a Comparison of Gaussian And Mean Curvature Estimation Methods on Triangular Meshes of Range Image Data

Evgeni Magid, Octavian Soldea, and Ehud Rivlin.
A Comparison of Gaussian and mean curvature estimation methods on triangular meshes of range image data.
CVIU, 107(3):139-159, 2007

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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, coputer graghics, geometric modeling, and industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Four different algorithms and their modifications were tested on triangular meshes that represent tessellations 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 from which these meshes originated. The algorithms were also tested on range images of geometric objects. The results were compared with the analytic values of the Gaussian and mean curvatures of the scanned geometric objects. This work manifests the best algorithms suited for Gaussian and mean curvature estimation, and shows that different algorithms should be employed to compute the Gaussian and mean curvatures.

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Bibtex Entry

@article{MagidSR07a,
  title = {A Comparison of Gaussian and mean curvature estimation methods on triangular meshes of range image data},
  author = {Evgeni Magid and Octavian Soldea and Ehud Rivlin},
  year = {2007},
  journal = {CVIU},
  volume = {107},
  number = {3},
  pages = {139-159},
  keywords = {Geometric modeling; Principal curvatures; Gaussian 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, coputer graghics, geometric modeling, and industrial and biomedical engineering. This work considers different computational schemes for local estimation of intrinsic curvature geometric properties. Four different algorithms and their modifications were tested on triangular meshes that represent tessellations 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 from which these meshes originated. The algorithms were also tested on range images of geometric objects. The results were compared with the analytic values of the Gaussian and mean curvatures of the scanned geometric objects. This work manifests the best algorithms suited for Gaussian and mean curvature estimation, and shows that different algorithms should be employed to compute the Gaussian and mean curvatures.}
}