Abstract

This paper proposed an effective method called propagating deconvolution to recover single image degraded in a scattering medium. The propagating deconvolution is in the manner of the calculus, which is based on multi-layered decomposition of the scattering volume and modeled blurring function of a single-layer scattering volume. Parameters of the deconvolution algorithm are estimated just from in situ measurement of the pure scattered background from one single image.

© 2014 Optical Society of America

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References

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  1. S. G. Narasimhan, S. K. Nayar, “Chromatic framework for vision in bad weather,” in Proceedings of IEEE Conference on CVPR (IEEE, 2000), 598–605.
    [CrossRef]
  2. Y. Schechner, S. G. Narasimhan, S. K. Nayar, “Instant dehazing of images using polarization,” in Proceedings of IEEE Conference on CVPR (IEEE, 2001), 1, 325–332.
  3. R. Tan, “Visibility in bad weather from a single image,” in Proceedings of IEEE Conference on CVPR (IEEE, 2008), 1–8.
    [CrossRef]
  4. R. Fattal, “Single image dehazing,” J. ACM Siggraph 27(3), 1–9 (2008).
    [CrossRef]
  5. K. He, J. Sun, X. Tang, “Single image haze removal using dark channel prior,” in Proceedings of IEEE Conference on CVPR (IEEE, 2009), 1956–1963.
  6. W. Hou, D. J. Gray, A. D. Weidemann, R. A. Arnone, “Comparison and validation of point spread models for imaging in natural waters,” Opt. Express 16(13), 9958–9965 (2008).
    [CrossRef] [PubMed]
  7. K. Iqbal, R. Abdul Salam, A. Osman, A. Zawawi Talib, “Underwater image enhancement using an integrated color model” J. Comput. Sci. 34, 2–12 (2007).
  8. G. Wang, B. Zheng, F. F. Sun, “Estimation-based approach for underwater image restoration,” Opt. Lett. 36(13), 2384–2386 (2011).
    [CrossRef] [PubMed]
  9. M. Pinchas, B. Z. Bobrovsky, “A maximum entropy approach for blind deconvolution,” Signal Process. 86(10), 2913–2931 (2006).
    [CrossRef]

2011

2008

2007

K. Iqbal, R. Abdul Salam, A. Osman, A. Zawawi Talib, “Underwater image enhancement using an integrated color model” J. Comput. Sci. 34, 2–12 (2007).

2006

M. Pinchas, B. Z. Bobrovsky, “A maximum entropy approach for blind deconvolution,” Signal Process. 86(10), 2913–2931 (2006).
[CrossRef]

Abdul Salam, R.

K. Iqbal, R. Abdul Salam, A. Osman, A. Zawawi Talib, “Underwater image enhancement using an integrated color model” J. Comput. Sci. 34, 2–12 (2007).

Arnone, R. A.

Bobrovsky, B. Z.

M. Pinchas, B. Z. Bobrovsky, “A maximum entropy approach for blind deconvolution,” Signal Process. 86(10), 2913–2931 (2006).
[CrossRef]

Fattal, R.

R. Fattal, “Single image dehazing,” J. ACM Siggraph 27(3), 1–9 (2008).
[CrossRef]

Gray, D. J.

He, K.

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

Hou, W.

Iqbal, K.

K. Iqbal, R. Abdul Salam, A. Osman, A. Zawawi Talib, “Underwater image enhancement using an integrated color model” J. Comput. Sci. 34, 2–12 (2007).

Narasimhan, S. G.

S. G. Narasimhan, S. K. Nayar, “Chromatic framework for vision in bad weather,” in Proceedings of IEEE Conference on CVPR (IEEE, 2000), 598–605.
[CrossRef]

Y. Schechner, S. G. Narasimhan, S. K. Nayar, “Instant dehazing of images using polarization,” in Proceedings of IEEE Conference on CVPR (IEEE, 2001), 1, 325–332.

Nayar, S. K.

Y. Schechner, S. G. Narasimhan, S. K. Nayar, “Instant dehazing of images using polarization,” in Proceedings of IEEE Conference on CVPR (IEEE, 2001), 1, 325–332.

S. G. Narasimhan, S. K. Nayar, “Chromatic framework for vision in bad weather,” in Proceedings of IEEE Conference on CVPR (IEEE, 2000), 598–605.
[CrossRef]

Osman, A.

K. Iqbal, R. Abdul Salam, A. Osman, A. Zawawi Talib, “Underwater image enhancement using an integrated color model” J. Comput. Sci. 34, 2–12 (2007).

Pinchas, M.

M. Pinchas, B. Z. Bobrovsky, “A maximum entropy approach for blind deconvolution,” Signal Process. 86(10), 2913–2931 (2006).
[CrossRef]

Schechner, Y.

Y. Schechner, S. G. Narasimhan, S. K. Nayar, “Instant dehazing of images using polarization,” in Proceedings of IEEE Conference on CVPR (IEEE, 2001), 1, 325–332.

Sun, F. F.

Sun, J.

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

Tan, R.

R. Tan, “Visibility in bad weather from a single image,” in Proceedings of IEEE Conference on CVPR (IEEE, 2008), 1–8.
[CrossRef]

Tang, X.

