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Parameterization of Closed Surfaces for Parametric Surface Description

M. Quicken, Ch. Brechbühler, J. Hug, H. Blattmann and G. Székely
IEEE Computer Society Conference on Computer Vision and Pattern Recognition CVPR 2000
Hilton Head Island SC, USA, June 2000

Abstract

A procedure for the parameterization of surface meshes of objects with spherical topology is presented. The generation of such a parameterization has been formulated and solved as a large constrained optimization problem by Brechbühler, but the convergence of this algorithm becomes unstable for object meshes consisting of several thousand vertices. We propose a new more stable algorithm to overcome this problem using multi-resolution meshes. A triangular mesh is mapped to a sphere by harmonic mapping. Next, a mesh hierarchy is constructed. The coarsest level is then optimized using a modification of the original procedure to map object surfaces to the unit sphere. The result is used as a starting point for the mapping of the next finer mesh, a process which is repeated until the final result is obtained. The new approach is compared to the original one and some parameterized object surfaces are presented.


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@InProceedings{eth_biwi_00208,
  author = {M. Quicken and Ch. Brechb\"uhler and J. Hug and H. Blattmann and G. Székely},
  title = {Parameterization of Closed Surfaces for Parametric Surface Description},
  booktitle = {IEEE Computer Society Conference on Computer Vision and Pattern Recognition CVPR 2000},
  year = {2000},
  month = {June},
  pages = {354--360},
  volume = {1},
  publisher = {IEEE Computer Society},
  keywords = {surface description, parameterization}
}