Parameterization of Closed Surfaces for Parametric Surface Descriptio
Abstract
A procedure for the parameterization of surface meshes of objects with spherical topology is presented. The generation of such a parameterisation has been formulated and solved as a large constrained optimization problem by C. Brechbuhler (1995), 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.
Cite
Text
Quicke et al. "Parameterization of Closed Surfaces for Parametric Surface Descriptio." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2000. doi:10.1109/CVPR.2000.855840Markdown
[Quicke et al. "Parameterization of Closed Surfaces for Parametric Surface Descriptio." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2000.](https://mlanthology.org/cvpr/2000/quicke2000cvpr-parameterization/) doi:10.1109/CVPR.2000.855840BibTeX
@inproceedings{quicke2000cvpr-parameterization,
title = {{Parameterization of Closed Surfaces for Parametric Surface Descriptio}},
author = {Quicke, Michael and Brechbühler, Christian and Hug, Johannes and Blattman, Hans and Székely, Gábor},
booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
year = {2000},
pages = {1354-1360},
doi = {10.1109/CVPR.2000.855840},
url = {https://mlanthology.org/cvpr/2000/quicke2000cvpr-parameterization/}
}