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Blind Contrast Restoration Assessment by Gradient Ratioing at Visible Edges
Nicolas Hautière1, Jean-Philippe Tarel1, Didier Aubert1-2, Eric Dumont1
1Laboratoire Central des Ponts et Chaussées, Paris, France2Institut National de REcherche sur les Transports et leur Sécurité, Versailles, France
Presentation Overview
1. Problematic2. Visibility Model3. Visible Edges Ratioing4. Visual Properties of Fog5. Contrast Restoration 6. Visible Edges Segmentation7. Contrast Restoration Assessment8. Conclusion
Problematic
There is a lack of methodology to assess the performances of fog degraded images restoration.
Since fog effects are volumetric, fog can not be considered as a classical image noise or degradation which might be added and then removed.
Consequently, compared to image quality assessment or image restoration areas, there is no easy way, synthetic images from 3D models put aside, to have a reference image.
We propose such a contribution.
Visibility Model
Visibility can be related to the contrast C, defined by:
For suprathreshold contrasts, the Visibility Level (VL) of a target can be quantified by the ratio:
As Lb is the same for both conditions, then this equation reduces to:
ΔLthreshold depends on many parameters and can be estimated using Adrian’s empirical target visibility model (Adrian, 1989).
b
bt
b L
LL
L
LC
thresholdbactualbthreshold
actual LLLLCC
VL
thresholdactual LLVL tL
bL
Visible Edges Ratioing
To assess the performances of a contrast restoration method, we compute, for each pixel belonging to a visible edge in the restored image, the ratio:
ΔIo is the gradient in the original image.
ΔIr is the gradient in the restored image.
Assuming a linear camera response function:
An object is composed of edges, r becomes:
where ΔLthreshold would be given by Adrian’s model.
Finally, we have:
or IfIfr 11
oror LLIIr
thresholdothresholdr LLLLr
or VLVLr Hautière N, Dumont E (2007). Assessment of visibility in complex road scenes using digital imaging. In: The 26th session of the CIE (CIE’07), Beijing, China.
Visual Properties of Fog
Koschmieder’s law gives the apparent luminance L of an object located at distance d to the luminance L0 measured close to this object:
where L∞ is the atmospheric luminance and β is the extinction coefficient of fog.
Duntley developed a contrast attenuation law:
The CIE defined a standard dimension called “meteorological visibility distance“: dd eLeLL
10
dd eCeLLLC 0
Daylight
Scattering
Atmospheric veil
Direct transmission
3
05.0log1
metV
Assuming a linear camera response function, Koschmieder’s law becomes in the image plane:
Assuming a flat world scene, it is possible to estimate (β, A∞) thanks to the existence of an inflection point on this curve:
where depends on camera parameters and vh denotes the horizon line.
Contrast Restoration: Fog Density Estimation
dd eALfI
1Re
hi vv
dv
Id
20
2
2
Hautière N, Tarel JP, Lavenant J, Aubert D (2006b). Automatic Fog Detection and Estimation of Visibility Distance through use of an Onboard Camera. Machine Vision and Applications Journal 17:8–20.
• To restore the contrast, we propose to reverse Koschmieder’s law. In this way, R can be estimated directly for all scene points from:
• The remaining problem is the depth d of each pixel. For pixels not belonging to the sky region, i.e I<A∞, a scene model is proposed:
• d1 models the depth of pixels belonging to the road plane and d2 models the depth of the vertical surroundings.
where c is a clipping plane, > controls the relative importance of the flat world against the vertical surroundings.
)1( dd eAIeR
21,min ddd
cvvifvc
cvvifvv
d
hh
hh
01
222)()( hhh vvuu
oruu
d
Contrast Restoration: Principle
u
v
Contrast Restoration: Algorithm
• One method aims at restoring the contrast of the road surface, while enhancing contrast on vertical objects without distorting them.
• We seek the best scene maximizes the contrast and minimizes the number of distorted pixels, i.e. the optimal values of and c.
• The problem can be formulated as a minimization process:
where Q is an image quality attribute, the norm of the local normalized correlation between the original image I and the restored image R:
),( RIhQ
ccQc
c
,minarg**,
0
1
i i
i
RixRIixI
RixRIixIHRIh
22)()(
)()(),(
Hautière N, Tarel JP, Aubert D (2007). Towards fog-free in-vehicle vision systems through contrast restoration. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’07), Minneapolis, USA.
Contrast Restoration: Results
Visible Edges Segmentation: Principle and Implementation
By fog, the visible edges are the set of edges having a local contrast above 5%.
LIP model (Jourlin and Pinoli, 2001) defined the contrast associated to a border F which separates two adjacent regions:
where C(x,y)(f) denotes the contrast between two pixels x and y of the image f:
To implement this definition of contrast, Köhler’s segmentation method has been used (Köhler, 1981).
Instead of using this method to binarize images, we use it to measure the contrast locally:
yfxfyfxffC yx ,min,max,
fCVcard
fC yxVyx
F ),(),(
1
Hautière N, Aubert D, Jourlin M (2006a). Measurement of local contrast in images, application to the measurement of visibility distance through use of an onboard camera. Traitement du Signal 23:145–58.
Visible Edges Segmentation: Results
Restoration Assessement: Final Results
The computation of r enables thus to compute the increase of visibility level VL produced by the contrast restoration method.
e denotes the percentage of new visible edges, i.e. C>5%. o
or
n
nne
1.18.1 er 4.16.2 er 6.17.1 er
Histogram stretching 3.03.1 er 25.01.1 er 4.01.1 er
Proposed method
riPi
r
rn
r log1
exp
Conclusion
In this paper, we proposed: An efficient contrast restoration method, A methodology to assess its performances by gradient
ratioing at visible edges, A method to extract edges having a local contrast
above 5% based on LIP model.
In the future, we want to tackle: The detection of other meteorological phenomena such
as rain, night-fog, The restoration of other types of image degradation.