a Comparison of Gaussian And Mean Curvatures Estimation Methods on Triangular Meshes

Tatiana Surazhsky, Evgeni Magid, Octavian Soldea, Gershon Elber, and Ehud Rivlin.
A comparison of Gaussian and mean curvatures estimation methods on triangular meshes.
In ICRA, 1021-1026, 2003

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Abstract

Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Five different algorithms and their modifications were tested on triangular meshes that represent tesselations of synthetic geometric models. The results were compared with the analytically computed values of the Gaussian and mean curvatures of the non uniform rational B-spline (NURBs) surfaces, these meshes originated from. This work manifests the best algorithms suited for total (Gaussian) and mean curvature estimation, and shows that indeed different algorithms should be employed to compute the Gaussian and mean curvatures.

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Bibtex Entry

@inproceedings{SurazhskyMSER03i,
  title = {A comparison of Gaussian and mean curvatures estimation methods on triangular meshes.},
  author = {Tatiana Surazhsky and Evgeni Magid and Octavian Soldea and Gershon Elber and Ehud Rivlin},
  year = {2003},
  booktitle = {ICRA},
  pages = {1021-1026},
  keywords = {Geometric modeling, principal curvatures, Gaussian curvature, total curvature, mean curvature, polygonal mesh, triangular mesh, range data},
  abstract = {Estimating intrinsic geometric properties of a surface from a polygonal mesh obtained from range data is an important stage of numerous algorithms in computer and robot vision, computer graphics, geometric modeling, industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Five different algorithms and their modifications were tested on triangular meshes that represent tesselations of synthetic geometric models. The results were compared with the analytically computed values of the Gaussian and mean curvatures of the non uniform rational B-spline (NURBs) surfaces, these meshes originated from. This work manifests the best algorithms suited for total (Gaussian) and mean curvature estimation, and shows that indeed different algorithms should be employed to compute the Gaussian and mean curvatures.}
}