COMPUTER AIDED DIAGNOSIS SYSTEM IN DIGITALMAMMOGRAPHY

Joao Maria Patacho de Matos Rocha e Melo

Thesis to obtain the Master of Science Degree in

Electrical and Computer Engineering

Supervisors: Prof. Maria Margarida Campos da SilveiraProf. Nuno Miguel de Pinto Lobo e Matela

Examination Committee

Chairperson: Prof. Joao Fernando Cardoso Silva SequeiraSupervisor: Prof. Maria Margarida Campos da Silveira

Members of the Committee: Prof. Jorge dos Santos Salvador Marques

May 2017

To my parents.

For despite all the struggles a family can go through, my education was never at stake.

Acknowledgments

I would like to thank Professor Margarida Silveira, from IST, supervisor of this thesis. Her input

and recommendations were essential throughout this work. I would like to particularly thank her for her

patience and understanding for, due to professional reasons, I had many time constrains during this

work’s period. Professor Margarida was nothing but understanding and supportive of this fact. I also

want to thank Professor Nuno Matela, from IBEB, co-supervisor of this work. Professor Nuno’s input on

the medical subjects were essential for the completion of this project. I would like to thank him for the

several trips to the Hospital in order to collect data and experts’ opinions.

A special thank you to Professor Jose Roquette and Dr Isabel Estudante, from Luz-Saude, and Dr

Tiago Saldanha for their availability in providing expert medical opinion regarding several topics as well

as for their recommendation on the user side of this work’s final product.

I would like to thank Ana Colaco, Bsc. Ana volunteered to do an extensive research on the medical

aspects of breast cancer and shared such research with me and several other students.

I cannot thank my entire family enough, in particular my parents and my girlfriend, for their under-

standing on the work and time invested in this thesis. Many sacrifices are done by researchers, when

doing a project such as this one. Nevertheless, many are also done by the people around them and

such should be acknowledged. For this, I thank them. Also, a great thank to Ederzito A.M. Lopes. His

inspiring attitude towards his profession and his accomplishments were crucial for the conclusion of this

work.

Also, to my friends, particularly my colleagues at IST: Bernardo Almeida, Bernardo Marques, Hugo

da Silva, Joao Franco, Joao Oliveira, Jose Teixeira, Manuel Avila de Melo, Manuel Ribeiro, Manuel

Beja da Costa, Miguel Monteiro and Nuno Sousa. Their input, both technical and emotional and their

recommendations and advices were fundamental for the conclusion of both this thesis and my studies.

I would like to thank my company, BNP Paribas, my team and my co-workers, for their support and

for letting me dedicate time to this project, when it was necessary.

Last, but not least, I would like to thank all my teachers, Professors and everyone involved in my

education whom, without their support, my journey towards here would have been different and harder.

To all of you, thank you.

Abstract

Currently, early detection of breast cancer is one of the most important factors in the treatment of breast

cancer. Computer Aided Diagnosis (CAD) systems provide aid to doctors in diagnosing breast images

such as mammography and Digital Breast Tomosynthesis (DBT), in order to increase the diagnosis’

accuracy. This work describes a CAD system to locate lesions (masses) in 2D mammographies, based

on image processing and machine learning techniques. This thesis proposes a two stage combination of

classifiers to label mammograms. The first stage separates masses from healthy tissue while the second

distinguishes between malignant or benign masses. Each base classifier is trained with a different type

of feature, either Morphological, Intensity or Texture based. Two base classifiers, Adaboost and Decision

Trees, were tested. Results obtained on real mammograms from an international database showed an

improvement in the accuracy of the CAD system, from 82% to 85%, when compared to the use of a

single classifier. In this thesis, an hypothesis of a 3 model ensemble classifier is implemented to label

a database of mammograms into healthy tissue, malignant mass or benign mass. In this classification

stage, two classifiers (AdaBoost and Decision Tree) were tested. This hypothesis proved to increase the

accuracy of the CAD system, when comparing to a single model classifier, from 82% to 85%.

Keywords

Mammography; Breast Cancer; Computer Aided Diagnosis.

iii

Resumo

Nos dias de hoje, a detecao em estado inicial do cancro da mama e um dos aspectos mais decisivos

para minimizar os impactos e consequencias deste tipo de cancro. Sistemas de Diagnostico Auxiliado

por Computador providenciam suporte aos medicos, aquando o diagnostico via tecnicas de imagiologia

como mamografia e tomossıntese, para aumentar a precisao do diagnostico. Este trabalho descreve

um sistema de diagnostico auxiliado por computador para localizar lesoes (massas), em mamografias

2D, baseado em tecnicas de processamento de imagem e aprendizagem automatica. Esta dividido

em seis capıtulos: uma introducao as tecnicas de imagiologia, do ponto de vista medico e tecnico, um

resumo do estado da arte dos sistemas de diagnostico auxiliado por computador para mamografias

e tomossınteses, uma explicacao extensiva dos metodos usados para a construcao do sistema, os

resultados do mesmo e uma conclusao e futuras melhorias para a continuacao deste trabalho. Nesta

dissertacao, uma hipotese baseada em fundir 3 modelos num unico classificador e implementada, para

diagnosticar mamografias presentes numa basa de dados em: tecido saudavel, massa maligna ou

massa benigna. Nesta etapa de classificacao, dois classificadores (AdaBoost e arvores de decisao)

e tres tecnicas de fusao sao testados. Comprovou-se que esta hipotese melhora os resultados do

diagnostico auxiliado por computador, quando comparado com a implementacao de apenas um modelo,

de 82% para 85%.

Palavras Chave

Mamografia; Cancro da Mama; Diagnostico Auxiliado por Computador;

v

Contents

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Breast and Breast Tumours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1 The breast and its anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.2 Breast Tumours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.3 BI-RADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Breast Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3.1 Mammography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3.2 Tomosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 Computer Aided Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 State-of-the-Art 13

2.1 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Feature Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 Learning and Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5 Summary of State-of-the-Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3 Pre-Processing and Segmentation 27

3.1 Pre-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 Feature Extraction and Classification 41

4.1 Feature Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.1.1 Morphological Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.1.2 Grey Level Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.1.3 Texture Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2.1 Decision Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.2.2 AdaBoost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

vii

4.2.3 Fusion Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5 Experimental Results 63

5.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.2 Pre-Processing and Segmentation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.3 Classification Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.3.1 Single Model Decision Tree Experiment . . . . . . . . . . . . . . . . . . . . . . . . 69

5.3.2 Decision Tree Ensemble Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.3.3 AdaBoost Ensemble Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.4 Comparison of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6 Conclusions and Future Work 77

viii

List of Figures

1.1 Relative survivals of female patients diagnosed with breast cancer up to one year earlier,

in Great Britain, brokedown by age category. . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 The anatomy of the breast. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Mammography performed on the left breast of a patient with a class 1 density breast. . . 8

1.4 Example of the 2 different perspectives taken on a mammography. . . . . . . . . . . . . . 8

1.5 Drawing of a mammograph examining the right breast of a patient. . . . . . . . . . . . . . 8

1.6 Angular capability of Siemens Model. This particular model creates up to 25 images. . . . 10

1.7 Example of a tomosynthesis exam where the relationship between the different slices can

be seen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.8 CAD output displayed where the previously marked lesion can be seen in green and the

CAD suggestion in red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.1 Example of a bilateral filter in which the centre in question is in a high intensity area but

close to the border. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 Example of a COIN filter being computed for a circle. . . . . . . . . . . . . . . . . . . . . . 18

2.3 Representation of the computation of the CRI. . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4 Representation of a labelled dataset and a new pattern, waiting to be classified. . . . . . 22

3.1 Scheme of the 4 steps approach applied in this thesis . . . . . . . . . . . . . . . . . . . . 29

3.2 Example of a a) digitalized mammography from Digital Database for Screening Mammog-

raphy (DDSM) and b) its histogram. As explained before, it can be seen that even within

the breast, darker areas may exist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3 Example of a) mammography and b) its histogram, where a Gaussian filter with a standard

deviation of 50 is applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

ix

3.4 Binary image obtained from dividing the mammography presented in 3.2(a) into back-

ground and foreground. Notice on the top right corner of a) that other elements were

wrongly identified as foreground. Hence the need to withdraw only the larger object as

seen in b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.5 Resultant image of separating breast (foreground) from background using Otsu’s method.

The green line represents the border of the mask computed from this breast. This process

is important for many of the methods following this one will be applied only to pixels within

the mask. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.6 2D spatial filter represented in a) 3D and b) from the x-y plane. In this figure, it is possible

to see that the further way a pixel is of the pixel of interest (center), the less its weight is

going to be. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.7 2D intensity filter representation in a) 3D and b) from the x-y plane. The pixels with the

highest weight value represented in this filter are the ones with the intensity value closest

to the value of the pixel of interest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.8 2D bilateral filter representation in a) 3D and b) in x-y plane. Combination of filters repre-

sented in figures 3.6 and 3.7, where it can be seen that pixels closer to the pixel of interest

in terms of spatial distance and intensity level value will have higher weights. . . . . . . . 35

3.9 Comparison between image from the database used in this thesis (to the left) and micro-

scopic fluorescent image (to the right) segmented using SBF . . . . . . . . . . . . . . . . 36

3.10 Gradient representation in a a) black and white image and b) its quiver representation

from Matlab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.11 Graphical representation of the gradient of a pixel computed using Intermediate Differ-

ences gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.12aGradient of an image. Each arrow represents the gradient vector in each pixel of the

surrounding area of the pixel of interest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.12bLine segments uniting each pixel with the pixel of interest. . . . . . . . . . . . . . . . . . . 38

3.13 Fusion of the gradient of each pixel and the line segment uniting each pixel with the pixel of

interest. Graphical representation of the angle used to compute the degree of convergence. 38

