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Fig. 11 Effect of the Laplacian
filter on an intervertebral disk space: a Original image.
b Laplacian of image (a), color-coded with green (negative values) and red (positive values)
intensity for syndesmophyte, GL
S
. Syndesmophytes are surrounded by soft tissue.
Considering the neighbors of syndesmophyte voxels we mark the
first soft tissue
layer, T
1
and second soft tissue layer T
2
. From those layers (T
1
and T
2
) we extract
the mean voxel intensity for soft tissue, GLT.
T
. For a voxel i labeled as syndesmo-
phyte or belonging to T
1
or T
2
, our density criterion is based on the measure Di
i
de
ned as:
GL
i
GL
T
D
i
¼
ð
12
Þ
GL
S
GL
T
where GL
i
is the grey level of voxel i. The higher the bone content of the voxel, the
higher Di
i
is.
The density and Laplacian criteria are combined in the following manner:
(a) First we consider all syndesmophyte, T
1
and T
2
voxels. If a voxel i (syndes-
mophyte, T
1
or T
2
) veri
es the conditions:
D
i
[
D
1
and L
i
\
0
ð
13
Þ
where D
1
is a threshold, it is classi
ed as syndesmophyte (L
i
is the Laplacian
at voxel i). Otherwise it is labeled as soft tissue. This
first step mainly corrects
leaks. An example is shown in Fig.
12
.
(b) The labeling of soft tissue layers T
1
and T
2
and the computing of GLT
S
and GL
T
are updated based on the new more accurate segmentation resulting from step
(a). We then process the
first soft tissue layer T
1
. If a voxel i of T
1
veri
es the
conditions:
D
i
[
D
2
and L
i
\
0
ð
14
Þ
