A topological sampling theorem for Robust boundary reconstruction and image segmentation

作     者：Meine, Hans Koethe, Ullrich Stelldinger, Peer 

作者机构：Univ Hamburg Cognit Syst Lab D-22527 Hamburg Germany Heidelberg Univ D-69120 Heidelberg Germany 

出 版 物：《DISCRETE APPLIED MATHEMATICS》 (离散应用数学)

年 卷 期：2009年第157卷第3期

页      面：524-541页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Alpha-shapes Geometric sampling theorem Delaunay triangulation Edgel linking Topology preservation 

摘      要：Existing theories on shape digitization impose strong constraints on admissible shapes, and require error-free data. Consequently, these theories are not applicable to most real-world situations. In this paper, we propose a new approach that overcomes many of these limitations. It assumes that segmentation algorithms represent the detected boundary by a set of points whose deviation from the true contours is bounded. Given these error bounds, we reconstruct boundary connectivity by means of Delaunay triangulation and alpha-shapes. We prove that this procedure is guaranteed to result in topologically correct image segmentations under certain realistic conditions. Experiments on real and synthetic images demonstrate the good performance of the new method and confirm the predictions of our theory. (c) 2008 Elsevier B.V. All rights reserved.