Biomedical Engineering Reference
In-Depth Information
Figure 18.
Binary image after alignment. The last image is the overlapping image after
alignment.
To extract the shape variabilities, Φ is subtracted from each of the
n
signed
distance functions to create
n
mean-offset functions
{
Ψ
1
,
Ψ
2
,...,
Ψ
n
}
. These
mean-offset functions are analyzed and then used to capture the variabilities of the
training shapes.
Specifically,
n
column vectors are created,
ψ
i
, from each Ψ
1
. A natural
strategy is to utilize the
N
1
×
N
2
rectangular grid of the training images to generate
N
=
N
1
×
N
2
lexicographically ordered samples (where the columns of the image
grid are sequentially stacked on top of one another to formone large column). Next,
we define the shape-variability matrix
S
as
S
=[
ψ
1
, ψ
2
,..., ψ
n
]. The procedure
for creation of the matrix
S
is shown in Figure 20.
An eigenvalue decomposition is employed to such that
n
SS
T
=
U
Σ
U
T
,
(32)
