Automatic Liver Parenchyma Segmentation from Abdominal CT
Images Using Support Vector Machines
Suhuai Luo
1
, Qingmao Hu
2
, Xiangjian He
3
, Jiaming Li
4
, Jesse S. Jin
1
, Mira Park
1
1: The University of Newcastle, Australia, 2: Chinese Academy of Sciences,
3: University of Technology Sydney, 4: CSIRO ICT Centre Australia
Abstract—This paper presents an automatic liver
parenchyma segmentation algorithm that can segment liver in
abdominal CT images. There are three major steps in the
proposed approach. Firstly, a texture analysis is applied to
input abdominal CT images to extract pixel level features. In
this step, wavelet coefficients are used as texture descriptors.
Secondly, support vector machines (SVMs) are implemented to
classify the data into pixel-wised liver area or non-liver area.
Finally, integrated morphological operations are designed to
remove noise and finally delineate the liver. Our unique
contributions to liver segmentation are twofold: one is that it
has been proved through experiments that wavelet features
present good classification result when SVMs are used; the
other is that the combination of morphological operations with
the pixel-wised SVM classifier can delineate volumetric liver
accurately. The algorithm can be used in an advanced
computer-aided liver disease diagnosis and liver surgical
planning system. Examples of applying the proposed algorithm
on real CT data are presented with performance validation
based on the comparison between the automatically segmented
results and manually segmented ones.
I. INTRODUCTION
In a computer-aided liver disease diagnosis and liver
surgical planning system such as a system for liver
transplantation, an accurate and automatic approach of liver
parenchyma segmentation is crucial. In practice, the liver
delineation in computer tomography (CT) images is very
difficult because of two main reasons. One is that the gray
level intensities of liver parenchyma are overlapped with
those of the surrounding tissues and organs such as the heart
and kidney. The other is that the liver is non-rigid in shape
and variant in position. The boundary between the liver and
its neighbouring structures is sometimes barely noticeable in
CT images [1,2]. Various algorithms have been proposed to
deal with the liver segmentation [3-8]. However, great
challenges remain in liver segmentation on the aspects of
accuracy, robustness, and automation.
In this paper, we present an automatic liver parenchyma
segmentation algorithm that can delineate liver in abdominal
CT images. In section 2, we describe the algorithm in detail,
including its flow diagram and its three major steps. In
section 3, we describe the procedure and results of the
experiments of applying the proposed algorithm on real CT
data as well as the related performance discussion. Finally in
section 4, we conclude by summarising the approach and
pointing out possible future pursuits in liver segmentation.
II. T
HE METHODOLOGY
In developing an automatic segmentation of CT images of the
liver, we have focused our attention mainly on three aspects. First,
there are no defined intensity or geometry descriptions to delineate
liver in CT images. Therefore, a simple approach such as an
intensity threshold will not apply. Second, both texture features and
distribution or resolution features are important in isolating the
liver from other surrounding areas. With this consideration,
Wavelet coefficients are investigated and used as texture
descriptors. The last aspect is that the combination of a pixel-wised
classifier with a shape-wised refiner will deliver a robust yet
accurate segmentation of the liver. This leads to our approach of
combining SVM classifier with morphological operators. This
section details the concepts and implementations in these regards.
A. Overview
Fig. 1 illustrates the overview of the proposed approach of
liver segmentation. It contains three major steps: texture
feature extraction, support vector machine classification,
and combined morphological operations.
Fig. 1 The overview of the proposed liver segmentation
The automatic segmentation process starts with extracting
texture features from input CT slices. We propose to use
Wavelet coefficients as texture features. Support vector
machines are used to classify each pixel into either liver
(with value of 1 assigned) or non-liver (with value of 0
assigned). Here the parameters of the SVM have been
Texture feature extraction
Support vector machine classification
Volumatric
abdominal CT
images
Integrated morphological operations
Segmented
liver
parenchyma
978-1-4244-3316-2/09/$25.00 ©2009 IEEE
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derived in a training process, of which the details will be
given in the following description. Since the SVM is a
pixel-wised classifier, i.e., it classifies the CT slices pixel by
pixel, and the classification will not be perfect on test data,
there will be both false negative error (FNE) inside the liver
parenchyma and false positive error (FPE) outside the liver
parenchyma. Therefore, a set of specifically designed
morphological operations is used to refine the result of SVM
classification to get the delineation of the liver. The
following three sections detail these step
s.
