Automatic Brain White Matter Hypertinsities Segmentation using Deep

Learning Techniques

Jos

e A. Viteri

, Francis R. Loayza

2 a

, Enrique Pelaez

1 b

and Fabricio Layedra

Facultad de Ingenier

ıa en Electricidad y Computaci

on, Escuela Superior Polit

ecnica del Litoral, Guayaquil, Ecuador

Facultad de Ingenier

ıa en Mec

anica y Ciencias de la Producci

on, Escuela Superior Polit

ecnica del Litoral,

Guayaquil, Ecuador

Keywords:

Convolutional Neural Network, U-Net, WMH Segmentation.

Abstract:

White Matter Hyperintensities (WMH) are lesions observed in the brain as bright regions in Fluid Attenuated

Inversion Recovery (FLAIR) images from Magnetic Resonance Imaging (MRI). Its presence is related to con-

ditions such as aging, small vessel diseases, stroke, depression, and neurodegenerative diseases. Currently,

WMH detection is done by specialized radiologists. However, deep learning techniques can learn the patterns

from images and later recognize this kind of lesions automatically. This team participated in the MICCAI

WMH segmentation challenge, which was released in 2017. A dataset of 60 pairs of human MRI images was

provided by the contest, which consisted of T1, FLAIR and ground-truth images per subject. For segmenting

the images a 21 layer Convolutional Neural Network-CNN with U-Net architecture was implemented. For

validating the model, the contest reserved 110 additional images, which were used to test this method’s accu-

racy. Results showed an average of 78% accuracy and lesion recall, 74% of lesion f1, 6.24mm of Hausdorff

distance, and 28% of absolute percentage difference. In general, the algorithm performance showed promising

results, with the validation images not used for training. This work could lead other research teams to push

the state of the art in WMH images segmentation.

1 INTRODUCTION

White Matter Hyperintensities (WMHs) are lesions

observed in the brain, which stand out as areas of in-

creased brightness when commonly observed as sig-

nal hyperintensity on FLAIR (Fluid Attenuation In-

version Recovery) sequences of Magnetic Resonance

Imaging (MRI). The WMH lesions are presumed to

be of vascular origin and have been associated with

cognitive impairment, risk of stroke, dementia, and

geriatric disorders (Breteler et al., 1994). Studying

the WMHs lesions on these types of images, through a

correct and precise segmentation process, would pro-

vide the means for improving the understanding of the

brain damage and the associated cognitive and phys-

ical problems and the supporting benchmarks for di-

agnosing in early stages of the disease.

Recent research (Giorgio and De Stefano, 2013)

has shown the importance of quantifying the WMH,

https://orcid.org/0000-0002-6283-3679

https://orcid.org/0000-0001-9355-5440

especially when analyzing diseases related to neu-

rovascular and neurodegenerative disorders. The im-

portance lies in the diagnosis, progression, and treat-

ment monitoring of the neurological conditions, and

it correlates with different WMH features.

Image analysis plays an essential role during clin-

ical diagnosis. Recent research shows that image seg-

mentation used to study the brain structure revealed

promising results, particularly to follow-up patients

or visualizing tissue abnormalities and tumors (Daliri,

2012). These results allow tracking relevant features

of the segments; such as changes in volume, shape,

or distribution of the abnormalities during patients’

follow-up.

The MICCAI WMH Segmentation Challenge

was created to directly compare automatic segmen-

tation techniques for the White Matter Hyperintensi-

ties (WMH). Since its launch, several methods have

pushed the models’ performance based on Convolu-

tional Neural Networks-CNN, in particular the U-Net

https://wmh.isi.uu.nl/

244

Viteri, J., Loayza, F., Pelaez, E. and Layedra, F.

Automatic Brain White Matter Hypertinsities Segmentation using Deep Learning Techniques.

DOI: 10.5220/0010360302440252

In Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2021) - Volume 5: HEALTHINF, pages 244-252

ISBN: 978-989-758-490-9

architecture (Ronneberger et al., 2015a).

In this work, we propose a model based on a Fully

CNN architecture, tailored for segmentation. This pa-

per is organized as follows: Section 2 describes the re-

lated work about segmentation procedures using var-

ious techniques. Section 3 presents the methodology

proposed in this research. Section 4 discusses the re-

sults and ﬁndings, and Section 5 contains some con-

clusions and future work.

