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v
X
ray
, respectively. And for each X-ray landmark, we can calculate a projection ray
emitting from the focal point to the landmark. We then calculate the length between
v
1
Mean
and v
4
Mean
and denote it as l
1
;
Mean
. Using the known image scale, we also
calculate the length l
1
;
4
X
ray
between v
X
ray
and v
X
ray
. Then, we do:
Data Preparation. In this step, we assume that the line connecting the centers of
the vertebra body and the center of the spinal process tip is parallel to the input
fl
fluoroscopic image and is certain distance away from the imaging plane. Using this
assumption and the correspondences between the landmarks de
ned in the CT
v
X
ray
volume and those from the
fl
fluoroscopic image, we can compute two points
v
X
ray
on the projection rays of v
X
ray
and v
X
ray
, respectively (see Fig.
4
a),
which satisfy:
and
v
X
ray
v
X
ray
==
v
X
ray
v
X
ray
;
and
ð
3
Þ
F
d
v
X
ray
v
X
ray
j¼
l
1
;
4
X
j
ray
F
where
symbol indicates that the two lines are parallel; F is the calibrated
distance from the focal point to the imaging plane and d is the assuming distance
from the line connecting the center of the vertebra body and the center of the spinal
process tip to the imaging plane.
The current scale s between the mean model and the input image is then esti-
mated as,
“
//
”
l
1
;
Mean
v
X
ray
v
X
ray
j=
s
¼j
ð
4
Þ
Fig. 4 Iterative landmark-to-ray registration. a Schematic view of data preparation. b Schematic
view of finding 3D point pairs
