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

We define strong r-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.

• Type: Conference
• Year: 2003
• Where: DAGM
• Authors: Peer Stelldinger, Ullrich Köthe
• Keywords: Certain Gray Scale, DAGM 2003, Equal Topology, Geometric Distortions