Determination of surface roughness from reflected step edges

Abstract

We suggest that a vision system may be able to determine surface roughness by measurement of the sharpness of the edges of an image reflected in a rough surface. We choose step edges because they are present in many environments and because the methods of edge detection and localization are mature. We show that the amount of blur of reflected images of step edges does indeed increase with respect to surface roughness. The method that we propose for estimating the roughness of a surface assumes a common surface-roughness model of simple form and requires a known shape for the reflective surface and a known position for the viewer. We show the results of experiments performed with planar milled surfaces in a controlled environment and calculate the roughness parameter. We also show that our method can rank order the surfaces by roughness. Next we compare our results with the values of the roughness as measured with a stylus profilometer to test the accuracy of our method and of the model. We find that the results of the two methods are quite different. We discuss the possibility that this difference is due to the non-Gaussian character of the surface height distribution and describe current research into possible models of the surfaces. We conclude by issuing a warning to computer vision researchers that the most common model of surface roughness might be inadequate for describing many real surfaces.