Optimal parameter selection for derivative estimation from range images

Range images may be used for a variety of applications in object recognition, inspection and reverse engineering. In many of these applications it is important to obtain good estimates of the local surface curvature. Good curvature estimates require good derivative estimates, but the estimation of derivatives from sampled data is highly susceptible to noise. In this paper, we introduce a new way of characterizing range data by a single parameter. From this characterization we show how to make an optimal choice of whatever parameters there are in a particular derivative estimation method, and obtain an estimate of the error one might expect. Finally, we show how the analysis may be applied to measuring derivatives on a cylinder.