crossref]
  16. J. Liang, L. Ren, E. Qu, B. Hu, and Y. Wang, “Method for enhancing visibility of hazy images based on polarimetric imaging,” Photonics Res. 2(1), 38–44 (2014).
    [Crossref]
  17. The AQI criterion can be read at http://en.wikipedia.org/wiki/Air_quality_index (2.2 Mainland China).
  18. A. Santos, C. Ortiz de Solórzano, J. J. Vaquero, J. M. Peña, N. Malpica, and F. del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188(3), 264–272 (1997).
    [Crossref] [PubMed]
  19. Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30(3), 570–587 (2005).
    [Crossref]

2015 (1)

2014 (4)

S. Fang, X. S. Xia, X. Huo, and C. W. Chen, “Image dehazing using polarization effects of objects and airlight,” Opt. Express 22(16), 19523–19537 (2014).
[Crossref] [PubMed]

J. Fade, S. Panigrahi, A. Carré, L. Frein, C. Hamel, F. Bretenaker, H. Ramachandran, and M. Alouini, “Long-range polarimetric imaging through fog,” Appl. Opt. 53(18), 3854–3865 (2014).
[Crossref] [PubMed]

J. Liang, L. Y. Ren, H. J. Ju, E. S. Qu, and Y. L. Wang, “Visibility enhancement of hazy images based on a universal polarimetric imaging method,” J. Appl. Phys. 116(17), 173107 (2014).
[Crossref]

J. Liang, L. Ren, E. Qu, B. Hu, and Y. Wang, “Method for enhancing visibility of hazy images based on polarimetric imaging,” Photonics Res. 2(1), 38–44 (2014).
[Crossref]

2013 (1)

2012 (1)

K. Nishino, L. Kratz, and S. Lombardi, “Bayesian defogging,” Int. J. Comput. Vis. 98(3), 263–278 (2012).
[Crossref]

2010 (1)

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

2009 (1)

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
[Crossref] [PubMed]

2007 (1)

K. Garg and S. K. Nayar, “Vision and rain,” Int. J. Comput. Vis. 75(1), 3–27 (2007).
[Crossref]

2005 (1)

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30(3), 570–587 (2005).
[Crossref]

2003 (1)

1997 (1)

A. Santos, C. Ortiz de Solórzano, J. J. Vaquero, J. M. Peña, N. Malpica, and F. del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188(3), 264–272 (1997).
[Crossref] [PubMed]

1986 (1)

C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54(3), 222–227 (1986).
[Crossref]

Alouini, M.

Bohren, C. F.

C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54(3), 222–227 (1986).
[Crossref]

Bretenaker, F.

Carré, A.

Chen, C. W.

del Pozo, F.

A. Santos, C. Ortiz de Solórzano, J. J. Vaquero, J. M. Peña, N. Malpica, and F. del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188(3), 264–272 (1997).
[Crossref] [PubMed]

Fade, J.

Fang, S.

Fraser, A. B.

C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54(3), 222–227 (1986).
[Crossref]

Frein, L.

Garg, K.

K. Garg and S. K. Nayar, “Vision and rain,” Int. J. Comput. Vis. 75(1), 3–27 (2007).
[Crossref]

Hamel, C.

He, K.

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

Hu, B.

J. Liang, L. Ren, E. Qu, B. Hu, and Y. Wang, “Method for enhancing visibility of hazy images based on polarimetric imaging,” Photonics Res. 2(1), 38–44 (2014).
[Crossref]

Huo, X.

Ju, H. J.

J. Liang, L. Y. Ren, H. J. Ju, E. S. Qu, and Y. L. Wang, “Visibility enhancement of hazy images based on a universal polarimetric imaging method,” J. Appl. Phys. 116(17), 173107 (2014).
[Crossref]

Karpel, N.

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30(3), 570–587 (2005).
[Crossref]

Kratz, L.

K. Nishino, L. Kratz, and S. Lombardi, “Bayesian defogging,” Int. J. Comput. Vis. 98(3), 263–278 (2012).
[Crossref]

Li, Y.

Liang, J.

J. Liang, L. Y. Ren, H. J. Ju, E. S. Qu, and Y. L. Wang, “Visibility enhancement of hazy images based on a universal polarimetric imaging method,” J. Appl. Phys. 116(17), 173107 (2014).
[Crossref]

J. Liang, L. Ren, E. Qu, B. Hu, and Y. Wang, “Method for enhancing visibility of hazy images based on polarimetric imaging,” Photonics Res. 2(1), 38–44 (2014).
[Crossref]

Lombardi, S.

