AUTOMATED TUMOR SEGMENTATION USING LEVEL SET

METHODS

Stephane Lebonvallet, Sonia Khatchadourian and Su Ruan

CReSTIC,IUT de TROYES, 9 rue du Quebec,1026 TROYES CEDEX

Keywords:

Image, Partial differential equations, Level Sets, Segmentation.

Abstract:

In the framework of detection, diagnostic and treatment planning of the tumours, the Positron Emission To-

mography (PET) and Magnetic Resonance Imaging (MRI) have become the most efﬁcient techniques for

body and brain examination. Radiologists take usually several hours to segment manually the region of in-

terest (ROI) on images to obtain some information about patient pathology. It is very time consuming. The

aim of our study is to propose an automatic solution to this problem to help the radiologist’s work. This paper

presents an approach of tumour segmentation based on a fast level set method. The results obtained by the

proposed method dealing with both PET and MRI images are encouraging.

1 INTRODUCTION

PET (Positron Emission Tomography) and MRI

(Magnetic Resonance Imaging) scans are both stan-

dard imaging tools that physicians use to pinpoint dis-

ease states in the body and the brain. A PET scan

demonstrates the biological function of the body be-

fore anatomical changes take place, while the MRI

scan provides usually information about the brain tu-

mor. Accurate and automatic tumor segmentation is

a very important issue in many applications of medi-

cal image system for quantitative studies. As known,

manual tracing by an expert of a tumor in 3D is not

only exceedingly time consuming, but also exhaust-

ing for experts leading to human errors. Therefore, an

automatic segmentation is necessary.

Many segmentation methods have already been

used in medical imaging ﬁeld. A simple method is

the thresholding. (Malyapa et al., 2002) used a binary

threshold to segment tumorous areas in the pelvis re-

gion. This method allows the user to obtain results

very quickly but it is not very accurate. The seeded

region growing is one of segmentation methods. It

consists of choosing seeds, and growing them accord-

ing to a criteria. One solution adopted by (Adams

et al., 1994) is to choose the seeds as the local minima

and maxima and then to grow them until the regions

touch themselves. But when one need to delineate

just one region, one cannot venture to ﬁll the entire

image. That is why (Zorooﬁ et al., 2004) have cho-

sen the seeds upon the histogram and then let grow

until the criteria was no longer veriﬁed. This work

has been used to the segmentation of a non-necrotic

femoral head. Mathematical morphology segmenta-

tion based on watersheds (Roerdink et al., 2001)is

proposed in (Mancas et al., 2004)to segment PET

/CT images. The principle of the watershed tech-

nique is to transform the gradient of a grayscale im-

age into a topographic surface. An iterative water-

sheds is used in (Mancas et al., 2004). A very com-

mon way to segment medical images is to use an at-

las of the humain body as a priori knowledge. (Bon-

diau et al., 2005), (Erhardt et al., 2001) and (Lorenzo

et al., 2004) have used such approach respectively on

the brain, the hip and the heart atlases. The statisti-

cal methods have been also studied to deal with the

medical images, because of noise presenting in im-

ages. (Ruan et al., 2000) propose a statistical segmen-

tation based on Random Markov Fields to segment

brain RM images. The fuzzy segmentation offers an

interesting point of view to take into account ambigu-

ities of objets to segment. As shown in (Dou et al.,

2004), membership functions are modelled to express

the fuzzy signals of the brain tumor observed in differ-

128

Lebonvallet S., Khatchadourian S. and Ruan S. (2007).

AUTOMATED TUMOR SEGMENTATION USING LEVEL SET METHODS.

In Proceedings of the Second International Conference on Computer Vision Theor y and Applications, pages 128-133

DOI: 10.5220/0002068301280133

 SciTePress

ent types of images. Among various image segmenta-

tion techniques, active contour model [2] has emerged

as a powerful tool for semi-automatic object segmen-

tation. The basic idea is to evolve a curve, subject

to constraints from a given image,for detecting inter-

esting objects in that image. It consists in the reso-

lution of systems of partial differential equations for

which interface propagation phenomenon has to be

described. The active contour models are often imple-

mented based on level set method ((Sethian, 1999)),

which is a powerful tool to capture deforming shape.

But it has the disadvantage of a heavy computation re-

quirement even using the narrowband evolution. The

fast marching method is proposed for monotonically

advanced fronts ((Sethian, 1999)), and is extremely

faster than level set evolution. Generally, there are

three key problems needed to be solved to implement

the curve evolution methods. The ﬁrst one is the ini-

tialization of the seed points. The second one is the

formulation of the speed function. And the last one is

the determination of the stopping criterion.

