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validation. The dependency on static values (thresholds) limits the capability of
segmentation methods when they are tested on different datasets. Furthermore,
performing many sequential steps to achieve the segmentation task increases the
error rate due to propagation of the error from each step to the next. Another study
by Weiss et al. [
100
] proposed a semi-automatic technique for disc labeling. The
upper and lower halves of the spine are separately labeled after histogram pro-
cessing,
filters and the use of threshold values. They tested their algorithm on
fty
MRI cases.
In surgery planning, Pekar et al. [
77
] developed a labeling method for the whole
spine. Initially, a set of disc candidates are located by a
filter using eigenvalues
analysis of the Hessian matrix. Then using prior structural knowledge of the spine,
they picked the disc centers from the candidates. After that labeling takes place
starting from the
first spine point and moving upward/downward. They also used a
distance constraint for locating the next disc, otherwise a new point is introduced
and that disc is considered missing due to abnormality. They used 15 subjects for
validation producing 60 image volumes for lumbar and cervical areas with two
poses for each subject.
Bhole et al. [
9
] presented a method for automatic detection and labeling of
lumbar vertebrae and discs from clinical MRI by combining tissue property and
geometric information from T1-Weighted (T1 W) sagittal, T2-Weighted (T2 W)
sagittal and T2 W axial MRI protocols. They achieved 98.8 % accuracy for disc
labeling on 67 sagittal images. However, they relied on speci
c threshold values
extracted from the dataset which prevents the extension for their method to another
dataset with variable parameter settings.
Schmidt et al. [
82
] introduced a probabilistic inference method using a part-
based model achieving up to 97 % disc detection rate on 30 cases. In another similar
approach, Oktay and Akgul [
76
] proposed a method using Pyramidal Histogram of
Oriented Gradients (PHOG) based on SVM and a probabilistic graphical model and
achieved 95 % accuracy on forty cases.
Localization and labeling has been better understood in the literature. The
author
s research group developed and tested a myriad of techniques. Koh et al.
[
54
] proposed a joint attention and active contour models to segment the low back
spine and subsequently label discs in later research efforts. However, the initial
contour is highly sensitive to the inhomogeneous MRI signal intensity. Further-
more, [
5
] proposed a novel probabilistic model of the lumbar discs. This model
adequately insulates the localization variables from the pixel intensities while at the
same time modeling the exact disc geometry rather than solely pixel-level labels.
Let
'
T
D
¼
fli;
d
1
;
...
;
d
6
g
. be the set of disc variables with each d
i
¼
ð
Þ
2
d
0
;
x
i
;
y
i
;
i
½
representing the disc center (it could also include disc angle, boundary, etc.),
d
0
is a label for non-disc pixels. Inferring
1
;
6
from an image is our ultimate goal, but
we avoid doing it directly due to its large computational complexity. We thus
introduce a set of auxiliary variables, called disc-label variables and denoted by
L
¼
fli;
l
i
;
8
i
2 Kg
D
1, +1} for non-
disc or disc, respectively. The disc-labels make it plausible to separate the disc
. Each disc-label variable can take a value of {
−
