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Single Image Haze Removal
Using Dark Channel Prior
Kaiming He
Jian Sun
Xiaoou Tang
The Chinese University of Hong Kong
Microsoft Research Asia
The Chinese University of Hong Kong
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]
Previous Works
• Single image
– Maximize local contrast [Tan, CVPR 08]
– Independent Component Analysis [Fattal, Siggraph 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 (rgb, local patch)
– min (r, g, b)
min (r, g, b)
Dark Channel
• min (rgb, local patch)
– min (r, g, b)
– min (local patch) = min filter
15 x15
darkest dark channel
Dark Channel
• min (rgb, local patch)
– min (r, g, b)
– min (local patch) = min filter
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 (rgb, local patch)
– min (r, g, b)
– min (local patch) = min filter
dark channel
)Jmin(minJ c
cdark
– Jc: color channel of J
– Jdark: dark channel of J
A Surprising ObservationHaze-free
A Surprising ObservationHaze-free
A Surprising ObservationHaze-free
A Surprising ObservationHaze-free
A Surprising ObservationHaze-free
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
Compute dark channel
Transmission Estimation
0)Jmin(min c
c
Dark Channel Prior
0
Compute dark channel
tt
1)A
Jmin(min)
A
Imin(min
c
c
cc
c
c
Transmission Estimation
Estimate transmission
)A
Imin(min1
c
c
ct
Transmission Estimation
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
Transmission Optimization
• L - matting Laplacian [Levin et al., CVPR ‘06]
• Constraint - soft, dense (matting - hard, sparse)
LtttttT
2~)(
Data term Smoothness term
Transmission Optimization
before optimization
Transmission 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
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