121

CHAPTER 5

SEGMENTATION OF BRAIN

TUMORS USING DRLSE

Papers Published out of this work

1. Usha Rani.N, Dr.P.V.Subbaiah,Dr.D.VenkataRao and Nalini.K,

“Optimal Segmentation of Brain Tumors using DRLSE Level Set”,

International Journal of Computer Applications (IJCA),Vol. 29,

No.9,Sep. 2011, pp6-11

2. Ms.N.Usha Rani,K.Nalini, and Ch.S.Srivalli,“Segmentation of

Medical Images using Variational Level Sets”,National Conference

on Communications & Energy Systems,VLITS, pp29-30,April 2011.

CHAPTER-5

122

SEGMENTATION OF BRAIN TUMORSUSING DRLSE

5.1. INTRODUCTION

Segmentation of medical images is a challenging task due to the

poor image contrast and artefacts that result in missing or diffusion of

organs or tissue boundaries. The role of medical imaging has been

drastically improved in the diagnosis and treatment of a disease. It also

opened an array of challenging problems such as the computation of

accurate models for the segmentation [44] of anatomic structures from

medical images.Active Contour (deformable) models have recently become

one of the most studied techniques for segmentation due to their ability

to adapt to the specific shape of the object of interest.

Deformable models offer an attractive approach

insolvingsegmentationproblems because these models are able to

represent the complex shapes and broad shape variability of anatomical

structures. Two dimensional and three dimensional deformable

modelshave been used to segment, visualize, track, and quantify a

variety of anatomic structures ranging in scale from the macroscopic to

the microscopic. These include the brain, heart, face, cerebral, coronary

and retinal arteries, kidney, lungs, stomach, liver, skull, vertebra, objects

such as braintumors, a foetus and even cellular structures such as

neurons and chromosomes.

123

In medical imaging, deformable models have been used to track

the non-rigid motion of the heart, the growing tip of a neurite and the

motion of erythrocytes. They have been used to locate structures in the

brain and to register images of the retina, vertebra and neuronal tissues.

Deformable models overcome many of the limitations of traditional low-

level image processing techniques by providing compact and analytical

representations of object shape by incorporating anatomic knowledge

and by providing interactive capabilities. The continued development and

refinement of these models should remain as an important area of

research.

5.2. APPLICATIONS OF ACTIVE CONTOUR SEGMENTATION

Active contour segmentation [66, 68, 69, 72, and 73] is one of the

active growing research area. Some of the practical applications of active

contour segmentation in medical imaging are listed below.

o To locate tumors and other pathologies

o To measure tissue volumes

o Computer-guided surgery

o Diagnosis

o Treatment planning

o Study of anatomical structure

5.3. CONVENTIONAL MEDICAL IMAGE SEGMENTATION

124

The segmentation of anatomic structures i.e. the partitioning of the

original set of image points into subsets corresponding to the structures

is an essential first stage of most medical image analysis tasks such as

registration, labelling, and motion tracking. Segmenting structures from

medical images and reconstructing compact geometric representation of

these structures is a difficult task due to the sheer size of the datasets

and the complexity and variability of the anatomic shapes of interest.

Furthermore, the shortcomings of typical sampled data, such as

sampling artefacts, spatial aliasingand noise may cause the boundaries

of structures are to be indistinct and disconnected. The challenge is to

extract theboundary [69] elements belonging to the same structure and

integrate these elements into a coherent and consistent model of the

structure.

Traditional low-level image processing techniques consider only the

local information can make incorrect assumptions during the integration

process and generate infeasible object boundaries. As a result, these

model-free techniques usually require considerable amount of expert

intervention. Furthermore, the subsequent analysis and interpretation of

these segmented objects is hindered by the pixel or voxellevel structure

representations generated by most image processing operations

At present most clinical segmentation [70] is performed by using

manual slice editing. In this scenario, a skilled operator, using a

125

computer mouse or trackball, manually traces the region of interest on

each slice of an image volume. In this process many problems may be

occurred due to human involvement. The problems are listed below.

