A

FAST AND ROBUST METHOD FOR VOLUMETRIC MRI BRAIN

EXTRACTION

Sami Bourouis and Kamel Hamrouni

Ecole Nationale d’Ing

´

enieurs de Tunis

Laboratoire de Syst

`

emes et de Traitement du Signal : LSTS

ENIT, BP-37, Le Belv

´

ed

`

ere 1002 Tunis, Tunisia

Keywords:

Magnetic Resonance Imaging (MRI), 3D Segmentation, Brain extraction, Expectation Maximization, Level-

set method.

Abstract:

This paper presents a method for magnetic resonance imaging (MRI) segmentation and the extraction of main

brain tissues. The method uses an image processing technique based on level-set approach and EM-algorithm.

The paper describes the main features of the method, and presents experimental results with real volumetric

images in order to evaluate the performance of the method.

1 INTRODUCTION

In brain imaging, image analysis such as segmenta-

tion of anatomical structures is a very important yet

open research problem and is often a ﬁrst step in the

study of brain anatomy and function. In the context

of neuro-imaging, 3D segmentation of white matter,

gray matter, CSF, etc. is extremely important and has

received much interest in the literature for the recon-

struction, visualization, interpretation of the brain ac-

tivity, and quantitative analysis such as volume mea-

surements. On the other hand, Magnetic Resonance

Imaging (MRI) has become of great interest in many

research areas. This modality allows neuroscientists

to see inside a living human brain, to better localize

speciﬁc areas inside the brain and to understand the

relationship between them. However, brain segmenta-

tion and especially the extraction of anatomical struc-

tures from MRI images are a complex problem, be-

cause medical images usually involve a large amount

of data and they sometimes present various artefacts

in the imaging process such as noise, partial volume

effects, intensity inhomogeneities, and because of the

highly convoluted nature of the brain cortex itself.

Thus, it is very difﬁcult to obtain a powerful segmen-

tation tools to be used in clinical routine. This asser-

tion is even more valid in the case of 3D segmentation

of cerebral structures.

In the last several years, many algorithms have

been proposed in this growing area, offering a di-

versity of methods and various evaluation criteria.

For example, several general surveys are reported in

(Pham et al., 1998; Sarang, 2000; Suri et al., 2002).

Shattuck et al. (Shattuck et al., 2001) have developed

a Brain Surface Extraction algorithm (BSE) based

on statistical classiﬁcation, mathematical morphol-

ogy and connected component operations. In gen-

eral, these methods work efﬁciently for some segmen-

tation tasks, but partially fail for ”hard cases”. In

addition, there is currently no segmentation method

that provides acceptable results for every type of

medical dataset. 3D brain segmentation using de-

formable model approach is an appropriate frame-

work for merging heterogeneous information and pro-

vides a consistent geometrical representation suitable

for a surface-based analysis. Deformable models are

classiﬁed as either parametric active contours or ge-

ometric active contours according to their representa-

tion. Parametric active contours (snakes), originally

proposed by Kass et al. (Kass et al., 1987), are repre-

sented explicitly as parameterized curves. However,

their typical problem consists in its evolution and ﬁ-

nal results are depended on initial shape parameter-

ization. Recently, several attempts have been made

to apply geometric deformable models to brain image

segmentation. In particular, Level-set method (Osher

and Sethian, 1988) is becoming very popular thanks

to its advantages over an explicit representation of

the interface. Indeed, no parametrization is needed,

topology changes are handled automatically, number

461

Bourouis S. and Hamrouni K. (2008).

A FAST AND ROBUST METHOD FOR VOLUMETRIC MRI BRAIN EXTRACTION.

In Proceedings of the Third International Conference on Computer Vision Theory and Applications, pages 461-466

DOI: 10.5220/0001078604610466

Copyright

c

SciTePress

of dimensions is accommodated, and intrinsic geo-

metric properties such as normal and curvature can

be computed easily from the level set function. In

addition, the level-set method has a sub-voxel pre-

cision in its segmentation, a property that very few

segmentation methods provide. An interesting work

on cortex segmentation using deformable models ap-

pears in (Davatzikos and Bryan, 1996) and (Sandor

and Leahy, 1997). Also, Xu et al. (Xu et al., 1999)

have presented a method for reconstructing cortical

surfaces from MR brain images by combining fuzzy

segmentation method, an isosurface algorithm, and a

deformable surface model. In recent studies, several

level set-based methods have been proposed. But, the

problem is that most of these techniques require that

the model should be initialized near the solution or

supervised by an interactive interface. In addition,

computational procedure is another limitation of us-

ing deformable level-set models.

The goal of this work is to provide an automatic

segmentation, based on a level-set deformable model,

for extracting accurately fronts from MR images.

