The Determination of Surface Roughness from Reflected Step Edges

The abdiw to measure the roughness of surfaces will be imporrant for general purpose machine vision systems, in which a robot attempts to passively gain information about its environment. Although the rradirional srudy ofpmfilometT is weil developed, its methods are unsuiiable for this endeavor; since they reqiiire specialized apparatuses such as h e r interferometers and styluses. We propose a method for the visual determination oj .surface roughness which does not require strong rnvimnmental constrainrr such as coherent lighr and small samples of the surface in queslion. We derrnnine surface roughness by the measurement of the sharpness of the edges of an i m g e reflected in a rough srrrfoce. We choose step edges since thex will be present in many envimnmenrs, and becuuse the methods ofedge detection and localization are mature. For there initial experimenfs, we assume a common surface roughness model of simplefcnn, which we believe models milled or mlled surfaces. We show that i fwe also cumme a known shnpe forthe refictive surface anda known position for the tiewer; we nmy d c u late a roughness parameter: For our surface mughness m d e L we show that the resulting infenrip disrribution may be given in closed form. We then show the results of experiments paformed with phnar surfaces in a controlled environment and give the calculated mughness paramete,: We compare these results with the values of fhe roughness as measured with a sV1u.r projlumeter: andfmd that the results are quite different. We discuss the possibilities ihat this difference is due to the non-Gaussian ctmracter of the surface height distribution. and the possibiliiy that rhe diffeEnce arises from the drfference in measurement procedures. We nert show some extensions to other type of mughnessfunctions, ond discuss some new methods of roughness eslimation which may yield injonnation about a broader class of roughness models. Finaiij, we discuss the addilional issues in extending and applying this approach to a gzneral vision system.