A modified distance regularized level set model for liver segmentation from ct images

Signal & Image Processing : An International Journal (SIPIJ) Vol.6, No.1, February 2015
DOI : 10.5121/sipij.2015.6101 1
A MODIFIED DISTANCE REGULARIZED LEVEL
SET MODEL FOR LIVER SEGMENTATION
FROM CT IMAGES
Nuseiba M. Altarawneh1
, Suhuai Luo1
, Brian Regan1
, Changming Sun2
1
School of Design Communication and IT,
The University of Newcastle, Callaghan NSW 2308, Australia
2
CSIRO Digital Productivity Flagship,
Locked Bag 17, North Ryde, NSW 1670, Australia
ABSTRACT
Segmentation of organs from medical images is an active and interesting area of research. Liver
segmentation incurs more challenges and difficulties compared with segmentation of other organs. In this
paper we demonstrate a liver segmentation method for computer tomography images. We revisit the
distance regularization level set (DRLS) model by deploying new balloon forces. These forces control the
direction of the evolution and slow down the evolution process in regions that are associated with weak or
without edges. The newly added balloon forces discourage the evolving contour from exceeding the liver
boundary or leaking at a region that is associated with a weak edge, or does not have an edge. Our
experimental results confirm that the method yields a satisfactory overall segmentation outcome.
Comparing with the original DRLS model, our model is proven to be more effective in handling over-
segmentation problems.
KEYWORDS
Liver segmentation, level set method, Distance Regularized Level Set (DRLS) model, and balloon forces
1. INTRODUCTION
Human liver constitutes one of the most prominent organs. The liver is one of the most important
organs in the human body. The liver is located in the upper right quadrant of the abdominal
cavity and is the largest organ in the body. The liver has a weight of about 2% or 3% to the total
body weight [1]. The liver is an unshaped organ since its shape is mainly determined by the
surrounding structures such as the lower ribs and the diaphragm. The liver can be small and only
located in the right half part of the abdomen or extend all to the left and cover the spleen [2].
The volume of a healthy liver correlates to the individually required organ functions when a liver
grows during childhood and adolescence; it adapts to the needs and increases in size. Later, when
an adult gains or loses weight, the organ will also change to match the new metabolic demand. It
performs several key functions in the human body. Beside its main purpose as a filter for blood
and a store for minerals and vitamins, other duties of the liver include separating bile and

2
proteins, processing of sugar and decompositions of medications. Unfortunately, the liver is
prone to many life-threatening diseases, most notably, hepatitis C, cirrhosis, and cancer.
During the last few years, computer-aided surgical planning systems (CAD) have contributed
significantly in diagnosing and treatment of liver diseases[3]. These cutting-edge methods portray
the structure of liver and its vessels often in the form of 3D visualizations, provide insights into
surgical simulations with cutting guidelines. This in turn leads to a significantly shorter planning
time. On this regard, accurate segmentation of a liver from its surrounding organs in compute
tomography (CT) images represents one of the most daunting tasks.
Developing an effective method to segment liver from CT images is a daunting task. This is
primarily due to the very similar intensity values between the liver and its adjacent organs, the
complexity in the geometrical structure of the liver, significant variations in shape and volume of
liver between individuals, and the injection of contrast media. Several artefacts of pulsation and
motion, and partial volume effects also contribute the difficulties encountered in carrying out
automatic liver segmentation in CT images. It follows that liver segmentation from medical
images is an active area of research.
Methods and approaches utilized in liver segmentation in the CT images are generally
categorized into two main classes: semiautomatic and fully automatic liver segmentation
methods. Semi-automatic liver segmentation methods entail a rather limited user intervention to
complete the task. This intervention may vary from a manual selection for seed points to a
manual refinement of a binary mask for the liver. The term “fully automated” denotes a liver
segmentation process that is implemented without any intervention by an operator. This property
is regarded as a benefit of fully automated methods as it saves processing times and causes results
to be free from any errors and biases that may be introduced by the intervention of the user.
Herein, we survey recent advances in methods used in liver segmentation. These methods fall in
three main categories; namely, gray level based methods, model based methods, and texture
based methods [4]. It is apparent that each category of liver segmentation methods has its own
advantages and shortcomings. It follows that some methods may perform well in certain
applications while fail poorly on other cases.
The gray level based methods [5-15] deploy features from an image directly. Consequently, gray
level based methods are widely used in liver segmentation. These methods rely mainly on the
evolution of gray level toward targets. Whilst gray level methods are generally fast, the presence
of changes in gray level intensity of targets may affect their performance. Despite of using prior
knowledge, success of gray level methods is significantly hindered if the liver occupies a small
percentage of the image. Gray level is applied either manually or via an automatic rough
segmentation. The purpose of these two procedures is to gather information germane to the gray
level. The profound reliability of these methods is often over shadowed by their time-expensive
nature. In most cases, gray level methods necessitate substantial computational time.
Several gray level based methods utilises gradient information as a well-defined approach to deal
with image boundaries. However, this approach becomes impractical upon the presence of
numerous boundaries. Under these conditions, gray level based methods may readily converge to
wrong boundaries, resulting in over- or under segmentation. This could be corrected by refining
the results through manual work or via the implementation of other methods.

