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Free Space Detection Free Space Detection for autonomous for autonomous
navigation in daytime navigation in daytime foggy weatherfoggy weather
Nicolas Hautière, Jean-Philippe Tarel, Didier Aubert
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Light under Daytime FogLight under Daytime Fog
Daylight
Scattering
Atmospheric veil
Direct transmission
3
Light attenuation by the Light attenuation by the atmosphereatmosphere
Koschmieder’s law:Koschmieder’s law:
LeeLL dd )1(0
Apparent luminance
Object luminance
Atmospheric luminance
Object distance
Extinction coefficient
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Visibility Range under Daytime Visibility Range under Daytime FogFog
deCL
LLC
0
LeeLL dd )1(0 From the Koschmieder’s law ( ) let express the contrast of an object against the sky:From the Koschmieder’s law ( ) let express the contrast of an object against the sky:
contrast Attenuationcontrast Attenuation
Visibility distance: “the greatest distance at which a black object of suitable dimensions can be recognized by day against the horizon sky” (CIE, 1987)
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)05.0log(1
metV
For a black object (C0=1) and a visibility contrast threshold of 5%:
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Flat road assumptionFlat road assumption
Assuming a flat road, the Assuming a flat road, the depth of a road point is:depth of a road point is:
where:where: vh the horizon line the pixel size.
h
hh
vv
vvvvd
if
if
cos
H
z
x f
d
S
X
YZ
C
y
v
u vh
H
M
Road plane
Imageplane
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Extraction of a region of interestFitting of a measurement bandwidth
VVmetmet = = 50m50m
Estimation of the meteorological visibility distance
Exploitation of the atmospheric Exploitation of the atmospheric veilveil
Re 1d dI f L A e
Measurement and derivation of intensity curveExtraction of the inflection point
B&W image
Assuming that the camera Assuming that the camera response function is linear, response function is linear, the Koschmieder’s law the Koschmieder’s law becomes within the image becomes within the image space:space:
Method: instanciation of the Koschmieder’s law
[Hautière et al., 2006a] Hautière, N., Tarel, J.-P, Lavenant, J. and Aubert, D. (2006). Automatic Fog Detection and Measurement of the visibility Distance through use of an Onboard Camera. Machine Vision Applications Journal, 17(1):8-20
2
2
20 i hv vI
v
estimation thanks to the estimation thanks to the inflection point inflection point vvii::
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Recovery of the object luminanceRecovery of the object luminance (1)(1)
Extinction coefficient is now determined
The Atmospheric luminance AA∞∞ is given by the is given by the bandwidth above the horizon linebandwidth above the horizon line
Lets compute Lets compute RR by reversing the Koschmieder’s by reversing the Koschmieder’s law:law:
There is still one unknown: d
)1(
)1(
eAeIR
eAeRI
dd
dd
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Recovery of the object luminanceRecovery of the object luminance (2)(2)
eAIAR d
The previous equation may be rewriting as follows:
The contrast after restoration with respect to the background sky is thus:
The contrast restoration is exponential
eCeAAIAARC dd
r //
=0.05 (visibility = 60m), A=255
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Free space segmentationFree space segmentation
By using a flat world assumption the vertical objects are falsely restored (their distance being largely overestimated)
Their intensity becomes null after the restoration process
This drawback may be used in our advantage to segment the vertical object
The free space is thus segmented by looking for the biggest connected component in front of the vehicle (whatever the method).