Paraspinal Muscle Segmentation in CT Images Using GSM-Based Fuzzy C-Means Clustering
Journal of Computer and Communications, 2014, 2, 70-77
Published Online July 2014 in SciRes. http://www.scirp.org/journal/jcc
http://dx.doi.org/10.4236/jcc.2014.29010
How to cite this paper: Wei, Y., Tao, X.P., Xu, B. and Castelein, A.P. (2014) Paraspinal Muscle Segmentation in CT Images
Using GSM-Based Fuzzy C-Means Clustering. Journal of Computer and Communications, 2, 70-77.
http://dx.doi.org/10.4236/jcc.2014.29010
Paraspinal Muscle Segmentation in CT
Images Using GSM-Based Fuzzy
C-Means Clustering
Yong Wei1, Xiuping Tao2, Bin Xu3*, Arend P. Castelein1
1Depart men t of Computer Science and Information Systems, University of North Georgia, Dahlonega, USA
2Depart men t of Chemistry, Winston-Salem State University, Winston-Salem, USA
3Depart men t of Spine Surgery, Jinling Hospital, School of Medicine, Nanjing University, Nanjing, China
Email: *xubin2020@gmail.com
Received April 2014
Abstract
Minimally Invasive Spine surgery (MISS) was developed to treat disorders of the spine with less
disruption to the muscles. Surgeons use CT images to monitor the volume of muscles after opera-
tion in order to evaluate the progress of patient recovery. The first step in the task is to segment
the muscle regions from other tissues/organs in CT images. However, manual segmentation of
muscle regions is not only inaccurate, but also time consuming. In this work, Gray Space Map (GSM)
is used in fuzzy c-means clustering algorithm to segment muscle regions in CT images. GSM com-
bines both spatial and intensity information of pixels. Experiments show that the proposed GSM-
based fuzzy c-means clustering muscle CT image segmentation yields very good results.
Keywords
CT Image, Segment ation, Gray Space Map (GSM), Fuzzy C-Means Clustering, Minimally Invasive
Spine Surgery (MISS)
1. Introduction
For patients with spine disorders such as lumbar spondylolisthesis, instability and spinal stenosis, surgery is one
of the options for treatment. The traditional transforaminal lumbar interbody fusion (TLIF) and posterior lumbar
interbody fusion (PLIF) require a wide decompression and bilateral nerve-root retraction to access the disc space
[1]. Minimally Invasive Spine surgery (MISS) was developed to decrease postoperative pain and allow quicker
recovery by limiting soft-tissue retraction and dissection [2]. One of the main goals of MISS is to reduce trauma
to the two posterior paraspinal muscle groups, including the deep paramedian transversospinalis muscle group
and the more superficial and lateral erector spine muscles [2]. Researchers have been using magnetic resonance
imaging (MRI) to assess the postsurgical appearance of the multifidus muscle [3], and compared muscle dam-
ages in two groups of patients treated with a posterior lumbar interbody fusion, those who had had a traditional
*
Corresponding author.
Y. Wei et al.
71
midline approach and those who had had a Wiltse approach [4].
Physicians can use the computed tomography (CT) images to estimate volume of muscles surrounding the
spine before and after the operation. The thickness of reconstruction of CT slices is determined during scanning.
If the size of muscle region in CT images can be measured, the volumetric estimation of muscle tissues sur-
rounding the spine can be obtained by calculating the sum of the products of the slice thickness and the muscle
region size of each CT slice. Hence, segmenting the muscle region in CT images becomes the key step in the
procedure.
In a CT image the intensity is a grey value representing the attenuation in the voxel [5]. A voxel is a small
rectangular pixel in three dimensions. The gray level intensity of a pixel in a CT image is determined by the
Hounsfield number [6]. The Hounsfield number specifies the attenuation in the material in relation to the attenu-
ation in water. The coefficient is material specific and a certain material thereby results in a certain pixel value
in a CT image.
The task of image segmentation is to group pixels into regions for future processes. In each partitioned region
of an image, pixels have similar characteristics based on given criteria. It is assumed that characteristics of pix-
els in different tissue object within an image will present themselves as clusters. Therefore segmenting tissue
object in a CT image becomes the problem of finding a set of clusters.
The k-means algorithm is the most commonly used clustering algorithm since it is easy to implement and
found to be effective in many applications. The fuzzy version of k-means clustering (fuzzy c-means, FCM) is
widely adopted for medical image segmentation [7]-[9]. Unlike the k-means clustering method, which forces
pixels to belong to one class, FCM classifies pixels to belong to multiple classes with degrees of membership.
