Abstract

The radiance received by the sensor is influenced by the atmospheric interaction including the effects of absorption and scattering. Based on the analysis of the radiance along the transmission path, we propose an image degradation model and a recovery method for remote sensing and bad weather condition in which the effect of multiple scattering cannot be ignored. Several real outdoor images are restored to verify the effectiveness of the proposed model and method. The results turn out to be significantly improved in contrast and sharpness.

© 2012 OSA

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References

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  1. A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, and S. M. Adler-Golden, “Modtran4 user’s manual,” Air Force Research Laboratory, 1999.
  2. J. P. Oakley and B. L. Satherley, “Improving image quality in poor visibility conditions using a physical model for contrast degradation,” IEEE Trans. Image Process.7(2), 167–179 (1998).
    [CrossRef] [PubMed]
  3. K. K. Tan and J. P. Oakley, “Physics-based approach to color image enhancement in poor visibility conditions,” J. Opt. Soc. Am. A18(10), 2460–2467 (2001).
    [CrossRef] [PubMed]
  4. J. Kopf, B. Neubert, B. Chen, M. Cohen, D. Cohen-Or, O. Deussen, M. Uyttendaele, and D. Lischinski, “Deep photo: model-based photograph enhancement and viewing,” ACM Trans. Graph.27, 116 (2008).
  5. S. G. Narasimhan and S. K. Nayar, “Contrast restoration of weather degraded images,” IEEE Trans. Pattern Anal. Mach. Intell.25(6), 713–724 (2003).
    [CrossRef]
  6. 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), 325–332.
  7. R. T. Tan, “Visibility in bad weather from a single image,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), 1–8.
  8. S. Shwartz, E. Namer, and Y. Y. Schechner, “Blind haze separation,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006), 1984–1991.
  9. R. Fattal, “Single image dehazing,” ACM Trans. Graph.27(3), 72 (2008).
    [CrossRef]
  10. K. He, J. Sun, and X. Tang, “Single image haze removal using dark channel prior,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2009), 1956–1963.
  11. S. G. Narasimhan and S. K. Nayar, “Chromatic framework for vision in bad weather,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2000), 598–605.
  12. S. G. Narasimhan and S. K. Nayar, “Shedding light on the weather,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2003), 665–672.
  13. S. Metari and F. Desch, ênes, “A new convolution kernel for atmospheric point spread function applied to computer vision,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 2007), 1–8.
  14. R. C. Gonzalez and R. E. Woods, Digital Image Processing, Second Edition, (Publishing House of Electronics Industry, 2002), Chap. 5.
  15. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (IOP, 1998), Chap. 5.
  16. A. Levin, D. Lischinski, and Y. Weiss, “A closed form solution to natural image matting,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006), 61–68.
  17. W. Dong, Y. Chen, Z. Xu, H. Feng, and Q. Li, “Image stabilization with support vector machine,” J. Zhejiang Univ.-Sci. C Comput. & Electron.12(6), 478–485 (2011).
    [CrossRef]

2011

W. Dong, Y. Chen, Z. Xu, H. Feng, and Q. Li, “Image stabilization with support vector machine,” J. Zhejiang Univ.-Sci. C Comput. & Electron.12(6), 478–485 (2011).
[CrossRef]

2008

J. Kopf, B. Neubert, B. Chen, M. Cohen, D. Cohen-Or, O. Deussen, M. Uyttendaele, and D. Lischinski, “Deep photo: model-based photograph enhancement and viewing,” ACM Trans. Graph.27, 116 (2008).

R. Fattal, “Single image dehazing,” ACM Trans. Graph.27(3), 72 (2008).
[CrossRef]

2003

S. G. Narasimhan and S. K. Nayar, “Contrast restoration of weather degraded images,” IEEE Trans. Pattern Anal. Mach. Intell.25(6), 713–724 (2003).
[CrossRef]

2001

1998

J. P. Oakley and B. L. Satherley, “Improving image quality in poor visibility conditions using a physical model for contrast degradation,” IEEE Trans. Image Process.7(2), 167–179 (1998).
[CrossRef] [PubMed]

Chen, B.

J. Kopf, B. Neubert, B. Chen, M. Cohen, D. Cohen-Or, O. Deussen, M. Uyttendaele, and D. Lischinski, “Deep photo: model-based photograph enhancement and viewing,” ACM Trans. Graph.27, 116 (2008).

Chen, Y.

W. Dong, Y. Chen, Z. Xu, H. Feng, and Q. Li, “Image stabilization with support vector machine,” J. Zhejiang Univ.-Sci. C Comput. & Electron.12(6), 478–485 (2011).
[CrossRef]

Cohen, M.

