Roughness as a Shape Measure

In this paper, we present a measure to quantify the multi-neighborhood level roughness of the surface using mean curvature. The surface is scaled to a unit sphere to enable comparison between different models with scale taken out of the comparison equation. Our roughness measure can be used as a shape indicator of the surface as it gives information regarding the vertex distribution at multiple neighborhood levels. In addition to computing the surface roughness, we use our measure as a unifying method to analyze different smoothing algorithms on different models including the effect of different vertex updating methods. We also use our measure to illustrate the differences in roughness at different neighborhood levels due to the irregular sampling of the surface. We specifically target triangle surface mesh representation for this paper, as it is the most common and other polygonal models can be converted to it by using local triangulation. Results are presented to demonstrate the usefulness of our roughness measure.