Local characterization of a maximum set of digital (26, 6)-surfaces

We introduce a new family SS of surfaces in the discrete space Z3Z3 for the usual (26, 6)-adjacency that strictly contains the family of simplicity 26-surfaces and other objects considered as surfaces in the literature. Actually, SS characterizes the strongly 6-separating objects of a family SU of digital surfaces defined by means of continuous analogues. The family SU consists of all objects whose continuous analogue is a surface in some homogeneous (26, 6)-connected digital space as defined in the approach to Digital Topology introduced in [R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, Weak Lighting Functions and Strong 26-surfaces. Theoretical Computer Science   283 (2002) 29–66.]. Therefore, SS is the largest possible set of surfaces in Z3Z3 in that setting.