Also, we aim to outline the importance of reducing

processing time in medical image analysis. Like sev-

eral other recent approaches, our design is a success-

ful combination of two approaches, which produces

good results and requires less computing time. Here,

unsupervised classiﬁcation based on expectation-

maximization (EM) and deformable level-set meth-

ods are integrated into the same pipeline. More pre-

cisely, we apply the EM algorithm and a connected

component analysis on MRI scans to generate inputs

to our deformable model. The synergy between dif-

ferent methodologies tends to result robustness and

optimize processing time that several medical appli-

cations required them.

This paper is organized as follows. In Section II,

we describe our proposed segmentation framework.

In Section III, we present and discuss obtained results

by our framework. Finally, in Section IV, we conclude

our paper and point out future research directions.

2 SEGMENTATION BASED ON

LEVEL-SET APPROACH

Automatic 3D segmentation of the brain from MR

scans is a challenging problem that has received enor-

mous amount of attention lately. Here, we present

our automatic 3D segmentation procedure based on

a deformable level-set method to extract accurately

main tissues from MR images. We notice that a large

number of computations are often needed to solve

the variational equations involved in the Level-Set

model. Nevertheless, good initialization could im-

prove quality results. Furthermore, only few itera-

tions are needed to converge to a sub-pixel accurate

solution. For this reason, we plan to include prior in-

formation about the expected shape. Our proposition

to overcome difﬁculties consists ﬁrst on reducing ini-

tial data set to a smaller size. It is an important task in

image analysis that allows overcoming the limitations

of the processing time and become more and more

important, especially, in the case of multidimensional

signal processing. Thus, estimating parameters on the

new sample can be done easily and rapidly.

Our brain extraction algorithm uses three stages to

segment image. The ﬁrst one is the dada smoothing

and the all non-brain tissue removal (i.e. skin, bone,

fat, etc.) from initial data set. In the second stage, we

apply a downsampling process that reduces data size

and furthermore overcomes computation time. The

ﬁnal stage consists of segmenting, with more preci-

sion, brain structures by using level-set method. Fig-

ure 1 illustrates the major computational steps in the

proposed method.

Volumetric MRI

data

DownSampling

volume

Brain tissues

Estimating

Clustering

Deformable Level-set

model

Reconstructed

surface

Deformable surface

Initialization

Parameters

Preprocessing

Figure 1: General principle of our method.

2.1 Preprocessing Data

Generally, the data volume can contain various

amounts of noise. To eliminate noise, a smoothing

ﬁlter is applied (Perona and Malik, 1990). This ﬁl-

ter is supposed to remove only high-frequency noise

and should not affect relevant major geometrical fea-

tures. Authors formulate the anisotropic diffusion ﬁl-

ter as diffusion process that encourages intra-region

smoothing while inhibiting inter-region smoothing.

The diffusion function is given as :

∂I(

¯

X,t)

dt

= ∇(C(

¯

X,t).∇I(

¯

X,t)) (1)

Where, I(

¯

X,t) is the MR image.

¯

X refers to the im-

age axes (i.e. x,y,z ) and t refers to the iteration

step. C(

¯

X,t) is called the diffusion function and is a

VISAPP 2008 - International Conference on Computer Vision Theory and Applications

462

monotonically decreasing function of the image gra-

dient magnitude. It allows for locally adaptive diffu-

sion strengths: edges are selectively smoothed or en-

hanced based on the evaluation of the diffusion func-

tion.

Figure 2 illustrates the effect of the anisotropic

diffusion ﬁlter on MRI brain. In our case, the param-

eter time step was 0.125, the number of iterations was

5, and the conductance value was 3.0. In This result

we show how the volume data is smoothed and edges

are preserved.

Figure 2: Effect of the anisotropic diffusion ﬁlter on an MRI

brain image. (left) original data, (right) smoothed data.

2.2 Non-Brain Tissue Removal

Removal of non brain tissue from the MR volume

can facilitates later stages in the algorithm as fewer

voxels and fewer tissue types are involved. On the

other hand, only brain tissue is retained and all non-

brain tissues are masked out. A number of techniques

have been proposed for brain mask extraction from

MRI data. Here, we have applied the standard tech-

nique called -Brain Extraction Tool (BET)- which has

been proposed by Smith et al. (Smith, 2002). This

algorithm uses deformable model technique, which

evolves to ﬁt the brain’s surface by the application of

a set of locally adaptive model forces. It can remove

skull, scalp, and other tissue from the MR image. An

illustration of this process is shown in ﬁgure 3.

Figure 3: Removal of extracerebral tissues. (left) original

image, (right) cerebral structures.

