Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation
Abstract
Estimating principal curvatures and principal directions of a surface from a polyhedral approximation with a large number of small faces, such as those produced by iso-surface construction algorithms, has become a basic step in many computer vision algorithms, particularly in those targeted at medical applications. We describe a method to estimate the tensor of curvature of a surface at the vertices of a polyhedral approximation. Principal curvatures and principal directions are obtained by computing in closed form the eigenvalues and eigenvectors of certain 3/spl times/3 symmetric matrices defined by integral formulas, and closely related to the matrix representation of the tensor of curvature. The resulting algorithm is linear, both in time and in space, as a function of the number of vertices and faces of the polyhedral surface.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Cite
Text
Taubin. "Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation." IEEE/CVF International Conference on Computer Vision, 1995. doi:10.1109/ICCV.1995.466840Markdown
[Taubin. "Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation." IEEE/CVF International Conference on Computer Vision, 1995.](https://mlanthology.org/iccv/1995/taubin1995iccv-estimating/) doi:10.1109/ICCV.1995.466840BibTeX
@inproceedings{taubin1995iccv-estimating,
title = {{Estimating the Tensor of Curvature of a Surface from a Polyhedral Approximation}},
author = {Taubin, Gabriel},
booktitle = {IEEE/CVF International Conference on Computer Vision},
year = {1995},
pages = {902-907},
doi = {10.1109/ICCV.1995.466840},
url = {https://mlanthology.org/iccv/1995/taubin1995iccv-estimating/}
}