Minimal Offsets That Guarantee Maximal or Minimal Connectivity of Digital Curves in nD

摘要

In this paper we investigate an approach of constructing a digital curve by taking the integer points within an offset of a certain radius of a continuous curve. Our considerations apply to digitizations of arbitrary curves in arbitrary dimension n. As main theoretical results, we first show that if the offset radius is greater than or equal to n~(1/2)/2; then the obtained digital curve features maximal connectivity. We also demonstrate that the radius value n~(1/2)/2 is the minimal possible that always guarantees such a connectivity. Moreover, we prove that a radius length greater than or equal to (n-1)~(1/2)/2 guarantees 0-connectivity, and that this is the minimal possible value with this property. Thus, we answer the question about the minimal offset size that guarantees maximal or minimal connectivity of an offset digital curve.