Shape Preservation During Digitization: Tight Bounds Based on the Morphing Distance

Peer Stelldinger and Ullrich Köthe

in: B. Michaelis, G. Krell (eds.): Pattern Recognition, Proc. of 25th DAGM Symposium, Magdeburg 2003, Lecture Notes in Computer Science 2781, pp. 108-115, Heidelberg: Springer, 2003 (note: this article is © Springer-Verlag)

Abstract

We define strong r­similarity and the morphing distance to bound geometric distortions between shapes of equal topology. We then derive a necessary and su#cient condition for a set and its digitizations to be r­similar, regardless of the sampling grid. We also extend these results to certain gray scale images. Our findings are steps towards a theory of shape digitization for real optical systems.

This paper builds on the paper "Shape Preserving Digitization of Ideal and Blurred Binary Images" which should be read before.

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