1. Blind Contrast Restoration Assessment by Gradient Ratioing at Visible Edges Nicolas Hautière 1, Jean-Philippe Tarel 1, Didier Aubert 1-2, Eric Dumont 1 1 Laboratoire Central des Ponts et Chaussées, Paris, France 2 Institut National de REcherche sur les Transports et leur Sécurité, Versailles, France

2. Presentation Overview 1. Problematic 2. Visibility Model 3. Visible Edges Ratioing 4. Visual Properties of Fog 5. Contrast Restoration 6. Visible Edges Segmentation 7. Contrast Restoration Assessment 8. Conclusion

3. 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.

4. 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 L b is the same for both conditions, then this equation reduces to:  ΔL threshold depends on many parameters and can be estimated using Adrian’s empirical target visibility model (Adrian, 1989).

5. 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:  ΔI o is the gradient in the original image.  ΔI r is the gradient in the restored image.  Assuming a linear camera response function:  An object is composed of edges, r becomes: where ΔL threshold would be given by Adrian’s model.  Finally, we have: 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.

6. Visual Properties of Fog  Koschmieder’s law gives the apparent luminance L of an object located at distance d to the luminance L 0 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“: Daylight Scattering Atmospheric veil Direct transmission

7.  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 v h denotes the horizon line. Contrast Restoration: Fog Density Estimation 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.

8. 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: d 1 models the depth of pixels belonging to the road plane and d 2 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. Contrast Restoration: Principle u v

9. 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: 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.

10. Contrast Restoration: Results

11. 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: 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.

12. Visible Edges Segmentation: Results

13. 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%. Histogram stretching Proposed method

14. 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.