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Liver Tumor segmentation in CT images using probabilistic
methods
Itay Ben-Dan ∗Elior Shenhav †
July 9, 2008
Abstract
Liver tumors segmentation is an important prerequisite for planning of surgical inter-
ventions. For clinical applicability, the segmentation approach must be able to cope with
the high variation in shape and gray-value appearance of the liver. We present a fully
automatic 3D segmentation method for the liver tumors from contrast-enhanced CT data.
The method consists of two main stages.
First an initial histogram and statistical distribution functions are created, and from
them a new image is created where, in each voxel, a weighted function is attached in accor-
dance with the probability of the voxel grey level. Next, we use the active contour method
on the new image, where the active contour evolution is based upon the minimization of
variances between the liver tumor and its closest neighborhood.
1 Introduction
Techniques of Image processing and data analysis are more and more used in medical practice.
Mathematical algorithms of features extraction and measurements can exploit data to detect
pathology in an individual, the evolution of the disease, or to compare a normal subject to an
abnormal one.
We are using the assumption that the liver can be segmented ([MC],[FPFW],[LLS],[1], previous
contest) and we will follow this assumption in the rest of the paper.
1.1 Description of the problem
Liver cancer is one of the most popular cancer diseases and causes a large amount of death
every year [2]. In order to make decisions such as liver resections, doctors will need to know
the tumor volume, and further, the functional liver volume. Thus, an important task in ra-
diology is the determination of tumor volume. Accurate segmentation of liver tumor from an
abdominal image is one of the most important steps in 3Drepresentation for liver volume
measurement, liver transplant, and treatment planning. Since manual segmentation is incon-
venient, time consuming and depends on the individual operator to a large extent, automatic
segmentation is much more preferred.
The main issue of automatic liver tumor segmentation from contrast-enhanced CT data
is that the intensity values of the liver tumors are often similar to those of healthy parts of
∗Mathematics Dept., Technion—Israel Institute of Technology, Haifa 32000, Israel. itaybd@gmail.com
†Biomedical Dept., Technion—Israel Institute of Technology, Haifa 32000, Israel.
shenhave@technion.ac.il.
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the liver. Approaches which are only based on local intensity or intensity gradient features
are usually not sufficient to differentiate between liver tissue and other anatomical structures
in those regions. In order to alleviate this problem prior knowledge about the typical shape
and the intensity of a liver tumors may be incorporated into the process to constrain the
segmentation process where the image information is not reliable.
1.2 Previous Work
A significant number of techniques has been proposed to deal with this and similar problems.
The whole set of approaches can be roughly divided into three groups, variational geometric
approach, texture analysis, machine learning.
Here we combine methods of prior analysis and energy based segmentation. Energy based
segmentation we use here based on [TCLV],[CV]. Efficient numerical methods were devel-
oped for blood vessels segmentation [HKPG], and for liver segmentation []. A combination of
Bayesian approaches and deformable surfaces for tumor segmentation was reported in [PHS],
[PSDF].
In this paper we adopt the Chan-Vese method and develop a new model using the intensity
likehood ratio test. Unlike the model in [LM], the energy based segmentation is preformed on
a probability image which yields a better and less noise sensitive results.
2 Methodology
Our approach for evaluating models for automatic liver segmentation consists of the following
stages: first, a probability image of the organ of interest is obtained by applying a binary
classification model (liver/non-liver) obtained using pixelbased priors. Since the classifier
model does not incorporate any spatial information, Chan-Vese segmentation algorithm is
applied on the organ probability image to overcome this drawback and remove the noise
introduced by misclassified pixels.
In this paper following([LM],[PHS]), we show how using the following two phases enables
us to extract the tumor up to relatively small mistakes.
2.1 Modeling tumor appearance in CT by weighted non-parametric density
estimate
Data obtained from manually segmented cases, was used as a reference to apply a learning
procedure method. The manually segmented data consists of the V OIin only. We then obtain
another volume of interest , V OIout, which is considered to contain only non-lesion tissue, by
first dilating generously the original mask V OIin using a 3Dstructuring element and then
excluding V OIin from the dilated mask. Morphological operations are restricted to respect
other pre-segmented structures, including body outline, bone and other detected hotspots. A
probabilistic model of tissue attenuation in CT in both the segmented tumor (i.e. lesion) as
well as in the background (i.e. non-lesion) can be obtained in terms of CT intensity likelihood
functions using weighted non-parametric density estimates. Let the CT value, I CT (x), at a
voxel, x, be I(x), then we can approximate the likelihood of this intensity,
in a lesion, or outside a lesion by:
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f(α|in −tumor) = 1
|V OIin|Zα+γ1
α−γ1
dV OIin
f(α|out −tumor) = 1
|V OIout|Zα+γ2
α−γ2
dV OIout
Where αis the intensity value, V OIin is the measure of the region of the tumor and
V OIout is the measure of the region outside the tumor, and γ1, γ2are parameters determined
by |V OIin|,|V OIout|respectively.
A joint-likelihood ratio r(x) is calculated on a voxel-by-voxel basis in the CT domain to
provide a measure of voxel being contained in tumor tissue as opposed to being in background,
r(x) = f(x|in tumor)−f(x|out tumor).
The choice of r(x) is based on tests we made.
By this we can overcome problems of small variance, and also enhancing difference between
the tumor and other parts (blood vessels) of the liver. This method prove its usefulness
especially when when a variety of tissues surrounding the tumor.
