The Determination of Surface Roughness from Reflected Step Edges

Abstract

The ability to measure the roughness of surfaces will be important for general purpose machine vision systems, in which a robot attempts to passively gain information about its environment. Although the traditional study of profilometry is well developed, its methods are unsuitable for this endeavor, since they require specialized apparatuses such as laser interferometers and styluses. We propose a method for the visual determination of surface roughness which does not require strong environmental constraints such as coherent light and small samples of the surface in question. We determine surface roughness by the measurement of the sharpness of the edges of an image reflected in a rough surface. We choose step edges since they will be present in many environments, and because the methods of edge detection and localization are mature. For these initial experiments, we assume a common surface roughness model of simple form, which we believe models milled or rolled surfaces. We show that if we also assume a known shape for the reflective surface and a known position for the viewer, we may calculate a roughness parameter. For our surface roughness model, we show that the resulting intensity distribution may be given in closed form. We then show the results of experiments performed with planar surfaces in a controlled environment and give the calculated roughness parameter. We compare these results with the values of the roughness as measured with a stylus profilometer, and find that the results are quite different. We discuss the possibilities that this difference is due to the non-Gaussian character of the surface height distribution, and the possibility that the difference arises from the difference in measurement procedures. We next show some extensions to other types of roughness functions, and discuss some new methods of roughness estimation which may yield information about a broader class of roughness models. Finally, we discuss the additional issues in extending and applying this approach to a general vision system.