The level set methods have been widely applied

in medical imagery (Suri et al., 2002) in different do-

mains : the brain (Xie et al., 2005), the bone (Morigi

et al., 2004), the vascular trees (Farag et al., 2004)

and so on... The most common way to initialize the

level set is the manual selection of a ROI which seems

to be relevant ((Xu et al., 2000), (Farag et al., 2004)

and (Xie et al., 2005)). Sometimes a simple mouse

click combined with a fast marching approach (Fan, )

is used. In this case the ﬁnal contour determined by

the fast marching step is the initial front of the level

set. Those methods are semi-automated while we are

focused on the automated methods. (Morigi et al.,

2004) proposed an automated method but the imag-

ing system is not the same as the subject of our study.

Our work consists of detecting tumors from the

whole body image volume acquired by a PET/CT de-

vice. We have no a priori knowledge on the loca-

tion of the tumor zone to detect. A contour evolution

model using a level set method with an initialization

based on thresholding is proposed in this paper.

The paper is organized as the following. Firstly,

an overview of our study is described. Secondly, the

principle of the level set method and its implementa-

tion will be exposed. The different steps of our ap-

proach and the associated results are then presented.

Finally we will conclude and give some perspectives.

2 OVERVIEW OF THE STUDY

2.1 Segmentation Framework

Our aim is at detecting the tumorous areas in the body

and in the brain from PET images and MRI images.

Any a priori knowledge about locations of the tumors

are taken into account. As the PET images are usually

noisy and bad contrasted, the methods based on the

image intensity or gradient are not efﬁcient in these

cases. The statistical methods cannot be neither used

efﬁciently due to the small size of the tumor : they

are too small to get statistical properties comparing

with all images. The solution of the evolving contours

is interesting in this case because they can grow to

the expected size of the tumorous areas with help of

geometrical and intrinsic properties.

For segmenting the 3D images, we complete it

through a 2D slice-by-slice process. The proposed

framework consists of 3 steps: seed detection giving

a set of seeds which are susceptible belonging to the

tumor; seed selection allowing to obtain one seed con-

sidered as the initial tumor contour; contour evolution

according to an active contour model.

The seed detection consists of ﬁnding ROIs us-

ing intensity information. The areas of high glucose

activity lead to high gray levels observed in PET im-

ages. A thresholding of images can be carried out to

obtain the ROIs. The problem is how to choose the

threshold. As known, the histogram can give the in-

formation about the distribution of grey levels. The

maximum of the histogram is ﬁrstly found, which rep-

resents body tissus. Supposing that the number of pix-

els belonging to tumor regions has less than that of the

pique of histogram. The threshold is then deﬁned as

the gray level on which the number of pixels equals to

the maximum multiplied by a proportionality factor α

which is given by experiences.

After the thresholding of images, several seeds are

obtained in which some of them do not belong to the

tumor. The big regions representing some anatomi-

cal regions which give high intensity, and very small

regions due to noise, are detected as seeds. The big

regions can be easily moved out from the seeds. A di-

latation, morphological mathematics operator, is car-

ried out to eliminate the small seeds. This seed se-

lection step allows us to delete aberrant seeds and to

keep that of tumorous areas. From the obtained initial

contours (seeds), a level set method is used to grow

them to ﬁnd the tumor contours. In the next section,

this method is presented in details.

AUTOMATED TUMOR SEGMENTATION USING LEVEL SET METHODS

129

3 CONTOUR EVOLUTION

BASED ON LEVEL SET

METHOD

The level set method has been introduced by (Os-

her et al., 1988) in order to solve the partial dif-

ferential equations. It refers to the theory of the

curve evolution. The algorithm proposed by Sethia

((Sethian, 1999) has been widely applied to many do-

mains ((Fan, ), (Xu et al., 2000))

3.1 Theory

Considering a curve represented by a level set func-

tion Φ, which is deﬁned as a distance function :

For a point p, if Φ > 0, p is outside the contour,

if Φ = 0, p is on the contour,

if Φ < 0, p is inside the contour.

From a geometric point of view, the evolution of a

contour can be described as follows :

∂x

∂t

= VN (1)

with x a point of the contour, V the speed function, N

the normal vector of the curve at x. The evolution of

the curve depends on the normal vector N of the curve

and the curvature K at each point of the curve, with :

N =

∇Φ

|∇Φ|

K = ∇

∇Φ

|∇Φ|

− 2Φ

+ Φ

(Φ

+ Φ

)

3/2

To describe the evolution of the curve we need to

initialize it. The initial curve is deﬁned as zero level

set :

Φ((x(t)),t = 0) = 0 (2)

To associate the zero level set to the evolving

curve at each time and to derive the motion equation

for this level set function, the zero level set has to te

be re-initialized at each time step :

Φ((x(t)),t) = 0 (3)

After derivation of the equation 3 :

+V∇Φ((x(t)),t) = 0 (4)

where V = x

′

(t) · N is deﬁned as a speed function.

This speed function is the key of the implementation

of the level set method.

3.2 Speed Function

The speed function V depends on :

• local properties given by local geometrical infor-

mation (curvature, normal of the curve),

• global properties depending on the form and the

position of the front,

• independent properties deﬁned as a ﬂuid velocity

that transport passively the front.

