Topologically Correct Image Segmentation Using Alpha Shapes

Peer Stelldinger, Ullrich Köthe, Hans Meine

in: A. Kuba, L. Nyul, K. Palagyi (Eds.): Discrete Geometry for Computer Imagery, Proc. DGCI 2006, Lecture Notes in Computer Science 4245, pp. 542-554, Berlin: Springer, 2006. (note: this article is © Springer-Verlag)

Abstract

Existing theories on shape digitization impose strong constraints on feasible shapes and require error-free measurements. We use Delaunay triangulation and alpha-shapes to prove that topologically correct segmentations can be obtained under much more realistic conditions. Our key assumption is that sampling points represent object boundaries with a certain maximum error. Experiments on real and generated images demonstrate the good performance and correctness of the new method.

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