Image Processing Reference
In-Depth Information
Algorithm 11: Medial Axis Transform (MAT) from Distance Transform
(DT) of an Object
Algorithm: MAT through DT (MATDT)
Input: Bilevel image.
Output: A set of medial points with centers and radii of the maximal
disks.
1. Compute the distance transform of the image.
2. Scan the distance mapped array as follows:
2a. For each point q in the distance mapped array, check whether its
distance value (D(q)) is a maximum among its neighbors. The
neighborhood type is determined as (D(q)−1) mod p, where p is
the length of the neighborhood sequence B.
2b. If the point is a local maximum, declare it as a medial point and
store the center of the disk and the radius at that point as
D(q)−1 .
End MAT through DT (MATDT)
from the values of the radius of a Euclidean circle (specified in the form of
(a,b) as discussed in Section 6.1.4), the maximum radii of its 4-neighbors and
8-neighbors, which could be contained in the circle, are computed and used.
It requires additional storage space for storing the tables or arrays of these
mappings.
6.2.2 Reduced Centers of Maximal Disks (RCMD)
As shown in Fig. 6.6, medial disks in a MAT, may overlap among them-
selves. One of the properties of these disks is that none of them are contained
in any other from the set. However, it does not ensure its coverage by more
than one disk from the remaining members. This implies that a disk that is
covered by a few other medial disks, becomes redundant in the reconstruction
of the object from the MAT. A set of medial disks that can fully reconstruct
the object and has no redundant disk, is called a reduced set of centers of
maximal disks (RCMD) [204]. An algorithm based on a greedy approach for
obtaining an RCMD from the MAT is discussed in [26]. We outline the ap-
proach in the context of 2-D images here.
In this technique a temporary array is used for recording the number of
medial disks covering a pixel. We refer to this array as the count array. This
is computed while performing the reconstruction of object points from the
medial disks of the MAT. Next, each medial circle is checked to see whether it
has all the pixels inside with counts of more than one. In that case, the circle is