1.1 Related Work

Segmentation techniques of brain images, such as

the Hidden Markow Random Fields (Zhang et al.,

2001), or through Probabilistic Methods (Ashburner

and Friston, 2005), or K-Nearest Neighbors-KNN

(Cocosco et al., 2003; Vrooman et al., 2007), are

mostly related to understanding the main brain struc-

tures, like the gray and white matter, cerebrospinal

ﬂuid, and the surrounding tissues. However, the ob-

tained results showed a need for automatic WMH

segmentation; several techniques based on thresh-

olds have been proposed with modest results, most

of them still waiting for clinical trials (Chancay et al.,

2015; Zijdenbos and Dawant, 1994). Contemporary

advanced techniques using artiﬁcial intelligence for

pattern recognition have been proposed in numerous

studies (Li et al., 2018c; Jin et al., 2018; Li et al.,

2018a; Xu et al., 2017b); these techniques use differ-

ent deep learning architectures; such as CNN models,

and pattern recognition based on texture classiﬁca-

tion (Bento et al., 2017). Several of these techniques

have been mainly derived from the MICCAI chal-

lenge (Berseth, 2017). However, the accuracy of the

segmentation, including detecting false positives or

true negatives, is still the most signiﬁcant challenge.

Even though most of these deep learning techniques

based on similar approaches, the pre-processing pro-

cedures, hyper-parameter calibration, and optimiza-

tion techniques applied to the models’ basic architec-

ture provide outstanding segmentation results. There-

fore, in this work, we propose a revised architecture

based on a Fully Convolutional Neural Network for

segmentation (Long et al., 2014) to push the current

performance of the models considered state of the art.

Segmenting images to localized WMH lesions

have been tackled through several machine learning

approaches, and the analysis of FLAIR images is a

common technique used for this kind of segmentation.

Jack, C. et al. (Jack et al., 2001) shows that segmenta-

tion can be performed by analyzing the FLAIR hyper-

intensities histograms and establishing an intensity

threshold. Morel B. et al. (Morel et al., 2016), used

morphological operators to segment the WMH le-

sions on Transverse Relaxation Time, or T2 brain im-

ages. Ghafoorian, M. (Ghafoorian et al., 2017a) have

proposed the use of CNN combined with anatomical

location data, and more recent techniques, proposed

by the same authors (Ghafoorian et al., 2017b), made

use of transfer learning with a personalized top seg-

ment, based on a dense convolutional architecture as

the output. Xu Y. et al. (Xu et al., 2017a) also pro-

posed to use transfer learning from the Visual Geome-

try Group-VGG architecture, pre-trained from the Im-

ageNet dataset, with a dense convolutional network

for segmenting 3D brain images.

In this work, we propose an architecture based on

a fully connected convolutional network, taking ad-

vantage of one of its characteristics, the shifting in-

variance, aimed at preserving the spatial relationships

of relevant patterns, such as lesions, need to be prop-

agated deep and up to the output layer.

The architecture of the model, as shown in the

next section, uses an end-to-end technique for seg-

menting T1 and FLAIR images sequences. The seg-

mentation process takes about 12 seconds to com-

plete, and this proposed architecture reached the ninth

place at the MICCAI WMH Challenge up to Novem-

ber 2020.

2 METHODOLOGY

The methodology was divided into three main phases.

The ﬁrst was data preparation and pre-processing;

the second was data modeling using deep learning

techniques; and, the third was evaluating the trained

model, which was performed locally by the con-

test organizers. All this work was developed with

python as the programming language (Van Rossum

and Drake Jr, 1995). For data preparation and

pre-processing, the following libraries were used:

nipype (Gorgolewski et al., 2016), numpy (Oliphant,

2006), scipy (Virtanen et al., 2020) and simpleITK

(Lowekamp et al., 2013). Keras (Chollet et al., 2015),

with tensorﬂow (Abadi et al., 2016) as engine, was

used for the deep learning model. Additionally, pan-

das (McKinney et al., 2010) and seaborn (Waskom

et al., 2017) were utilized during the data evaluation

step. Data preparation, validation, and evaluation of

the model were primarily performed in a computer

with Ubuntu 18, 16 GB of RAM, and an Nvidia 1060

GPU with 6GB of GDRR5 memory. For more de-

manding tasks, a Microsoft Azure virtual machine

instance was used. The instance used was a Stan-

dard NC6 Ubuntu 18, 56 GB of RAM, an Nvidia

Tesla K80 with 12 GB of GPU memory (Microsoft,

2020).

