Hazy Images

• Low visibility

• Faint colors

Goals of Haze Removal

• Scene restoration

• Depth estimation

depth

Haze Imaging Model

)1( tt AJI

TransmissionScene radianceHazy image

Atmospheric light

Transmission

Haze Imaging Model

)1( tt AJI

Depth

td ln

Ambiguity in Haze Removal

input

scene

radiance

depth

….

Previous Works

• Using additional information

– Polarization filter [Shwartz et al., CVPR’06]

– Multiple images [Narasimhan & Nayar, CVPR’00]

– Known 3D model [Kopf et al., Siggraph Asia’08]

– User-assistance [Narasimhan & Nayar, CPMCV’03]

Previous Works

• Single image

– Maximize local contrast [Tan, CVPR 08]

Previous Works

• Single image

– Maximize local contrast [Tan, CVPR 08]

– Independent Component Analysis [Fattal, Siggraph 08]

Priors in Computer Vision

• Smoothness prior

• Sparseness prior

• Exemplar-based prior

Ill-posed

problem

well-posed

problem

prior

Dark Channel Prior

Dark Channel

• min (rgb, local patch)

Dark Channel


– min (r, g, b)

min (r, g, b)

Dark Channel


– min (r, g, b)

– min (local patch) = min filter

15 x15

darkest dark channel

Dark Channel


– min (r, g, b)


dark channel

))(Jmin(min)(J c

}bg,r,{c)(yyx

x dark

– Jc: color channel of J

– Jdark: dark channel of J

Dark Channel


– min (r, g, b)


dark channel

)Jmin(minJ c

cdark

– Jc: color channel of J

– Jdark: dark channel of J

A Surprising ObservationHaze-free

A Surprising Observation

0

0.2

0.4

0.6

0.8

1

0 64 128 192 256

Prob.

Pixel intensity of dark channels

86% pixels

in [0, 16]

5,000 haze-free

images

Dark Channel Prior

• For outdoor haze-free images

0)Jmin(min c

c

What makes it dark?

• Black object

• Colorful object

• Shadow

Dark Channel of Hazy Image

• The dark channel is no longer dark.

hazy image dark channel

Transmission Estimation

)1( tt AJIHaze imaging model

tt 1A

J

A

Ic

c

c

c

Normalize

tt

1)A

Jmin(min)

A

Imin(min

c

c

cc

c

c

Compute dark channel

tt

1)A

Jmin(min)

A

Imin(min

c

c

cc

c

c



0)Jmin(min c

c

Dark Channel Prior

0


tt

1)A

Jmin(min)

A

Imin(min

c

c

cc

c

c


Estimate transmission

)A

Imin(min1

c

c

ct


input I testimated

)A

Imin(min1

c

c

ct

Estimate transmission

Transmission Optimization

)1( tt AJIHaze imaging model

)1( BFIMatting model

+Refined

transmission

+

tri-map


• L - matting Laplacian [Levin et al., CVPR ‘06]

• Constraint - soft, dense (matting - hard, sparse)

LtttttT

2~)(

Data term Smoothness term


before optimization


after optimization

hazy image dark channel

brightest pixels

Atmospheric Light Estimation

brightest pixel

A: most hazy

Scene Radiance Restoration

)1( tt AJI

Scene radiance TransmissionHazy image

Atmospheric

light

Results

input

Results

recovered image

Results

depth

Results

input

Results

recovered image

Results

depth

Results

input

Results

recovered image

Results

depth

Comparisons

input [Fattal Siggraph 08]

Comparisons

input our result

Comparisons

input [Tan, CVPR 08]

Comparisons

input our result

input our result[Kopf et al, Siggraph Asia 08]

Comparisons

Results: De-focus

recovered scene radiance

input

depth

input

depth

Results: De-focus

de-focus

Results: Video

output

input

input our result transmission

• Inherently white or grayish objects

Limitations

• Haze imaging model is invalid

– e.g. non-constant A

input our result

Limitations

Summary

• Dark channel prior

– A natural phenomenon

– Very simple but effective

– Put a bad image to good use

Thank you

Single Image Haze Removal Using Dark Channel Prior參考

Documents

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