B. Wavelet Texture Feature Extraction
Texture extraction is the process of quantifying the
texture patterns within a specified neighbourhood of size N
by N pixels around a pixel of interest. There mainly exist
four categories of texture analysis, namely, structural,
statistical, model-based, and transform-based approaches
[9]. In our study, Wavelet coefficients are used as texture
descriptors to segmenting the liver. This section describes
the definitions and calculations of the Wavelet features.
To deal with both the texture characteristics and spatial
structures of the liver and its surrounding tissues, Wavelet
transform [12] is used to derive inputs to the SVM classifier.
Comparing to other transforms such as Fourier [13] and
Gabor [14], Wavelet transform has two advantages in
segmentation application. One is that it can represent
textures at the most suitable scale by varying the spatial
resolution. The other is that wavelets best suite for texture
analysis in a specific application can be chosen because of a
wide range of choices for the wavelet function.
The wavelet transform replaces the Fourier transform's
sinusoidal waves by a family generated by translations and
dilations of a window called a wavelet. The wavelet
transform is defined by
dt
s
ut
tffsuWf
s
su
)()(,),(
*
1
,
−
==
∫
+∞
∞−
ψψ
(EQ 1)
Where the base atom
ψ is a zero average function,
centered around zero with a finite energy. The family of
vectors is obtained by translations and dilatations of the base
atom:
)(
1
)(
,
s
ut
s
t
su
−
=
ψψ
(EQ 2)
In image processing applications, the wavelet transform is
usually computed with dyadic wavelet transform which is
implemented by filter banks. The filtering is done along both
rows and columns with pairs of lowpass filter and highpass
filter [12]. As illustrated in Fig. 2 (a), a one-scale image
wavelet decomposition results four blocks of components:
LL which is the downsampling of the lowpass filtering along
both rows and columns, LH which is the downsampling of
the lowpass filtering along rows and highpass filtering along
columns, HL which is the downsampling of the highpass
filtering along rows and lowpass filtering along columns,
and HH which is the downsampling of the highpass filtering
along both rows and columns. Such filtering or
decomposition can be done further on LL, resulting a higher
scale representation of the original image as shown in Fig. 2
(b).
Fig. 2 The wavelet coefficients derived with decomposition
(a) output of one-scale decomposition (b) output of
two-scale decomposition
C. SVM Classification
Support vector machines (SVMs) [15] are a set of related
supervised learning methods used for classification and
regression. Viewing input data as two sets of vectors in an
n-dimensional space, an SVM will construct a separating
hyperplane in that space, one which maximizes the margin
between the two data sets.
Assume the training set is {(x
i
,y
i
}, i =1,2,…l}, where x
i
is
the input with x
i
∈Rn, y
i
is the output with y
i
∈R, here
R={-1,+1}, and l is the number of input samples. Then an
optimal hyperplane in canonical form must satisfy the
following constraints:
0)( =+ bx
ω
φ
(EQ 3)
Where b∈ R,
ω
is a normal vector,
)(x
φ
is an inner
product that maps the input space into a high dimension
linear space.
SVM converts the task of finding the optimal hyperplane
into a task of quadratic programming problem as:
)min(
1
2
2
1
∑
=
+
l
i
i
C
ξω
, subject to
ii
bx
ξ
ω
−≥+ 1)(
,
}1,1{−∈
i
y
(EQ 4)
Where
0≥
i
ξ
is slack variable,
0>C
is penalty.