Automatic Brain White Matter Hypertinsities Segmentation using Deep Learning Techniques

245

2.1 The Dataset

The images used for training and validation came

from a dataset provided by the MICCAI WMH Chal-

lenge (Kuijf et al., 2019), which consisted of images

of 60 subjects, acquired from three different 3T scan-

ners and places: Amsterdam (AMS GE3T), Utrecht,

and Singapore. Each scanner contributed with a set of

20 pairs of images per subject. Fig. 1, shows a sample

of the images.

Figure 1: Sample of one slice of the dataset used as input for

training. T1-weighted, FLAIR and a manually segmented

mask of the WMH (Ground-truth).

It is important to note that scanners and volun-

teers came from three different hospitals and MRI

scanners: two from the Netherlands and one from

Singapore. As described in (Kuijf et al., 2019), the

parameters’ settings of the acquisition images like

voxel size, slice number, and echo time were differ-

ent for each scanner. The images acquired per subject

were: 3D-T1-weighted images and 2D-multi-slice

FLAIR images. Further, the provided images were

pre-processed previously to correct the bias ﬁeld in-

homogeneities, re-sampled, and coregistered between

them using SPM12 software. Additionally, the con-

test provided the ground-truth images obtained from

each FLAIR image, which were manually segmented.

The segmentation was done by two expert observers,

O1 and O2. The process was made following the

STandards for ReportIng Vascular changes on nEu-

roimaging (STRIVE) conventions (Wardlaw et al.,

2013) — the observer O1 segmented all images using

a contour drawing technique delineating the outline

of each WMH. The second observer O2 performed a

peer review over the manual delineations of O1, fol-

lowing a peer project methodology. A detailed de-

scription of the manual segmentation can be found in

(Kuijf et al., 2019). These images contained binary

masks of the WMH lesions, which correspond to the

ground-truth.

Additionally, the organizers kept in reserved 110

cases from ﬁve different scanners; these images were

not provided to the participants. 30 out of the 110

cases, were from each of the scanners mentioned be-

fore, and 20 from two additional scanners (from Am-

sterdam, but with different characteristics, such as

less magnetic ﬁeld strength). All of these images

were also pre-processed using the same procedure de-

scribed before. The contest reserved these images for

testing purposes and metrics calculation.

2.2 Data Preparation and Further

Pre-processing

Before training the model, data from all sources were

merged into one dataset, consisting of 60 pairs of im-

ages: one T1-weighted image and FLAIR per subject.

All slices for each image were resized to 200x200

pixels across the y and z axis, using the numpy li-

brary in python. Further, we selected a ﬁeld of view

from all images that contained the brain, cropping

the volume to discard the neck. We also performed

additional pre-processing procedures on all images;

such as, a Gaussian normalization to reduce noise,

highlight small brightness spots and smooth the im-

ages, and a morphological normalization to reduce

the black and low-intensity brain regions produced by

cerebral atrophy. This morphological normalization

was performed with the scipy python library.

2.3 Data Augmentation

To prevent the model from overﬁtting and to increase

the size of the training and testing datasets, we ap-

plied some data augmentation strategies with two ap-

proaches. The ﬁrst includes standard operations, like

rotation, scaling, and shearing to all images. Each

transformation increased up to 60 additional images

to the original dataset, increasing from 60 to 240

images for each MRI channel. We also included

more complex data augmentation procedures; such as,

linear and nonlinear transformations over the origi-

nal data. For the linear transformations, we used a

pointwise product between the FLAIR and T1 im-

ages. And, we applied a diffeomorphic transforma-

tion for the nonlinear data augmentation, normaliz-

ing from the native space to the MNI 152 standard

space (Fonov et al., 2011; Fonov et al., 2009), using

the nipype library. After these procedures, we created

a separate dataset with the linear and nonlinear trans-

formations.

2.4 Network Architecture

The proposed model’s architecture was designed to

use two types of images as input per subject: T1-

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246

weighted and FLAIR images with the correspond-

ing pre-processed procedures explained before. Addi-

tionally, both images need to be coregistered between

them, including a ﬁeld bias inhomogeneities correc-

tion.

