Estimation of the luminance map for a Lambertian photometric model: application to the study of road surface roughness

The study of rough textured surfaces such as road coverings, is generally made on gray-level images. This supposes that the variations of gray levels are representative of the local variations of the relief. This assumption is justified, in the case of surfaces that are uniformly colored, but finds its limit in the case when these surfaces present variations of color or aspect. The corresponding image then presents variations of gray levels that can be related to the color variations or to the relief variations or both. It becomes difficult in this case to work out the criteria of roughness based on image analysis. It is then necessary to develop, before any study of roughness, an estimation of the luminance map linked to color variations. To do that, we have linked the gray-level value to the height variation of the road-covering surface. Thus, we express the luminance distribution according to these height variations, obtained through a laser sensor, and to the image gray level. This method enables us to compute the distribution of the luminance map. We characterize this distribution by considering statistical parameters of its histogram. Then we test the effectiveness of our approach by comparing the evolution of the criterion of roughness on road surfaces, first without considering the luminance distribution and then by taking it into account. The results obtained show that this approach leads to a good discrimination by the criterion of roughness in the case of colored surfaces. ©