Applying Lagrange multipliers, the optimal quadratic
programming problem with the above linear conditions can
be solved as the following dual optimal problem:
)},(max{
11
2
1
1
jiji
l
i
j
j
ji
l
i
i
xxKyy
∑∑∑
===
−
ααα
, subject to
C
i
≤≤
α
0
, and
0
1
=
∑
=
i
l
i
i
y
α
(EQ 5)
Where
i
α
is support value, the x
i
corresponding to
C
i
≤≤
α
0
is called support vector (SV), and the x
i
corresponding to
C
i
<<
α
0
is called normal support
vector (noted as NSV).
)],([
1
j
NSVxSVx
ijji
N
xxKyyb
ij
NSV
∑
∑
∈∈
−=
α
(EQ 6)
LL LH
HL HH HL HH
LH
LL
LL
LL
LH
LL
HL
LL
HH
(a) (b)
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Where NNSV is the number of NSV,
),(
ji
xxK
is kernel
function.
The training process will derive
i
α
, b, and
),(
ji
xxK
.
Then the SVM as a classifier can classify any input data x
with the following classify function:
)},({)(
1
xxKysignxf
ii
l
i
i
∑
=
=
α
(EQ 7)
D. Integrated Morphological Operations
A SVM is a pixel-wised classifier. This results in two
issues that need to be resolved in liver parenchyma
segmentation. One is that the classification is not perfect,
resulting misclassified pixels both within the liver and
outside the liver. The other is that the shape and spatial
information is not considered, making the classification
sensitive to the noise produced by the misclassified pixels.
Therefore, a set of specifically designed binary
morphological operations [16] is used to refine the result of
SVM classification to get the delineation of the liver.
The integrated morphological operation starts with
“dilate” and “erode” on the output of pixel-based SVM
classifier. Fig. 3(a) presents an original slice of abdominal
greyscale CT image. In the image, liver is at the top-left
corner, indicated with the white curve. Fig. 3(b) shows the
output of SVM on the image. From the figure, it can be seen
that the SVM can classify most of the liver pixels correctly
but with some errors outside liver as well. By applying
“dilate” and then “erode”, the dotted pattern inside the liver
is converted into connected region as shown in fig. 3(c).
Morphologic operations are described by the shape and size
of the structural element used. When a “dilate” or “erode”
operator is used, the size of the structural element has to be
chosen carefully: if the structural element is too small, there
will form multiple regions inside the liver; if the structural
element is too large, other organs and tissues will be wrongly
combined into liver. We used a square structural element
with a diameter of 6 pixels for the operation. This value was
determined according to both the anatomical structural
knowledge of the abdomen and the CT image resolutions.
The second step of the integrated morphological operation
is to get rid of non-liver areas but keep the liver. This can be
easily done by retaining the largest object inside the
abdominal volume composed of multiple scans. Fig. 3 (d)
shows the outcome.
Up to this point, it can be seen from fig. 3(d) that there are
still some black holes inside the liver. These are the pixels
which are liver yet are misclassified as non-liver. To rectify
on these positions, “hole filling” operation is applied. Its
result is shown in fig. 3(e).
The last step is to delete the spurs and smooth the contour
along edges. Here the “erode” operator is applied first, then
the “dilate” operator. Fig. 3(f) shows the final segmented
liver area, where the white curve is the liver contour that was
manually segmented by radiologist.
III. E
XPERIMENTS
The proposed automatic liver parenchyma segmentation
algorithm was applied to human abdominal CT images
obtained from [17]. All the images were enhanced with
contrast agent and scanned in the central venous phase on a
variety of scanners ranging from 4 to 16 and 64 detector
rows. All the data were acquired in transversal direction. The
pixel spacing varied between 0.55 and 0.80 mm, the
inter-slice distance varied from 1 to 3 mm.
In designing the support vector machine classifier, an
open source software LIBSVM [18] was used as a platform
to derive proper parameters.
