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2. Probabilistic graphical model is a general tool to model a multi-component
structure like spine such that both the local feature information of each
individual component and the constraints among components can be encoded in
a model parameter space.
3. Probabilistic graphical model also enables various inference methods to
nd the
optimal model parameters that can
fit the model to the observation.
The current vertebral body or intervertebral disc identi
cation approaches
usually face the following challenges:
Unknown object number. Detecting an unknown number of vertebrae or
intervertebral discs invokes a model selection problem. In [
1
,
2
], either the
lumbar or the whole spine is investigated such that the number of intervertebral
discs is taken as
fixed. This is the reason why the authors can build their
graphical models with a
fixed number of nodes and avoid the model selection
problem. In [
6
], the number of vertebrae is detected by a Generalized Hough
Transform (GHT) along the detected spinal cord. The robustness of the exact
number determination is highly dependent on the image quality.
Off-line training. Due to the complexity of the spinal structure, most of the
existing work on spine area asks for the involvement of prior knowledge which
is usually obtained by off-line training. In [
1
,
2
], both the low-level image
observation models and the high-level disc context potentials need to be trained
using training data. In [
6
], statistical surface models for each vertebra, the
sacrum, the vertebra coordinate system and GHT models are obtained from
the training data. Besides the fact that the model training and model building are
complex problems themselves, the dependency on training data makes these
approaches only applicable to the data with similar characteristics to the training
data.
firstly we designed a graphical model to
model a spinal structure, which can adaptively determine the number of visible
vertebrae during the inference procedure; (2) secondly, in the graphical model, both
the low-level image observation model and the high-level vertebral context
potentials need not to be learned from training data. Instead they are designed such
that they can be learned from the target image data during the inference procedure.
Our contributions in this chapter are: (1)
2 Method
2.1 Graphical Model
Similar to [
2
], we build a graphical model G
¼f
V
;
E
g
with N nodes for the spinal
structure as shown in Fig.
1
. Each node V
i
;
¼
;
; ...;
1 represents a con-
nected disc-vertebra-disc component of the spinal structure, in which both the discs
and the vertebral body are modelled as rectangular shapes. We assign a parameter
i
0
1
N