3.14 Illustration of Convergence Index (COIN) filter being computed for an approximately cir-

cular lesion. This figure exemplifies a case where the centre is correctly found, but the

border is not. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.15 Illustration of an iris filter being computed for the same approximately circular lesion as

in figure 3.14. This figure exemplifies a case where both the centre and the border are

found. In this illustration, only 8 orientation points are used, hence, the border is not

entirely found, although, if N →∞ , it would. . . . . . . . . . . . . . . . . . . . . . . . . . 40

x

3.16 Illustration of an adaptive ring filter being computed for the same approximately circular

lesion as in figure 3.14 and 3.15. In this illustration, the Rmin and Rmax are used to limit

the area in which the border can be found. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.1 Mathematical morphology operation a) ”dilatation” and b) ”erosion” performed between

image A, a square, and the structuring element B, a disk. . . . . . . . . . . . . . . . . . . 44

4.2 Example of a round region where mathematical morphology opening was applied. At it

can be visualized, the image does not differ from its original one. . . . . . . . . . . . . . . 45

4.3 On the contrary of the region presented in figure 4.2, when opening is applied to an

approximately round region, some changes can be observed already. . . . . . . . . . . . 45

4.4 Opposing the two cases earlier, figures 4.2 and 4.3, when opening is applied to a spicu-

lated region, a significant difference can be seen. . . . . . . . . . . . . . . . . . . . . . . . 46

4.5 Examples of histograms of Region of Interest (ROI)s with the same mean intensity value

but with different levels of standard deviation. On the left, an histogram with a small value

of standard deviation. On the right, an histogram with a standard deviation value 5 times

higher than the one on the left. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.6a Example of the angle’s histogram of an image. On the left, the histogram of an image

with a random texture (presented on the right). By this histogram, it is possible to see that

there are gradients pointing to all directions in the image on the left. . . . . . . . . . . . . 49

4.6b Illustration of how an analysis on the histogram of the gradients’ angle of an image can be

descriptive of such image. In this case, on the right an image with stripes and on the left,

its histogram. It can be easily seen that, comparing to figure 4.6a, this histogram outputs

more information regarding the organization of its image. . . . . . . . . . . . . . . . . . . 49

4.7 Representation of the classification flow used in this work. The features of the ROI are

used as input for 3 classifiers, whose outputs are combined and in which the ROI is

classified as a Mass or as Healthy Tissue. In case of a mass, the process moves along

and the features are used as inputs to another 3 classifiers, that, after its outputs are

combined, define if the ROI is malignant lesion or a benign one. . . . . . . . . . . . . . . . 51

4.8 Example of a DT with three nodes and four leafs. . . . . . . . . . . . . . . . . . . . . . . . 52

4.9 Gini function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.10 Ilustration of the Single Model Decision Tree used in this work . . . . . . . . . . . . . . . . 53

4.11 Schema of the classifier used in the Decision Tree Ensemble experiment. . . . . . . . . . 53

4.12 Ilustration of the AdaBoost Classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.13 Illustration of the first learner being computed. In this example, all the patterns have the

same weight (represented by the patterns size) . . . . . . . . . . . . . . . . . . . . . . . . 56

xi

4.14 Illustration of the second learner of an AdaBoost. In this figure, the patterns previously

miss-classified in figure 4.13 have a larger classification weight, as represented by their

size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.15 Illustration of the third learner of the AdaBoost. As it can be seen, the patterns miss

classified both in figure 4.13 or 4.14 have larger weights than the others. . . . . . . . . . . 57

4.16 Schema of the classifier used in the AdaBoost Ensemble experiment. . . . . . . . . . . . 58

5.1 Histogram of the 3 classes of exams contained in DDSM database. . . . . . . . . . . . . . 65

5.2 Effect of filtering on the segmentation of a breast image with a malignant lesion a) without

the bilateral filter b) with the bilateral filter. In this figure, it can be seen the output of the

segmentation in green and the ground truth in blue. . . . . . . . . . . . . . . . . . . . . . . 67

5.3 Effect of filtering on the segmentation of a breast image with a malignant lesion a) without

the bilateral filter b) with the bilateral filter. In this case, the filter had no effect on the

segmentation output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.4 Effect of filtering on the segmentation of a breast image with a malignant lesion a) without

the bilateral filter b) with the bilateral filter. In this case, the segmentation algorithm does

not locate the correct ROI in the filtered image. . . . . . . . . . . . . . . . . . . . . . . . . 68

5.5 DT a) not pruned, b) pruned, with three possible outputs: 0,1 and 2 or healthy tissue,

malignant mass and benign mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.6 Relative weights of the learners of the AdaBoost classifier a) in total b) by model. . . . . . 73

xii

List of Tables

1.1 Percentage value of the 3 most common types of cancer. The values represent the

amount of cases of a certain type of cancer in a universe of cancer diagnosed patients. . 3

2.1 Table presenting chronologically several important contributions in the field of CAD of

breast cancer in mammography and DBT in the past recent years . . . . . . . . . . . . . 25

5.1 The female population at MGH and WFUSM by race . . . . . . . . . . . . . . . . . . . . . 66

5.2 Confusion matrix of the decision tree presented in the Single Model Decision Tree exper-

iment. This model obtained a classification rate of 82%. . . . . . . . . . . . . . . . . . . . 70

5.3 Table presenting the per class accuracy results of the Single Model Decision Tree experi-

ment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.4 Confusion matrix of the classifier presented in the Decision Tree Ensemble Experiment.

The final classifier obtained a classification rate of 82%. . . . . . . . . . . . . . . . . . . . 71

5.5 Table presenting the accuracies per class and per model obtained from the results of the

Decision Tree Ensemble Experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.6 Confusion matrix of the morphological, intensity and texture features model presented in

the Decision Tree Ensemble Experiment. Each model obtained a classification rate of

80%, 73% and 71%, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.7 Confusion matrix of the AdaBoost Ensemble Experiment classifier. This model obtained

a classification rate of 85%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.8 Table presenting the accuracies per class and per model obtained from the results of the

AdaBoost Ensemble Experiment classifier. . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.9 Table for comparison of general accuracies and per class accuracy of the three experiments 74

5.10 Confusion matrix for all three experiments, considering only two masses. . . . . . . . . . 75

xiii

xiv

Acronyms

ACC Accuracy

AT Adaptive Thresholding

AUC Area Under the Curve

BI-RADS Breast Imaging Reporting and Data System

CAD Computer Aided Diagnosis

CC Craniocaudal

CRI Candidate Ratio Index

COIN Convergence Index

DBT Digital Breast Tomosynthesis

DDSM Digital Database for Screening Mammography

DT Decision Tree

EM Expectation Maximization

FCM Fuzzy C-Means

FFDM Full-Field Digital Mammography

FP False Positive

GFA Gradient Field Analysis

IBEB Instituto de Biofısica e Engenharia Biomedica

IEEE Institute of Electrical and Electronics Engineers

ICIP International Conference on Image Processing

xv

IST Instituto Superior Tecnico

IJBBE International Journal of Biology and Biomedical Engineering

HOG Histogram of Oriented Gradients

LCF Local Convergence Filters

LDA Linear Discriminant Analysis

MGH Massachusetts General Hospital

MRI Magnetic Resonance Imaging

MLO Mediolateral Oblique

MLP Multi-layer Perceptron

MP Medical Physics

PV Projection View

RBF Radial Basis Function

RGI Radial Gradient Index

RLS Run Length Statistics

ROI Region of Interest

SBF Sliding Band Filter

SC Surface Change

SGLD Spatial Grey Level Dependence

SPIE Society of Photo-Optical Instrumentation Engineers

SSD Sum of Squared Differences

SVM Support Vector Machine

TP True Positive

VOI Volume of Interest

WFUSM Wake Forest University School of Medicine

xvi

1Introduction

Contents

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Breast and Breast Tumours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Breast Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Computer Aided Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1

2

1.1 Motivation

According to the World Health Organization, cancer incidence worldwide increased from 12.7 million

cases in 2008 to 14.1 million in 2012. If this increase continues, this will bring the number of cancer

cases close to 25 million over the next two decades [1]. According to the same source, in the year of

2012, 8.2 million people died of cancer, which represents a cancer mortality rate of 64.5%. Despite the

fact that lung cancer is the most common type of cancer [2] and the one with the lowest survival rate [3],

breast cancer represents 25% of all cancer cases in the female population, being the most common

cancer for women, as shown in table 1.1. 1

Table 1.1: Percentage value of the 3 most common types of cancer. The values represent the amount of cases ofa certain type of cancer in a universe of cancer diagnosed patients.

GenderBoth (%) Male (%) Female (%)

Typesof

Cancer

Breast 11.9 - 25.2Lung 13.0 16.7 8.8

Colorectum 9.7 10.0 9.2

In 2012, Breast Cancer’s survival rate was 87% for people who were diagnosed 5 years earlier

(or more) in the United States [4], and 78% for people diagnosed 10 years earlier (or more) in Great

Britain [3]. One of the most peculiar aspects of this type of cancer is that, if caught in its early stages,

the survival rate is very high, but it drops at a steep rate when diagnosed in later stages, lowering to as

much as half the value when the patient is of advanced age. Figure 1.1 exemplifies this.

Figure 1.1: Relative survivals of female patients diagnosed with breast cancer up to one year earlier, in GreatBritain, brokedown by age category. Source: Public Health England [5]

1Male population not displayed for breast cancer, for not statistically significant

3

This data points towards an important conclusion. Quicker and more efficient diagnosis methods,

for breast cancer prevention and early detection, are very important and should be increasingly used,

given the amount of breast cancer cases. Currently, the most common breast imaging technique used

for breast cancer diagnosis is the mammography, a 2D X-ray technique used to visualize lesions in

the patient’s breast [6]. Being an imaging technique, mammography implies a doctor to spend time

evaluating the exam itself in order to obtain a diagnosis. This means more expenses for the hospital

(doctor’s allocated time to this task) and that fatigue and lack of time for evaluations are important

factors in the diagnosis sensitivity.

Due to all these reasons, the need for Computer Aided Diagnosis (CAD) systems to complement

mammography is expected to rise. A CAD system uses image processing techniques and machine

learning algorithms to perform an analysis on the exam and helps the doctor with its diagnosis. Other

CAD systems have already been implemented in several imaging techniques, increasing 6% to 17% the

number of correct diagnoses depending on the type of cancers.

4

1.2 Breast and Breast Tumours

1.2.1 The breast and its anatomy

The breast is composed by several different regions, types of tissues and muscles, as seen in figure

1.2. On one hand, the adipose tissue is composed by muscles and fat, and it represents the less

dense sections of the breast. On the other hand, glandular tissue is denser and it is where glands and

lactiferous ducts2 can be found.

