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A new algorithmic approach to the computation of Minkowski functionals of polyconvex sets. (English) Zbl 1104.65012

A new approach to the computation of Minkowski functionals for finite unions of convex sets in \(\mathbb{R}^d\), \(d\geq 2\), is presented. The proposed algorithm allows the simultaneous computation of all Minkowski functionals, except for the volume, and is quite flexible since it depends on an \(d\)-ple of free parameters which have the meaning of dilation radii. The computations can be arranged in such a way that one single scan of the image is required. Some suggestions for an appropriate choice of dilation radii and an upper bound on the computational error are given. In particular, the case \(d= 2\) is widely studied and the results of numerical experiments are presented, discussed and compared to those of conventional computation methods.

MSC:

65D15 Algorithms for approximation of functions

Software:

GeoStoch
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References:

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