An Edge-preserving Filtering Framework
for Visibility Restoration
Linchao Bao, Yibing Song, Qingxiong Yang (City University of Hong Kong)
and
Narendra Ahuja (University of Illinois at Urbana-Champaign)
Contents
• Proposed Edge-preserving
Filtering Framework
• Application on Dehazing
From Gaussian to Bilateral
• Gaussian filtering
• p, q: pixel location
• Ω: the neighborhood of pixel p
• Gσ: Gaussian function
p
q
From Gaussian to Bilateral
• Bilateral filtering
• Gσ_s ,Gσ_r : Gaussian function
• Wp: Weight normalization factor
p
q
[Tomasi and Manduchi ICCV’98]
Edge-preserving Filtering
Applications
•
•
•
•
•
•
•
•
Detail enhancement [Farbman et al. 08]
HDR tone mapping [Durand and Dorsey 02]
Image abstraction/stylization [Winnemoller et al. 06]
Joint filtering (upsampling, colorization) [Kopf et al. 07]
Photo-look transferring [Bae et al. 06]
Video enhancement [Bennett and McMillan 05]
Haze removal (Dehazing) [Tarel and Hautiere 09]
Shadow Removal [Yang et al. 12]
Bilateral Filtering
σr
0.1
0.01
σs 0.05
0.1
0.2
0.4
Input image
Input image (color visualized)
σs
0.01
0.05
0.1
σr
0.1
0.2
0.4
Bilateral Filtering
Smaller σr
Larger σr
Edge blurred
Not smoothed
Bilateral filtered
Our Filtering Framework
Our bilateral filtered
Idea
Find the optimal filtered value for each pixel, such that
Weighting function
Cost function
• Ω: The neighboring pixels of p
• Perform aggregations on costs of neighboring pixels w.r.t.
different x values, and then select the optimal x* as the output
filtered value!
• Reminder: Gaussian and bilateral filter are just aggregations using
different weighting functions!
First example
Neighborhood of p
p
Where
is x* ?
q
First example
Neighborhood of p
p
Where
is x* ?
q
First example
Neighborhood of p
x*
q
α = 2.0
First example
Neighborhood of p
x*
x*
q
α = 2.0
α = 1.0
First example
Neighborhood of p
x*
x*
α = 2.0
α = 1.0
α = 0.5
20
15
x*
q
10
5
0
 =0.5
0
100
200
300
First example
α = 2.0 Box filter (Mean filter)
α = 1.0 Median filter
α = 0.5 ?
Our Framework
Find the optimal filtered value for each pixel, such that
Weighting function
(
Cost function
can be any local-neighborhood-aggregation-based filter)
Specific Form (power cost function)
can be
•
•
•
•
•
Box filter
Gaussian filter
Bilateral filter
Guided filter
…
α < 2.0 Edge-preserving
α = 2.0 Original filter
Examples
Gaussian
Input filtered
Examples
Ƒ is Gaussian
Input filter, α = 0.5
Examples
Bilateral
Inputfiltered
Examples
Ƒ is bilateral
Inputfilter, α = 0.5
Examples
Ƒ is bilateral filter, α = 0.5
Edge-preserving Filtering
Applications
•
•
•
•
•
•
•
•
Detail enhancement [Farbman et al. 08]
HDR tone mapping [Durand and Dorsey 02]
Image abstraction/stylization [Winnemoller et al. 06]
Joint filtering (upsampling, colorization) [Kopf et al. 07]
Photo-look transferring [Bae et al. 06]
Video enhancement [Bennett and McMillan 05]
Haze removal (Dehazing) [Tarel and Hautiere 09]
Shadow Removal [Yang et al. 12]
Haze Removal (Dehazing)
The widely adopted model [Narasimhan and Nayar 02]
Atmospheric light
(global constant)
Haze image
(input)
Dehazed image
(desired result)
Transmission map
(haze attenuation)
Haze Removal (Dehazing)
The widely adopted model [Narasimhan and Nayar 02]
• First estimate A and transmission map t
• Ill-posed – additional assumption/prior needed
 Dark channel prior [He et al. 09] => Rough estimate of
 Smoothness [Fattal 08] [Tan et al. 08]
 White balanced input image [Tarel and Hautiere 09] => A = (1, 1, 1)
• We prefer fast filtering-based method [Tarel and Hautiere 09]
Filtering-based Method [Tarel and Hautiere 09]
Haze image I
(input)
Filtering-based Method [Tarel and Hautiere 09]
1)
W
Filtering-based Method [Tarel and Hautiere 09]
1)
2)
A
Filtering-based Method [Tarel and Hautiere 09]
1)
2)
B
Filtering-based Method [Tarel and Hautiere 09]
1)
2)
3)
Filtering-based Method [Tarel and Hautiere 09]
1)
2)
3)
4)
J
Filtering-based Method [Tarel and Hautiere 09]
1)
2)
3)
4)
Edge-preserving Filtering
W
Median filtered
(Tarel’s method)
Bilateral filtered
Edge-preserving Filtering
W
Median filtered
(Tarel’s method)
Ours
(F is BLF,
α=1)
Bilateral
filtered
Replace the filtering step
1)
2)
3)
4)
Replace the filtering step
1)
2)
3)
4)
Result
Input
Tarel’s method
Our result
(0.35 sec 1-megapixel@CPU)
(0.78 sec 1-megapixel@CPU)
Thank you!
Presented by Linchao Bao (@ City University of Hong Kong)
Implementation
• Straightforward implementation:
FUNCTION J = OurFilteringFramework(I, F, α)
init output image J;
init image MinMap with maximum cost value;
FOREACH output candidate value x,
calculate intermediate image Ȋ=|x-I|^α;
obtain M by filtering Ȋ using F;
FOREACH pixel p,
if M(p)<MinMap(p) then MinMap(p)=M(p), J(p)=x;
ENDFOR
ENDFOR
ENDFUNC
Fast Algorithm
• Fast approximation algorithm: (see paper for details)
• Do not filter for each candidate x value
• Sampling and interpolation:
• Assume local pixels are similar, then for each pixel p, filtered
follows curve
, and
• Filter at N sampling intensity levels, then use three x values and their
costs to calculate x* using the above curve (choose three points near the
bottom of the curve)
• Experiments show that
can usually generate good results
• N>=16 can generally produce high-quality results (PSNR>40dB)