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)

3

)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

6

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).

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Free space segmentationFree space segmentation(Foggy weather)(Foggy weather)

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Free space segmentationFree space segmentation(rainy weather)(rainy weather)

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