Digital lighting functions

Abstract

Abstract. In this paper a notion of lighting function is introduced as an axiomatized formalization of the "face membership ruleg' suggested by Kovalevsky. These functions are defined in the context of the framework for digital topology previously developed by the authors. This enlarged framework provides the (a, fl)-connectedness (~, fl E {6, 18, 26}) defined on 2[ 3 within the graph-based approach to digital topology. Furthermore, the Kong-Roscoe (c~,fl)-surfaces, with (a,~) 5~ (6,6), (18,6), are also found as particular cases of a more general notion of digital surface.

Topology on Digital Label Images

“…Some ways to associate labels to points in X that are not xels are discussed in [44,51]. We have proposed, in [22], our own modus operandi to embed a binary digital image defined on Z n in a binary image defined on F n .…”

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

“…Several examples of (homogeneous) (26, 6)-connected digital spaces (R 3 , f) can be found in [1,3,5] as well as examples of (k, k)-connected spaces for k, k ∈ {6, 18, 26}.…”

“…This notion of digital surface is closely related to the families of 26-connected digital surfaces quoted in the Introduction. Actually, each of these families agrees or is contained in the set of digital surfaces of a particular homogeneous (26, 6)-connected digital space; see [1,3,5]. Moreover, in [6] we give a homogeneous (26, 6)-connected digital space E U = (R 3 , f U ) whose set of digital surfaces is the largest in this class of digital spaces.…”

Universal Spaces for $(k, \overline{k})-$ Surfaces

“…It suffices to find an object O ⊇ O such that st 3 (β; O ) = st 3 (β; O) and f (O , δ) = 1 for each cell δ ∈ {β, α 1 , α 2 }. In these conditions, it is readily checked that β(O, O ) is either empty or equal to the non-connected set {α 1 …”

“…and, in addition, it is homogeneous in 1 We often drop the "f " from the notation and also write the sense that the continuous analogue of any object O does not change under isometries ϕ :…”