Application of Particle Filter for Vertebral body Extraction: A Simulation Study

doi:10.4236/jcc.2014.22009

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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.

Email: [email protected]

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

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

. 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

( )

xy

and the orientation variation

( )



of the vertebra from frame

were de-

tected by particle filter, which are formulated in a state

vector as

[ ]

,, T

t ttt

X xy

=

. (1)

The particles are then resampled and the state estimate

is approximated from the posterior distribution by a

set of particles

() ()

{X ,}

n nN

t tn

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

() ()

(| )

t tt

pZ X

∝

, (2)

and

, (3)

where is a Dirac delta function. The kinematic

parameters in state vector at frame

are computed

using the minimum mean square error (MMSE) estimate

( )( )

ˆNnn

t tt

≈

∑

. (4)

The control vector for frame

, is obtained from

the one at

-1t

C -1t

, and after which

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

)(n

)(

∑

−≈ N

ttt XXZXp

)()(

:1 )()|(

δω

)(•

Application of Particle Filter for Vertebral body Extraction: A Simulation Study

OPEN ACCESS JCC

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







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

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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