Parameter-free and Multigrid Convergent Digital Curvature Estimators

Jérémy Levallois, David Coeurjolly, Jacques-Olivier Lachaud

18th International Conference on Discrete Geometry for Computer Imagery (DGCI 2014) September 2014

Abstract

In many geometry processing applications, the estimation of differential geometric quantities such as curvature or normal vector field is an essential step. Focusing on multigrid convergent estimators, most of them require a user specified parameter to define the scale at which the analysis is performed (size of a convolution kernel, size of local patches for polynomial fitting, etc). In a previous work, we have proposed a new class of estimators on digital shape boundaries based on Integral Invariants. In this paper, we propose new variants of these estimators which are parameter-free and ensure multigrid convergence in 2D. As far as we know, these are the first parameter-free multigrid convergent curvature estimators.

Type

Conference paper

Publication

18th International Conference on Discrete Geometry for Computer Imagery (DGCI 2014)

Caption: (Left) Mean curvature mapped on “bunny” at different resolution using Hˆl∗ (yellow color is the highest curvature, blue the lowest). (Right) First principal direction on “bunny” using kˆl∗ estimator.

@inproceedings{dcoeurjo_DGCI14_parameter,
      author = {Jérémy Levallois and David Coeurjolly and Jacques-Olivier Lachaud},
      booktitle = {18th International Conference on Discrete Geometry
for Computer Imagery (DGCI 2014)},
      editor = {E. Barcucci, S. Rinaldi, A. Frosini},
      language = {en},
      month = {September},
      publisher = {Springer Verlag},
      series = {Lecture Notes in Computer Science},
      title = {Parameter-free and Multigrid Convergent Digital Curvature Estimators},
      url = {http://liris.cnrs.fr/publis/?id=6703},
      year = {2014}
}