3
On the contrary, structure based methods [16-20] can generally handle cases with unclear liver
boundaries by utilising prior knowledge. Structure based methods can carry out tasks that could
not be performed by gray level based methods. However, these methods involve a great deal of
training data to cover all plausible conditions of the liver. Applying these methods hold profound
difficulty when handling non-standard liver’s shapes for the liver. In other words, it is very hard
to develop a “universal” segmentation model for liver based on structure based methods.
Instead of using gray level or shapes, texture based methods [21-24] utilises pattern recognition
and machine learning in their search for boundaries. As a result, these methods enable one to
collectively consider more features. Texture based methods can produce better results even when
the boundaries of liver are not clear. An accurate account of texture feature represents one of the
main challenges in these methods, in addition to the need for training data. Furthermore, selecting
a proper descriptor out of many, poses another problem. It is worthwhile noting that both
machine learning and pattern recognition still incur much weak processing ability if compared
with human brain and they are not able to achieve good segmentation result without the use of
other refined methods.
In most practical applications, gray level based methods often provide rather good segmentation
results. Structure based methods are mainly based on the shape of the object, a characteristic
affording them powerful performance. Methods that use texture properties work to simulate
processes in human’s brain. On the other hand, level set methods have been widely used in
segmentation of medical images [25-27]. Despite of their wide and effective uses, successful
application of level set relies heavily on the initial position.
Level set methods generally attain satisfactory if the initial contour is positioned near the target.
3D liver segmentation methods can be grouped into two classes, namely, direct 3D segmentation
and propagation of the 2D slice-based segmentation. In the first group, a 3D deformable surface
is first initialised in multiple 2D slices of the liver. This is followed by automatically updating the
initial 3D mesh by means of forces characterized by the image gradient and the smoothness of the
contour. As a result, direct 3D segmentation is time consuming and requires many user
interactions. This may render outcomes to be dependent on the user choices.
The second class of 3D liver segmentation stems from the slice-based propagation approach. In
this method, the 3D CT images are re-sliced into a number of 2D slices. A 2D segmentation is
applied on each slice that is initialized by a propagated boundary from the previous 2D slice. As
such, this technique reduces a 3D segmentation problem to a sequence of 2D segmentation
problems. Each of the reduced 2D segmentation sub-problems is significantly less sophisticated
than the original 3D segmentation problem. Furthermore, it is computationally less expensive to
integrate 2D shape information - as a shape constraint - into the 3D segmentation procedure.
Because the difference between adjacent slices is minimal, the final contour of one slice can
potentially afford useful information with regard to the initial contour position, prior intensity,
and shape information. Acquiring prior knowledge pertinent to these aforementioned factors
enhances the segmentation performance of the level set method of the following slices.
Our main contribution in this paper is to revisit the distance regularization level set [28] (DRLS)
model by deploying new balloon forces. These forces control the direction of the evolution and
slow down the evolution process in regions that are associated with weak or without edges. We
organise this contribution as follows, in Section 2 we present the DRLS model. Section 3

