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

Peer Stelldinger, Ullrich Köthe

Abstract: We define strongr-similarity and the morphing distance to bound geometric distortions between shapes of equal topology. We then derive a necessary and sufficient condition for a set and its digitizations to be r-similar, 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.