Digital Geometry in Image Processing

Digital Topology: Fundamentals 21

(a) (b)

FIGURE 1.18: Thinned pattern o btained by ESPTA (a) original 3-D object,

and (b) thinned pattern.

1.4.2 Adjacency Tree

Let C = {C

0

, C

1

, . . . C

k

} be the set of k disjoint connected components

of foreground and background of a 2-D digital picture P = (G

2

, m, n, S). It

may be noted tha t foreground components are m-connected and the back-

ground c omponents are n-connected. We further denote F ⊂ C as the set

of foreground components and B ⊂ C as the set of background components.

Two components C

i

and C

j

form an edge, if there exist p ∈ C

i

and q ∈ C

j

such that they are adjacent. In this case, if C

i

is a foreground co ...