Mohammed Benjelloun, Sa
ıd Mahmoudi and Fabian Lecron
Faculty of Engineering, University of Mons, 9 rue de Houdain, Mons, Belgium
Segmentation, Vertebrae, Active shape model, Edges.
This paper describes a new method for cervical vertebra segmentation in digitized X-ray images. We propose a
segmentation approach based on Active Shape Model method whose main advantage is that it uses a statistical
model. This model is created by training it with sample images on which the boundaries of the object of
interest are annotated by an expert. The specialist knowledge is very useful in this context. This model
represents the local statistics around each landmark. Our application allows the manipulation of a vertebra
model. The results obtained are very promising.
Nowadays, the radiography of the spinal column is
one of the fastest and the cheapest way for a special-
ist to detect vertebral abnormalities. Furthermore, as
far as the patient is concerned, this procedure has the
advantage to be a safe and non-invasive. For these
reasons, this exam is widely used and remains incon-
testable in the scope of treatments and/or urgent diag-
noses. Despite these precious advantages, a meticu-
lous and tiresome analysis is required by the practi-
tioner. The nature of the radiographs is the origin of
the problem. In fact, they are obtained by impress-
ing the density of the tissues on a radiographic film.
A bone is defined by a white color, a soft tissue by a
gray level and an empty space by a black color. It is
a fact that the images present low contrasts and some
areas might be partially hidden by other organs of the
human body. As a result, the vertebra edge is not al-
ways obvious to see or detect.
The problem of vertebra segmentation in digitized
X-ray images is of great importance for the special-
ists. The extraction of quantitative data gives them a
valuable computer-aided diagnosis.
There is a myriad of segmentation methods. Of
course, they are not all recommended for the medi-
cal image processing and all the more so they don’t
all meet the difficulties concerning the X-ray images.
The reader is lead to discover (Pham et al., 2000) for
an overview of the current segmentation methods ap-
plied to medical imagery.
The vertebra segmentation has already been
treated in various ways. The level set method is a nu-
merical technique used for the evolution of curves and
surfaces in a discrete domain (Sethian, 1999). The
advantage is that the edge has not to be parameterized
and the topology changes are automatically taken into
account. Some works related to the vertebrae are pre-
sented in (Tan et al., 2006).
The active contour algorithm deforms and moves
a contour submitted to internal and external energies
(Kass et al., 1988). A special case, the Discrete Dy-
namic Contour Model (Lobregt and Viergever, 1995)
has been applied to the vertebra segmentation in (Ben-
jelloun and Mahmoudi, 2008). A survey on de-
formable models is done in (McInerney and Ter-
zopoulos, 1996).
Other methods exist and without being exhaustive,
let’s just mention the generalized Hough transform
(Tezmol et al., 2002), or the use of the polar signa-
ture (Mahmoudi and Benjelloun, 2008).
The difficulties resulting from the use of X-ray im-
ages force the segmentation methods to be as robust as
possible. In this paper, we consider a technique based
on the Active Shape Model (ASM) (Cootes et al.,
1995). An active shape model is a statistic model de-
signed from sample of images. This preconception
regarding the shape to search in the image (a verte-
bra in our case) gives the method based on ASM an
important robustness.
We will see that the effectiveness of the method
highly depends on the initialization. The computer-
Benjelloun M., Mahmoudi S. and Lecron F. (2010).
In Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing, pages 501-506
DOI: 10.5220/0002765505010506
aided diagnosis has to fulfill the same characteristic
than the radiography technique, i.e. the simplicity and
the rapidity. Therefore, it is crucial to automate and
to provide the results in acceptable times. Extensive
research related to this issue has been done in (Long
and Thoma, 2000; Long and Thoma, 2001).
This paper is structured as follows. In section 2,
we explain the principles of the active shape model
approach and our proposed segmentation method us-
ing this approach. In section 3, the results of the seg-
mentation on data sets of cervical images are com-
mented. Finally, section 4 presents our conclusions.
In this paper, we propose a new segmentation ap-
proach based on the active shape model theory. The
goal of this method is to identify vertebra edges
from the cervical spinal X-ray images. An Active
Shape Model is a statistical model that describes ob-
jects shape. Basically, an active shape model (ASM)
(Cootes et al., 1994) is a statistical model generated
from a set of training samples. A series of correspond-
ing points, called landmark points, are identified on
the boundary of the target object in each training im-
age. Then the training samples are regarded as vec-
tors and statistical parameters of the vector distribu-
tions are computed using principal component analy-
sis. By changing the parameters, new shapes can be
synthesized. After the ASM is trained, it can be used
to locate objects in a new image. The contour ex-
traction process using ASM is a process of synthesiz-
ing an optimal shape that is most similar to the shape
in the image. The statistical difference between the
synthesized shape and the original model can be cal-
culated. By restricting the difference to small values,
the deformation can be limited to an acceptable range.
