Biomedical Engineering Reference
In-Depth Information
Figure 17.
Binary images for training before alignment. The last image is the overlapping
image before alignment.
to accurately capture high-curvature locations, difficulty in handling topological
changes, and the need for point correspondences. In order to overcome these
problems, an Eulerian approach to shape representation based on the level set
methods of Osher and Sethian [41] can be utilized.
The signed distance function is chosen as the representation for shape. In
particular, the boundaries of each of the aligned shapes are embedded as the zero
level set of separate signed distance functions
, with negative
distances assigned to the inside and positive distances assigned to the outside of
the object. The mean level set function of the shape database as the average of
these signed distance functions can be computed as
{
Ψ
1
,
Ψ
2
,...,
Ψ
n
}
n
¯
Φ=
n
Ψ
i
. Figure 19
illustrates the implicit level set representation of the average shape and the zero
level set represents the boundary of the average model.
i
=1