5.3.1. Drawbacks of ConventionalLow-Level Segmentation

Segmentation using traditional low-level image processing

techniques such as thresholding, region growing, edge detection

and mathematical morphology operations, also require

considerable amountof expert interactive guidance. Furthermore,

automating these model-free approaches is difficult because of the

shape complexity and variability within and across individuals.

The manual slice editing suffers from several drawbacks. These

include the difficulty in achieving reproducible results, operator

bias, forcing the operator to view each 2D slice separately to

deduce and measure the shape and volume of 3D structures and

operator fatigue.

Noise and other image artefacts can cause incorrect regions or

boundary discontinuities in objects recovered by these methods.

A deformable model based segmentation scheme, used in concern

with image pre-processing can overcome many of the limitations of

manual slice editing and traditional image processing techniques. These

connected and continuous geometric models consider an object

boundary as a whole and can make use of prior knowledge of object

126

shape to constrain the segmentation problem. The inherent continuity

and smoothness of these models can compensate for noise, gaps and

other irregularities in object boundaries.

5.4. DYNAMIC ACTIVE CONTOUR BASED IMAGE SEGMENTATION

The specific category of image segmentation methods widely used in

medical imaging is the active contour deformable models. Though

originally developeddeformable models areused in computer vision and

computer graphics applications, the potentiality of the deformable

models for use in medical image analysis has been quickly realized. They

can be applied for the segmentation of images generated from varied

imaging modalities such as X-ray, computed tomography (CT),

angiography, magnetic resonance (MR), and ultrasound. In this thesis,

algorithms for two-dimensional segmentation and reconstruction of

braintumorsof CT, MRI and PET brain images are presented. The

segmentation of brain tumors from CT and MRI scans using model based

active contours is shown in Fig.5.1. Depending on how the model is

defined in the shape domain, the two general classes of active contour

models to perform segmentation are (1) the parametric deformable

models or active contours and (2) the geometric or implicit models are

used.

127

(a) CT (b) PET

5.1. Segmentation of Brain Tumors from CT and PET Scans.

The idea behind active contoursor deformable models for image

segmentation is quite simple. The user specifies an initial guess for the

contour which is then moved by image driven forces to the boundaries of

the desired objects. In such models, two types of forces are considered

the internal forces, defined within the curve, are designed to keep the

model smooth during the deformation process, while the external forces,

which are computed from the underlying image data, are defined to move

the model toward an object boundary or other desired features within the

image.

5.4.1. Parametric Active Contour (PAC) Model Based Segmentation

Parametric deformable models are very popular and have

been successfully used in medical image segmentation for some time.

Intuitively, parametric models are widely known as active contours or

500 iterations

20 40 60 80 100 120 140

20

40

60

80

100

120

140

2500 iterations

10 20 30 40 50 60 70 80 90

20

40

60

80

100

120

128

snakes are used for the segmentation in the two-dimensional image

domain. These are curves whose deformations are determined by the

displacement of a discrete number of control points along the curve.

Apart from active contours, parametric models can alsobe surfaces with

the control points defining two-dimensional (in the shape domain)

deformable grids, for two-dimensional image segmentation or hyper-

surfaceswith the control points defining three-dimensional,

interconnected, clouds of points, for the segmentation of higher-

dimensional image data (e.g., image stacks). Thesegmentation of human

vertebrausingparametric models is shown in Fig.5.2.below. Fig.5.2. (a) is

the initial curve.Fig.5.2.(b) and Fig.5.2.(c) represents the evolution and

Fig.5.2.(d) represents the object segmentation.

