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Parameterization of Closed Surfaces for Parametric Surface Description

M. Quicken, Ch. Brechb├╝hler, 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


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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  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}