A Maximum Set of (26,6)-Connected Digital Surfaces

Local Characterization of a Maximum Set of Digital (26,6)-Surfaces

“…Despite of all surfaces in S U are Jordan objects, some of them might be considered as pathological examples since the deletion of one of their points might yield an object that still separates its complement into two 6-components. In Section 5, we state a characterization of the subset of non-pathological surfaces of S U , which still strictly contains the family of simplicity 26-surfaces [6]. As a conclusion, the results in [6] and this work lead to a good and general enough approach to a notion of digital surface since:…”

“…In Section 5, we state a characterization of the subset of non-pathological surfaces of S U , which still strictly contains the family of simplicity 26-surfaces [6]. As a conclusion, the results in [6] and this work lead to a good and general enough approach to a notion of digital surface since:…”

“…Within the framework for Digital Topology proposed in [3] we have recently found in [6] a homogeneous (26, 6)-connected digital space E U whose set of digital surfaces S U is the largest in that class of digital spaces. In particular, the Jordan-Brouwer and Index Theorems, proved in [3] and [2] for digital manifolds of arbitrary dimensions, automatically hold for these surfaces.…”

“…In spite of these nice properties, the digital surfaces in S U were defined in [6] by constructing a continuous analogue, and thus it might not be considered a completely digital notion. In this paper we give a purely digital characterization of the family S U by the use of plates and graphs extending the Kong and Roscoe method in [8] (see Theorem 3).…”

“…This paper provides a local characterization for a set of digital surfaces S U defined in [6] by mean of continuous analogues. For this, we firstly identify the set of admisible plates for any surface S ∈ S U (i.e., the intersection S ∩ C of S with a unit cube C of Z 3 ).…”