Fig.5.2. Segmentation of Human Vertebra using Parametric

Evolution Model

The main advantage of parametric models is that they are usually

very fast in their convergence, depending on the predetermined number

of control points. However they have several disadvantages. The most

significant difficulty with the PAC segmentation is in

(a)

(b)

(c)

(d)

129

segmentingtopologically complex structures. Other disadvantages are

that implementation in 3-D is difficult. However, an obvious weakness of

these models is that they are topology dependent. A model can only

capture a single ROI, and therefore, in images with multiple ROIs,

multiple models have to be initialized, one for each ROI.To overcome

these difficulties, geometric deformable models are introduced which are

based on the level set method proposed by Sethianet al. [38].

5.4.2. Geometric Active Contour (GAC) Model Based Segmentation

In this work,a class of active contour model, namely the geometric

models are more used for the segmentation of brain tumors from the

scan images. There are two main advantages in using these models for

segmentation.

First, the shape can be defined in a domain with

dimensionality similar to the dataset space (for example, for

2D segmentation, a curve is transformed into a 2D surface),

which can provide a more mathematically straightforward

integration of shape and appearance (image features) in the

model definition.

Second, the shape can be implicitly defined, with the

control/deformation points at the image pixel positions.

These representations are topology independent, i.e.,they

130

can capture multiple ROIs with a single model, and therefore

they can be robust to initializations.

The segmentation of the brain from CT scan using geometric

active contours is shown in Fig.5.3. The initially initialized curve

automatically evolves and segments the brain using geometric level

sets.Fig.5.3.(a) represents the initial curve and Fig.5.3.(c) represents the

final object.

Fig.5.3. Segmentation of Human Brain using Geometric LevelSet

Level Set Method

In the level set method, the object is segmented from the

imagesusing curve evolution. The object is to be segmented is initialized

with a closed curve. The curve is evolved based on internal and external

forces and finally stops evolution when the curve reaches the object

boundaries. The internal forces used for the evolution are computed from

the model. The external forces are computed from the image data.The

(a) Initial

Curve

(b) Intermediate evolution

(c) Final Segmentation

131

evolution follows the LaGrange equation (4.1). The discrete

representation of the equation (4.1) is represented below.

0,,

,

1

,

n

jiji

n

ji

n

jiF

t ------------------(5.1)

This mathematical modelling uses on a discrete grid in the domain

of x(x,y) and difference approximations for example, by using an uniform

mesh spaces h, with grid nodes i, j and employees standard notation nij

in the approximation to the solution ( tnjhih ,, ), where t is the time

step.

This representation can 1) break or merge during evolution

naturally and 2) it remains a function on a fixed grid hence numerical

methods can be applied efficiently. The advantage of Eulerian[]

formulation is ),( tx remain a function as it evolves hence it can be

represented on a discrete grid.

Although level set methods have been used to solve a wide range of

medical imaging problems, their applications have been plagued with the

irregularities of the LSF that are developed during the level set evolution.

The PDE can develop shocks during sharp and flat shape evolution

132

which needs re-initialization. Re-initialization is performed by

periodically stopping the evolution and reshaping the degraded LSF as a

signed distance function [5-7]. Re-initialization causes serious problems

and also affects the numerical accuracy in an undesirable way. Hence

the Eulerian PDE is converted as Variational level set method[76,

77,79,80] based on energy minimization [13,14] doesn’t need re-

initialization[64] and are convenient for adding external shape, colour or

texture information into the model.

Variational Method

The variational formulation for geometric active contours forces the

level set function to be close to a signed distance function[74] and

therefore completely eliminates the need of the costly re-initialization

procedure. The variational formulation consists of an internal energy

term that penalizes the deviation of the levelset function from a signed

distance function [78] and an external energy term that drives the motion

of the zero level set toward the desired image features, such as object

boundaries. The resulting evolution of the variationallevel set function is

the gradient flow that minimizes the overall energyfunction. The

advantage of this method over conventional levelsets is fast since larger

time steps can be used in evolution PDE. The mathematical formulation

133

of variational method is represented as follows.Let R be the image

domain, Ω be the subset of index R. ∂ Ω is the boundary.