Three slices from one data set (liver-orig002, named as
a
b
c
d
e f
Fig. 3 Refining the output of SVM classification with
combined morphological operations
(a) an original slice of abdominal greyscale CT image; (b)
output of SVM on the image; (c) output of “dilate” and
“erode”; (d) output of getting rid of non-liver areas; (e)
output of “hole filling” operation; (f) output of “smoothing”
operation Note: the white curve in (a) and (f) is the liver
boundary manually segmented by radiologist
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Data2) were used as training data. Testing was done on the
data set and another data set (liver-orig003, named as
Data3). Performance validation was done by comparing the
automatically segmented results with the results manually
segmented by experience radiologist. Three metrics are
resigned to evaluate the algorithm’s performance, of which,
the first two are used to evaluate the performance of SVM
classifier, and the third one is used to evaluate the
performance of the proposed automatic liver parenchyma
segmentation algorithm as a whole.
(a) False positive volume fraction (FPVF)
FPVF is defined as the amount of the pixels that are
falsely classified by SVM as the liver, as a fraction of the
total amount of pixels that are manually identified as the
liver by radiologist. It can be expressed as:
man
manSVM
L
LL
FPVF
−
=
Where L
man
denotes the total amount of pixels that are
manually identified as the liver by radiologist, i.e., the
number of 1’s in the classification bench mark dataset. L
SVM
denotes the total amount of the pixels that are classified by
SVM as the liver.
manSVM
LL −
is the set difference
between L
SVM
and L
man
.
(b) False negative volume fraction (FNVF)
FPVF is defined as the amount of the pixels that are
falsely classified by SVM as the liver, as a fraction of the
total amount of pixels that are manually identified as the
liver by radiologist. It can be expressed as:
man
SVMman
L
LL
FNVF
−
=
Where
SVMman
LL −
is the set difference between
L
man
and L
SVM
.
(c) True positive volume fraction (TPVF)
TPVF is defined as the amount of the pixels that are
classified as liver by both the proposed automatic liver
parenchyma segmentation algorithm and radiologist, as a
fraction of the total amount of pixels that are manually
identified as the liver by radiologist. It can be expressed
as:
man
manproposed
L
LL
FPVF
∩
=
Where L
proposed
denotes the total amount of the pixels that
are classified by the proposed automatic liver parenchyma
segmentation algorithm as the liver.
Segmentation performance evaluation was done on
different data sets and texture features. Table 1 shows the
performance metrics of the proposed liver segmentation
algorithm.
Table 1 Performance metrics (%) of the proposed liver
segmentation algorithm
FPVF FNVF TPVF
Data2 11.5 5.3 96.3
Data3 15.5 7.8 94.1
Note that Data2 contains the three training images, Data3
contains the images of another subject. From the table we
can observe that: (a) SVM classifier alone is not enough to
delineate the liver parenchyma. Misclassification happened
at both inside the liver (which is measured by FNVF) and
outside the liver (which is measured by FPVF); (b) On true
positive volume fraction, the approach presented about two
percent better performance on partly trained data set (i.e.,
Data2) than non-trained data set; (c) The proposed approach
achieved as high as 94.1% true positive volume fraction on
non-trained data set, and 96.3% on partly trained data set.
IV. C
ONCLUSIONS
This paper has introduced an automatic liver parenchyma
segmentation algorithm to segment liver in abdominal CT
images. It is based on efficient texture feature analysis,
support vector machines, and integrated morphological
operations. The approach is unique in that it uses the
combination of integrated morphological operations with
pixel-wised SVM classifier to delineate volumetric liver
accurately. Experiment results on liver segmentation on real
CT images have demonstrated the effectiveness of the
algorithm. The algorithm can be used in an advanced
computer-aided liver disease diagnosis and liver surgical
planning system. Future work and further improvements
needed for the method include: theoretical and implemental
study on the support vector machine classifier to make the
pixel based classifier more robust on test data; calculation
speed improvement to SVM on both training and testing;
and testing on more data.
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