In the followed section briefly reviews the ASM seg-
mentation scheme.
2.1 Active Shape Model Method
The ASM method is composed of 4 steps (Figure 1):
1. Learning: placing landmarks on the images in or-
der to describe the vertebrae
2. Model Design: aligning all the marked shapes for
the creation of the model
3. Initialization: the mean shape model is associated
with the corners of the searched vertebrae. This
step can be manual or semi-automatic
4. Segmentation: each point of the mean shape
evolves so that its contour fits the edge of the ver-
Figure 1: The steps of our framework.
2.1.1 Learning
A set of image samples has to be described by some
landmarks. It is therefore common to choose as land-
marks the corners of the vertebra and a reasonable
number of equidistant points between these corners.
Figure 2 shows an example of this process.
Figure 2: Vertebra marking.
Each shape in the set is represented by a vector x
= (x
, y
, y
;. . . ;x
, y
;. . . ;x
, y
2.1.2 Model Design
When the annotation phase is completed, it is neces-
sary to align the shapes to make a correct statistical
treatment since they are indeed positioned at various
locations and orientations of an X-ray image. The al-
gorithm is as follows:
1. Align each shape of the sample on the first one.
2. Repeat until convergence:
(a) Compute the mean shape.
(b) Adjust the mean shape to the first shape.
(c) Align each shape on the mean shape.
Once the set of aligned shapes is available, the
mean shape is calculated using the arithmetic mean
of coordinates describing each element of the sample
(see equation 2).
x =
A set of possible models is derived from this mean
shape by the moving of points through specific di-
rections called modes of variations. These directions
BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing
are equivalent to the eigenvectors of the variance-
covariance matrix of the sample. Finally, the model
is described by the mean shape x , the matrix P of the
most significant eigenvectors p
corresponding to the
eigenvalues λ
and a vector b of weight factors b
. We
x = x + Pb (3)
P = (p
, p
, ··· , p
b = (b
, b
, ··· , b
The equation 3 is used to decide if an object from
an image can be considered as convenient. As the
coordinates of the landmarks of an object are known
and as the eigenvectors are unit vectors, it is possible
to determine the vector b by the equation 4.
b = P
(x x) (4)
The values of the factors b
allow to know if an
object is convenient to the model. The values of b
vary in the following manner (Cootes et al., 1994):
2.1.3 Initialization
For the initialization process, we propose a semi-
automatic process based on two points placed by the
user on the left side of each vertebra on the superior
and inferior corners. The mean shape is positioned
according to this information.
2.1.4 Segmentation
Having generated a flexible shape model, we would
like to find examples of the modeled form when it is
present in the images. So, after the initialization step,
shapes are fitted in an iterative manner, starting from
the mean shape.
For each landmark belonging to the mean shape,
it is necessary to analyze the surrounding texture. It
is always important to consider changes in the level
of gray in the same direction to ensure a coherent re-
search. Therefore, it was chosen to analyze the tex-
ture around landmarks along the normal of the con-
tour at that point (see Figure 3). Thus, a profile is de-
fined as a vector containing the gradient of intensity
for each point in the normal. Each landmark is moved
to the direction perpendicular to the contour to n
sitions on either side, evaluating a total of 2n
+ 1 po-
sitions. We can notice that these positions correspond
to the profile of each landmark on the mean shape.
In our experiments, we chose n
= 7. The landmark
Figure 3: Normal of the contours for each point of the pro-
is moved to the position with the lowest Mahalanobis
distance (Cootes et al., 1995). After moving all the
landmarks, the shape is fitted to the displaced points
(by respecting the equation 5), yielding an updated
The search algorithm is given here:
Search, along each normal of the shape, the best
profile according to the computed mean shape.
The new sections are landmarks and profiles
Search shape model best suited to points found in
the previous step. This will form the basis for the
next iteration.
While the convergence condition is not met and
the maximum number of iterations is not reached.
It remains to determine when to suspend the con-
duct of the search algorithm previously presented.
The first condition of convergence proposed is to
stop the search when all the landmarks remain fixed.
However, it appears that this condition is too strict.
We have therefore decided to stop searching when a
small percentage of the landmarks continues to move.