Figure 2: U-Net Neural Network Architecture.

For this research, we designed three different seg-

mentation models based on a fully CNN architec-

ture, as proposed by (Long et al., 2014; Milletari

et al., 2016); and, in particular the U-net architec-

ture (Ronneberger et al., 2015b), which had proven

to be highly useful in biomedical image segmenta-

tion. In this work, the U-Net architecture performed

the best, a model with 21 layers, including 15 con-

volutional layers, three upsampling layers, and three

pooling layers. Fig. 2 shows a general representation

of this model’s architecture. For the ﬁrst two layers

we used 5x5 convolutional ﬁlters, while for the rest a

set of 3x3 convolutional ﬁlters were used. After each

convolutional layer, a Rectiﬁed Linear Unit (RELU)

activation function was applied (Agarap, 2018). The

yellow boxes in Fig. 2 represent the max pooling or

downsamplig procedures, and the green boxes the up-

sampling operation, both with 2x2 ﬁlters. The num-

ber of ﬁlters in each layer goes from 64 in the two ﬁrst

convolutional layers to 128, 256, and 512 ﬁlters in the

left side of the U-Net. We use Adam Stochastic Gra-

dient Descent for the learning process of the model

(Kingma and Ba, 2014). The learning rate was set to

0.0002. The training was performed with 30 batches,

and the parameter’s search was performed during 50

epochs. The other two models were designed with a

similar conﬁguration, but with some modiﬁcations of

the hyper-parameters, as discussed in the next section.

Once the models were trained, cross-validated and

tested, the models were put into an inference stage,

where the architectures were also tested with new T1

and FLAIR images, which were not seen during the

previous phases, to let them recognize the WMH le-

sions, as well as to perform the segmentation in the

images.

2.5 Evaluation

The models were evaluated using six metrics as

deﬁned by the MICCAI WMH segmentation chal-

lenge. Those metrics were: Dice Similarity Coefﬁ-

cient (DSC), Hausdorff Distance (HD), Average Vol-

ume Difference (AVD), Sensitivity for detecting indi-

vidual lesions, (Recall), and the F1-score. The Dice

similarity metric measures the overlap between the

manual segmentation and the model segmentation.

The Hausdorff Distance measures how far two sub-

sets of a metric space are from each other. As used in

this challenge, the Hausdorff Distance is modiﬁed as

to obtain the most robust version using the 95th per-

centile instead of the maximum 100th percentile dis-

tance. The Average Volume Difference metric mea-

sures the percentage difference in the volume of the

manual segmentation lesions compared to the model

segmentation. As for the Recall metric, this measures

the ability of a model to ﬁnd all relevant cases within

the data. And, the F1 index is a way to combine the

recall with its precision, which is deﬁned as the har-

monic mean of both, as deﬁned in (Li et al., 2018b).

The model evaluation was performed in two parts.

First, a local testing was made using the three differ-

ent U-nets architectures, tuning the hyper-parameters

to push for the ground-truth masks and for the met-

rics obtained by the 2017’s challenge winner (Li et al.,

2018b). Then, once our best model was tuned for the

best performance, it was evaluated by the WMH chal-

lenge organizers, using their own additional test im-

ages, which placed our architecture ninth on the over-

all challenge up to November 2020.

3 RESULTS AND DISCUSSION

3.1 Local Results

Before conﬁguring our three U-Net based models, we

evaluated the Re f erence models, to set the basis for

comparing our models. We evaluated the model pre-

sented by (Li et al., 2018b), which was taken as refer-

ence. Then, the challenge’s Re f erence model, which

we use it to obtain the metrics as described by the

challenge. Based on these baseline architectures, our

ﬁrst proposed model was created based on the U-net

architecture as shown in Fig. 2; this ﬁrst model was

called (U − net#1), and its architecture was conﬁg-

ured to take two channels as input: a FLAIR image

and an augmented image obtained by a dot product

of the T1 and the FLAIR. This architecture produced

low performance as compared to the reference mod-

els and did not require further analysis.

Automatic Brain White Matter Hypertinsities Segmentation using Deep Learning Techniques

247

Figure 3: General results of the internal testing.

Figure 4: Figure shows a comparison of the same slice of

two images between the ground-truth (Original) and auto-

matic segmentation performed by U −net#2 and U −net#3.

