Journal of Computer and Communications, 2014, 2, 48-51
Published Online January 2014 (http://www.scirp.org/journal/jcc)
http://dx.doi.org/10.4236/jcc.2014.22009
OPEN ACCESS JCC
Application of Particle Filter for Vertebral body
Extraction: A Simulation Study
Hongyan Cui1, Xiaobo Xie1, Shengpu Xu1, Yong Hu1,2
1Institute of Biomedical Engineering, Chinese Academy of Medical Sciences & Peking Union Medical College, Tianjin, PR China;
2Department of Orthopaedics and Traumatology, The University of Hong Kong.
Received November 2013
ABSTRACT
Lumbar vertebra motion analysis provides objective measurement of lumbar disorder. The automatic tracking
algorithm has been applied to Digitalized Video Fluoroscopy (DVF) sequence. This paper proposes a new
Auto-Tracking System (ATS) with a guide device and a motion analysis to automatically measure human lumbar
motion. Digitalized Video Fluoroscopy (DVF) sequence was obtained during flexion-extension lumbar movement
under guide device. An extraction of human vertebral body and its motion tracking were developed by particle
filter. The results showed a good repeatability, reliability and robustness. In model test, the maximum fiducial
error is 3.7% and the repeatability error is 1.2% in translation and the maximal repeatability error is 2.6% in
rotation angle. In this simulation study, we employed a lumbar model to simulate the motion of lumber flexion-
extension with the stepping translation of 1.3 mm and rotation angle of 1˚. Results showed that the fiducial error
was measured as 1.0%, while the repeatability error was 0.7%. The sequence can be detected even noise con-
tamination as more as 0.5 of the density. The result demonstrates that the data from the auto-tracking algorithm
shows a strong correlation with the actual measurement and that the Vertebral Auto-Tracking System (VATS) is
highly repetitive. In the human lumbar spine evaluation, the study not only shows the reliability of Auto-Tra ck-
ing Analysis System (ATAS), but also reveals that it is robust and variable in vivo. The VATS is evaluated by the
model, the simulated sequence and the human subject. It could be concluded that the developed system could
provide a reliable and robust system to detect spinal motion in future medical application.
KEYWORDS
Vertebral Auto-Tracking System (VATS); Particle Filter; Sequential Important Resampling;
Lumbar Spine; Vertebral Body
1. Introduction
The lumbar spine instability is an ill-defined clinical ent-
ity and most likely is related to the huge number of pa-
tients with chronic low back pain. Low back pain is one
of the most common disorders associated with absence
from work and need for social benefit in modern society.
It affects 40% - 85% of adult population in Hong Kong
and in industrial countries [1].
Current definitions of spinal instability are based on “a
loss of stiffness” [2]. Thus, in an unstable condition a
small load results in a large displacement. There has been
difficulty in translating this definition into criteria that
can be applied to clinical diagnosis and consequent
choice of treatment [3]. Clinically, physical signs such as
a visible slip, catch, click, or shaking of the section dur-
ing motion are commonly used for diagnosing spinal
instability [1].
The diagnosis of lumbar instability commonly depends
on the chief complaints by patients and plain X-ray radi-
ography in two dimensions [4]. Radiographs were taken
at several different poses, taking full extension and full
flexion as an example, which is a definite and convenient
way to obtain some information of the spine motion but
not reflects the continuous process of vertebrae.
Due to the application and expansion of medical tech-
nology [5-7], digitalized video fluoroscopy (DVF) se-
quence [8-13] was recommended to image spine motion
for kinematic data acquisition. DVF was proposed to
investigate spine in kinematics by Breen et al. in 1989
[13]. The advantages are of low level of intervention,
low-dose X-ray, and continuously imaging for moving
vertebrae. The special imaging technology laid the

Application of Particle Filter for Vertebral body Extraction: A Simulation Study
OPEN ACCESS JCC
49
groundwork to record the spine motion in vivo. On the
other hand, many biomedical engineering researchers in
[9,12,14-20] have analyzed spine biomechanics and pre-
sented avenues of identification and mark of vertebral
corners as well as tracking algorithm for the vertebrae.
Therefore, this new system, named as Auto-Tracking
Analysis System (ATAS), was designed to mainly study
the lumbar vertebrae’s movement in model and in vivo.
