Symmetry Measure Computation for Convex Polyhedra

Authors:
Alexander V. Tuzikov;Stanislav A. Sheynin
Affiliations:
Institute of Engineering Cybernetics, Academy of Sciences of Republic Belarus, Surganova 6, 220012 Minsk, Belarus. tuzikov@mpen.bas-net.by;Institute of Engineering Cybernetics, Academy of Sciences of Republic Belarus, Surganova 6, 220012 Minsk, Belarus. sheynin@mpen.bas-net.by
Venue:
Journal of Mathematical Imaging and Vision
Year:
2002

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Abstract

The paper discusses measures and indices of different kind of symmetry (central, reflection, rotation, mirror rotation) for 3D convex shapes. The measures are based on Minkowski addition and inequalities for volume and mixed volume and are valid for convex shapes only. Symmetry index computation in 3D case is a complicated optimization problem. Taking advantage of convex polyhedra we investigate the situations when these indices can be computed efficiently.