A topological sampling theorem for Robust boundary reconstruction and image segmentation

Authors:
Hans Meine;Ullrich Köthe;Peer Stelldinger
Affiliations:
University of Hamburg, 22527 Hamburg, Germany;University of Heidelberg, 69120 Heidelberg, Germany;University of Hamburg, 22527 Hamburg, Germany
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

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 @a-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.