2.3 Downsampling Volume

In computer graphics, downsampling (or ”resam-

pling”) is the process of reducing an image to a

smaller size. Changing the pixel dimensions of an

image is called also resampling. The downsampling

process is an important task in image analysis that

decreases computation time and improves rendering

performance. Therefore, an improvement in speed

could be gained by downsampling the initial volu-

metric data before any other processing. The gain in

speed could be obtained by the reduction of the num-

ber of voxels. For example if the dimension of an

input MRI volume is 256 x 256 x 150 voxels and if

this MRI was downsampled from 1.0 mm

3

to (2.0 x

2.0 x 5) mm

3

in the x-, y- and z-directions respec-

tively, then the output volume dimensions are 128 x

128 x 30 voxels. Therefore, downsampling the input

volume of 9,830,400 voxels to an output volume of

491,520 voxels drops out 95% of the voxels from the

input volume. Thus, next statistical estimation will be

performed by the resampled data and level-set evolu-

tion will be done on original smoothed volume.

2.4 Estimation Maximization

The classiﬁcation step is intended to provide an initial

model that can be reﬁned using level-set. In the case

of unsupervised classiﬁcation, the Expectation Max-

imization (EM) algorithm (Dempster et al., 1977), is

an efﬁcient iterative procedure to compute the Max-

imum Likelihood (ML) estimate in the presence of

hidden data f. In short, the EM algorithm alternates

between two steps: an expectation (E) step and a max-

imization (M) step. In the E-step, the missing data

are estimated given the observed data and current esti-

mate of the model parameters. In the M-step, we com-

pute the maximum likelihood estimates of the param-

eters by maximizing the expected likelihood found in

the E-step. The parameters found in the M-step are

then used to begin another E-step, and the process

is repeated. The method classiﬁes resampled image

into white matter (WM), grey matter (GM) and cere-

brospinal ﬂuid (CSF).

Let us consider the mean parameter µ

k

and the

variance parameter σ

k

of the intensity distribution

of the k-th tissue class grouped in θ

k

such as θ

k

=

{µ

k

,σ

k

}. We denote also π

k

the prior probability of

each class k and γ

k

i

the posteriori probability calcu-

lated in each voxel i for each class k. In the expec-

tation step, we calculate the posteriori probability ac-

cording to the following formulas:

γ

k

i

= P(x

k

/y

k

,θ

k

) =

π

k

i

f

k

(y

i

/θ

k

)

∑

K

l=1

π

l

i

f

l

(y

i

/θ

l

)

(2)

A FAST AND ROBUST METHOD FOR VOLUMETRIC MRI BRAIN EXTRACTION

463

In the maximization step, we estimate data driven

parameters by:

π

k

=

∑

K

l=1

γ

k

i

N

µ

k

=

∑

K

l=1

γ

k

i

y

i

∑

K

l=1

γ

k

i

σ

2

k

=

∑

K

l=1

γ

k

i

(y

i

−µ

k

)(y

i

−µ

k

)

∑

K

l=1

γ

k

i

(3)

2.5 Clustering

Gaussian parameters obtained previously on the

downsampled volume are generally identical to those

obtained on whole volume. In this way, an improve-

ment in speed could be gained in the clustering step.

At this step, classiﬁcation is restricted to three classes:

gray matter (GM), white matter (WM) and CSF. Sev-

eral classiﬁers could do this task such as k-means,

Fuzzy k-means, k-NN, etc. However, we show that

a simple clustering based on euclidian distance is suf-

ﬁcient. More precisely, each voxel is assigned to one

class based on its minimum euclidian distance. This

simple way decreases also computation time and pro-

vides good results. Figure 4 illustrates the effect of

this clustering with three classes. The mean values

are estimated by the EM algorithm.

Figure 4: Clustering of the MR image (original image is

shown in ﬁgure 3).

2.6 Level-set Method

The aim of this step is to extract accurately the bound-

ary of the region-of-interest by using a deformable

level-set model. Therefore, we exploit previous ini-

tialization to accelerate and to guide the process evo-

lution. Level set method, initially introduced by Os-

her and Sethian (Osher and Sethian, 1988), has been

used in many applications: physics, graphics, com-

puter vision, image analysis, restoration, etc. It be-

comes also one of the popular frameworks for image

segmentation. Theoretically, the level set function ψ

will change with time according to the speed term F

(as illustrated in the eq. 6) and the front Γ is always

represented by the zero isosurface. ψ and Γ are de-

ﬁned as follows:

ψ :

Ω × [0,+∞[→ IR

(x,y,t) 7→ ψ(x,y,t)

ψ(x,y,t = 0) = ±d(x, Γ)

(4)

Γ(t) = {(x,y) ∈ Ω;ψ(x, y,t) = 0} (5)

Figure 5: Level-set concept.

