Abstract
The paper considers a problem of minimization the volume of Minkowski sum or mixed volume functionals for convex polyhedral shapes. It is assumed that one of the shapes can be rotated about arbitrary axis through arbitrary angle. This problem is of interest for some approaches developed for shape pose determination, invariant shape comparison, shape symmetry analysis. It is shown that the problem can be solved efficiently, i.e. there exists a finite number of rotation axes and rotation angles which are candidates for the best solution. Some implementations problems of the developed algorithm and results of experiments are discussed.
The authors were supported by the INTAS grant N 96-785.
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© 2002 Kluwer Academic/Plenum Publishers
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Tuzikov, A.V., Sheynin, S.A. (2002). Minkowski Sum Volume Minimization for Convex Polyhedra. In: Goutsias, J., Vincent, L., Bloomberg, D.S. (eds) Mathematical Morphology and its Applications to Image and Signal Processing. Computational Imaging and Vision, vol 18. Springer, Boston, MA. https://doi.org/10.1007/0-306-47025-X_5
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DOI: https://doi.org/10.1007/0-306-47025-X_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-7862-4
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