Estimating affine-invariant structures on triangle meshes
Thales Vieira, Dimas Martinez, Maria Andrade, Thomas Lewiner
Abstract:
Affine invariant measures are powerful tools to develop robust shape descriptors that can be applied, for example, to shape matching, shape retrieval, or symmetry detection problems. In this work we introduce estimators for the affine structure of surfaces represented by triangle meshes, i.e. affine co-normal and normal vectors, affine curvature tensors, affine mean and Gaussian curvatures, and affine principal directions and curvatures. The proposed method estimates the affine normal using a finite differences scheme together with a least-squares approximation, followed by a weighted average strategy to approach discrete affine curvature tensors. When compared to the exact geometric measures of analytic models, experiments on regular meshes obtain small error, which decreases for finer meshes, and outperforms the state-of-the-art method in some cases. Experiments to evaluate affine invariance show that the difference between measures before and after equi-affine transformations remains small even after large deformations.Downloads:
BibTeX:
@inproceedings{affine_mesh_sibgrapi,author = {Thales Vieira and Dimas Martinez and Maria Andrade and Thomas Lewiner},
title = {Estimating affine-invariant structures on triangle meshes},
year = {2016},
month = {october},
booktitle = {Sibgrapi 2016 (Computers & Graphics)},
publisher = {Elsevier},
address = {Sao Paulo, Brazil},
doi = {10.1016/j.cag.2016.07.008},
url = {\url{http://thomas.lewiner.org/pdfs/affine_mesh_sibgrapi.pdf}}
}