Image Processing Reference
In-Depth Information
structure of the skeleton has a thickness of a unit pixel and it preserves the
topological properties of the objects, such as connectivity of patterns and the
cavities or holes inside. As discussed there, skeletonization is usually carried
out by iterative deletion of points lying at the present outermost layer of the
skinned object. If the removal of a point does not introduce any decomposition,
opening in a hole, or erosion of the pattern, the point is safe for deletion. Such
a point is said to be simple. The checking for condition of removal of a point
is a sequential operation of considering the effect of progressive deletion of
points. One such condition for testing a point to be declared as simple in
an 8-connected pattern is given in Section 1.4.1, in the discussion of the safe
point thinning algorithm (SPTA). We consider here another example of the
safe point testing condition using the Hilditch number [98]. It is the number
of components among the 8-neighbors of a point. If this number is more than
one, the point is not safe for deletion, otherwise it is declared as a simple point.
The method for obtaining the Hilditch number is explained with the help of
Fig. 6.10. Let m
i
, 1 ≤i ≤ 8 be variables with the values from the neighboring
pixels as either 1 (belonging to foreground) or 0 (belonging to background).
Then the Hilditch number X
H
(q) is given by the following [204]:
4
X
H
(q) =
b
j
(6.3)
j=1
where,
1
if (m
2j−1
= 0) and ((m
2j
= 1) or (m
2j+1
= 1)).
b
j
=
(6.4)
0
otherwise.
In the above computation m
9
is equated to m
1
.
In the conventional thinning algorithms [130] (refer to the safe point thin-
ning algorithm (SPTA) discussed in Section 1.4.1 of Chapter 1) the boundary
points are classified into several groups depending upon the position of the
background pixel in its neighborhoods. For example, if any of the 4 neigh-
bors belongs to the background, the pixel is called an edge boundary point.
Moreover, if its left edge neighbor is 0, it is also called a left edge boundary
point. Similarly, other types are right, top, and bottom edge boundary points.
A boundary pixel could belong to more than one categories as a combination
of edge points may be empty. Usually at each iteration the deletion of bound-
ary points are carried out sequentially for the same types of boundary points.
Thus an iteration consists of scanning all groups of boundary points, one after
another. The strategy is followed to avoid any bias or preferential treatment
in the deletion or retainment of pixels along a specific direction in the image.
This aims at keeping the thinned pattern in equidistant regions of the objects
from the boundary points. However, layer-wise removal of simple points do
not require any check on the types of edge points, as candidates for deletion.
The kth layer of the DT provides a set of pixels, which could be checked for
their safe removal without bothering about the directionality of removal. In