4
demonstrates our adapted theoretical approach. Section 4 depicts selected experimental results,
and finally concluding remarks are presented in Section 5.
2. DISTANCE REGULARIZED LEVEL SET METHOD
Li et al. [28] proposed a level set method termed as Distance Regularized Level Set (DRLS)
model. The DRLS model uses an edge-based active contour method to drive the level set function
(LSF) to the desired boundary, and provides a simple and efficient narrowband implementation
without re-initialization.
Let :φ Ω→ℜ be a level set function defined on domainΩ . An energy function ( )ε φ is defined
as:
( ) ( ) ( ) (1)p extRε φ β φ ε φ= +
where 0β > is a constant and ( )pR φ is the level set regularization term, defined by
( ) (| |) (2)pR p dxφ φ
Ω
= ∇∫
where p signifies an energy density function :[0, ) ,p ∞ → ℜ defined as
The minimization of the energy ( )ε φ can be achieved by solving a level set evolution equation.
For a LSF, an external energy function is defined by
( ) ( ) ( ), (4)ext g gL Aε φ λ φ α φ= +
where λ andα are the coefficient of the length term ( )gL φ and area term ( )gA φ , which is given
by
( ) ( ) | | (5)gL g dxεφ δ φ φ= ∇∫
and
( ) ( ) (6)gA gH dxφ φ= −∫
where [0,1)g ∈ is an edge indicator function given by

5
*
2
1
, (7)
1
g
G Iσ
=
+ ∇
where Gσ is a Gaussian kernel with a standard deviationσ , and I is the input image. The Dirac
delta function εδ and Heaviside function Hε in Eqs. (5) and (6) are approximated by the
following smooth function εδ and Hε , respectively, as in many level set methods:
and
where ε is a constant, typically set to 1.5. The length term ( )gL φ was first introduced by
Caselles et al. [29] in their proposed geodesic active contour (GAC) model. ( )gL φ is the line
integral of the function g along the zero level contour of φ , which is minimized when the zero
level set of φ is located at the object boundaries which in turn keeps the curve smooth during the
deformation.
The area term ( )gA φ calculates the weighted area inside the evolving contour. It is introduced to
speed up the motion of the zero level contour when the contour is far away from the desired
object boundaries and slow down the expanding and shrinking of the zero level contour when it
arrives at object boundaries where g is smaller. ( )gA φ represents a balloon forces in which the
sign of α controls the direction of the level set evolution (shrinking or expanding). The level set
evolution equation in the DRLS model is defined by:
.div( ( ) ) ( ). .div ( ). . (10)
| |
pd g g
t
φ φ
β φ φ δ φ λ δ φ α
φ
 ∂ ∇
= ∇ ∇ + + 
∂ ∇ 
The problem with the DRLS model in the case of liver segmentation is that the curve will evolve
and deviate from the liver boundary in the region with weak or without edges. In this
contribution, we will modify the distance regularization level set method [28] (DRLSM) by
adding a new balloon force to guide the evolution process and discourage the evolving contour
from leaking at a region with a weak or without an edges and from going far from the liver
boundary.

6
3. THE PROPOSED MODEL
In this paper, we propose a new balloon force that controls the direction of the evolution and
slows down the evolving contour at weak or blurred edges. Since the liver has a very similar
intensity with its adjacent organs, this could easily result in over and/or under segmentation
results. The DRLS model does not perform well with liver segmentation.
We will modify the DRLS model to segment the liver contour in each 2D slice by using a new
balloon force that controls the direction of the evolution and slows down the evolution process in
the region with weak or without edges, which subsequently discourage the evolving contour from
leaking at a region with a weak or without an edge and from deviating from the liver boundary.
Our balloon term will be built using the probability density function. The methodology
encompasses steps described in the following sections.
3.1 PRE-PROCESSING
The intensity distribution of the liver is irregular due to noises, so liver segmentation without pre-
processing is difficult. A smoothing step, in theory, would make the intensity distribution less
variable. In our work, a Gaussian filter is used as a smoothing step.
3.2 SEGMENTATION OF THE REFERENCE SLICE
This step is the most important step in our 3D liver segmentation method. The segmented liver
contour will be the initial contour for the adjacent slice so the segmentation result should be
accurate. The starting slice or the reference slice can be selected as the middle or the largest slice
of the liver volume. In this contribution we used the Active Shape Model (ASM) [30] to segment
the reference slice.
3.3 2D SLICE BASED PROPAGATION APPROACH
Since the variation of shape and intensity between the adjacent slices are very small we can use
these information from the previous slice to segment the next slice. In our method we compute
the mean intensity and the variance of the segmented slice. According to [31],
about 98% of liver pixel is located in Generating an
evolution region by expanding the previous segmented slice by a number of pixels and compute
the probability density function inside this region using the following equations:
21
( )
2
1
, if [ -3 , 3 ]
( ) (11)2
0, otherwise
x
e x
B X
µ
σ
µ σ µ σ
σ π
−
−
∈ +
= 