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

Wang, G.

Weidemann, A. D.

Zawawi Talib, A.

K. Iqbal, R. Abdul Salam, A. Osman, A. Zawawi Talib, “Underwater image enhancement using an integrated color model” J. Comput. Sci. 34, 2–12 (2007).

Zheng, B.

J. ACM Siggraph

R. Fattal, “Single image dehazing,” J. ACM Siggraph 27(3), 1–9 (2008).
[CrossRef]

J. Comput. Sci.

K. Iqbal, R. Abdul Salam, A. Osman, A. Zawawi Talib, “Underwater image enhancement using an integrated color model” J. Comput. Sci. 34, 2–12 (2007).

Opt. Express

Opt. Lett.

Signal Process.

M. Pinchas, B. Z. Bobrovsky, “A maximum entropy approach for blind deconvolution,” Signal Process. 86(10), 2913–2931 (2006).
[CrossRef]

Other

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

S. G. Narasimhan, S. K. Nayar, “Chromatic framework for vision in bad weather,” in Proceedings of IEEE Conference on CVPR (IEEE, 2000), 598–605.
[CrossRef]

Y. Schechner, S. G. Narasimhan, S. K. Nayar, “Instant dehazing of images using polarization,” in Proceedings of IEEE Conference on CVPR (IEEE, 2001), 1, 325–332.

R. Tan, “Visibility in bad weather from a single image,” in Proceedings of IEEE Conference on CVPR (IEEE, 2008), 1–8.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Layered decomposition of the scattering medium between the target and the sensor.

Fig. 2
Fig. 2

(a) is an original fog image, (b)-(d) are the successive recovered images of (a), choosing α = 0.3, for m = 1, 2, 3, respectively. The propagation stops at (c) associated to the maximum S.

Fig. 3
Fig. 3

column (a) are the original images; column (b) are the results by Fattal [4]; column (c) are the results by He [5]; column (d) are refined results by our method.

Fig. 4
Fig. 4

(a) is a selected patch from the column (a), the second row of Fig. 3, (b)-(d) are the recovered results by methods of Fattal [4], He [5], and our method, respectively.

Equations (21)

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

g(x,y)=f(x,y)h(x,y)+n(x,y)
E=Jexp(βz)+A(1exp(βz))
h Δ (x,y)=(1/ π θ Δ )exp{ ( x 2 + y 2 )/ θ Δ }( θ Δ 0,ifΔ0, h Δ (x,y)δ( x,y ))
H Δ (u,v)=exp[ θ Δ π 2 ( u 2 + v 2 ) ]
H z (u,v)=exp(βz)exp{zρ π 2 ( u 2 + v 2 )}(ρ= θ Δ   /Δ)
d n z (x,y)={k(x,y)Idz} h z (x,y)
d N z (u,v)=K(u,v)Adz H z (u,v)
N z (u,v)=AK(u,v) 0 z e β+ρ π 2 ( u 2 + v 2 )z dz= AK(u,v) β+ρ π 2 ( u 2 + v 2 ) (1 e [ β+ρ π 2 ( u 2 + v 2 ) ]z )
S d = N z (0,0)=( k 0 A /β ){1exp(βz)}
P n (u,v)={ A 2 σ 2 / [β+ρ π 2 ( u 2 + v 2 )] 2 } (1exp{[βz+zρ π 2 ( u 2 + v 2 )]}) 2
g= f (m1) * h m + s d (m) f (m1) = f (m2) * h m1 + s d (m1) f (1) =f* h 1 + s d (1)
H α (u,v)=exp{ α( 1+ ρ β π 2 ( u 2 + v 2 ) ) } (α=βΔ)
s d (m) = k 0 A z z+Δ exp{βz} dz= k 0 A β exp{βz}( 1exp{βΔ} )
P n (m) (u,v)= A 2 σ 2 ( z z+Δ exp{βzzρ π 2 ( u 2 + v 2 )} dz ) 2 = A 2 σ 2 ( β+ρ π 2 ( u 2 + v 2 ) ) 2 [ exp{βzρz π 2 ( u 2 + v 2 )} ( 1exp{βΔρΔ π 2 ( u 2 + v 2 )} ) ] 2
H α (u,v)=exp{α( 1+ η 1 π 2 ( u 2 + v 2 ) )}
s d (m) = η 3 exp{mα}(1exp{α})
P n (m) (u,v)= η 2 2 [1+ η 1 π 2 ( u 2 + v 2 )] 2 [ exp{mα( 1+ η 1 π 2 ( u 2 + v 2 ) ) ( 1exp{α( 1+ η 1 π 2 ( u 2 + v 2 ) )} ) ] 2
d N z ' (u,v)=K(u,v)Aexp(βz)dz H z (u,v)
S= i=1 L p i ln p i
f (m+1) (x,y)= f (m) (x,y) s d (m) ,m=0, 1, 2
F (m+1) (u,v)= H α (u,v) | H α (u,v) | 2 + P n (m) (u,v)/ P f (m) (u,v) F (m) (u,v)

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