Information Technology Reference
In-Depth Information
V is a partial syndesmophyte voxel. To determine what proportion of V is
syndesmophyte, we subdivide V into smaller rectangles. A voxel V of dimensions
p
x
, p
y
and p
z
can be subdivided into M
3
equal subvoxels of dimensions
p
M
,
p
M
and
p
M
.
For this, we simply take as locations of the vertices of the new subvoxels the
coordinates
where M is an integer controlling the number of
subdivisions and (i, j, k) are integers. The choice M = 10, which means each voxel
is divided into M
3
= 1,000 subvoxels, is a good trade-off between computational
speed and gain in precision. The better precision results produced by
p
y
M
;
p
x
p
z
M
i
M
;
j
k
finer subdi-
visions (larger M) are limited by diminishing returns. Then, for each subvoxel, it is
straightforward to determine if it is above or below P using the same scalar product
(Eq.
9
). However, since we do not want to pursue the subdivision process further, it
is not necessary to test all 8 vertices. We only test one, corresponding to the
smallest (i, j, k). For every subvoxel of V, if the test is positive in sign we increment
N
S
that we de
ne as the number of subvoxels of V found to be syndesmophyte
(conversely to determine the proportion of a voxel below the local level of EP1/
RL1, we would increment when the test is negative in sign). The corresponding
partial syndesmophyte volume is:
N
S
M
3
PSV
¼
p
x
p
y
p
z
ð
10
Þ
Figure
9
illustrates the difference between whole voxel and subvoxel cutting.
Fig. 9 Comparison between subvoxel and whole voxel cutting. a Coronal view of a CT scan of an
IDS. b Lateral view of the 3D surface reconstruction of the registered right-hand side
syndesmophytes. View of the registered syndesmophyte upper surfaces after c subvoxel and
d whole voxel cutting from the vertebral body. The view is from the direction of the blue arrow in
(a) and (b)