Then a second model was conﬁgured, which we

called (U − net#2), and it was tune-designed to ac-

cept our pre-processed FLAIR and T1 images as in-

puts, which was deﬁned in our pre-processing phase,

with promising results. Fig. 3 shows the segments

obtained by this models as compared to the original

or ground-truth.

A third model then was evaluated, a model called

(U − net#3), which was designed to use an Exponen-

tial Linear Unit ELU (Clevert et al., 2015), as ac-

tivation function in the convolutional steps, and the

he − normal as kernel initializer (He et al., 2015)

in the last step. This model performed better than

the reference, but not as good as the model called

U − net#2. Fig. 4 also shows the segments obtained

by this models as compared to the original or ground-

truth.

Therefore, our second model was uploaded to the

WMH challenge platform. Figures 3 and 5 show the

results of the testings performed locally and the re-

sults assessed by the WMH organizers.

For local testing purposes, eight images were se-

lected randomly and used to compare the resulting

segments from the four models. The eight images

were obtained from the three scanners proportionally,

making sure to have at least two subjects for the input

scanner. The metrics used in the local testing were

the same as they were deﬁned by the challenge orga-

nizers; that is, the Dice, Hausdorff Distance, Average

Volume Difference, F1 score, and Recall. The results

could be seen in Fig. 3. This ﬁgure shows a gen-

eral summary of all metrics assessed locally in our

experiments. The Ams preﬁx are patients from the

Amsterdam scanner, Sin is from the Singapore scan-

ner, and Ut is from the Utrecht scanner. Additionally,

the table in Fig. 3, shows the average results for all

metrics from each model. Fig. 4 shows the segments

from two MRI images: Singapore (subject #60) and

Amsterdam (subject #132). The original label is the

manual segmentation done by experts and provided

by the challenge organizers. As it is shown in Fig. 4,

our U − net#2 and U − net#3 models obtained com-

parable segmentation results as to the experts’ deﬁned

segments.

As it is seen in Fig. 3A, the Dice metric, in our

U − net#2 and #3 models, performed better than the

Re f erence model. Also, the performance gain was

in general better. These metrics were 4.84% and 3%,

respectively better than the Re f erence model.

On the other hand, the Hausdorff distance, as seen

in Fig. 3B, was signiﬁcantly better. For example,

a subject from the Amsterdam group has a Hausdorff

Distance of 65.52 mm in the Re f erence segmentation.

While in model U − net#2, such difference reached

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248

0.98 mm, which represents an improvement of 67.10

times over the actual Re f erences. On average, the

Hausdorff Distance between the manual segmenta-

tion and the automatic segmentation, obtained in this

work, was 4.62 times better than the Re f erence.

The Average Volume Difference is observed in

Fig. 3C. In this metric, we obtained more varia-

tion. For example, in two patients from the Amster-

dam scanner, the U −net#2 performed better than the

rest of the models. The U − net#3 worked very well

on images from the Utrecht scanner. However, in gen-

eral, both the U − net#2 and #3 performed better seg-

menting than the Re f erence. While the average AV D

of the validation patients in the Re f erence model was

28.23 % in our model U − net#2 was 15.44 %and

22.63 % in the U − net#3. Although, Both methods

performed better compared to the Re f erence model.

The F1 score can be seen in Fig. 3F. The aver-

age value of the eight validation subjects’ images was

0.68, while our score was 0.80. In absolute terms, the

U −net#2 improved 17.3 % and the U −net#3, 6.16%

as compared to the Re f erence.

Finally, the recall metric can be seen in Fig. 3D.

This metric was the only one which did not im-

prove, as compared to the Re f erence models using

the U − net#2 model. In average the value obtained

with our model was 0.83, while the Re f erence model

was 0.88. However, the U −net#3 performed better in

the recall metric, we obtained 0.90, representing 1.3%

improvement as compared to the re f erence model.