Based on these properties, the speed function can

be expressed as follows :

V = V

prop

curv

adv

(5)

with V

prop

= V

constant speed propagation

curv

= −εK curvature dependent speed

adv

= U(x,y,t) · N advection speed

Since the speed function decreases to zero at the

boundary of the area to segment, the components of

the speed function are proposed as follows:

ε = ε

pij

with ε

constant , (6)

pij

1+ Gij

with G

the image gradient(7)

at pixel (i, j) ,

= β∇V

pij

with β constant . (8)

and beta are constant parameters to be deﬁned

according to used images. For further details on the

implementation of the speed function, see (Sethian,

1999) and (Xu et al., 2000).The stopping criteria de-

pends on the speed function, therefore indirectly on

the intrinsic parameters of the images. The evolution

of contours stops when the speed function V = 0.

3.3 The Narrow Band

The problem of this method is that it takes a long time

to compute if the update of the level set function is

made on the entire image. The solution proposed by

(Chopp, 1993) is to compute the level set function in a

narrow band around the front. The level set function

is only updated when it reaches the boundary of the

narrow band. This narrow band approach can reduce

importantly the computing time. It has been used in

shape recognition by (Malladi et al., 1994) and an-

alyzed by (Adalsteinsson et al., 1995) with success.

Therefore, the narrow band is also adopted to the our

method in the process of evolution.

VISAPP 2007 - International Conference on Computer Vision Theory and Applications

130

4 EXPERIMENTAL RESULTS

4.1 Data

The data PET, we use for our experimentation, con-

sist of three PET image volumes corresponding to

three patients who reach some tumors. The size of

the images is of 144x144 pixels and their resolution

is above 7mm per pixel for both PET and Ct images.

One volume is composed of about 190 slices. Visu-

ally, the three tumors observed in images are well seg-

mented, conﬁrmed by hospital experts. The MRI im-

ages are acquired on a 1.5T GE (General Electric Co.)

machine using an axial FLAIR. The image volume

consists of 512 (pixels) x 512(pixels) x 24 (slices)

with a voxel size of 0.470.47 5.5 mm3. Three vol-

umes of one patient acquied during a medical treat-

ment at three time points are used in our experience.

Six months separates each time point. The volume

variations can be then calculated from segmentation

results.

4.2 Choice of Parameters

Different values of the parameters have studied and

tested before validate these ones : α = 0, 0025 for

the seed detection parametrization, ε

= 0,05 and β =

0,005 for the level set parametrization. Those values

are chosen according to the images to be dealed with.

They can keep the same if the images to be treated are

acquired from the same imaging machine.

4.3 Segmentation

Ten PET slices of a patient who reaches a lung tumor

are presented here (ﬁgure 1). For giving a good vi-

sualization, the gray levels are inverted. The tumor

appears dark. The results obtained in different steps

are shown from the ﬁgure 2 to 4:

• seed detection,

• seed selection,

• tumor segmentation with the level set method.

The seed detection (ﬁgure 2) allows us to deter-

mine ROIs which could be contained by tumorous ar-

eas. It is achieved thanks to the gray level informa-

tion of the entire image volume. We know that higher

gray levels represent areas of higher glucose activity

and the tumors have abnormal glucose activity. But

as foreseen the ROIs obtained are not necessarily tu-

mors. The seed selection (ﬁgure 3) can help the deci-

sion of seed as explained previously.

The level set method is carried out image by image

for all the voulme from the initialization given by the

seed selection. We can see on ﬁgure 4 that the tumor

is well segmented. The same approche is performed

on MRI data. For example, for one patient, the varia-

tion is decreased about 15.42 percent six months after.

This measure provides a very important information

for the experts to evaluate the medical treatment.

5 CONCLUSION AND FUTURE

WORKS

This paper presents a work on the automatic segmen-

tation of tumorous areas for whole body and brain.

The tumors are well segmented even if it remains in

the results healthy regions. Two possibilities have

been evoked to solve this :

- Improving the seed detection by using a multi-scale

binarization method (see (Jolion, 1994) and (Trier

et al., 1995)) for example. Indeed the question of seed

detection has been brieﬂy considered to test the level

set method.

- Implementing a very robust classiﬁcation method.

A SVM classiﬁcation has already evoked : previous

works on medical image classiﬁcation, lead in the lab-

oratory, gave encouraging results (AitAouit, 2004).

If the initialization step is not robust enough, the clas-

siﬁcation step is necessary to select tumor contour.

Finally the level set should be implemented as a

real 3-dimensional method in order to consider the

whole 3D information. That allows to ameliorate the

performances of the coutour evolution.

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Figure 1: patient 3 stack sample illustrating a lung tumor.

Figure 2: Seed detection on this sample.

Figure 3: Seed treatment.

Figure 4: level set segmentation.

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133