A Sampling Framework for Accurate Curvature Estimation in Discrete Surfaces
IEEE Transactions on Visualization and Computer Graphics
Efficient search and verification for function based classification from real range images
Computer Vision and Image Understanding
Computer Vision and Image Understanding
Exact and interpolatory quadratures for curvature tensor estimation
Computer Aided Geometric Design
Moving parabolic approximation of point clouds
Computer-Aided Design
Curvature-aware adaptive re-sampling for point-sampled geometry
Computer-Aided Design
Estimating principal properties on triangular meshes
ICHIT'11 Proceedings of the 5th international conference on Convergence and hybrid information technology
Cooperative exploration of level surfaces of three dimensional scalar fields
Automatica (Journal of IFAC)
Curvature tensor computation by piecewise surface interpolation
Computer-Aided Design
| Hi-index | 0.00 |
Principal curvatures and the local Darboux frame are natural tools to be used during processes which involve extraction of geometric properties from three-dimensional (3-D) range data. As second-order features their estimations are highly sensitive to noise and therefore, until recent years, it was almost impractical to extract reliable results from real 3-D data. Since the use of more accurate 3-D range imaging equipment has become more popular, as well as the use of polyhedral meshes to approximate surfaces, evaluation of existing algorithms for curvature estimation is again relevant. The work presented here, makes some subtle but very important modifications to two such algorithms, originally suggested by Taubin (1995) and Chen and Schmitt (1992). The algorithms have been adjusted to deal with real discrete noisy range data, given as a cloud of sampled points, lying on surfaces of free-form objects. The results of this linear time (and space) complexity implementation were evaluated in a series of tests on synthetic and real input. We also present one of many possible uses for these extracted features in an efficient and robust application for the recovery of 3-D geometric primitives from range data of complex scenes. The application combines the segmentation, classification and fitting processes in a single process which advances monotonously through the recovery procedure. It is also very robust and does not use any least-squares fittings. The conclusion of this study is that with current scanning technology and the algorithms presented here, reliable estimates of the principal curvatures and Darboux frame can be extracted from real data and used in a large variety of tasks.