The initial levelset function is defined as

),(),(0 yxcyx o ),( yx

= 0 ),( yx

= ),( yxco ),( yx

The variational penalty function term (internal energy) of φ

penalizes the deviation of the LSF from a signed distance function. The

penalty term not only eliminates the need for re-initialization, but also

allows the use of a simpler and more efficient numerical scheme in the

implementation.The penalty term is defined as follows

dxdy2

12

1

The energy function is the sum of penalizing term and external

potential energy is defined as follows

m -----------------(5.3)

where is a constant and is positive, controls the deviation of from

SDF. m is a certain energy that would drive the motion of the zero

level curve of φ, hence called as external energydepends on the image

134

data.The external energy term in terms image parameters is defined as

follows.

ggg L )(,, -------------- (5.4)

where gis an edge indicator function obtained from image data. Whereλ

>0 and are constants, and the termsAg(φ) in (5.4) is introduced to

speed up the curve evolution.Lg(φ) computes the length of the zero level

curve of φ.In image segmentation, active contours are dynamic curves

that move toward the object boundaries. To achieve this goal, we

explicitly define an external energy that can move the zero level curves

towards the object boundaries. For an image I, and g be the edge

indicator function defined as

21/1 IGg

The first variation known as Gateaux derivative [18] of the energy

functional E, is the curve evolution w.r.t time.

t

The penalizing term is used as a metric to characterize how close a

function φto a signed distance function in Ω € R2. This metric will play a

key role in our energy based variational level set formulation. However,

this penalty term may not followthe SDF hence cause an undesirable

side effect on the LSF when concavities involved. This problem can be

addressed in the distance regularized LSF.

135

5.4.3.DISTANCE REGULARIZED LEVELSET EVOLUTION (DRLSE)

The penalizing term in the variational method affects the numerical

accuracy at concavities can be corrected by using distance regularizing

term. The computation of distance functions is simple and fast.In this

section segmentation problem is solved using the distance regularization

term. It is defined with a potential function such that the derived level set

evolution has a unique forward-and-backward (FAB) diffusion effect,

which is able to maintain a desired shape of the level set function,

particularly a signed distance profile near the zero level set. This yields a

new type of level set evolution called Distance Regularized Level Set

Evolution (DRLSE) [75].The level set evolution in it is derived as the

gradient flow that minimizes energy functional with a distance

regularization term and an external energy that drives the motion of the

zero level set towards desired locations.

The distance regularization effect eliminates the need for re-

initialization and thereby avoids its induced numerical errors. Relatively

large time steps can be used in the finite difference scheme to reduce the

number of iterationswhile ensuring sufficient numerical accuracy. This

section presents the mathematical modelling of DRLSE. The energy

function E( ) in DRLSE is defined in terms distance regularizing term is

as follows.

136

extpR -------------(5.5)

where pR is the level set distance regularization term

is a constant,

ext is the external energy

The level set regularization term pR is defined as

dxPRp

where P is a potential energy function is designed such that it achieves a

minimum when the zero level set of the LSF is located at desired

position.

The Gateaux derivative for DRLSE evolution is defined as follows

extpR

Pis a potential (or energy density) function p [0, ], Eext( ) is the

external energy designed such that it achieves a minimum when zero

Level set of LSF is located at desired positions. Regularization term

maintains the required | | =1 in the vicinity of zero level set and also

emerges smooth movement of the curve. The double well potential

function with | | =0 is responsible for the forward and backward

(FAB) diffusions in case of conventional levelset. The DRLSE not only

eliminates the need for re-initialization but also allows the use of more

137

general functions as the initial Level Set Functions. This method is more

efficient in segmenting objects.

5.5. RESULTS

In this chapter,work is carried out on brain tumor

segmentationfrom medical brain scans by the application of distance

based levelsets. Particularly in this chapter DRLSE levelsets with energy

penalizing and distance regularizationis used for the segmentation of

brain tumors from CT,PET and MRI scan images. Segmentation of brain

tumors using variational method and DRLSE from MRI, PET and CT is

shown qualitatively in Fig.5.4.Column 1 indicates the original images

with tumors represented in polygons or ellipse. Column 2 represents

segmentation of tumors shown with red curve using DRLSE method.