Figure 1.2: The anatomy of the breast. Source: Interventional Ultrasound of the Breast [7]

The measurement of the ratio between glandular and adipose tissue is called density. A patient’s

breast can be of density 1 to 4, with the following specifics:

• Density 1: Significantly larger presence of adipose tissue. A breast with these characteristics is

little dense and fat.

• Density 2: Equally distributed amounts of glandular and adipose tissue, in an organized and

distinct manner. In this type of breast, there is more glandular tissue in comparison with density 1

breast, but adipose and glandular tissue do not mix nor overlap.

• Density 3: Equally distributed amounts of glandular and adipose tissue, such as in density 2

breasts, but in a de-organized manner. Several regions of each type of tissue with no apparent

order or criteria are present in a breast of density 3.

• Density 4: Larger presence of glandular tissue and lactiferus ducts.

2Channel that transports breast milk from its origin (glandular cells) to the nipple

5

1.2.2 Breast Tumours

A tumour is a conglomerate of cells that is out of the ordinary. Contrary to common belief, a tumour

does not necessarily pose health issues, nor troubles. There is a variety of tumours which have different

behaviours, shapes, locations, etc, and each of them is treated and analysed in a different way. A tumour

(also called lesion or mass) is of one of two types:

• Benign lesion: this lesion is encapsulated. It means it does not spread nor grows out of control.

• Malignant lesion: commonly known as cancer, these types of lesions grow uncontrolled and

disproportional to what the human body expects. These cells can invade surrounding tissue and/or

metastatize to other tissues in other parts of the body.

This thesis focus in tumours located in the breast area. As with other tumours, they can be either

malignant or benign and are more common among the female population than other tumours due to the

anatomy of the breast. The lactiferus ducts are auspicious environments for tumours to develop due to

the large number of glandes and to the presence of breast milk which contains calcium and can solidify

into lesions as well.

Lesions in the breast can be divided into two major categories, where both can be benign or malig-

nant:

• Masses: structures with an oval and round shape. Can be of various sizes.

• Microcalcifications: conglomerates of calcium originated from breast milk. These lesions are

significantly smaller than masses and can form clusters which can become malignant.

1.2.3 BI-RADS

The Breast Imaging Reporting and Data System (BI-RADS) is a classification system of the appar-

ent malignancy of the lesion of a patient. After reviewing a radiology exam (mammography, Magnetic

Resonance Imaging (MRI) or breast ultrasound), the radiologist determines, in a scale from 0 to 6, how

malignant (or not) the findings in the exams are. This classification system is divided into the following

items:

• BI-RADS 0: This level of BI-RADS indicates that the study is not complete. More information (or

more exams) are still required or undergoing.

• BI-RADS 1: This indicates that no lesion was found by visual inspection of the exam. The patient

should continue the routine screenings, but there is no factor that indicates any other action should

take place.

• BI-RADS 2: When this level is discriminated, it indicates that the doctor found an irregularity but

with no reason for further precautions. This means the patient should continue routine screenings.

6

This is important because it tells the next doctor that sees the next exam, that something was

previously found. This way the doctor can check if it evolved to something worse, if it stayed the

same or if it vanished.

• BI-RADS 3: This level of BI-RADS indicates that something slightly suspicious was found in the

patient’s exam. No immediate action is required, but the patient is asked to repeat the exam in a 6

month period for further confirmation.

• BI-RADS 4: This indicates that the findings in the patient’s mammogram are suspicious of being

malignant. When this level is attributed, the patient will undergo a biopsy 3 exam for confirmation

of the malignancy of the lesion.

• BI-RADS 5: When this level is discriminated, it indicates that, in the expert’s opinion, the findings

appear malignant. This is the maximum level of BI-RADS that can be assigned to a patient without

undergoing a biopsy (only by visual inspection). Similar to level 4, the next step is to perform a

biopsy to confirm (or not) the malignancy of the lesion.

• BI-RADS 6: The highest level of BI-RADS that can be assigned to a patient is level 6. This means

the patient was diagnosed with breast cancer and should discussed (or already did) a treatment

plan with an expert.

1.3 Breast Imaging

1.3.1 Mammography

Currently, the most common and effective form of breast cancer diagnosis is the digital mammogra-

phy [8]. This exam consists in X-ray images of the breast that can be taken from two standard directions

(Craniocaudal (CC) view and Mediolateral Oblique (MLO) view) and many supplementary views [9]. As

seen in figure 1.4, a CC view mammography will obtain an image overlap from top to bottom of the

breast, compared to the MLO which will in turn obtain a 45º side-view image of the breast. These

processes are done for two reasons:

• Some sections of the breast can only be seen from one of the projections

• It may be important for the doctor to have a different perspective of a certain lesion, which can only

be done through a different view (or DBT).

As mentioned in section 1.1, breast cancer is a common issue among the female population. For

this reason, it is generally advised for women to perform annual routine mammographies from the age

of 40. Nevertheless, if a patient of any gender feels a lump in the breast region and/or has genetic

3A biopsy is an exam where a needle is used to collect a sample of the suspicious tissue. This is the highest form of confirmationof breast cancer available, excluding actual surgery.

7

tendency to have breast cancer, he or she should get advice from a specialist on whether a screening

mammography should take place.

Figure 1.3: Mammography performed on the left breastof a patient with a class 1 density breast.Source: Canada Health [10]

Figure 1.4: Example of the 2 different perspectivestaken on a mammography. CC in red andMLO in blue. Source: Statistical modelsof mammographic texture and appearance[11]

Figure 1.5: Drawing of a mammograph examining the right breast of a patient. Source: Canadian Cancer Society[12]

When a mammography is to be performed, the patient’s breast must be placed in a device called

mammograph (figure 1.5). Here, the breast is compressed between the detector and the compression

plates and beamed with radiation, which will later be constructed into an image. This process is both

painful and brings health risks due to the patients’ exposition to malignant radiation levels.

The revolution of the digital era has also affected the way mammographies are performed. Previously,

silver foils were beamed with x-ray radiation, a process which would darken the foil accordingly to the

level of radiation that would reached it. This means that areas that were exposed to a lot of radiation

would turn almost black and areas with less exposition would remain silver coloured. This detects

masses and microcalcifications, for these lesions are much denser than normal breast tissue, hence,

8

less radiation would go through and reach the silver foil. The final result would be a generally dark

image (where no lesion or glands are present), lighter sections where skin and glandular tissue can be

encountered and a very light region if a mass or microcalcifications existed.

Later, digital mammography was introduced, where the silver foil was replaced by an electronic circuit

with radiation micro-detectors that represent a pixel in the digital image. For the patient and for the

radiologist, the process is the same: radiation is beamed over the detector and through the breast.

This process results in different levels of radiation reaching each micro-detector. In the final result,

a micro-detector that was beamed with a high level of radiation outputs a dark pixel and vice-versa.

This convention was chosen in order to keep consistency and similarities to mammographies performed

before the digital era.

Finally, after the exam is performed by a radiology technician, it is observed by a radiologist. This

specialist will give it a BI-RADS classification (as explained in section 1.2.3), a small description and

indicates what should happen next:

• Nothing

• Keep routine mammographies

• Perform another mammography

• Undergo a biopsy exam for tissue evaluation

If the result of the biopsy is positive, the patient is diagnosed with breast cancer and he or she are

redirected to a specialist in oncology (speciality of medicine that focus on cancer treatment).

So far, mammographies’ sensitivity is around 88 to 93.1%, in general, being these values significantly

lower for denser breasts [13] [14], which indicates that even when a doctor observes a mammography

image, he or she may not detect with 100% certainty if there is a lesion or not. This thesis focus on a

computer aided diagnosis technique to improve this situation.

1.3.2 Tomosynthesis

A different breast imaging technique was introduced in the most recent years to resolve a common

issue with the mammography exam: tissue overlap. Tissue overlap happens when several layers of

denser tissues are over each other, creating the illusion of a very dense volume instead of a summation

of slightly denser tissue segments. This different technique, Digital Breast Tomosynthesis (DBT) has

been introduced due to its capability to reconstruct the breast in a 3D environment. This way, it is

possible to distinguish tissue overlap from lesions, hence improving a doctor’s ability to classify what is

being observed and perform a better diagnosis of the situation.

Tomosynthesis is also an x-ray based technique which beams the patient’s breast with radiation from

different angles so that several images can be taken from different perspectives (Projection View (PV)

images).

9

Figure 1.6: Angular capability of Siemens Model. This particular model creates up to 25 images. Source: To-mossıntese no Diagnostico do Cancro da Mama [15]

The first part of this process is similar to a mammography exam: the patient’s breast is placed

between an electronic radiation detector and it is compressed in order to obtain several digital images

of the breast.

Afterwards, the radiation beamer swipes over the breast, with an angular window that can go from

[-7.5º ; +7.5º]4 up to [-25º ; +25º]5, as seen in figure 1.6. This technique, creates up to 25 PV images,

which means that it is possible to have up to an image for every 2 degrees. [15] [16]

After the data from the detector is obtained, there is a need to reconstruct the images into a 3D

volume. Such a process can be done through several algorithms such as Niklason algorithm, filtered

back projection or matrix inversion tomosynthesis [17] and it compiles a 3D volume with 40 to 70 2D

slices, where the slices are separated by approximately 1 mm. [8]

Figure 1.7: Example of a tomosynthesis exam where the relationship between the different slices can be seen.Source: Washington Radiology Associates [18]

4In Hologic Models5In Siemens Models

10

It is based on this reconstruction that a radiologist will perform the diagnosis. Resorting to image

processing techniques, he or she can vary the contrast of the images to what suits him/her best and can

easily swipe through the different slices to find any anomalies and report them to any doctor of another

area of expertise.

1.4 Computer Aided Diagnosis

In order to improve diagnosis’ accuracy, a concept was introduced called Computer Aided Diagnosis.

CAD is the use of techniques and algorithms to show/indicate where abnormalities are located. In

breast imaging, CAD is built by gathering several mammographies and use them as a training set. By

fetching characteristics of these exams, regions suspicious of being lesions can be displayed to doctors

in order to help them detect abnormalities and to speed up the diagnosis process. This way, suspicious

lesions that doctors would not notice without CAD are enhanced and wrong diagnosis due to fatigue and

tiredness can be reduced.

