Estimating the principal curvatures and the Darboux frame from real 3D range data

As products of second-order computations, estimations of principal curvatures are highly sensitive to noise. Due to the availability of more accurate 3D range imaging equipment, evaluation of existing algorithms for the extraction of these invariants and other useful features from discrete 3D data, is now relevant. The work presented here, makes some subtle but very important modifications to two such algorithms, originally suggested by Taubin [14] and Chen and Schmitt [2]. The algorithms have been adjusted to deal with real discrete noisy range data. The results of this implementation were evaluated in a series of tests on synthetic and real input yielding reliable estimations. Our conclusion is that with current scanning technology and the algorithms presented here, reliable estimates of the principal curvatures and the Darboux frame can be extracted from real data and used in a variety of more comprehensive tasks.