Specifically, we compare the shape obtained in the
current iteration with all the forms built with previ-
ous iterations. For each of them, we compute the
number of points that differ from those recently ob-
tained. We then seek the minimum of these values. If
the corresponding shape is close to the present shape,
we then compare the number of points that differ be-
tween these two shapes. If the first value is less than
10% of the second, the convergence condition is met.
To avoid an indefinite search if the vertebrae are not
found, a maximum number of iterations can be fixed.
If this number is reached, the search ends and the re-
sult of the current iteration is proposed as a final so-
lution. In practice, when an initialization is done cor-
rectly, the method converge after 50 to 250 iterations.
We proposed and developed a segmentation method
based on the active shape model theory. Our goal was
to produce a tool for vertebra detection in X-ray im-
ages corresponding to the cervical spinal column. We
validated our method by using a test database com-
posed of more than 10 000 X-ray images from the
online database NHANES II of the National Library
of Medicine (NLM, ). Our application was developed
in order to allow the use of a vertebra model. Figure 5
shows the segmentation results obtained by this kind
of modelization.
We study in our experiments the influence of some
parameters in the final segmentation result, such as
the number of sample images, the profile structure and
the number of landmarks by vertebra used to define
the mean shape model.
For bothly a powerful and useful segmentation,
the choice of images sample should be the task of
a specialist. The dataset size recommended for the
training set varies from one database to another. Nev-
ertheless, the larger the sample, the best the built
model. We proposed a sample composed of 25 im-
ages for our tests. This number provided good seg-
mentation results. It is obvious that this number can
be augmented, but by increasing the mean shape com-
puting time.
By the same way, the number of landmarks has
a direct influence on the quality of the segmentation
results obtained by the search process. It is evident
that the greater this number, the better the segmen-
tation result. Nevertheless, it would be necessary to
find a good compromise, in order to obtain a reason-
able computing time for the search phase process. We
carry out this compromise by using 20 landmarks for
each vertebra.
The last parameter influencing the segmentation
results is the structure of the profiles used for the
search process phase. This one depends on two pa-
rameters: the number of points by profile and the dis-
tance between these points. We can also notice that
to ensure an independence of this spacing with re-
spect to the image size, this distance is proportional
to the vertebra size. After various tests, we conclude
that a profile of seven points spaced by a distance
equal to 5% of the vertebra size is a good compro-
(a) Image 1. (b) Image 2.
(c) Image 3.
Figure 4: Test images.
Table 1: Vertebra recognition rate.
Vertebra Type Recognition Rate
C3 96%
C4 98%
C5 96%
C6 98%
C7 86%
mise. Figure 5 shows the segmentation results for the
three images corresponding to the cervical spinal col-
umn (Figure 4) on the basis of the parameters pre-
sented above. After convergence, all the vertebrae are
detected perfectly. The segmentation results for the
chosen images tests show that vertebra edges are de-
tected perfectly by applying the proposed segmenta-
tion approach, based on a vertebra model and using
the Active Shape Model approach. The Table 1 pro-
poses the vertebra recognition rate of our method on
50 images.
BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing
(a) Image 1.
(b) Image 2.
(c) Image 3.
Figure 5: Segmentation results.
The goal of this paper was to present a semi-automatic
technique applied to cervical vertebra edge detection
in X-ray images. To this aim, we used a segmentation
approach based on Active Shape Model. This method
is composed of two stages: a stage of modeling and
another of search. We proposed an approach which
consists on modeling all the shapes of vertebrae by
only one vertebra model. The multiple tests which
we carried out on a large dataset composed of varied
images prove the effectiveness of the suggested ap-
proach. We can also notice that the proposed method
allows a fast contours extraction and is more repro-
ducible than the manual method. This method can be
adapted to other component of the spinal column: like
dorsal or lumbar.
The principal inconvenient of this ASM based
segmentation approach is the stage of training, which
is time consuming. Another important problem of this
approach is the impact of pose initialization in ASM:
the closer the mean shape is placed to the actual ob-
ject, the better the chances of having a successful seg-
mentation are. In our case, we solve this problem by
proposing a semi-automatic approach. So, we suggest
to place the mean shape model on the image by using
the vertebra left corners edges which are placed by the
user. This approach produces a very good initializa-
tion of the search process.
In our future works we want to investigate a
method aiming to propose an automatic approach of
segmentation. To this end, we can use some corner
detectors. We also consider the use of these segmen-
tation results in order to analyze the mobility of the
cervical spinal column. Another perspective of our
work consists in using the Graphics Processing Unit:
GPU, in order to accelerate the process of mean shape
calculation, and also the ASM search stage.
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