Image Processing Reference
In-Depth Information
6.2 Medial Axis Transform (MAT)
Medial Axis Transform (MAT)[21] of an image consists of a set of maximal
disks (or hyperspheres) that could be contained within the pattern (or fore-
ground). An interesting property of a medial point (the center of a maximal
disk (CMD)) is that it touches the boundary of the object at two or more
points (refer Fig. 6.6). This property leads to the development of a simple
FIGURE 6.6: A few examples of maximal disks of an object in 2-D Euclidean
space.
but straightforward algorithm for the computation of MAT. Let the bound-
ary points of the object form a set ∆. For every foreground point q (∈ Σ),
its closest boundary point(s) in ∆ are computed. If p has more than one such
point, it is declared as a medial point and the distance of the boundary point
is taken as the radius of the medial (or maximal) disk at that point. In the
formation of this set of medial points, the distance function plays an impor-
tant role. The number of medial points and the shape of axes depend upon the
choice of the distance function. The MAT could be computed more e
ciently
using distance transforms. This we discuss in the following subsections.
