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Fig. 14 Preparation of
training data [
2
]. An expert
radiologist manually selects a
set of 16 points based on a
predefined model for locating
these points
modeling by the ASM, and vertebra boundary delineation by a Gradient Vector
Flow (GVF-)snake [
1
,
2
].
The vertebrae localization step provides a point inside each vertebra. This step
utilized an earlier work on disc localization from clinical MRI [
5
]. After producing
a point inside each disc, they take the average point between each two discs and
consider this as the vertebra localization point as shown in Fig.
15
.
The next step is to model the vertebra point distribution by an ASM [
20
]. In this
work, they produced a separate model for each vertebra level. A radiologist pre-
pares the training data where he manually marks 16 landmark points for each
vertebra as shown in Fig.
14
. These points are named from k
1
to k
16
. Similar to
[
20
], they initially calculated the mean shape
N
P
1
x where N is the size of the
training data. Then each vertebra shape xi,
i
, where i
¼
1
x
is recursively
aligned to the mean shape x using generalized Procrustes analysis to remove
translational, rotational, and isotropic scaling from the shape.
Then, they model the remaining variance around the mean shape for each ver-
tebra with principal components analysis (PCA) to extract the Eigen vectors of the
covariance matrix associated with 98 % of the remaining point position variance
according to the standard method for deriving the ASM
2
f
1
;
...
;
N
g
;
'
s
linear
shape
representation.
However, they did not use the original CT image for training the ASM of each
vertebra. Rather, they applied the range
filter R
first on the image to obtain a better
edge enhancement for vertebrae. R is the range
filter operator where the intensity
levels in each 3
×
3 window are replaced by the range value (maximum
-
minimum)
