Document Type
Article
Publication Title
2016 29th SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI)
Version
Final Published Version
Publication Date
2016
Abstract
We analyze the correctness of an O(n log n) time divide-and-conquer algorithm for the convex hull problem when each input point is a location determined by a normal distribution. We show that the algorithm finds the convex hull of such probabilistic points to precision within some expected correctness determined by a user-given confidence value phi. In order to precisely explain how correct the resulting structure is, we introduce a new certificate error model for calculating and understanding approximate geometric error based on the fundamental properties of a geometric structure. We show that this new error model implies correctness under a robust statistical error model, in which each point lies within the hull with probability at least φ, for the convex hull problem.
Publisher's Statement
Copyright 2016 Taylor & Francis Group. The published version of this article can be found here: http://doi.org/10.1109/SIBGRAPI.2016.016
DOI
http://doi.org/10.1109/SIBGRAPI.2016.016
Citation
F. B. Atalay, S. A. Friedler and D. Xu, "Convex Hull for Probabilistic Points," 2016 29th SIBGRAPI Conference on Graphics, Patterns and Images (SIBGRAPI), Sao Paulo, 2016, pp. 48-55.