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2.4 Syndesmophyte Segmentation
Once corresponding pairs of vertebrae are registered, syndesmophytes can be cut
from the vertebral bodies using the ridgeline of the baseline vertebra (using the year
1 or 2 ridgelines is also possible). The algorithm identi
es syndesmophytes in each
IDS unit. The cutting algorithm marks as syndesmophyte bone voxels lying
between the two end plates that bound each IDS. Because of the high precision
required by our application, we found it necessary to operate this cutting with
subvoxel accuracy. We also address the problem of differing degrees of smoothness
in the reconstructions and partial volume effect, and re
ne the segmentation of
syndesmophytes [
33
].
2.4.1 Syndesmophyte Cutting
Each IDS is bounded by the lower end plate of the superior vertebra, that we note
EP1, and the upper end plate of the inferior vertebra, noted EP2. The corresponding
ridgelines are respectively noted RL1 and RL2. The cutting algorithm marks as
syndesmophyte those previously segmented voxels that are between those 2 end
plates. Each candidate voxel is considered in relation to the local ridgelines. If it is
below the local level of EP 1/RL1 and above the local level of EP2/RL2 it is
marked as syndesmophyte.
However the representation of a continuous space by discrete voxels can
introduce inaccuracies in this algorithm. In the
first version of our algorithm, a
whole voxel was considered either totally above or below the local ridgeline level
[
32
]. However, in reality, most voxels close to the ridgeline level are neither
completely above nor completely below that level. Rather, part of the voxel is
above while the other part is below. The following algorithm achieves syndes-
mophyte cutting with subvoxel accuracy. We show how to determine the proportion
of a voxel above the local level of EP2/RL2. Determining the proportion of a voxel
below the local level of EP1/RL1 is straightforwardly similar.
First we extract the normal to the end plate EP2, N, using a least square estimate
method [
32
]. Let V be a voxel under consideration. We determine the local ridgeline/
end plate level in the following way. The point of RL2 closest to V is found.
Neighboring points of EP2/RL2 are averaged to form the point R
V
, which, as an
average, is an estimate more robust to noise. N and R
V
de
ne a plane P (orthogonal
to N and containing R
V
), that can be used to cut syndesmophyte from vertebral body.
We now determine the position of V relative to this plane. V is a rectangle de
ned by
8 vertices Vi
i
with i
2f
1
;
...
;
8
g:
The sign of the scalar product:
!
N
sV
ðÞ¼
ð
Þ
ð
Þ
sign
R
V
V
i
9
tells us if Vi
i
is above or below the plane P. If all signs are positive or negative, then
voxel V is either completely a syndesmophyte voxel or not. If we have a mix, then