2.2 3DImage variational segmentation
Our method is based on geometric active surfaces that evolve according to geometric partial
differential equations until they stop at the boundaries of the objects. We use a minimal
variance term that measures the homogeneity inside and outside the object. The measure we
use is the minimal variance term proposed by Chan and Vese [TCLV]. It penalizes lack of
homogeneity inside and outside the evolving surface. In [TCLV], the image is divided into two
segments, the interior and exterior of a closed surface. This model minimizes the variance in
each segment. The model was generalized in [3][CV] to piecewise constant segmentation of
more than two segments and higher dimensions. Given a 2Dgray level image I(x, y) : Ω →R2
, Chan and Vese proposed to use a minimal variance criterion given by the functional,
EM V (C, c1, c2) = Z ZΩC
(I(x, y)−c1)2dxdy +Z ZΩ\ΩC
(I(x, y)−c2)2dxdy +vZC
ds
(11) where Cis the contour separating the two regions, ΩCis the interior of the contour C, and
RCds measures the length of the separating contour, where vis a constant that determines
the regularization level. While minimizing this functional, c1and c2obtain the mean intensity
values of the image in the interior and the exterior of C, respectively. The optimal curve would
separate the interior and the exterior with respect to their relative expected values.
Our method integrates two ’methods’: a bayesian prior based tumor modelling, a homo-
geneity term based on the Chan-Vese functional. In the next section we discuss the experi-
mental results.
3 Experimental Results
Our primary results are based on the CT images from the contest. In order to obtain priori
knowledge we analyzed the intensity values of the liver tumors and of the healthy parts in the
given test data.
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The intensity values of the liver tumors are often similar to those of healthy parts of the
liver, here we introduce some statistics (including the three relevant cases from the original
data set) which demonstrate the problem of using variance minimization methods on the orig-
inal picture: The intensity variance of ’tumor’ pixels is:
Case 1: 5.1955 ∗10−5
Case2: 5.1477 ∗10−5
Case4: 1.0655 ∗10−4
The intensity variance of the ’non-tumor’ pixels is:
Case 1: 8.6659 ∗10−4
Case2: 6.2∗10−3
Case4: 1.2∗10−3
One of the main problems is the small relative difference between the intensity of the
tumor and the healthy part this cause that any energy based segmentation of the normalized
intensity values will not work. We will demonstrate other problems which make methods as
multiplication of all pixels by some large constant inefficient.
Therefore, with our method, given the assumptions approved by the provided data and
figures, the result is that the distribution functions of the grey level of the tumors and the
healthy parts are different. Just as well, the distribution functions of the the tumors are similar
up to the expectation (by similar we mean that there is an isometry of the approximated
functions s.t they are 0<10−4close in the L1metric). This enables us segmenting the liver
tumor, the accuracy of the segmentation depends on the accuracy of estimated the distribution
function. In figure (3) we show graphically the advantage of our method.
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Figure 1: Grey level distribution of tumors 1,2,4
Figure 2: Grey level distribution of tumors is marked by the blue curve and the distribution
of the healthy part is marked by the red curve
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Figure 3: probability image of neighborhood of the liver tumor
An example for the segmentation is shown in figures ??,5
An example of one advantage of our method of using the probability image can be seen in
the following figures 6,?? where the tumor is near the boundary of the liver and the tumor is
surrounded by two different regions which both apply to the out tumor class.
The results comparison metrics and scores for all the ten test cases.
Overlap Volume Ave. Surf. RMS Surf. Max. Surf.
Error Diff. Dist. Dist. Dist.
Tumor (%) Score (%) Score (mm) Score (mm) Score (mm) Score Total Score
IMG05_L1 30.66 76 17.37 82 2.36 40 3.24 55 12.08 70 65
IMG05_L2 40.77 68 35.78 63 1.53 61 1.92 73 5.80 85 70
IMG05_L3 52.48 59 51.06 47 2.33 41 3.00 58 7.77 81 57
IMG06_L1 86.91 33 86.90 10 3.25 18 3.51 51 6.88 83 39
IMG06_L2 41.85 68 2.80 97 1.11 72 1.79 75 8.94 78 78
IMG07_L1 39.18 70 36.54 62 5.27 0 6.34 12 23.50 41 37
IMG07_L2 30.21 77 0.53 99 1.45 63 2.02 72 8.81 78 78
IMG08_L1 24.96 81 23.36 76 2.87 28 3.55 50 12.77 68 60
IMG09_L1 97.49 25 94.59 2 7.37 0 8.46 0 17.28 57 17
IMG10_L1 46.66 64 46.28 52 2.81 29 3.42 52 9.94 75 54
Average 49.12 62 39.52 59 3.04 35 3.73 50 11.38 72 56
4 Conclusion and discussion
The benefits of this algorithm can be summarized as follows: Automatic detection of interior
contours, robust with respect to noise, ability to detect and represent complex topologies
(boundaries, segments) and extraction of geometric measurements such as length, diameter,
area, volume intensity, of a detected tumor.
6
image.jpg
Figure 4: Tumor in the Coronal Cut
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image segmented.jpg
Figure 5: Tumor Segmentation Coronal Cut
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image edge.jpg
Figure 6: tumor is in the image edge
image segmented edge.jpg
Figure 7: segmented tumor in the image edge
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Further possible improvements could be in Validation of vessels segmentation, Liver parti-
tioning to functional parts and Integration with pre-operative planning modules. And maybe
Using the algorithm to segment other organs.
5 Acknowledgements
We would like to thank Dr. Moshe Lapidot at the Rambam Hospital, Haifa, Israel.
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