The advantage of FCM-based segmentation algorithm over thresholding is that there is no need to choose the
empirical threshold. This feature is useful especially when large amount of images are processed.
In this work, Gray Space Map (GSM) is introduced to be used by the fuzzy c-mean segmentation algorithm to
incorporate both pixel intensity and region connectivity information. The CT images are from patients who have
had minimally invasive spine surgery. Experimental results show that the FCM-based image segmentation algo-
rithm incorporated with GSM yields promising results. Segmented posterior paraspinal muscle regions can be
used to estimate volume of muscles in order to evaluate damages to them after spine surgery.
The remainder of the paper is as follows. Section 2 provides a brief description of the challenges in muscle
region segmentation on CT images and the proposed fuzzy c-means segmentation algorithm using GSM. Section
3 discusses the experimental data preparation and results. Section 4 concludes the paper with an outline for fu-
ture work.
2. Paraspinal Muscle Region Segmentation
2.1. Fuzzy C-Mean Clustering
Fuzzy c-means (FCM) is a clustering method that allows a data point to belong to more than one cluster. Each
point has a degree of belonging to a cluster. The membership function is defined as below:
( )
21
1
1
m
Cxc
ij
xc
ik
k
ij
u
=




=
, (2.1)
where
ij
u
is the degree of data point
i
x
in cluster
j
,
1
1
C
ij
j
µ
=
=
,
j
c
is the center of cluster
j
.
represents the Euclidean distance between data point
i
x
and cluster center
j
c
. C is the total number of clusters.
Parameter m is a weighting exponent on each membership and controls the shape of the fuzzy membership func-
tion. When the value of m approaches 1, the algorithm becomes similar to k-means. The FCM algorithm mini-
mizes the following objective function:
2
11
NC
ij ij
ij
ux c
= =
∑∑
,
1m≤ <∞
(2.2)
where N and C are the total number of data points and clusters respectively.
Y. Wei et al.
72
2.2. Challenges of Paraspinal Muscle Region Segmentation in CT Images
Figure 1 is a CT image obtained from a patient who has had a minimal invasive spine surgery. In the image,
there are paraspinal muscles, spine and other tissues and organs. The histogram of the image (Figure 2) shows
that the intensities of the region of interest and other tissues/organs are similar, i.e. no obvious threshold of in-
tensity could distinguish other tissues from the region of interest.
In order to incorporate spatial information of pixels in the ROI, we can select an initial seed point within the
ROI. Figures 3-6 are visualizations of the ROI using various parameters. Figure 3 is a map of spatial Euclidean
distance from the seed point to other pixels. It does not reflect the dimension or shape of the muscle group. Fig-
ure 4 is the Euclidean distance map from the initial seed in the Gray level space. The map shows that the muscle
group region has similar parameter values to other soft tissues and organs, such as kidneys. The map based on
the mean Euclidean distance in Gray level space from a window centered in the initial seed to all the other win-
dows centered in all the other pixels in the image is shown in Figure 5. Window size is 7 × 7. It is similar to
Figure 4 except that the map is blurred because of the averaging operation. Statistical feature such as standard
derivation of pixel gray intensity values does not help in segmenting the region of muscles neither as shown in
Figure 6.
2.3. Gray Space Map (GSM)
The Gray Space Map (GSM) uses image topological information. The assumption for GSM is that pixels inside
Figure 1. CT Image of a MISS Patient, show-
ing paraspinal muscles and other tissues and
organs.
Figure 2. Histogram of the CT Image in Fig-
ure 1.
010 2030 4050 60 7080 90100
0
1
2
3
4
5
6
7
8x 10
4
Y. Wei et al.
73
Figure 3. Spatial Euclidean distance map from
the initial seed.
Figure 4. Gray intensity Euclidean distance
map from the initial seed.
Figure 5. Gray intensity mean Euclidean dis-
tance map from the initial seed, window size is
7 × 7.
SDMap
EDMap
EDMAp
w
indow
Y. Wei et al.
74
Figure 6. Standard derivation distance map
between the initial seed and other pixels, win-
dow size is 7 × 7.
the region of interest not only have similar gray level intensities but also connect to other pixels inside the region
[10]. It is necessary to emphasize that it is not assumed that pixels in other regions have different intensity val-
ues from pixels inside ROI. This is important because as we have seen, other tissues and organs have similar
gray level values as the region of muscles.