J. Kopf, B. Neubert, B. Chen, M. Cohen, D. Cohen-Or, O. Deussen, M. Uyttendaele, and D. Lischinski, “Deep photo: model-based photograph enhancement and viewing,” ACM Trans. Graph.27, 116 (2008).

Cohen-Or, D.

J. Kopf, B. Neubert, B. Chen, M. Cohen, D. Cohen-Or, O. Deussen, M. Uyttendaele, and D. Lischinski, “Deep photo: model-based photograph enhancement and viewing,” ACM Trans. Graph.27, 116 (2008).

Deussen, O.

J. Kopf, B. Neubert, B. Chen, M. Cohen, D. Cohen-Or, O. Deussen, M. Uyttendaele, and D. Lischinski, “Deep photo: model-based photograph enhancement and viewing,” ACM Trans. Graph.27, 116 (2008).

Dong, W.

W. Dong, Y. Chen, Z. Xu, H. Feng, and Q. Li, “Image stabilization with support vector machine,” J. Zhejiang Univ.-Sci. C Comput. & Electron.12(6), 478–485 (2011).
[CrossRef]

Fattal, R.

R. Fattal, “Single image dehazing,” ACM Trans. Graph.27(3), 72 (2008).
[CrossRef]

Feng, H.

W. Dong, Y. Chen, Z. Xu, H. Feng, and Q. Li, “Image stabilization with support vector machine,” J. Zhejiang Univ.-Sci. C Comput. & Electron.12(6), 478–485 (2011).
[CrossRef]

Kopf, J.

J. Kopf, B. Neubert, B. Chen, M. Cohen, D. Cohen-Or, O. Deussen, M. Uyttendaele, and D. Lischinski, “Deep photo: model-based photograph enhancement and viewing,” ACM Trans. Graph.27, 116 (2008).

Li, Q.

W. Dong, Y. Chen, Z. Xu, H. Feng, and Q. Li, “Image stabilization with support vector machine,” J. Zhejiang Univ.-Sci. C Comput. & Electron.12(6), 478–485 (2011).
[CrossRef]

Lischinski, D.

J. Kopf, B. Neubert, B. Chen, M. Cohen, D. Cohen-Or, O. Deussen, M. Uyttendaele, and D. Lischinski, “Deep photo: model-based photograph enhancement and viewing,” ACM Trans. Graph.27, 116 (2008).

Narasimhan, S. G.

S. G. Narasimhan and S. K. Nayar, “Contrast restoration of weather degraded images,” IEEE Trans. Pattern Anal. Mach. Intell.25(6), 713–724 (2003).
[CrossRef]

Nayar, S. K.

S. G. Narasimhan and S. K. Nayar, “Contrast restoration of weather degraded images,” IEEE Trans. Pattern Anal. Mach. Intell.25(6), 713–724 (2003).
[CrossRef]

Neubert, B.

J. Kopf, B. Neubert, B. Chen, M. Cohen, D. Cohen-Or, O. Deussen, M. Uyttendaele, and D. Lischinski, “Deep photo: model-based photograph enhancement and viewing,” ACM Trans. Graph.27, 116 (2008).

Oakley, J. P.

K. K. Tan and J. P. Oakley, “Physics-based approach to color image enhancement in poor visibility conditions,” J. Opt. Soc. Am. A18(10), 2460–2467 (2001).
[CrossRef] [PubMed]

J. P. Oakley and B. L. Satherley, “Improving image quality in poor visibility conditions using a physical model for contrast degradation,” IEEE Trans. Image Process.7(2), 167–179 (1998).
[CrossRef] [PubMed]

Satherley, B. L.

J. P. Oakley and B. L. Satherley, “Improving image quality in poor visibility conditions using a physical model for contrast degradation,” IEEE Trans. Image Process.7(2), 167–179 (1998).
[CrossRef] [PubMed]

Tan, K. K.

Uyttendaele, M.

J. Kopf, B. Neubert, B. Chen, M. Cohen, D. Cohen-Or, O. Deussen, M. Uyttendaele, and D. Lischinski, “Deep photo: model-based photograph enhancement and viewing,” ACM Trans. Graph.27, 116 (2008).

Xu, Z.

W. Dong, Y. Chen, Z. Xu, H. Feng, and Q. Li, “Image stabilization with support vector machine,” J. Zhejiang Univ.-Sci. C Comput. & Electron.12(6), 478–485 (2011).
[CrossRef]

ACM Trans. Graph.

R. Fattal, “Single image dehazing,” ACM Trans. Graph.27(3), 72 (2008).
[CrossRef]

J. Kopf, B. Neubert, B. Chen, M. Cohen, D. Cohen-Or, O. Deussen, M. Uyttendaele, and D. Lischinski, “Deep photo: model-based photograph enhancement and viewing,” ACM Trans. Graph.27, 116 (2008).