ψ(t) takes opposite signs on each side of Γ(t) (Fig.5).

The evolution of ψ(t) can be expressed as:

∂ψ

∂t

= F|∇ψ| = αP(x)|∇ψ| + βk|∇ψ| (6)

Where P(x) is a propagation (speed) term that con-

trols surface expansion/contraction and k is a curva-

ture term that controls the smoothness of the surface.

α and β are scalar constants. The standard convention

for level-set segmentation is that positive propagation

term causes the surface to expand while negative term

causes the surface to contract.

Different implementations of the level-set func-

tion are proposed in literature (Sethian, 1996). We no-

tice that most of them are relatively sensitive to initial

conditions. For best efﬁciency, the initial front should

be the best guess possible for the solution. Here, we

expect two inputs for our implementation. The ﬁrst is

an initial front, which is given by previous step (i.e.

statistical classiﬁcation), and the second is a feature

image from which the propagation term P(x) is cal-

culated (see eq. 4). In the feature image, values that

are close to zero are associated with object bound-

aries and speed term is calculated as the laplacian of

the image. The goal is to attract the evolving level set

surface to local zero-crossings in the laplacian image.

One nice property of using the laplacian is that there

are no free parameters in the calculation and it is of-

ten used for edge detection. Finally, positive values

in the output image are inside the segmented region

and negative values are outside. The zero crossings of

the image correspond to the position of the level set

front.

VISAPP 2008 - International Conference on Computer Vision Theory and Applications

464

2.7 3D Volume Rendering

Representing the surface as an explicit geometry is

efﬁcient when used with the conventional computer

graphics approaches for shading and viewing. Fur-

ther, it greatly reduces the necessary data storage and

provides a data structure that can be measured. At

this step, our segmentation is transformed into a tri-

angulation using an isosurface ”marching cubes” al-

gorithm (Lorensen and Cline, 1987). More precisely,

an isosurface is a surface that passes through all lo-

cations in space where a continuous data volume is

equal to a constant value. However, the output trian-

gulated surfaces usually contains multiple small ”use-

less” meshes that are physically disconnected from

each other. In order to reduce aliasing artefacts and

produce a smooth surface estimation, we have ap-

plied the algorithm proposed by Whitaker (Whitaker,

2000).

3 EXPERIMENTAL RESULTS

At this stage, we have validated the performance of

the proposed method on some 3D MRI data sets.

Clustering process is limited to provide only three

classes: GM, WM and CSF because our ﬁrst objective

is to prove speed and not to extract all internal tissues.

In the ﬁrst experiment, two different axial MRI data

sets consisting of 181 slices have been tested. The

voxel size is 1 mm

3

. Figure 7 shows the ﬁnal seg-

mented white matter tissue.

Figure 6 shows the cpu time and the gaussian pa-

rameters obtained by our method. Processing was

performed on a 1.5 Mhz Intel Pentium HP with 512

MB of RAM. The second column of the table presents

different sample sizes of two initial data sets. The

fourth column is reserved for the computation time.

The three last columns illustrate mean values of the

three classes (CSF, GM, WM) which are estimated by

EM. According to these results, we notice that mean

values of each class are almost the same ones to all

samples and a notable gain in computation time was

performed. However, the current process can provide

poorer quality. For example, when we resample an

image to larger pixel dimensions, the image will lose

some detail and sharpness.

For instance, these ﬁrst results are encouraging but

further investigation is required to extend the algo-

rithm to a large range of data.

Figure 6: CPU times (in seconds) and parameter estimation

provided by our algorithm : application on two normal MR

Data with different samples.

4 CONCLUSIONS

In this paper, we have proposed method for 3D MRI

brain segmentation problem. We have explored the

use of deformable level-set models to segment ac-

curately different brain tissues. The algorithm gives

satisfying results for brain tissues segmentation. It is

also relatively computationally efﬁcient and fast. At

this stage, we have only presented preliminary results

to demonstrate its potential: Even if they have not yet

been compared to manual or other automatic segmen-

tation results, we think that they are encouraging and

faster than manual procedures.

However, clinical validation remains to be done,

which will require additional work. Future valida-

tions will compare our segmentation with manually

labelled data and other segmentation results. Future

work could be the integration of anatomical knowl-

A FAST AND ROBUST METHOD FOR VOLUMETRIC MRI BRAIN EXTRACTION

465

Figure 7: White matter segmented using our implementa-

tion.

edge to improve segmentation performance. Finally,

the same framework can be used and extended to seg-

ment and quantify abnormal brains.

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