In figure 1.8 is displayed the output of the CAD system built in this thesis, where it is possible to see

the contour of the breast (skin) and the lesion previously marked by a doctor in green and the suspicious

region detected by the CAD system in red.

Figure 1.8: CAD output displayed where the previously marked lesion can be seen in green and the CAD sugges-tion in red.

The several processes used to reach this output are explained throughout the next chapters. It is

important to enhance that CAD systems do not replace doctors, nor should their outputs be displayed to

patients, for an interpretation of these results should still take place by an expert.

11

12

2State-of-the-Art

Contents

2.1 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3 Feature Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.4 Learning and Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.5 Summary of State-of-the-Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

13

14

Introduction to State-of-the-Art

The two breast cancer screening techniques presented earlier, mammography in section 1.3.1 and

Digital Breast Tomosynthesis (DBT) in section 1.3.2 are conceptually different but use the same acqui-

sition techniques. Given this, when building a CAD for either, one should consider methods applied in

the other, for some of the issues and procedures to solve them might be the same.

This chapter summarizes methods, procedures and algorithms used by several authors throughout

the last years. It is divided into 4 sections: Pre-processing, Segmentation, Feature Extraction and

Learning and Classification, where each presents the steps taken for mass detection in either one of the

screening techniques. Each section includes a small explanation of its purpose and descriptions of what

the authors did in their studies.

2.1 Pre-processing

The pre-processing stage is the earliest one. This increases its importance for any alterations in

the data will influence all following stages. Many techniques presented in this section can be adapted

from mammography to DBT (and vice-versa) within two conceptions: either apply 2D procedures to

mammography and to the layers of the DBT exam, or scale (if possible) the implementation of a 2D

algorithm in a 3D environment. The main goal of pre-processing is to perform noise reduction, image

normalization, object enhancement, background-foreground separation among others.

Jun Wei et al. in [19] developed a CAD system for mass detection in Full-Field Digital Mammography

(FFDM). In this study, the authors start by applying Otsu’s method to compute the separation between

the background and the foreground (breast) of the image. This is done by labelling the several regions

of high intensity of the binary image and consider the region with the largest area to be the breast. An

enhancement technique used by R. Alam et al. in [20] is to use a linear transformation filter to enhance

the low and the high grey level areas of the image. The same parameters used in this technique are

applied to all images, independently of their initial contrast. This enhancement proved to increase the

sensitivity of the system and helps to visualize the elements.

When pre-processing DBTs, H.P. Chan et al. in [21] use a median filter. This is a clean-up technique

that performs noise removal whilst preserving edges. Another filtering technique is the bilateral filter. In

this filter, the value of each pixel is replaced by a weighted average of the surrounding pixels. The weights

can be computed via a Gaussian function and depend on the Euclidean distance and the intensity

values. To compute a bilateral filter, one can use the expression presented in 2.1.

15

IBL(x) =∑xi∈Ω

I(xi)× fr(I(xi)− I(x))× gs(|xi − x|) (2.1)

where

• IBL(x) is the filtered image

• I(x) is the original image

• x is the pixel being considered

• xi are the surrounding pixels

• Ω is the window of analysis

• fr is the kernel used to smooth differences in intensities

• gs is the spatial kernel for smoothing differences in coordinates

An example of a bilateral filter is shown in figure 2.1

Figure 2.1: Example of a bilateral filter in which the centre in question is in a high intensity area but close to theborder. In a) it is possible to see a sharp transition between a dark and a bright region. In b), an exampleof a bilateral filter where one can see that the pixels with the same intensity as the centre, have higherweights. In c) the result of the bilateral filter applied to the transition shown in a). Source: [22]

S. Vedantham et al. in [6] and R. Thyagarajan et al. in [23] use a bilateral filter to remove ”X”-shaped

out-of-slices artifacts that happen due to the reconstruction process in DBTs. In order to perform edge

enhancement, these authors used an unsharp masking technique along the x-y plane. This masking

technique increases high frequency noise, so the authors used an anisotropic diffusion to decrease

such effect. This diffusion, used for noise regularization, minimizes the effect of noise while at the

same time preserves the edges (important for the segmentation stage). A last pre-processing technique

these authors suggest is background correction via the user’s input. By clicking on the location of the

Volume of Interest (VOI) the user wants to analyse (a potential lesion), a normalization is performed.

The expression to compute this normalization is presented in equation 2.2.

I(x, y) =I(x, y)− IminImax − Imin

, I ∈ V OI (2.2)

This normalization is done to correct the differences in the average of the layers’ intensity which can

be problematic when performing segmentation.

16

X. Qin et al. in [24] use 4 different approaches to increase image quality in DBTs. First, an angular

constrained bilateral filter is needed due to limited angle imaging which causes out-of-slice artefacts.

Second, due to intensity based classification later in the process, cupping artefacts need to be corrected,

since the intensity values differ from the centre of the breast to the margins (in the reconstructed image).

The cupping artefacts are corrected using a non-parametric coarse-to-fine approach with an entropy

related cost function. Third, histogram equalization is used to enhance details and local contrast. Fourth,

authors also use a bilateral filter to remove noise in the x-y plane.

I. Reiser et al. in [25] study DBTs and perform two pre-processing techniques. First, a logarithmic

transform is applied to the PV images to enhance the contrast. Second, morphological denoising is

done to remove single and double pixel noise peaks, leaving three pixel regions (or larger) intact.

2.2 Segmentation

Segmentation is the name given to the act of taking out/identifying an object within an image. The

goal of this second step is to identify Regions of Interest (ROIs)1. Some segmentation techniques are

not object dependent and aim to segment any element found in the image. The techniques presented in

the following studies may derive from others, but are directed to find regions suspicious of being masses

in mammograms or DBTs.

M. R. Hejazi et al. in [26] built a CAD system for mass detection in mammographies where the

authors start by marking foreground objects using morphological operations such as erosion and dilation.

Later, regional maximums of intensity are considered the centre of the suspicious object and, from this

centre, inner and outer borders of the object are found by considering other pixels to be a part of the

same object if the difference in the average of the histograms (including and excluding the pixel) did not

overcome a certain threshold. This method outputs a region suspicious of being a mass.

Another segmentation technique is called Gradient Field Analysis (GFA). This analysis considers

areas of high convergence of the gradient to be the best mass candidates. It can be performed either

in 2D images or 3D Volumes. Jun Wei et al. in [19] use a gradient analysis technique to find the centre

and borders of ROIs. The technique was introduced by H. Kobakate et al. in [27] and it is called a COIN

filter (in its simpler version) or an iris filter (in a complex version) for it simulates the same adaptation

capacity of the human eye by calculating the convergence of gradient around each pixel, as displayed in

figure 2.2. This technique is used because it starts by searching for possible centres of ROIs and further

it finds the borders of the object whose centre was previously found. In 2008, H-P Chan et al. in [21]

proposed to use 3D GFA to segment masses in DBT. The approach suggested is to use GFA to pre-

1In the scope of this work, ROI is any region suspicious of being a mass.

17

screen the mass candidates. Choosing a maximum of 30 sites with the highest gradient convergence,

3D GFA is used to select the mass candidates which will be further analysed. These authors suggest

the use of the same method to perform segmentation of mass candidates in 2D PV images. B. E.

Caroline et al. in [8] suggest the use of GFA to segment both 2D PV images and 3D volumes. The

authors suggest performing segmentation with a very high sensitivity rate, which means that the number

of false positives becomes also very high, most likely. This does not become a problem since these false

positives should be eliminated further ahead. The approach suggested in 2D is to detect the centre of

the ROI by computing the value of convergence of the gradient into a certain pixel. This value is called

Radial Gradient Index (RGI). The lesion candidates will be the ROIs centred in the pixels which exceed

a certain RGI value. The authors started by using a threshold of 10 %, which means selecting the top

10% pixel values (of RGI value) as centres of suspicious mass candidates. In 3D volumes, the detection

is similar to the description in 2D.

Figure 2.2: Example of a COIN filter being computed for a circle. P1 and P2 represent two pixels of interest beingconsidered for the centre. This technique considers the angle θ between the gradient vector in a givenpoint (k, l) and a straight line uniting (k, l) to the centre of interest. If that angle is close to zero (itscosine close to one), it means the gradient in (k, l) is pointing towards the centre of interest. In thiscase, P1 is chosen as the centre, for it was the point with most gradients point towards it. This iscomputed by summing the cosines of all the cases analysed. The norms and directions of the vectorsare not in scale and are simply illustrative.

R. Alam et al. use an adaptive local thresholding to find masses for these are denser than the

surrounding tissue, which means they will be a locally bright spot. This adaptive technique uses two

windows (a large and a small one) centred in the same pixel. It considers the pixels inside the small

window to be a mass if the difference between the intensity of small window and the large window to

overcome a certain threshold. This threshold is image dependent, which originates the name of the

technique.

A different approach which is used by several authors to segment lesions, or simply segment different

18

tissues, are clustering techniques. This segmentation is performed by grouping pixels that have the

same characteristics together. For example, S. Vedantham et al. in [6] use Fuzzy C-Means (FCM) for

lesion segmentation by clustering pixels with similar grey levels. The authors use FCM with two clusters

in order to segment the lesion from the background tissue. After FCM, a binary mask is created with the

cluster label. Then, several morphological operations are applied to this mask, such as area filtering,

binary opening followed by binary closing to remove salt and pepper noise and also binary erosion and

binary dilation to perform mask smoothing. This is done to respond to the fact that FCM may create

isolated pixels, hence morphological operations are required.

Another clustering technique is Expectation Maximization (EM). It was used by R. Thyagarajan and

Dr. S. Murugavalli in [23]. These authors used FCM or EM due to their robustness and efficiency

and because these techniques are effective in segmenting noisy reconstructed images and incomplete

datasets. After using FCM, the authors also performed morphological operations for the same reasons

presented in [6]. Segmentation is performed using EM for maximizing and enhancing the affected areas

and is used to distinguish the anatomical structures of the breast.

