Information Technology Reference
In-Depth Information
Likelihood Estimation
A likelihood estimation model integrating 2D morphological and feature informa-
tion was included in order to measure the error given from the current data. This
estimate expresses the measure of similarity between the current model points
w
i
^
and an estimate w
i
ð
which encodes expert morphological knowledge of the
relationships between the L landmarks [
31
]. Each landmark i is assigned to a
speci
x
Þ
depending on the landmark type (i.e. pedicle tip), and is
based on local vertebral height, width, orientation and relative distances between
landmarks. The model also measures the similarity response of a rotation and scale
invariant wavelet coef
c function of w
i
ð
x
Þ
cient feature c
msd
ð^
w
i
Þ
speci
c to the landmark type, at
location
^
w
i
on the image. The probability of this likelihood estimate is:
(
"
#
)
2
Y
L
w
PA
ð
w
PA
Þþw
SAG
ð
w
SAG
1
2
Þ
i
i
D
morphology
/
exp
D
w
ð
14
Þ
2
r
i¼1
where
w
PA
ð^
w
PA
i
Þ
and
w
SAG
ð^
w
SAG
i
Þ
are the similarity measures for the landmark
coordinates on the coronal and sagittal plane de
ned as:
w
PA
i
w
PA
i
w
PA
i
w
PA
i
w
PA
ð^
Þ
¼
ð^
ð
ÞÞ
c
msd
ð^
Þ
ð
Þ
x
15
w
SAG
i
w
SAG
i
w
SAG
i
w
SAG
i
w
SAG
ð^
Þ
¼
ð^
ð
x
ÞÞ
c
msd
ð^
Þ:
ð
16
Þ
Þ
¼
P
j
d
j
f
j
ð
Þ
¼
P
j
d
j
s
j
ð
In Eqs. (
15
) and (
16
), w
PA
i
and w
SAG
i
are the
estimates of the landmark coordinates on the coronal and sagittal plane respectively
based on morphological distribution of the neighbouring j landmarks. Each land-
mark j is assigned with prior knowledge distances f
j
ð
ð
x
x
Þ
ð
x
x
Þ
Þ
and s
j
ð
Þ
x
x
for the PA and
SAG views respectively, pondered by the prede
ned weights
d
.
5 Results
5.1 Self-calibration of the Radiographic Scene
5.1.1 Validation Methodology
A clinical validation using real data has assessed the clinical validity of the pre-
sented self-calibration algorithm. A comparison between a previously validated
system using an explicit calibration based on manually identified landmarks in a
fixed radiographic setup [
8
], and the proposed system based on uncalibrated X-rays
was made by generating a 3D model of the spine using both techniques. The data
used for the clinical study consisted of 60 pairs of digitized X-rays of adolescents