Continuous digitization in Khalimsky spaces

Authors:
Erik Melin
Affiliations:
Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden
Venue:
Journal of Approximation Theory
Year:
2008

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Abstract

A real-valued function defined on R^n can sometimes be approximated by a Khalimsky-continuous mapping defined on Z^n. We elucidate when this can be done and give a construction for the approximation. This approximation can be used to define digital Khalimsky hyperplanes that are topological embeddings of Z^n into Z^n^+^1. In particular, we consider Khalimsky planes in Z^3 and show that the intersection of two non-parallel Khalimsky planes contains a curve homeomorphic to the Khalimsky line.