2.3 Feature Extraction

After performing segmentation, some characteristics must be extracted from the regions or volumes

segmented. These characteristics are called ”features”. For CAD systems for mammographies or DBTs,

one can divide the features into 3 big groups:

• Morphological Features

• Grey Level Features

• Texture Features

This section is divided into 3 parts, in order to present the features used by different authors in their

studies, by group.

The first ones, morphological features, are all the features related to space, physical and shape

context. For mammography, M. R. Hejazi in [26] extracts 4 morphological features: Area, Shape, Edge

Distance Variation and Spread Pattern. Area is simply the total number of pixels in a segmented ROI.

Shape is extracted for discriminating circular masses from non-circular ones. This feature is calculated

by computing the distance between the centre of a region and the points at the border. Edge Distance

Variation indicates the difference between intensity levels at the border because usually tumours are

well-defined structures. This feature is computed by subtracting the intensity level of the pixel at the

border by the local mean. In this case, the computation of the local mean is not specified. Spread

19

Pattern analysis the inner and outer border, both previously computed, which indicates if a tumour is

benign (encapsulated and does not spread) or malignant (risk of spreading cancerous cells to other

parts of the body). D. Saraswathi et al. in [28] and [29] write about features extracted in mammograms

and in DBT. As morphological features, Area, Centroid Position, Orientation, Perimeter, Euler Number,

Projection, Thinness and Aspect Ratio are extracted.

For DBT, B. E. Caroline et al. in [8], suggest the extraction of the Candidate Ratio Index. This index

is the number of times a certain region is presented in the same position throughout all the PV images.

The computation of this index is shown in figure 2.3. As it can be seen, structure 1 is a mass so when

analysing PV images from the source in both positions 2 and 10, it will appear in the same location.

The same does not happen for structures 2 and 3, which are dense tissue. From position 2, structure

2 overlays structure 3, which creates the illusion of a denser tissue, possibly a mass. This hypothesis

is eliminated with the PV image from the source in position 10, where these two dense tissues do

not overlay each other. Therefore, this feature holds information on the morphology of the suspicious

structure and it is used to eliminate false positives that may be caused by overlaying tissue. H-P Chan

et al. in [21] extracted morphological features such as: Volume (in terms of number of voxels in the

object), Volume difference before and after 3D morphological opening, the surface area, the maximum

perimeter of the segmented object throughout all the slices and the compactness (percentage overlap

between the object with a sphere of the same volume, both centred in the same centroid).

Figure 2.3: Representation of the computation of the CRI. Structure 1 is a mass and structures 2 and 3 are densetissue. With the Projection View image obtained from source position 2, the combination of structures2 and 3 would appear to be a mass when in fact it would just be a representation of overlaying densetissue. Source: B. E. Caroline et al. in [8]

Grey level features are all the features related to the intensity of the region being analysed. D.

20

Saraswathi et al. in [28] and [29] extract the Mean, the Standard Deviation, Skewness, Energy and

Entropy from the ROI’s histogram. X. Qin et al. in [24] extracted 8 grey level features for further tissue

classification: Skewness, Contrast, Correlation, Entropy, Sum Entropy, Difference Entropy, Information

Measures of Correlation and Mean Intensity of each region. H-P Chan et al. in [21] also extracted grey

level features from the object’s histogram such as, maximum, minimum and average grey level intensity

of the 3D object, contrast between the object and its surroundings, Skewness, Kurtosis, Energy and

Entropy.

Texture features do not have a direct definition. The concept of texture is very vague and some

authors have tried to define texture qualitatively [30] but no definition ever stood out. This means that

texture features can be all the features that have information regarding the environment of the segmented

image. The periodicity of the image, the total gradient intensity, etc, can be considered as texture

features. Jun Wei et al. presented in [19] a way of using the wavelet transform to better extract texture

features from mammograms by performing an analysis on the Spatial Grey Level Dependence (SGLD)

in several frequency bands. This matrix contains informations regarding how often do pixels with the

same intensity repeat itself, which, when analysed locally, contain information on the irregularity or

homogeneity of a certain ROI. H-P Chan et al. in [21] extract two types of texture features: Run

Length Statistics features and SGLD matrices’ features. Of the first type, short run emphasis, long run

emphasis, grey level non-uniformity, run length non-uniformity and run percentage are extracted from

the Sobel gradient image. Run Length Statistics (RLS) features are extracted for they are effective in

differentiating spiculated from non-spiculated objects. When a structure is spiculated, it means that it

has spikes or points on its surface, which may be an indicator of malignancy [14]. In this study, 13 SGLD

features are extracted from each ROI. The final SGLD feature vector contains the average between

all the slices of each of the 13 features. D. H. Kim et al. in [31] propose to extract texture features

from both breasts and analyse their dissimilarities. In order to characterize the bilateral asymmetry

between VOIs on the left and on the right breast, three features are extracted: Histogram Dissimilarity,

Sum of Squared Differences (SSD) and Dissimilarity of Single View. Histogram dissimilarity has a low

value when VOIs are similar, so it is expected to output high value for masses. Given that masses are

asymmetric structures, the SSD between two VOIs should have higher values if one of the VOI contains

a mass. The Dissimilarity of Single-View is the absolute difference between a feature value of a VOI and

the feature value of that VOI’s version on the other breast. Many of these features are suppose to output

zero in a case where a VOI would become a False Positive (FP) for it is expectable that FPs have similar

tissue aspect in both the left and right breast.

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2.4 Learning and Classification

Learning and Classification is used in order to identify whether a region is cancerous or not. Most

CAD systems used for breast cancer are supervised, which means a labelled dataset is required, where

one has several patterns with the corresponding (correct) label. As exemplified in figure 2.4, one can

identify to which class a region belongs, giving it a label (classifying it). Naturally, these methods have a

certain error associated to them, which is what must be reduced.

Figure 2.4: Representation of a labelled dataset and a new pattern, waiting to be classified.

M. R. Hejazi et al. in [26] propose a mass detection method for mammograms, where several ma-

chine learning techniques are combined using explicit knowledge from experts in the field. The authors

start by ruling out patterns (consider them healthy tissue) if the area of the ROI is not between a max-

imum and a minimum threshold. The edge intensity variation and shape of the patterns that overcome

this test are used as features of two different Multi-layer Perceptron (MLP) that output the characteristics

of the tumour in a categorical way 2 3. This categorization is then used in a rule-based classifier built

by experts where situations such as ”if a tumour has only one segment circular and both segments are

clearly defined, then it is a malignant tumour” are used to make the final decision of the whole CAD

system. The sample used by these authors is a small one, being the authors able to identify 14 out of

15 benign tumours and 4 out of 5 malignant ones.

Nicholas Petrick et al. in [32] use the features extracted as an input to a Linear Discriminant Analysis

(LDA) classifier. These authors only separate masses from healthy tissue, using texture features and

this classifier, at a True Positive (TP) rate of 90%, outputs 3.77 FPs per image.

2For shape: inner and outer segments circular, only one circular or none.3For edge intensity variation: both segments clearly defined, only one or neither.

22

H-P Chan et al. in [21] implement an ensemble classifier for classification of masses in DBT. Using

both 2D techniques to identify lesions in PV images and 3D techniques to identify lesions in 3D volumes,

the study suggests a combined approach to classify masses and reduce the number of FPs. The

authors use a dataset of 100 DBT cases and use only MLO DBT views. In 3D, in order to classify which

VOIs contained masses or not, the authors use an LDA based classifier, using the mass candidates as

patterns, and perform a leave-one-out cross-validation technique to train the classifier and to perform a

stepwise feature selection. This way, features can be selected from the feature pool and LDA weights

can be estimated. Alongside, in order to detect masses in 2D PV images, a rather similar process

occurs. Using only the ROIs considered as candidates after the segmentation step, a leave-one-out

method (with these ROIs as patterns) is implemented in order to build an LDA classifier. Geometry is

used to know the 3D location of the already classified 2D PV images. In order to obtain a classification

whether a candidate is a mass or not, the labels obtained from 3D VOIs and 2D ROIs are matched using

the following criteria: if the centroid of the 3D VOI classified as positive falls within the area classified

as a mass in 2D as well, the global system classifies that VOI as a positive. If the contrary happens,

which means, if a ROI is classified as positive and its centroid falls within a VOI which is also classified

as positive, the system also classifies this region as a mass. Only in the case where an object was

classified as positive in one of the approaches but is does not match any corresponding object from

the other approach, the object is not considered as a mass. At a sensitivity of 90 %, the presented

implementation obtained 4.05, 3.40 and 2.04 false positives per breast, for the 2D, 3D and combined

approach, respectively. This proved that the combined approach reduced the number of false positives

per breast.

D. H. Kim et al. in [31] use a dataset composed of 160 reconstructed volumes from the two views (CC

and MLO) from 40 patients, to perform mass detection. In this dataset, 54% of the volumes are biopsy-

proven to contain a malignant mass. For classification, a Support Vector Machine (SVM) algorithm with

radial basis function is used to distinguish masses from FPs. 5-fold cross-validation is applied to find

the optimal parameters of the SVM. The authors perform three experiments: one in which only single-

view features are used, another where bilateral features are used and a last one where single-view and

bilateral-view features from VOIs previously selected as mass candidates are used. The Area Under

the Curve (AUC) for each of the experiments is 0.809, 0.785 and 0.826 respectively. The FP per breast

are 1.99, 2.21 and 1.67 respectively. As it can be seen by the results, the use of both single-view and

bilateral features outputs the best results in terms of AUC and eliminating False Positives.

23

2.5 Summary of State-of-the-Art

Table 2.1 presents four types of studies:

1. CAD systems for segmenting masses in mammograms.

2. CAD systems for the classification of masses in mammograms.

3. CAD systems for segmenting masses in DBT.

4. CAD systems for the classification of masses in DBT.

As one can see, the false positives that occur are still an existing problem even in the most recent

studies. On the other hand, very often, the patient’s dataset size is not statistically significant in many of

the studies.

24

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26

3Pre-Processing and Segmentation

Contents

3.1 Pre-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

27

28

Overview

This work has the general architecture presented in figure 3.1. It is divided into 4 steps, as detailed.

Each section of this chapter and the next explains one of the steps in the following order.