IEEE Trans. Image Process.

J. P. Oakley and B. L. Satherley, “Improving image quality in poor visibility conditions using a physical model for contrast degradation,” IEEE Trans. Image Process.7(2), 167–179 (1998).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell.

S. G. Narasimhan and S. K. Nayar, “Contrast restoration of weather degraded images,” IEEE Trans. Pattern Anal. Mach. Intell.25(6), 713–724 (2003).
[CrossRef]

J. Opt. Soc. Am. A

J. Zhejiang Univ.-Sci. C Comput. & Electron.

W. Dong, Y. Chen, Z. Xu, H. Feng, and Q. Li, “Image stabilization with support vector machine,” J. Zhejiang Univ.-Sci. C Comput. & Electron.12(6), 478–485 (2011).
[CrossRef]

Other

A. Berk, G. P. Anderson, P. K. Acharya, J. H. Chetwynd, L. S. Bernstein, E. P. Shettle, M. W. Matthew, and S. M. Adler-Golden, “Modtran4 user’s manual,” Air Force Research Laboratory, 1999.

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), 325–332.

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

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

K. He, J. Sun, and X. Tang, “Single image haze removal using dark channel prior,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2009), 1956–1963.

S. G. Narasimhan and S. K. Nayar, “Chromatic framework for vision in bad weather,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2000), 598–605.

S. G. Narasimhan and S. K. Nayar, “Shedding light on the weather,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2003), 665–672.

S. Metari and F. Desch, ênes, “A new convolution kernel for atmospheric point spread function applied to computer vision,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 2007), 1–8.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, Second Edition, (Publishing House of Electronics Industry, 2002), Chap. 5.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (IOP, 1998), Chap. 5.

A. Levin, D. Lischinski, and Y. Weiss, “A closed form solution to natural image matting,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2006), 61–68.

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Figures (8)

Fig. 1
Fig. 1

(a) The radiance arriving at the sensor. (b) The corresponding relationship between image pixels and object pixels.

Fig. 2
Fig. 2

The procedure of image recovery.

Fig. 3
Fig. 3

(a) The original image. (b) The enlarged image.

Fig. 4
Fig. 4

The flowchart for solving our degradation model.

Fig. 5
Fig. 5

(a) The haze-free outdoor image. (b) The hazy outdoor image. (c) The dark channel of (a). (d) The dark channel of (b).

Fig. 6
Fig. 6

(a) The original degraded image. (b) The transmittance t calculated by Eq. (15). (c) The refined transmittance t’ obtained from Eq. (16).

Fig. 7
Fig. 7

Image recovery results. (a) Input degraded image. (b) The result by He et al.. (c) The result by Metari and Deschênes. (d) Our result.

Fig. 8
Fig. 8

More results. First row: three test images. Second row: the corresponding results by He et al.. Third row: the corresponding results by Metari and Deschênes. Fourth row: the corresponding results of our approach.

Tables (2)

Tables Icon

Table 1 Contrast data influenced by atmospheric transmission

Tables Icon

Table 2 Image quality assessment results for images in Figs. 7 and 8 (the number in bold denotes the largest value of each row)

Equations (19)

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Contrast= ( E a + E 0 )( E b + E 0 ) ( E a + E 0 )+( E b + E 0 ) ,
I(i,j)=J(i,j)t(i,j)+A[1t(i,j)],
p o (i,j)= f o (i,j)t(i,j) = f o (i,j)exp[μL(i,j)],
I= I 0 APSF,
q o = p o h o ,
q o | r×c = ( p o | (r+k1)×(c+k1) h o | k×k ) n| r×c =[ ( f o | (r+k1)×(c+k1) t| (r+k1)×(c+k1) ) h o | k×k ] n| r×c ,
q o =[( f o t) h o ]n,
q a ={[ f a (1t)] h a }n,
g= q o + q a + N CCD =[( f o t) h o ]n+{[ f a (1t)] h a }n+ N CCD .
g =( f o t) h o +[ f a (1t)] h a + N CCD .
G= g [ f a (1t)] h a ,
f o t=deconv(G, h o ),
f o = deconv(G, h o ) max(t, t 0 ) .
min c { min yΩ [ f o c (y)]}=0,
t=1ω min c { min yΩ [ g c (y) f a c ]},
(L+λU) t =λt,
APSF(i,j;σ,T)= exp[ ( i 2 + j 2 ) kT 2 | A(kT,σ) | kT ] 4 Γ 2 (1+ 1 kT )A (kT,σ) 2 ,
A(kT,σ)= [ σ 2 Γ( 1 kT )/Γ( 3 kT )] 1/2 ,
T=ln t ,

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