ESTIMATION OF CURVATURES IN POINT SETS BASED ON GEOMETRIC ALGEBRA

Helmut Seibert, Dietmar Hildenbrand, Meike Becker, Arjan Kuijper

2010

Abstract

For applications like segmentation, feature extraction and classification of point sets it is essential to know the principal curvatures and the corresponding principal directions. For the purpose of curvature estimation conformal geometric algebra promises to be a natural mathematical language: Local curvatures can be described with the help of osculating circles or spheres. On one hand, conformal geometric algebra is able to directly compute with these geometric objects, as well as with lines and planes needed for the description of vanishing curvature. On the other hand, distance measures for fitting these objects into point sets can be handled in a linear way, leading to efficient algorithms. In this paper we use conformal geometric algebra advantageously in order to locally compute continuous curvatures as well as principal curvatures of point sets without the need of costly pre-processing of raw data. We show results on artificial and real data. Numerical verification on artificial data shows the accuracy of our approach. Furthermore, the results are obtained in a fast manner and are also visually satisfactory.

Paper Citation

in Harvard Style

Seibert H., Hildenbrand D., Becker M. and Kuijper A. (2010). ESTIMATION OF CURVATURES IN POINT SETS BASED ON GEOMETRIC ALGEBRA . In Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2010) ISBN 978-989-674-028-3, pages 12-19. DOI: 10.5220/0002817800120019

in Bibtex Style

@conference{visapp10,
author={Helmut Seibert and Dietmar Hildenbrand and Meike Becker and Arjan Kuijper},
title={ESTIMATION OF CURVATURES IN POINT SETS BASED ON GEOMETRIC ALGEBRA},
booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2010)},
year={2010},
pages={12-19},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002817800120019},
isbn={978-989-674-028-3},
}

in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2010)
TI - ESTIMATION OF CURVATURES IN POINT SETS BASED ON GEOMETRIC ALGEBRA
SN - 978-989-674-028-3
AU - Seibert H.
AU - Hildenbrand D.
AU - Becker M.
AU - Kuijper A.
PY - 2010
SP - 12
EP - 19
DO - 10.5220/0002817800120019