• Pre-Processing: techniques to clean noise and enhance suspicious regions are used to improve

ROI detection and lesion classification.

• Segmentation: a searching algorithm is implemented to locate such ROIs within the image.

• Feature Extraction: specific characteristics of regions are extracted to use as input of the classi-

fiers.

• Classification algorithms: two algorithms are set up to classify classify the detected lesions.

Figure 3.1: Scheme of the 4 steps approach applied in this thesis

3.1 Pre-Processing

The pre-processing step is divided into two parts: identifying the breast area and cleaning the image

for better ROI detection (segmentation).

To identify the breast, Otsu’ method was used [19]. This method separates the background pixels

from the foreground (breast). It assumes that there are two-classes of pixels in the image (background

and breast) and exhaustively searches for the intensity value which separates the two classes better.

This means that Otsu’s method tries every value between 0 and 255 and chooses the one which min-

imizes the variance of the set of pixels below that value and the set of pixels above that value. The

conceptual idea is to identify that there are two modes in the image’s histogram, and find the intensity

level that separates the two. In this case, the breast is considered to be the larger region with higher

intensity level. In figures 3.2(a) and 3.2(b), background and foreground modes can be visually identified:

background being the bin most to the left (dark pixels), in intensity value 0, and foreground being the

maximum located in the bin centred in intensity level 25.

29

Several local maxima can be seen in the histogram. To solve this, there is the need of applying a

Gaussian filter to the whole image, as seen in figures 3.3(a) and 3.3(b). This process blurs the image

which brightens possible dark zones within the breast. The result is shown in figure 3.3(a), where it can

be seen that the breast becomes a generically bright spot.

(a) Digitalized Mammogram (b) Histogram of digitalized mammogram

Figure 3.2: Example of a a) digitalized mammography from DDSM and b) its histogram. As explained before, it canbe seen that even within the breast, darker areas may exist

30

(a) Blurred Digitalized Mam-mogram

(b) Histogram of digitalized mammogram and Otsu’smethod border

Figure 3.3: Example of a) mammography and b) its histogram, where a Gaussian filter with a standard deviation of50 is applied. In this image, it can be seen that the breast area becomes a generically high intensityregion. Histogram displays Otsu’s method’s threshold in red at intensity level of 3. Pixels with intensitylevel from 0 to 3 belong to the background, pixels with intensity levels from 3 to 255 belong to theforeground. It is visually possible to realize that the transitions smooth due to the filter, hence, it iseasier to find the local maxima.

31

(a) Binary mask with all components (b) Binary mask only with biggest com-ponent

Figure 3.4: Binary image obtained from dividing the mammography presented in 3.2(a) into background and fore-ground. Notice on the top right corner of a) that other elements were wrongly identified as foreground.Hence the need to withdraw only the larger object as seen in b).

Figure 3.5: Resultant image of separating breast (foreground) from background using Otsu’s method. The greenline represents the border of the mask computed from this breast. This process is important for manyof the methods following this one will be applied only to pixels within the mask.

32

Next, a filter will be applied in order to reduce noise. The bilateral filter [24] was chosen due to its

ability to reduce noise without losing information of the edges, which is important for the following step

(Segmentation). This goal is achieved by combining two Gaussian filters in order for two criteria per pixel

to be considered: intensity and spatial distance. These criteria are used to compute the weight of every

pixel in a given neighbourhood of the pixel being analysed. In an image processing context, the concept

of a filter is to perform a sum of products within a certain window. In this case, the filter size is 81 × 81

pixels. This means that every pixel 40-pixels away in any direction of the one of interest, is going to be

taken into account to compute its filtered value.

Let’s consider image I and filter f , where f has size 3 × 3, being its centre in f(1, 1). Considering

the pixel of interest to be (cx, cy), then the resultant image If , is the sum of products of the pixels of I

with filter f , centred in pixel (cx, cy), which is presented, generically, in equation 3.1.

If (cx, cy) =

1∑x=−1

1∑y=−1

I(cx − x, cy − y) × f(1− x, 1− y) (3.1)

The concept of the bilateral filter used in this work is to combine two filters into one. Let’s consider

filter f to be related to spatial distances, filter g to be related to intensity distances and filter r to be the

resultant filter, with the following expressions:

f(cx, cy, x, y) =e−|(cx,cy)−(x,y)|

2σ2s

, (x, y) ∈ Ω (3.2)

g(cx, cy, x, y) =e−(I(cx,cy)−I(x,y))2

2σ2I

, (x, y) ∈ Ω (3.3)

r(cx, cy, x, y) = f(cx, cy, x, y)× g(cx, cy, x, y), (x, y) ∈ Ω (3.4)

where σs and σI are the standard deviation to consider in spatial and intensity dimensions, respec-

tively and Ω is the window of analysis. In this work, σs = 20 and σI = 0.121. The illustration of the filters

can be seen in figure 3.6, 3.7 and 3.8, respectively.

After the resultant bilateral filter r is computed, the filtered image IBF is achieved through equation

3.5.

IBF (cx, cy) =∑x,∈Ω

∑y∈Ω

I(x, y)× r(cx, cy, x, y) (3.5)

1Fraction of the maximum intensity value of the entire image

33

(a) 3D representation (b) X-y plane representation

Figure 3.6: 2D spatial filter represented in a) 3D and b) from the x-y plane. In this figure, it is possible to see thatthe further way a pixel is of the pixel of interest (center), the less its weight is going to be.

(a) 3D representation (b) X-y plane representation

Figure 3.7: 2D intensity filter representation in a) 3D and b) from the x-y plane. The pixels with the highest weightvalue represented in this filter are the ones with the intensity value closest to the value of the pixel ofinterest.

34

(a) 3D representation (b)

Figure 3.8: 2D bilateral filter representation in a) 3D and b) in x-y plane. Combination of filters represented infigures 3.6 and 3.7, where it can be seen that pixels closer to the pixel of interest in terms of spatialdistance and intensity level value will have higher weights.

3.2 Segmentation

The segmentation step is done in order to identify ROIs suspicious of being a mass. This will allow

the CAD system to extract information of regions suspicious of being lesions, instead of performing a

greedy search on the entire image, which can become unfeasible in terms of computational time and

can output many FPs.

In order to perform segmentation, the Sliding Band Filter (SBF) is used as implemented by Tiago

Esteves et al. in [33]. In this study the authors use this technique to find cells in microscopic fluorescent

images, where the cells’ pixels (foreground) have a higher intensity than the background (tissue). These

are the same conditions of the masses in the mammography images used in this thesis, as it can be

seen in figure 3.9. The authors use this filter for its ability to handle illumination variations, noise and low

contrast.

35

Figure 3.9: Comparison between image from the database used in this thesis (to the left) and microscopic fluores-cent image (to the right) segmented by the authors in [33].

SBF is part of a larger group of filters called Local Convergence Filters (LCF). These filters perform

Gradient Field Analysis (GFA) which considers gradient orientation instead of gradient magnitude. This

is an important characteristic for segmenting ROIs in this work, for the filter becomes independent of

the gradient magnitude, and therefore, independent of image properties, such as maximum or minimum

image intensity level. In order to understand this concept, it is important to understand the concept of

image gradient.

The gradient of an image is used in order to know if there are local changes in the pixel intensity.

Assuming a grey scale image, by computing the gradient of a pixel, it is possible to know how big such a

change is (magnitude) and which is the direction of the change (orientation). This is exemplified in figure

3.10(a) and 3.10(b).

(a) Grey-scale image and its gradients (b) Matlab quiver representation

Figure 3.10: Gradient representation in a a) black and white image and b) its quiver representation from Matlab

To compute the gradient, let’s consider image I and 5I as the gradient of image I [34]. Since an

36

image gradient will have two directions, one can say that:

5 I =

[gxgy

]=

[ ∂I∂x∂I∂y

](3.6)

Following this, one computes the magnitude and direction of the gradient [30]. This can be done

through:

5 Imag =√g2x + g2

y (3.7)

5 Idir = tan−1

(gxgy

)(3.8)

A more graphical way to represent the gradient, is to think about the pixel’s neighbourhood. As

represented in figure 3.11, a simple way to compute the gradient is to analyse the difference between

the pixel above and the pixel bellow, and the difference between the pixel to left and the pixel to the

right. These differences are gy and gx respectively. The computation of the gradient using this method

is called the Intermediate differences gradient [35].

Figure 3.11: Graphical representation of the gradient of a pixel computed using Intermediate Differences gradient

The main goal of SBF is to compute the degree of convergence for each pixel. This measurement

indicates the convergence of the gradient vectors towards a certain pixel (pixel of interest). In other

words, it analyses the surrounding area of the pixel of interest and computes ”how many” gradients point

towards that same pixel. The pixel is considered to be the centre of a ROI if its degree of convergence is a

regional maximum. There are several variations of LCFs and the SBF used in this work is a combination

of 3 of them: COIN filter, iris filter and adaptive ring filter.

As presented in section 2.2, SBF’s basic principle is similar to the one presented by H. Kobakate et

al. in [27] (the COIN filter). It starts by computing the gradient for each pixel in a certain window, as

represented in figure 3.12a, followed by computing the line segment which unites each pixel with the

pixel of interest, as represented in figure 3.12b. The final goal is to compute the cosine of the angle

37

between the gradient vector and the line segment, hence computing ”how much” each gradient points

towards the pixel of interest. Let us call this value CI as presented in equation 3.9 where α represents

the angle between the gradient vector and the line segment and (x, y) are the spatial coordinates of a

pixel.

CI(xi, yi) = cos(α(xi,yi)) (3.9)

Figure 3.12a: Gradient of an image. Each arrow repre-sents the gradient vector in each pixel ofthe surrounding area of the pixel of inter-est.

Figure 3.12b: Line segments uniting each pixel with thepixel of interest.

Figure 3.13: Fusion of the gradient of each pixel and the line segment uniting each pixel with the pixel of interest.Graphical representation of the angle used to compute the degree of convergence.

To achieve the degree of convergence, a certain number N of orientation points is determined, from

which the maximum value of CI is computed. As shown in figure 3.14, the orientation points are spread

38

through the entire radial space around the pixel of interest. SBF uses one of COIN filter’s property which

is to find the maximum value of the sum of CI among all orientation points, as described in equation

3.10 and figure 3.14.

