Computing 3d symmetry sets; a case study

Authors:
Arjan Kuijper;Ole Fogh Olsen
Affiliations:
Image Group, IT-University of Copenhagen, Copenhagen, Denmark;Image Group, IT-University of Copenhagen, Copenhagen, Denmark
Venue:
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Year:
2005

Citing 5
Cited 2

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Computation of the shock scaffold for unorganized point clouds in 3D

CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition

Alternative 2D Shape Representations using the Symmetry Set

Journal of Mathematical Imaging and Vision
Deriving the Medial Axis with geometrical arguments for planar shapes

Pattern Recognition Letters

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Abstract

In this paper we discuss the implementation of methods to derive 3D Symmetry Sets, given a parameterized shape, as well as an unorganized point cloud. It presents a geometric method to derive the Symmetry Set, that is an extension of the one given in [6]. Although the mathematics is a simple extension of the 2D case, the visualization, numerical computations and their stability are much more complicated. An example is given by means of an ellipsoid. In this example the Symmetry Set can be computed exactly and results can be compared to the ground truth.