Introduction to digital level layers

Abstract

We introduce the notion of Digital Level Layer, namely the subsets of ℤd characterized by double-inequalities h1 ≤ f(x) ≤ h2. The purpose of the paper is first to investigate some theoretical properties of this class of digital primitives according to topological and morphological criteria. The second task is to show that even if we consider functions f of high degree, the computations on Digital Level Layers, for instance the computation of a DLL containing an input set of points, remain linear. It makes this notion suitable for applications, for instance to provide analytical characterizations of digital shapes. © 2011 Springer-Verlag.