A new algorithmic approach to the computation of Minkowski functionals of polyconvex sets

Authors:
Simone Klenk;Volker Schmidt;Evgueni Spodarev
Affiliations:
Universität Ulm, Abteilung Stochastik, Ulm, Germany;Universität Ulm, Abteilung Stochastik, Ulm, Germany;Universität Ulm, Abteilung Stochastik, Ulm, Germany
Venue:
Computational Geometry: Theory and Applications
Year:
2006

Citing 3
Cited 1

Marching cubes: A high resolution 3D surface construction algorithm

SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Morphological Image Analysis: Principles and Applications

Morphological Image Analysis: Principles and Applications
Image Analysis and Mathematical Morphology

Image Analysis and Mathematical Morphology

Algorithms for the computation of the Minkowski functionals of deterministic and random polyconvex sets

Image and Vision Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

An algorithm is proposed for the simultaneous computation of all Minkowski functionals (except for the volume) of sets from the convex ring in Rd discretized with respect to a given regular lattice. For this purpose, a polyhedral approximation is used to reconstruct their boundary structure. In the planar case d = 2, the performance and precision of the algorithm is studied on various examples of particular polyconvex sets. The algorithm is implemented in Java for two different approximation systems. The results of numerical experiments are compared with those obtained by other methods known in the literature.