The results from the ATAS provide the objective basis
for the diagnosis in lumbar disorder.
In this study, an attempt was made to gain the motion
trajectories of lumbar vertebrae in model to test the ro-
bustness and the reliability of the ATAS. Thereafter, the
practicability is illustrated by importing a healthy human
DVF sequence to the auto-tracking system.
2. Methods
2.1. Image Preprocessing
The DVF image sequence is contaminated by noises
generated from the DVF system. On the other hand, due
to low X-ray dose imaging mode is employed in our se-
tup, the contrast between vertebra and surrounding tissue
is degraded. In order to enhance the image quality to fa-
cilitate automated with regarding to the operation of the
software, Landmarking the vertebrae in a DVF sequence
is the basis of kinematic analysis whether in automatic or
manual tracking. In this paper, the ‘Manual’ panel locat-
ing algorithm in the GUI is not used, which will be use-
ful for poor DVF sequence images. When the image is
poor and cannot be automatically tracked, the markers
are placed on the vertebrae’s four corners (two dorsal
corners and two ventral corners) on each vertebra body in
every frame of the DVF sequence. We can put landmark
manually but with time-consuming and error-prone.
Nevertheless, the manual tracking is also an important
part in the ATAS because the vertebrae images of pa-
tients’ DVF sequences are usually presented without sa-
tisfactory quality. As well, Trajectory analysis is of great
value to the original results once the tracking process
finished. The “LPR-RICI Analysis” processes the origi-
nal data by local polynomial regression analysis to gain a
smooth curve graph. We can obtain the translation and
angle of the rotation in a curve graph from “Trajectory
Analysis” and “LPR-RICI Analysis”. At last, the data
can be output to Excel for further flexible analysis. For
more information about operating procedures, please
view “Help” on the interface.
2.2. Automated Tracking
In the present study, we modify the well validated auto-
mated vertebra tracking algorithm using particle filter
proposed by Lam et al. [16].
The acquired DVF sequence is in passed to the auto-
mated tracking module through the GUI software to es-
timate the position and orientation of the vertebrae in
each frame of the sequence once the vertebrae of interest
have been manually identified in the first frame as shown
in Figure 1. The locations of the control points are stored
in a control vector
C0
. This initialization step defines the
vertebra boundary as a close contour for matching with
the same vertebra in subsequent frames using the obser-
vation model described in Lam et al. [16].
In summary, the posterior distribution of the x- and y-
displacement
( )
,
tt
xy
and the orientation variation
( )
t
θ 
of the vertebra from frame
t
to
+1 t
were de-
tected by particle filter, which are formulated in a state
vector as
[ ]
,, T
t ttt
X xy θ =
. (1)
The particles are then resampled and the state estimate
is approximated from the posterior distribution by a
set of particles
() ()
t1
{X ,}
n nN
t tn
w
=
weight with and
. Sequential Importance Resampling (SIR)
was applied to each time step to prevent the degeneracy
problem, and then the weight of each particle n can be
calculated as
() ()
(| )
nn
t tt
pZ X ω ∝
, (2)
and
, (3)
where is a Dirac delta function. The kinematic
parameters in state vector at frame
t
are computed
using the minimum mean square error (MMSE) estimate
( )( )
1
1
ˆNnn
t tt
n
XX
N
ω
=
≈
∑
. (4)
The control vector for frame
t
,
C t
, is obtained from
the one at
-1t
,
C -1t
, and after which
Ct
and
are passed back to the particle filter for the next
iteration.
3. Anatomical Lambo-sacral Model
Extraction and Performance Assessment
The DVF of model was obtained by the previous intro-
duced medical system (45 kV, 80 mA, Exposure time:
3ms, Protocol Name: 25 Pediatric < 4y). During the DVF
collecting process, the L1-L5 region was maintained
within the field of view. For a sharp boundary and pre-
venting image from “white-out” in movement, a metal
harness was placed on the edge of each vertebra. The
assisting device also pulled and pushed the true-to-life
model of lumbar vertebral column (Anatomical lam-
bo-sacral model, Ortholink LLC, CA 90212, USA) to
t
X
ˆ
)(n
t
w
1
1
)(
=
∑
=
N
n
n
t
w
∑
=
−≈ N
n
n
tt
n
ttt XXZXp
1
)()(
:1 )()|(
δω
)(• δ
t
X
ˆ
t
X
ˆ
t
X
ˆ

Application of Particle Filter for Vertebral body Extraction: A Simulation Study
OPEN ACCESS JCC
50
Figure 1. Image of lumbar model with manually markers.
perform sagittal cycling flexion-extension motion. The
continuous dynamic lumbar sequence of the model is
assessed by the medical system 10 times, which includes
2 integral cycles each time. When the collection was fi-
nished, each vertebra trajectory was recorded by a real-
time depiction of the vertebral body with rigid fixation
pens.
