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ð
x
j
;
y
j
;
z
j
Þ
centerline are
, j =1
…
n, the curved reformation in the sagittal direction is
written as
I
Sag
ð
x
i
;
y
j
Þ
¼I
3D
ð
x
j
;
x
i
;
z
j
Þ
ð
7
Þ
where I
Sag
is the curved reformatted sagittal image, I
3D
is the original 3D image.
(x
i
, y
i
) is the 2D coordinate in the reformatted image. Similarly,
the curved
reformation in the coronal direction is written as
y
j
;
z
j
Þ
I
Cor
ð
x
i
;
y
j
Þ
¼
I
3D
ð
x
i
;
ð
8
Þ
where I
Cor
is the reformatted coronal image. Figure
5
b, c show the regular coronal
reformation, together with the curved planar reformation in sagittal and coronal
directions. The curved reformations clearly better reveal the inter-vertebral disks.
To make use of the CPR for spinal column partitioning, the centerline of the
spinal canal is
first projected onto the reformatted images. Then the normal is
computed at every point on the centerline. The intensity along the normal direction
is then aggregated and recorded. Figure
5
d shows the aggregated intensity pro
le
(AIP) along the spinal cord at the reformatted coronal view. As observed, the
aggregated intensity at the disc location is lower than those at the vertebral body
location. However, the difference is still not prominent, especially at cervical spine
and highly curved region. We further convolve the aggregated intensity pro
le with
an adaptive disk function, which can be written as,
Þ
¼
1
x
2
½
T
=
2
;
T
=
2
f
ð
x
ð
9
Þ
1
Elsewhere
The function is a rectangle function with adaptive width T. In order to determine
T, we search the neighborhood in both directions on the AIP for local maximum
values.
The intervertebral disks are then located at the lowest response points on the
adjusted intensity pro
le and used to partition the spinal column. Figure
5
e, f show
the spine partition superimposed on reformatted CPR views and the spinal column
with vertebral partitions in a 3D view is shown in Fig.
5
g.
6 Metastasis Candidate Detection
After the spine is segmented, the following lesion detection processes are restricted
to the segmented spine excluding the spinal canal. We locate bone metastasis
candidates in three steps. First a watershed algorithm is applied to extract initial
super-pixels as metastasis candidates, followed by a merging routine based on
graph cut to alleviate over-segmentation. The resulting 2-D candidates are then
merged into 3-D detections. For each 3-D candidate, a set of features is computed