3.2 WMH Validations

In this section, we present a summary of the evalu-

ations made by the WMH challenge organizers. The

model submitted to evaluation was the U −net#2. The

evaluation method is based on the rankings of each

metric, as described before, using a score from 0 to

1. The best performing team is ranked with 0 and

the worst with 1. All other teams were ranked in be-

tween relative to their performance within that met-

ric range. Then to compute the ﬁnal score, the ﬁve

ranks were averaged in an overall ﬁnal score, as de-

scribed in (WMH Segmentation Challenge, 2020). In

general, this work was placed ninth out of 43 partici-

pant teams, and as reported in November 2020, with

a score of 0.0596. Even though the metrics mea-

sured locally favored us, we could not improve the

Re f erence performance with the organizers’ assess-

ment, as observed in the results section of the web

site: (https://wmh.isi.uu.nl). A summary of this re-

sults can be seen in Fig. 5. Each ﬁgure includes a box

plot for every metric against the scanners tested by the

organizers. It is important to note, that the organizers

tested with images acquired from scanners with a dif-

ferent technology than the used for our training pro-

cess, as it is seen in the table, in Fig. 5. All the images

provided by the contest were obtained by different

brands of 3 Tesla scanners. However for validation

purposes, the contest also included images obtained

from 1.5 Tesla (AMS GE1.5T) and a hybrid Positron

Emission Tomography/MRI (AMS PETMR). The or-

ganizer’s results includes the average for each scan-

ner and the ranking of each metric against the other

teams, our worst results are observed precisely for the

AMS GE1.5T and AMS PETMR, images from scan-

ners with different technology not used for training.

The Dice metric performed best for Singapore

subjects. All validation results seem to have some

standard deviation and outliers, considering the im-

ages’ origin. In our case, the Singapore patients and

the AMS GE3T patients have a Dice score of 0.80 and

0,79, respectively, demonstrating good performance.

The Dice score, however, for the AMS PETMR was

slightly lower, with a 0.71 value, than the rest of the

scanners.

As for the Hausdorff distance metric, our model

performed particularly good; in this metric our model

was placed in ﬁfth place with an overall rank of 0.017.

We also obtained a slightly better result in this met-

ric than the Re f erence, with an averaged distance of

6.30 mm, as compared to ours of 6.24 mm. The image

shows that the distance is almost always below the 20

mm mark, with some outliers reaching 40 mm.

In the average volume difference metric, the aver-

age value with all the testing patients was 28.26 %.

The performance was good in nearly all the scanners

except the AMS PEMTR scanner, in that case, the av-

erage volume difference was 60.79 %.

Considering the recall, the results obtained from

the Amsterdam images were above 0.80. However,

with the Utrecht images, we obtained a score of 0.71.

Also, it is noticeable that in this work, the perfor-

mance was better for the exclusive training scanners,

in which the other metrics did not perform well. Over-

all, for the local testing, the recall was the weakest

metric obtained in our model, with an overall rank-

ing of 0.137 compared to the other teams. However,

the score of 0.78 was not as far from the 0.87, which

is the current higher score obtained up to November

2020.

Finally, the F1 score had an average value of 0.74.

This metric was the one with a more standard devia-

tion. All the scanners had averaged performances be-

tween 0.7 and 0.8, except for the AMS PETMR scan-

ner with 0.65.

Automatic Brain White Matter Hypertinsities Segmentation using Deep Learning Techniques

249

Figure 5: Overall results assessed by WMH challenge organizers.

3.3 Conclusions

We developed and evaluated a Convolutional Network

architecture for segmenting automatically WMH,

from FLAIR and T1 images. In our local evalua-

tions, we obtained and improvement in 4 out of 5 met-

rics, as deﬁned by the WMH segmentation challenge.

That includes Dice, Hausdorff Distance, F1 score, and

Average Volume Difference. We were ranked ninth

place overall in the organizers’ assessment, obtaining

the best metric for the Hausdorff distance. As it can

be seen, our worst performance was with the images

coming from scanners not used during training, which

could be interpreted as over-ﬁtting the data. How-

ever, considering a good performance obtained with

this proposed architecture, the hyper-parameter tun-

ing and the re-training of the algorithm, with images

from additional scanners technology could improve

the algorithm performance. Therefore, the work pre-

sented here could lead to other researchers to improve

the state of the art, for all society’s beneﬁt.

ACKNOWLEDGEMENTS

We thank the MICCAI-2017 WMH Challenge orga-

nizer Dr. Hugo J. Kuijf to share us all the datasets

of images and making all the validation results. We

also thank Phd. Luis Mendoza for the supervision of

the project work and Kevin Cando as this work was

initialized by him as his ﬁnal degree project.

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