Surface digitizations by dilations which are tunnel-free

Abstract

In this article we study digital topology with methods from mathematical morphology. We introduce reconstructions by dilations with appropriate continuous structural elements and prove that notions known from digital topology can be defined by continuous properties of this reconstruction. As a consequence we determine the domains for tunnel-free surface digitizations. It will be proven that the supercover and the grid-intersection digitization of every surface with or without boundary is always tunnel-free. © Springer-Verlag Berlin Heidelberg 2000.