Biomedical Engineering Reference
In-Depth Information
Figure 7.
Example of grassfire propagation using an active contour model. The potential
surface shows the valley in the distance transform function. Other images show the evolution
of the snake toward the skeleton of the object. Reprinted with permission from [19].
Copyright c
1992, IEEE.
tion within the same framework to define the skeleton. However, this application
has the probability of suffering from situations where noise plays a dominant role
in determining the image gradient quality. Figure 7 depicts examples of skele-
tonization using this technique. Clearly, this formulation requires well-defined
boundaries, which are absent in most medical images.
Lobregt et al. [20] tried to implicitly address the challenge due to fuzzy bound-
aries in medical images by controlling the local curvature of the contour in a local
coordinate system. In this work, a local coordinate system was defined with res-
pect to the vertex of the contour, and the change of curvatures in local and global
coordinate systemwas taken into account. Thus, instead of global curvature varia-
tion, the contour deforms based on the variation in local and global curvature. This
in turn retains the length of the contour, which otherwise has a shrinking property.
It is important to mention that the curvature in this approach has been attributed
to a direction both globally and locally. The approach intends that internal forces
that act on the vertices should have the same (radial) direction as the curvature
vectors. This means that internal forces can be derived from the curvature vectors
by modifying only their lengths. Second, in order to reduce local curvature with-
out affecting areas of constant curvature, the lengths of the internal force vectors