DCCOIN (P1) = max0<R<Rmax

1

N ∗R

N∑i=1

R∑r=0

CI(xi, yi), where x2i + y2

i < R2 (3.10)

Figure 3.14: Illustration of COIN filter being computed for an approximately circular lesion. This figure exemplifiesa case where the centre is correctly found, but the border is not.

This method performs well when locating centres of regions, but it assumes a round shape (which

might not happen). For a better location of the border, the iris filter presents a solution where the border

of a non round shape can be found. The concept of this filter is to use the sum of the maximum value per

orientation point instead of the maximum value of the sum among all orientation points, as presented in

equation 3.11.

DCIRIS(P1) =1

N

N∑i=1

max0<R≤Rmax

[1

R

R∑r=0

CI(xi, yi),

]where x2

i + y2i < R2 (3.11)

39

Figure 3.15: Illustration of an iris filter being computed for the same approximately circular lesion as in figure 3.14.This figure exemplifies a case where both the centre and the border are found. In this illustration, only8 orientation points are used, hence, the border is not entirely found, although, if N → ∞ , it would.2

The last property used by SBF comes from the adaptive ring filter, a minimum and maximum radius

can be used to search for the border only in some specific locations in order to obtain better results. The

expression used to compute SBF is found in equation 3.12 and its concept is represented in figure 3.16.

DCIRIS(P1) =1

N

N∑i=1

maxRmin<R≤Rmax

[1

R−Rmin

R∑r=Rmin

CI(xi, yi),

]where x2

i + y2i < R2 (3.12)

Figure 3.16: Illustration of an adaptive ring filter being computed for the same approximately circular lesion as infigure 3.14 and 3.15. In this illustration, the Rmin and Rmax are used to limit the area in which theborder can be found.

2In reality, if N ≥ 2x+ 2y, being x, y the dimensions of the image, the border is correctly found.

40

4Feature Extraction and Classification

Contents

4.1 Feature Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

41

42

4.1 Feature Extraction

In the feature extraction stage, information from each ROI is collected in order to classify the ROIs

into healthy tissue, malignant masses or benign masses. This chapter describes 3 types of features:

Morphological, Intensity and Texture based. These, on the contrary of the previous stage, are extracted

from the raw image, and not the pre-processed one. This happens because, although pre-processing

techniques are important for ROI identification, they interfere with the information present in the image,

hence, raw data is used.

4.1.1 Morphological Features

Morphological features are extracted so that the system has information on the shape characteristics

of the ROI being analysed. Given that the images used have different sizes, if no action is taken,

morphological features will get affected. For example, if a lesion has an area of x pixels and a different

lesion (in a different image) as an area of 2x pixels, it becomes impossible to know if the second lesions is

twice as large, or if is is just an image with twice the size. In order to oppose this issue, two actions can be

taken: either the images are resized to the same value or all extracted features are normalized to the size

of the image. In this work, the second option is chosen, for resizing images implies oversampling and

sub-sampling techniques that might affect the information extracted. Given this, all the measurements

are normalized to the image size.

One feature to extract is the location of the centre (output of the segmentation stage). The x and

y coordinates are normalized to the image length and height, in order not to be affected by the image

dimensions.

The following feature to extract is the maximum radius. If a lesion is perfectly circular, to extract only

the distance between the centre and any point of the border would be enough. In this case, one extracts

the euclidean distance between the centre and its farthest point. The computation of this feature is

presented in equation 4.1,

R = argmax(√

(Bx − cx)2 + (By − cy)2)

(Bx, By)(4.1)

where Bx and By are the coordinates of the pixels of the border (computed in the segmentation stage)

and cx and cy, the coordinates of the centre.

After the maximum radius, the number of pixels that are part of the border are extracted: the perime-

ter. For this computation, the number of pixels correspondent to the border, which are output by the

segmentation algorithm is not enough, for these are just a subset of such border, as seen in image 3.15.

This way, the perimeter is computed by summing up the distances between a pixel of the border sample

43

and the following pixel, as presented in equation 4.2, where N is the number of orientation points.

P =

N∑i=1

(√(Bx(i)−Bx(i+ 1))2 + (Bx −Bx(i+ 1))2

)(4.2)

Next, the area is also to be extracted. Given that the region found is a closed region it is possible to

compute the amount of pixels inside this region. Like the previous features, it is normalized to the image

size.

Another feature to extract is the Surface Change (SC) after mathematical morphology is applied.

In this case, the difference between the original image and the image after opening of the ROI by a

disk with the size of 1/10th of the radius is extracted. The expression of the mathematical morphology

operation is presented in equations 4.3 and 4.4.

ROIMM = ROI disk = (ROI disk)⊕ disk (4.3)

SC = ROI− ROIMM (4.4)

”Opening”, in mathematical morphology terms, means to perform two operations between two im-

ages: erosion and dilatation [36]. In this thesis, opening is performed between a ROI and a structuring

element (disk). The first operation, dilatation, can be though as the union between the ROI and the disk

in every pixel. On the contrary, erosion can be considered the intersection between the two elements.

As an example, assuming image A as a square, figures 4.1(a) and 4.1(b) represent both operations.

(a) Dilation illustration (b) Erosion illustration

Figure 4.1: Mathematical morphology operation a) ”dilatation” and b) ”erosion” performed between image A, asquare, a the structuring element B, a disk. Source: Language and Media Processing Lab [36]

44

The goal of this operation is to analyse how ”round” a certain lesion is. By applying mathematical

morphology opening, the more round a certain region is, the less effect an opening will have. Hence,

by extracting the difference between the original image and the transformed image, one has information

on the roundness of the ROI. Figures 4.2(a) trough 4.4(b) exemplify the different outcomes of extracting

this feature.

(a) Original image (b) Image where mathematical mor-phology was applied

Figure 4.2: Example of a round region where mathematical morphology opening was applied. At it can be visual-ized, the image does not differ from its original one.

(a) Original image (b) Image where mathematical mor-phology was applied

Figure 4.3: On the contrary of the region presented in figure 4.2, when opening is applied to an approximatelyround region, some changes can be observed already.

45

(a) Original image (b) Image where mathematicalmorphology was applied

Figure 4.4: Opposing the two cases earlier, figures 4.2 and 4.3, when opening is applied to a spiculated region, asignificant difference can be seen.

The list of morphological features extracted is presented below:

• X and Y coordinates of the location of the center

• Maximum Radius

• Perimeter

• Area

• Surface Change

4.1.2 Grey Level Features

Grey level intensity features are also extracted. These features hold information regarding the inten-

sity values within the ROIs. Given that it is possible to define exactly which pixels are inside the ROI,

grey level features will be extracted for all pixels in it. Let’s consider a given ROI with N pixels.

The first features to extract are the mean (equation 4.5), the maximum and the minimum of the

intensity values of the ROI being analysed.

µ =1

N

N∑i=1

I(i), i ∈ ROI (4.5)

Another set of features, which also holds information regarding the ROI, are features from its his-

togram analysis: standard deviation, skewness and kurtosis. The standard deviation of intensity is the

feature illustrated in figure 4.5. Its computation is as defined in equation 4.6 and has the goal to measure

how spread the intensity levels are along the scale.

σ =

√√√√ 1

N − 1

N∑i=1

(I(i)− µ)2, i ∈ ROI (4.6)

46

Figure 4.5: Examples of histograms of ROIs with the same mean intensity value but with different levels of standarddeviation. On the left, an histogram with a small value of standard deviation. On the right, an histogramwith a standard deviation value 5 times higher than the one on the left.

The skewness of an histogram discriminates whether the histogram is equivalently or asymmetrically

distributed around the sample mean. The computation of skewness is presented in equation 4.7, being

E the expected value.

s =E(IROI − µ)3

σ3(4.7)

Similar to skewness, kurtosis is a feature that describes the shape of the histogram. It is a measure of

spikiness of the center of the histogram, allowing for its better description. Its computation process is

described in equation 4.8.

k =E(IROI − µ)4

σ4(4.8)

Another feature to extract relates to the connection between the intensity levels of the ROI and the

entire image: contrast. It is the ratio between the mean intensity value of the ROI (as presented in

equation 4.5) and the mean intensity value of the entire image.

The last intensity related single feature to extract is the energy, which is computed as presented in

equation 4.9.

Energy =

N∑i

I(i)2, i ∈ ROI (4.9)

Finally, a last set of features is extracted. A 10 bin histogram of the intensity levels of the ROI is

computed and the number of pixels present in each bin1 is considered as a feature. Given this, the list

of the grey level features to extract is presented below:1as described in section 4.1.1, the number of pixels is normalized to the image size

47

• Mean Intensity Value

• Maximum Intensity Value

• Minimum Intensity Value

• Standard Deviation of Intensity Values

• Skewness

• Kurtosis

• Contrast

• Energy

• 10 Intensity Histogram bins

4.1.3 Texture Features

Regarding texture features, one single feature and a set of features are extracted.

The entropy is a statistical measure of randomness of intensity levels. This randomness indicates

if the ROI is smooth or wrinkled. This measurement is computed according to equation 4.10, where p

represents the fraction of pixels which have level of intensity l. In this work, the intensity levels are not

considered in bins but all separate (from 0 to 255).

Entropy = −255∑l=0

(pl ∗ log(pl)) (4.10)

The last set of features to extract is an analysis made to the histogram of the angles of the gradients.

These are called Histogram of Oriented Gradients (HOG) features [37] and hold information on the

ROI’s organization. For example, in figure 4.6a, one can see an image and its histogram. Given the

randomness of this image, the histogram bin levels are uniform, for there are gradient angles in every

direction. On the other hand, in figure 4.6b, there is an organized image with stripes and hence, its

histogram bin levels are not uniform any more. It can be seen that the gradients of the image are always

in the same direction and therefore, the majority of its pixels will be in the same bin (for they have the

48

same gradient angle).

Figure 4.6a: Example of the angle’s histogram of an image. On the left, the histogram of an image with a randomtexture (presented on the right). By this histogram, it is possible to see that there are gradients pointingto all directions in the image on the left.