K. Nishino, L. Kratz, and S. Lombardi, “Bayesian defogging,” Int. J. Comput. Vis. 98(3), 263–278 (2012).
[Crossref]

Lu, H.

Malpica, N.

A. Santos, C. Ortiz de Solórzano, J. J. Vaquero, J. M. Peña, N. Malpica, and F. del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188(3), 264–272 (1997).
[Crossref] [PubMed]

Mudge, J.

Narasimhan, S. G.

Nayar, S. K.

Nishino, K.

K. Nishino, L. Kratz, and S. Lombardi, “Bayesian defogging,” Int. J. Comput. Vis. 98(3), 263–278 (2012).
[Crossref]

Ortiz de Solórzano, C.

A. Santos, C. Ortiz de Solórzano, J. J. Vaquero, J. M. Peña, N. Malpica, and F. del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188(3), 264–272 (1997).
[Crossref] [PubMed]

Panigrahi, S.

Peña, J. M.

A. Santos, C. Ortiz de Solórzano, J. J. Vaquero, J. M. Peña, N. Malpica, and F. del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188(3), 264–272 (1997).
[Crossref] [PubMed]

Qu, E.

J. Liang, L. Ren, E. Qu, B. Hu, and Y. Wang, “Method for enhancing visibility of hazy images based on polarimetric imaging,” Photonics Res. 2(1), 38–44 (2014).
[Crossref]

Qu, E. S.

J. Liang, L. Y. Ren, H. J. Ju, E. S. Qu, and Y. L. Wang, “Visibility enhancement of hazy images based on a universal polarimetric imaging method,” J. Appl. Phys. 116(17), 173107 (2014).
[Crossref]

Ramachandran, H.

Ren, L.

J. Liang, L. Ren, E. Qu, B. Hu, and Y. Wang, “Method for enhancing visibility of hazy images based on polarimetric imaging,” Photonics Res. 2(1), 38–44 (2014).
[Crossref]

Ren, L. Y.

J. Liang, L. Y. Ren, H. J. Ju, E. S. Qu, and Y. L. Wang, “Visibility enhancement of hazy images based on a universal polarimetric imaging method,” J. Appl. Phys. 116(17), 173107 (2014).
[Crossref]

Santos, A.

A. Santos, C. Ortiz de Solórzano, J. J. Vaquero, J. M. Peña, N. Malpica, and F. del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188(3), 264–272 (1997).
[Crossref] [PubMed]

Schechner, Y. Y.

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
[Crossref] [PubMed]

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30(3), 570–587 (2005).
[Crossref]

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

Serikawa, S.

Sun, J.

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

Tan, R. T.

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

Tang, X.

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

Treibitz, T.

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
[Crossref] [PubMed]

Vaquero, J. J.

A. Santos, C. Ortiz de Solórzano, J. J. Vaquero, J. M. Peña, N. Malpica, and F. del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188(3), 264–272 (1997).
[Crossref] [PubMed]

Virgen, M.

Wang, Y.

J. Liang, L. Ren, E. Qu, B. Hu, and Y. Wang, “Method for enhancing visibility of hazy images based on polarimetric imaging,” Photonics Res. 2(1), 38–44 (2014).
[Crossref]

Wang, Y. L.

J. Liang, L. Y. Ren, H. J. Ju, E. S. Qu, and Y. L. Wang, “Visibility enhancement of hazy images based on a universal polarimetric imaging method,” J. Appl. Phys. 116(17), 173107 (2014).
[Crossref]

Xia, X. S.

Zhang, L.