The algorithm starts with a pre-selected seed point inside the region of interest. Initial values of all pixels in
the image are set to zero. During each iteration, the GSM values of pixels which satisfy both of the following
conditions are incremented by 1. Condition 1: pixel gray level intensity difference from the seed point is within
a threshold T; Condition 2: the pixel belongs to a structure which overlaps the seed point. The GSM values are
defined in the following equation.
( )()
max
0
, ,,
I
T
GSMij gijT
=
=
whe r e
( )
, ,1,g ijT=
if
( )
,
T
ij R
AND
()
( )
,xy
I i jIseedseedT
− −≤
;
Otherwise,
( )
,, 0
g ijT=
(2.3)
In Equation (2.3), pixel
( )
,ij
belongs to gray level image I. T is a threshold of gray level intensity differ-
ence between the seed point and other pixels. Threshold T starts from zero up to the maximum possible value for
the pixel value data type
max
I
. If the data type is an unsigned eight bit integer,
max
I
is 255.
T
R
is a region
overlapping the seed point
( )
,
xy
seed seed
within threshold T. In our calculation,
( )
,GSMi j
is normalized to
the range of
[ ]
0, 1
. Pixels connected to the seed point with similar gray level intensities are assigned higher
GSM values than other pixels. In Figure 7, the region of paraspinal muscle group is clearly differentiated from
other regions. The histogram of the GSM image (Figure 8) shows pixels whose GSM values are greater than the
red line belong to the paraspinal muscle region. Comparison of histogram of gray intensities in Figure 1 with
that of GSM in Figure 8 confirms that GSM is useful in segmenting muscle region from other tissue s
3. Experimental Results
Images used in experiments are extracted from axial spinal CT scans of patients who have had minimal invasive
spinal surgery. SL represents the axial spatial location of the slice. ST is the slice thickness. Resolution of the
images is 512 × 512. Objects in an image include the paraspinal muscle groups, kidney, liver, pancreas, spine
STDMap
w
indow
Y. Wei et al.
75
Figure 7. GSM visualization of the CT image
illustrated in Figure 2.
Figure 8. Histogram of the GSM image of the
CT image illustrated in Figure 2.
and other tissues. CT image pixel values are determined by the Hounsfield coefficient of material. Hounsfield
units of some related substances [11] are shown in Table 1. In a CT image, it is easy to differentiate muscle
from fat and bones using gray intensities. However, the HU interval of muscles overlaps with organs such as
kidney, liver and pancreas, making it difficult to segment the muscle region from other tissues using gray inten-
sity alone. Hence topological information should be incorporated in the segmentation algorithm.
To reduce the effect of the initial seed selection, images are dilated. The user chooses an initial seed point
within the interested region, i.e. the paraspinal muscle region. GSM is calculated and normalized to range
[ ]
0, 1
.
For an image of size
ij×
,
Nij
. The input to the FCM clustering algorithm is a sequence of
k
p
,
1~kN=
, where
k
p
is the GSM value of pixel k in the image. Figure 9 shows a set of segmentation results.
Figure 9(a) shows the region of longissimus muscle and iliocostal muscle, which is the interested region. Or-
gan in Figure 9(b) is part of the gastrointestinal tract. Both Figure 9(c) and Figure 9(d) show images of kid-
neys. In Fig ure 9(e) and Figure 9(f), main tissues are psoas major, descending aorta, vertebral body and the
right side of sacrospinalis. Figure 9(h) sho ws the segmented region with the boundary highlighted.
4. Conclusions
In this paper, we use the GSM-based fuzzy c-means algorithm to perform CT image paraspinal muscle segmen-
tation to estimate muscle volume for patients who have had minimal invasive spinal surgery. Muscle tissues
have similar Hounsfield unit values with other organs. Thus using gray intensity alone cannot differentiate mus-
cles from other tissues. GSM utilizes both gray level intensity and image topological information. It is a prom-
ising candidate as a predicate used for segmentation.
GSM
Y. Wei et al.
76
Table 1. Hounsfield unit value ranges of tissues.
Tissue Type HU Value Range
Muscle 10 - 40
Bones 45 - 3000
Kidney 30 - 50
Li v er 20 - 60
Pancreas 10 - 40
Fat 220 - 30
(a) (b) (c) (d)
(e) (f) (g) (h)
Figure 9. Segmentation results.
Experimental results show that fuzzy c-means segmentation using GSM can effectively segment paraspinal
muscle regions. It provides a solid foundation for muscle volume estimation for physicians to evaluate muscle
damage due to spine surgery and monitor the progress of patient recovery. In the future, the technique will be
tested on large amount of image data.
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