1. Free Space Detection for autonomous navigation in daytime foggy weather Nicolas Hautière, Jean-Philippe Tarel, Didier Aubert

2. 2 Light under Daytime Fog Daylight Scattering Atmospheric veil Direct transmission

3. 3 Light attenuation by the atmosphere  Koschmieder’s law: Apparent luminance Object luminance Atmospheric luminance Object distance Extinction coefficient

4. 4 Visibility Range under Daytime Fog  From the Koschmieder’s law ( ) let express the contrast of an object against the sky:  contrast 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)  For a black object (C 0 =1) and a visibility contrast threshold of 5%:

5. 5 Flat road assumption Assuming a flat road, the depth of a road point is: Assuming a flat road, the depth of a road point is:where: v h the horizon line  the pixel size. z x f d  S X Y Z C y v u vhvh H M Road plane Image plane

6. 6 Extraction of a region of interest Fitting of a measurement bandwidth V met = 50m Estimation of the meteorological visibility distance Exploitation of the atmospheric veil Measurement and derivation of intensity curve Extraction of the inflection point B&W image Assuming that the camera response function is linear, the Koschmieder’s law becomes within the image 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  estimation thanks to the inflection point v i :

7. 7 Recovery of the object luminance (1)  Extinction coefficient  is now determined A ∞ is given by the bandwidth above the horizon line  The Atmospheric luminance A ∞ is given by the bandwidth above the horizon line  Lets compute R by reversing the Koschmieder’s law:  There is still one unknown: d

8. 8 Recovery of the object luminance (2)  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  =0.05 (visibility = 60m), A  =255

9. 9 Free 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).

10. 10 Free space segmentation (Foggy weather)

11. 11 Free space segmentation (rainy weather)

12. 12 Thank you for your attention