Local Characterization of a Maximum Set of Digital (26,6)-Surfaces
This paper provides a local characterization for a set of digital surfaces S U defined in  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 ℤ3 ). Then, the characterization is given in terms of a graph representing the intersection of plates. In addition, we establish a further condition that detects the digital surfaces in S U which are strongly separating objects.
The family S U consists of all objects which are a digital surface in some homogeneous (26,6)-connected digital space in the sense of . Moreover, the subset of strongly separating surfaces of S U contains the family of simplicity 26-surfaces and other surfaces in literature as well.
KeywordsDigital Object Unit Cube Adjacency Pair Digital Space Polyhedral Complex
- 1.Ayala, R., Domínguez, E., Francés, A.R., Quintero, A.: DGCI 1997. LNCS, vol. 1347, pp. 139–150. Springer, Heidelberg (1997)Google Scholar
- 2.Ayala, R., Domínguez, E., Francés, A.R., Quintero, A.: A Digital Index Theorem. Int. J. Patter Recog. Art. Intell. 15(7), 1–22 (2001)Google Scholar
- 7.Couprie, M., Bertrand, G.: Simplicity Surfaces: a new definition of surfaces in ℤ3. In: SPIE Vision Geometry, vol. 3454, pp. 40–51 (1998)Google Scholar
- 11.Rourke, C.P., Sanderson, B.J.: Introduction to Piecewise-Linear Topology. Ergebnisse der Math. 69 (1972)Google Scholar