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Distributed boundary tracking using alpha and Delaunay-Cech shapes


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Opened Access Distributed boundary tracking using alpha and Delaunay-Cech shapes
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Author: Chintakunta, Harish
Krim, Hamid
Date: 2013
Published in: Image-A : Applicable Mathematics in Image Engineering, 3 (6), 33-36
Document type: Article
Abstract: We demonstrate real time tracking of systematic failures in sensor networks, using distributed computation of the α−shape derived from the network. More generally, our work may be applied to tracking the boundary of any time varying object, whose data is captured in the form of a point cloud. We also demonstrate the use of a new geometric object called the Delaunay-Cech shape, which is geometrically more appropriate than an ˇ α−shape for some cases. For a given point set S in a plane, we develop a distributed algorithm to compute the α−shape of S. α−shapes are well known geometric objects which generalize the idea of a convex hull, and provide a good definition for the shape of S. We assume that the distances between pairs of points which are closer than a certain distance r > 0 are provided, and we show constructively that this information is sufficient to compute the alpha shapes for a range of parameters, where the range depends on r.
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