Column3 indicates the segmented tumors with variational method.

The quantitative analysis is represented in Table.5.1. The

performance is compared in terms of computation time and the

convergence of the model towards object boundaries when the curve

evolves.In case of simple tumors both the methods perform well in

segmenting thetumors. The computational times of same images in both

the methods is shown in Table.5.1.DRLSE method uses less time as

shown in column2, compared to the variational method column3. The

same fact is also indicated in the graph in Fig.5.5.

138

(a) (b) (c)

(a) Column1 - Original Images with Region of Interest

(b) Column2 - DRLSE Segmentation

(c) Column3 - Energy Variational Method

Fig.5.4. Segmentation of Tumors from MRI, CT, and PET

Images

MRI1

MRI1

MRI

PET

PET

PET

CT

CT

CT

MRI2

MRI2

MRI2

500 iterations

10 20 30 40 50 60 70 80 90

10

20

30

40

50

60

70

80

90

100

110

500 iterations

10 20 30 40 50 60 70 80 90

10

20

30

40

50

60

70

80

90

100

110

1000 iterations

20 40 60 80 100 120 140

20

40

60

80

100

120

140

139

Fig.5.6. represents the curve and levelset function evolution in

case of DRLSE.Fig.5.6.(a) represents the initial contour incase of MRI

with 2 tumors and (b) represents the curve evolution and segmentation

of 2 tumors. Fig.5.6.(c) and (d) represents the levelset functions before

with red and after segmentation. In (c) we can observe connected region

before evolution. In (d) unconnected region was shown after evolution of

curve.Table.5.2. indicates the DRLSE and Variational methods for

different iterations with MRI and PET images.

Fig.5.7. distinguishes the merits of the DRLSE method over the

variational method. When images having nearer gray levels variational

method is failed in segmenting the tumors as shown in Fig.5.7. (b)and

(d). This problem can be rectified in DRLSE shown in Fig.5.7. (a) and (c).

Table.5.1.Performance Comparison

Type of scan

Computation Time

DRLSE

Variational

MRI1

16.484000 37.281000

PET

10.094000 13.234000

CT

18.344000 34.652000

MRI2

15.782000 30.218000

140

Fig.5.5. Computational times of DRLSE and Variational Method

Table.5.2. Performance Comparison

(a) Initial

Contour (b) Curve Evolution

(b) Initial Level Set (d) Final Level Set

Fig.5.6. DRLSE Method

16.484

37.281

0

5

10

15

20

25

30

35

40

MRI1 PET CT

Type of Scan

Method No of iterations

Computation time(sec)

MRI DRLSE 5000 28.359

Variational 1500 129.016

PET DRLSE 1500 47.953

Variational 600 124.531

(a)

(b)

(c)

(d)

141

(a) and (c) DRLSE -Proper Segmentation

(b) and (d) Variational method -Improper Segmentation

Fig.5.7. DRLSE VsVariationalMethods

5.6.CONCLUSIONS

In this chapter an algorithm is proposed to segment the brain

tumors from scan images. The existed variational method, based on

energy function is incapable of segmenting the tumors which are having

near gray levels as shown in Fig.5.7. When humans affect with cancer,

they may posses multiple tumors in near region. In such situations the

existing one may not address the problem. The proposed distance based

method having good regularization hence this can solve the problem as

shown in Fig.5.7. The computation of distance functions is easy and less

complex. Hence they can be computed in a faster way with less

(a)MRI

(b)MRI

(c )PET

(d )PET

500 iterations

50 100 150 200 250 300

50

100

150

200

250

300

350

400

15000 iterations

20 40 60 80 100 120

20

40

60

80

100

120

140

1000 iterations

20 40 60 80 100 120

20

40

60

80

100

120

140

142

complexity. Hence it needs less computational time andmaintains good

regularization.