We then shrink the previous segmented slice and use it as the initial contour for its adjacent slices
in both directions.
µ σ
[ 3 , 3 ].µ σ µ σ− + [ 3 , 3 ].µ σ µ σ− +

7
3.4 MODIFIED DRLS MODEL
Since the liver boundary to be segmented is not far from the contour propagated from the
previous slice, a shape and intensity prior information will discourage the evolving contour from
leaking at a region with a weak edge or without an edge. We have modified the DRLSM by
adding the probability density energy term to the evolution equation and use it as a balloon forces
to control the direction and the speed of the evolution process
( ) . ( ) . ( ) . ( ) (12)P gE R L Bφ ρ φ λ φ α φ= + +
where ,ρ λ and α are the coefficients of the regularization term, the length term, and the
probability term, respectively. This energy functional can be minimized by solving the following
gradient flow:
.div( ( ) ) ( ). .div ( ). . ( ) (13)
| |
pd g B
t
ε ε
φ φ
ρ φ φ δ φ λ δ φ α φ
φ
 ∂ ∇
= ∇ ∇ + + 
∂ ∇ 
The above procedure is repeated until the contours in all 2D slices of the 3D image are
segmented. A 3D liver surface is reconstructed from the contours segmented from all 2D slices.
4. RESULT AND DISCUSSION
In the DRLS model, two segmentation stages are applied. The first stage is for evolving the
contour in the direction of the object boundary, speeding up the evolution process when the
evolving contour is far from the object boundary and slowing down the evolution process when
the evolving contour is close to the object boundary. The second stage concerns with the
refinement of the segmentation results. In each experiment, we selected values of ρ , λ and α
to be 0.02, 5 and -1 for the first stage and 0.02, 5 and 0 for the second stage, respectively. The
zero level set is initialized as a binary function and evolves according to the evolution equation
Eq. (13) for our model and Eq. (10) for the DRLS model.
Figure 1 presents segmentation results of the DRLS model and the proposed model in a liver CT
slice. Our model performs well and gives a satisfactory result comparing to the DRLS model. The
DRLS model fails to segment the liver boundary and the evolving contour leaks from the region
with weak edges. Our balloon force slows down the evolution process close to the liver boundary
and stops the evolving contour from going far in the region with weak or without edges.
Comparing with the DRLS model, our model is more effective in dealing with over segmentation
problem.

8
Figure 1. Comparisons of liver segmentation results between the DRLS model and the proposed method.
The first column shows the liver slice in a CT scan; the second column shows the evolving region in green
and the initial contour in red. The third column shows the ground truth segmented manually by a
radiologist in blue and the final segmentation result of the DRLS model in red and the fourth column shows
the ground truth segmented manually by the radiologist in blue and the final segmentation result with our
proposed method in red.
Figure 2 shows some examples of liver extraction results based on our proposed method. We
tested our model on a liver dataset containing 10 volumes of abdominal CT images. Each volume
has 64 slices and the size of each slice is 512x512 pixels. Each slice in the dataset is provided
with corresponding ground truth segmented manually by a radiologist. The model deals very well
with over segmentation problems. Our model can handle the over segmentation problem very
well in comparison with the DRLS model that is not able to handle this task well.

9
Figure 2. The experimental result of our proposed method on a sequence of liver slices for one person. The
green and red colours refer to the ground truth segmented manually by the radiologist and the final
segmentation result of our proposed method, respectively.
5. CONCLUSION
In a nutshell, the original DRLS model is modified by adding a novel balloon force. The most
advantageous feature of our method stems from its ability to guide the direction of the evolving
contour via several desired approaches. Our model slows down the evolving contour in regions
with blurred edges and dampens the evolving contour from exceeding boundaries of liver.
Experimental results have shown that our method produces satisfactory outcome, especially when
dealing with over-segmentation problems comparing with the DRLS model.
ACKNOWLEDGEMENTS
We would like to acknowledge and extend our gratitudes to the International Conference on
Signal, Image Processing and Multimedia (SPM-2015) for granting us a permission to publish a
modified version of the conference paper by Altarawneh et al. [32].

10
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International Conference on Signal, Image processing and Multimedia(SPM), Sydney, 2015.

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