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Fig. 4 Example of vertebral body segmentation (original image on the left, segmentation results
on the right)
than K
1
to approximately 0. K
2
can be evaluated as the mean gradient magnitude
inside a neighborhood around the seed placed by the user in the center of the
vertebral body. K
1
can be determined by a search algorithm. Along lines originating
from the center of the vertebral body, the maximal gradient magnitude is considered
as belonging to the object
'
is boundary and is recorded. The mean of the 10 % lowest
recorded values constitutes our estimate for K
1
[
32
]. The optimal values for
parameters
a
,
b
and
c
were determined experimentally [
32
]. Figure
4
shows an
example of segmentation obtained by the algorithm.
2.2 Segmentation of the Vertebral Body Ridgelines
The segmentation of vertebral body ridgelines is a preliminary step to both the
registration stage (Sect.
2.3
) and the syndesmophyte extraction stage (Sect.
2.4
).
The vertebral body ridgelines provide the landmarks that aid the registration process
and the reference level from which syndesmophytes are cut. We extract the ridg-
elines from the triangular meshes representing the surfaces of the vertebrae using
the same level set as Eq. (
1
), but transposed from the Cartesian domain of rect-
angular grids to the domain of a surface mesh. While in the usual image grids of CT
scans the relevant features are grey level gradients, on a surface mesh, the useful
features are curvature measures (the vertebral body surface is more curved at the
ridgelines than on the end plates). The curvature measure we used is curvedness
(C)[
47
]:
