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Approximating Imprecise Planar Tesselations with Voronoi Diagrams

Authors:
Narciso Javier Aguilera Centeno
Belén Palop del Rio
Hebert Pérez-Rosés

Keywords: Planar tesselations; Voronoi Diagram; Inverse Voronoi Diagram.

Abstract:
Natural growth processes tend to generate shapes in the form of imprecise planar tesselations, where the tiles do not match exactlyand leave some space among them. In this paper we model these tesselations by means of Voronoi Diagrams. We look for the set of 2D-sites whose Voronoi Diagram better approximates the given imprecise tessellation. Since we conjecture the Inverse Voronoi Problem (also known as Voronoi-fitting Problem) to be NP-hard, we describe in this paper a heuristic algorithm that looks for the optimal set of sites. We study the algorithm’s performance and validity on a set of tesselations extracted from real-life images. With the aid of these experiments, we find optimal values for a tunable parameter of the algorithm. In the long run, our main goal is to develop a tool that can automatically analize an image of a tessellation that is expected to be modelled with a Voronoi Diagram (e.g., pictures from chrystals, trees in a forest, etc), and decide whether the growth process was or was not affected by some external force. This inverse computation should be able tell how far is the image from its theoretical model.

Pages: 19 to 23

Copyright: Copyright (c) IARIA, 2016

Publication date: November 13, 2016

Published in: conference

ISSN: 2519-8645

ISBN: 978-1-61208-520-3

Location: Barcelona, Spain

Dates: from November 13, 2016 to November 17, 2016