About 27 control points were marked on the first
frame of each DVF sequence. The more precise the mark
is, the more accurate the results will be. An example of
locating the control points is shown in Figure 1. Each
vertebra used 2000 particles, and
222
,,
ttt
xy θ



was
set as [15,23].
Due to have no elasticity of the discs’ material of the
lumbar model, we select the first four moving cycles of
DVF sequences to compute the fiducial error and repea-
tability error and analyze Test-Retest Reliability. Fig ure
2 arrays partly frames from the DVF sequence of the
tracking process. The maximum of the fiducial error is
3.7% in x-translation. In the 20 integral cycles, the aver-
age ICC of the x- and y- translation are 0.99 (Std 0.009),
0.99 (Std 0.005) (p < 0.05) respectively between the au-
to-tracking and actual measurement.
Owing to the same reason to calculate the error, the
Root Mean Square differences (RMS) and the Standard
Error of the Measurement (SEM) of rotation angle [16],
as well as the x- and y-translation of the center among
first 4 cycles, calculated to test the variability and ro-
bustness of the VATS. The average RMS differences of
the x-translation, y-translation and angle of rotation are
0.69 (Std 0.4) mm, 0.64 (Std 0.3) mm, and 0.9˚ (Std 0.3˚)
Figure 2. Sequent frames of vertebra flexion.
while SEM is 0.47, 0.42, and 0.57˚ (p < 0.05).
4. Discussion
The using of particle filter can track the simulated lumbar
model and to detect the motion in various noising situa-
tion. Breen et al. [18], who introduced DVF to investi-
gate spine kinematics firstly, succeeded in using DVF to
acquire and analyze lumbar spine motion. Okawa et al.
[21] used a sandwich stand to assist in video fluoroscopy
acquisition from subjects with and without back pain.
Teyhen et al. [9] proposed methods for video fluorosco-
py image enhancement and distortion compensated
roentgen analysis as well as showing the reliability of
their methods and demonstrating an improvement in
video fluoroscopy image measurement. However, the
main drawback is that the vertebral motions can only be
recorded at certain fixed frames or time intervals. Lee et
al. [8] evaluated the inter-vertebral motion at certain
fixed anatomic ranges of motion of the lumbar spine,
which was not a time-dependent parameter. The VATS
did not show faults.
The translation and angle are accurate in a certain
range. The effect of out-of-plane is decreased but there
are still minor changes observed in the human DVF se-
quence. Eventually, other kinematical parameters such as
intervertebral angle and translation can be measured to
provide a more comprehensive evaluation.
The model and simulation study focus mainly on the
reliability and robustness of the Vertebral Auto-Tracking
System for the lumbar spine motion. In model test (unit:
millimeter in translation and degree in angle), the maxi-
mum fiducial error is 3.7% in translation. The maximal
repeatability error is 1.2% in translation and 2.6% in ro-
tation angle. The result presented the repeatability error
with 0.5%, 0.5%, 0.7% in x- and y-translation and rota-
tion angle respectively. It proved VATS measurement
system with highly repetitive. This simulation study eva-
luated the VATS under noise contamination with various
noise densities, results from VATS proved the robust of
the detection until noise density ≤ 0.5.

Application of Particle Filter for Vertebral body Extraction: A Simulation Study
OPEN ACCESS JCC
51
5. Conclusion
The proposed Vertebral Auto-Tracking System used par-
ticle filter to detect lumbar motion, which can provide a
useful tool for medical diagnosis. This study proved the
reliability and robustness by a simulation lumbar model.
The VATS is evaluated by the model and the simulated
sequence. The satisfactory of results proposed the poten-
tial value in the future clinical application.
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