Image Processing Reference
In-Depth Information
FIGURE 1.7: The border (orange pixels) and interior (black pixels) of a
connected component of foreground pixels in an (8,4) digital grid. (See color
insert.)
By using the 'surround' relationship, we can provide a more precise defi-
nition of a hole or cavity. In a 2-D digital picture, a finite background com-
ponent that is adjacent to and surrounded by a foreground component X is
called a hole in X. For a three-dimensional digital picture, such a background
component is called a cavity. In Fig. 1.6, the finite background component
containing those orange pixels is a hole in the set of foreground pixels forming
the connected component.
1.3.3 Boundary and Interior
In a digital picture, a foreground point is said to be isolated, if it has no
foreground neighbor. For example, in Fig. 1.3(b), two black foreground points
are isolated. We should note that in that figure the orange pixels are also part
of the foreground pixels and form a connected component using 4-adjacency.
We call a foreground point a border point, if it is n-adjacent to one or more
background points in a digital grid of (m,n) type of adjacency; otherwise,
it is an interior point. The boundary or border of a connected component
of foreground pixels X is formed by the set of all border points in X, and
similarly, its interior is formed by all interior points belonging to it. In Fig.
1.7, the border and interior of a connected foreground component are shown
by orange and black pixels, respectively.
