Authors:
Helmut Seibert
1
;
Dietmar Hildenbrand
2
;
Meike Becker
2
and
Arjan Kuijper
1
Affiliations:
1
Fraunhofer Institute for Computer Graphics Research, Germany
;
2
Technical University of Darmstadt, Germany
Keyword(s):
Principal curvature, Curvature estimation, Geometric algebra, Point set.
Related
Ontology
Subjects/Areas/Topics:
Computational Geometry
;
Computer Vision, Visualization and Computer Graphics
;
Image and Video Analysis
;
Image Formation and Preprocessing
;
Surface Geometry and Shape
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.
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