On surface curvature computation from level set contours

Abstract

The authors consider the 3-D shape representation problem for a class of range image where the natural model of the acquired range data is in the form of level set contours (equidistance contours), as exemplified by a moire interferometry range system. They present a novel surface curvature computation scheme that directly computes the surface curvatures (the principal curvatures, Gaussian curvature, and mean curvature) from the equidistance contours without any explicit computations or implicit estimates of partial derivatives. They show how the special nature of the equidistance contours, specifically. the dense information of the surface curves in the 2-D contour plane, turns into an advantage for the computation of the surface curvatures. The approach is based on using simple geometric construction to obtain the surface normals, the normal sections, and the normal curvatures. This method is general and can be extended to any dense range image data. Computation results on both real and synthesized equidistance range contours are shown. >