Am. J. Phys. (1)

C. F. Bohren and A. B. Fraser, “At what altitude does the horizon cease to be visible?” Am. J. Phys. 54(3), 222–227 (1986).
[Crossref]

Appl. Opt. (3)

IEEE J. Oceanic Eng. (1)

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng. 30(3), 570–587 (2005).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

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

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
[Crossref] [PubMed]

Int. J. Comput. Vis. (2)

K. Nishino, L. Kratz, and S. Lombardi, “Bayesian defogging,” Int. J. Comput. Vis. 98(3), 263–278 (2012).
[Crossref]

K. Garg and S. K. Nayar, “Vision and rain,” Int. J. Comput. Vis. 75(1), 3–27 (2007).
[Crossref]

J. Appl. Phys. (1)

J. Liang, L. Y. Ren, H. J. Ju, E. S. Qu, and Y. L. Wang, “Visibility enhancement of hazy images based on a universal polarimetric imaging method,” J. Appl. Phys. 116(17), 173107 (2014).
[Crossref]

J. Microsc. (1)

A. Santos, C. Ortiz de Solórzano, J. J. Vaquero, J. M. Peña, N. Malpica, and F. del Pozo, “Evaluation of autofocus functions in molecular cytogenetic analysis,” J. Microsc. 188(3), 264–272 (1997).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Photonics Res. (1)

J. Liang, L. Ren, E. Qu, B. Hu, and Y. Wang, “Method for enhancing visibility of hazy images based on polarimetric imaging,” Photonics Res. 2(1), 38–44 (2014).
[Crossref]

Other (5)

The AQI criterion can be read at http://en.wikipedia.org/wiki/Air_quality_index (2.2 Mainland China).

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

G. Woodell, D. J. Jobson, Z. Rahman, and G. Hines, “Enhancement of imagery in poor visibility conditions,” Sensors, and Command, Control, Communications, and Intelligence Technologies for Homeland Security and Homeland Defense 5778 (2005).

L. Schaul, C. Fredembach, and S. Süsstrunk, “Color image dehazing using the near-infrared,” in 16th IEEE International Conference on Image Processing (ICIP, 2009), pp. 1629–1632.
[Crossref]

T. Treibitz and Y. Y. Schechner, “Polarization: Beneficial for visibility enhancement?” in IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2009), 525–532 (2009).

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Figures (10)

Fig. 1
Fig. 1 The raw image of sky area I(0) snapped in the hazy weather.
Fig. 2
Fig. 2 (a) The AOP value of the incident light directly calculated by Eq. (7). (b) The AOP value of the incident light calculated by Eq. (7) after smoothing each pixel value of the four raw images.
Fig. 3
Fig. 3 (a-d) are the polarized images taken with the specific angle of the polarizer 0°, 45°, 90° and 135°, respectively.
Fig. 4
Fig. 4 (a) and (b) are the estimated A of the image before and after smoothing with ε = 1.61; (c) is the estimated A of the image after smoothing with ε = 3.61.
Fig. 5
Fig. 5 (a-c) are the results of the dehazing process using the A which shows in Fig. 4(a-c), respectively.
Fig. 6
Fig. 6 The relationship of the bias factor ε and the contrast of the image C.
Fig. 7
Fig. 7 (a-d) are the dehazing results of the sky region with ε = 1.61, 1.76, 1.77 and 1.90, respectively.
Fig. 8
Fig. 8 (a) The dehazing result using our optimized polarimetric dehazing method; (b) the dehazing result using the polarimetric dehazing method in [14].
Fig. 9
Fig. 9 (a) The raw polarized image in four is taken in the same haze weather as Fig. 3; (b) the dehazed image is dehazed by using the optimized polarimetric dehazing method.
Fig. 10
Fig. 10 (a) The raw polarized image in four is taken in extremely dense sea fog; (b) the dehazed image is dehazed by using the optimized polarimetric dehazing method.

Tables (1)

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Table 1 The contrast of the target buildings in the same hazy condition.

Equations (11)

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

I=D+A,
D=Lt( z ),
A= A [ 1t( z ) ],
t( z )= e βz .
L= IA 1A/ A .
S 0 = [ I(0)+I(90)+I(45)+I(135) ] /2 S 1 =I(0)I(90) , S 2 =I(45)I(135)
θ= 1 2 arctan S 2 S 1 .
A= I( 0 ) S 0 ( 1p ) /2 p A cos 2 θ A = I( 90 ) S 0 ( 1p ) /2 p A sin 2 θ A ,
A= I( 0 ) S 0 ( 1ε p A ) /2 ε p A cos 2 θ A = I( 90 ) S 0 ( 1ε p A ) /2 ε p A sin 2 θ A .
C( I )= 1 N x,y [ I( x,y ) I ¯ ] 2 I ¯ ,
V= I ( x,y ) max I ( x,y ) min I ( x,y ) max +I ( x,y ) min ,

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