Figure 4.6b: Illustration of how an analysis on the histogram of the gradients’ angle of an image can be descriptiveof such image. In this case, on the right an image with stripes and on the left, its histogram. It canbe easily seen that, comparing to figure 4.6a, this histogram outputs more information regarding theorganization of its image.

49

4.2 Classification

The CAD system implemented in this thesis for diagnosing breast cancer in mammography can

have its output vary between benign masses, malignant masses or healthy tissue. The classification

approach suggested in this thesis is to implement several classifier ensembles using different training

sets and different features. Each classifier is binary and outputs one of two options:

• Healthy tissue vs Mass

• Malignant mass vs Benign mass

This is done by building a 2-stage classifier ensemble, as seen in figure 4.7. The goal of the first

stage is to determine whether the ROI is a lesion or not, whereas the second stage determines its

malignancy. Given this, the first one distinguishes masses from healthy tissue and the other, benign

masses from malignant masses.

In both stages, the general approach is the same, but the datasets used are different. In the first

one, the dataset includes all patterns (healthy tissue, benign and malignant) and in the second one, only

benign and malignant are used. This division is made due to the final goal of the CAD system: to point

out the lesions to the doctor. This means that identifying a lesion is more important than saying whether

it is benign or malignant, given that if a lesion is detected, the doctor should be aware of it, regardless

of its malignancy. Due to these reasons, 2 stages are built since, this way, it is possible to parametrize

the CAD system to output the best results.

In each stage an ensemble of classifiers is used, where each base classifier in the ensemble uses

features from a different type. The output of the base classifiers is combined using combination tech-

niques (Majority Vote, Weighted Majority Vote, Naive Bayes Combination [38]). This way, the flow of

classification is compiled by a first stage divided into 3 classifiers (one for each type of feature: Morpho-

logical, Grey level and Texture) and a combination technique. Here, the patterns classified as healthy

tissue are considered non-lesions and leave the flow. The second stage which also contains 3 classifiers

and a combination technique, classifies the patterns into benign or malignant lesions. This second stage

performs worse, for lesions are more look a like among themselves than with healthy tissue.

In order to obtain the best results, two different types of classifiers (Decision Tree (DT) and AdaBoost)

are tested.

50

Figure 4.7: Representation of the classification flow used in this work. The features of the ROI are used as input for3 classifiers, whose outputs are combined and in which the ROI is classified as a Mass or as HealthyTissue. In case of a mass, the process moves along and the features are used as inputs to another 3classifiers, that, after its outputs are combined, define if the ROI is malignant lesion or a benign one.

4.2.1 Decision Tree

The decision tree used in this thesis uses the CART algorithm [39]. The general idea of a DT is to

use thresholds (for continuous features) or rules (for categorical features) to classify the patterns, as

shown in figure 4.8. A DT is a supervised method, which means it has to be trained beforehand. The

root of the tree (first node) is computed by selecting, from the feature pool, the rule which maximizes

the drop of impurity. After the node is selected, the same algorithm is applied to the subtree with the

corresponding subset of patterns, which were divided in the root. By doing this process, ones grows the

tree. One property of the CART algorithm is that only binary nodes are created.

The feature/rule used for each node is not arbitrarily chosen. Let’s assume an example: by using

the rule ”radius being larger than 50, the pattern is healthy tissue”, 54% of the patterns are wrongly

classified. On the other hand, by using ”mean intensity value larger than 180, the pattern is a mass”,

one sees that 70% of the classifications are correct. In this case, the second rule would be chosen, and

two subtrees would be built with two other nodes, and then four other, etc, etc. It is computationally heavy

(and unnecessary) to compute the classification of the tree in order to know which rule to choose. The

51

measurement function used by the CART algorithm to define the rule is called Gini2, which computes

a measure called impurity. The expression to compute Gini is presented in equation 4.11, where S

represents the subset of patterns, C represents the number of classes (in this case, 2) and ps is the

fraction of patterns in each class.

Gini(S) = 1−C∑k=1

ps(k)2 (4.11)

In order to choose the rule, one computes the drop of impurity. For example, splitting sample S with

respect to feature A can be computed via equation 4.12:

Drop(S,A) = Gini(S)−∑

v∈values(A)

|Sv||S|

Gini(Sv) (4.12)

in which, Sv is the subset generated if the rule is applied.

By maximizing the drop of impurity, one can find out which rule to use when building the node. In

figure 4.9, the Gini function can be seen.

Figure 4.8: Example of a DT with three nodes and fourleafs. Figure 4.9: Gini function

A decision tree is grown until it reaches a certain stopping criteria. Among these criteria, one can

have:

• A maximum number of splits is achieved

• A certain threshold of drop value is achieved

• Each leaf corresponds to one class only

This growth has to be controlled, for over-fitting might occur when growing a decision tree. In order

to control it, the tree can be pruned.

2Other algorithms use other measurement functions

52

In the current work, two classifiers were built using decision trees. The first experiment was a single

model hypothesis with a DT as a classifier, with a dataset containing all the patterns and three labels:

healthy tissue, benign lesions and malignant lesions.

Figure 4.10: Ilustration of the Single Model Decision Tree used in this work

A second experiment was done using a Decision Tree Ensemble in the same conditions: using all

the patterns and the three classes available, to test a simple version of the classifier ensemble and the

2 stage hypothesis. In this case, a total of 6 decision trees are trained: 3 for classifying the lesions into

healthy tissue or mass and 3 other for classifying lesions into benign masses and malignant ones. Each

model is trained with a specific set of features: morphological, intensity based or texture. A schema of

this classifier is presented in figure 4.11.

Figure 4.11: Schema of the classifier used in the Decision Tree Ensemble experiment.

53

In order to understand better the order of the actions taken in this experiment, algorithm 1 presents

the pseudo-code used in it.

Algorithm 4.1: Pseudo-code of the algorithm used in the Decision Tree Ensemble experiment.Data: Dataset off all patterns (and their features)Result: Label vector C, the accuracy, true positive and true negative

for kfold = 1−→ 10 do%Stage 1

t(1)←− decision tree trained with morphological features of all patterns;t(2)←− decision tree trained with intensity features of all patterns;t(3)←− decision tree trained with texture features of all patterns;

CMat←− Compute confusion matrix for each of the trees t(1), t(2), t(3) (to be used by thefusion technique);

OutputTree(1)←− classify validation set with t(1);OutputTree(2)←− classify validation set with t(2);OutputTree(3)←− classify validation set with t(3);OutputsS1←− Naive Bayes fusion off all three outputs;

%Stage 2;t(4)←− decision tree trained with morphological features of masses;t(5)←− decision tree trained with intensity features of masses;t(6)←− decision tree trained with texture features of masses;

CMat←− Compute confusion matrix for each of the trees t(4), t(5), t(6) (to be used by thefusion technique);

if pattern classified as mass thenOutputTree(4)←− classify validation set with t(4);OutputTree(5)←− classify validation set with t(5);OutputTree(6)←− classify validation set with t(6);

OutputsS2←− Naive Bayes fusion off all three outputs;Final Output←− OutputsS2;

elseFinal Output←− OutputsS1;

Compute the accuracy for this fold using Final Output and Label.

Average the accuracy

54

4.2.2 AdaBoost

The other method experimented in this work, AdaBoost [40] [41], is an ensemble classifier for binary

classification that trains T weak learners and combines their outputs into a strong classifier C. This

method can be considered a feature selection and learning algorithm, for each learner t chooses the

best feature (and its threshold) and performs a classification. Its name comes from the fact that it boosts

the classification performance of a single weak learner, in this case, single node decision trees, by

selecting the one with the highest classification rate (or lowest error). The learners are called ”weak”,

for they normally have a low classification rate, but the fusion of the outputs of the several learners

has proven to outcome robust results. Classifier C is a weighted combination of all weak learners that

outputs the classification solution. The added value of this ensemble method is that it accounts for the

output of learner t and, with it, adjusts the classification weights of each pattern, used in learner t + 1.

Figure 4.12 exemplifies this statement, where each learner picks a feature out of the feature pool.

Figure 4.12: Ilustration of the AdaBoost Classifier

In mathematical terms, each learner is a combination of patterns x, feature f , threshold θ and p, the

polarity indicating the direction of the inequality present in equation 4.13.

h(x, f, p, θ) =

1, if pf(x) < pθ

0, otherwise(4.13)

55

Adaboost is trained in an iterative way. During this process, two actions take place constantly:

• Computation of learner function h(t)

• Update of weights w(t)

The first one happens by minimizing the weighted classification error, present in equation 4.14 where

N is the total number of patterns, w(t)i is the classification weight for pattern i in learner t, di is the desired

output (pattern i’s correct label) and h(t) is the learner function.

ε(t) = minf,θ,p

N∑i=1

w(t)i |h

(t)(xi, f, θ, p)− di| (4.14)

It is worth noticing that the module portion of equation 4.14 is either 1 or 0. With this, h(t)(x, ft, θt, pt)

is chosen as learner t by being the one which minimizes function ε(t).

Figure 4.13 shows an example of the initial learner h(t), where the learner is represented by a border

that separates the patterns in the best way possible.

Figure 4.13: Illustration of the first learner being computed. In this example, all the patterns have the same weight(represented by the patterns size)

As mentioned before, in the beginning of each iteration, an update on the weights happens for w(t).

The weights are initialized according to the proportion of patterns from each class and are updated for

every t, as seen in equation 4.15,

w(t+1)i = w(t)β

(1− |h(t)

i −yi|)

(t) (4.15)

where β(t) = ε(t)

1−ε(t) .

In other words, this means that the weight in t + 1 is the same as the weight in t if the pattern is

incorrectly classified3 (|h(t)i − yi| = 1) or it is updated to a smaller relative value (dependent of ε(t)) as

represented in equation 4.16.

w(t+1)i =

wt, if |h(t)

i − yi| = 1 (incorrect classification)

wt × ε(t)

1−ε(t) , otherwise(4.16)

3Before the normalization step

56

Figure 4.14 and 4.15 illustrate the process of the weight update, when starting in figure 4.13, by

increasing the size of the pattern to exemplify the weight increment after normalization.

Figure 4.14: Illustration of the second learner of an AdaBoost. In this figure, the patterns previously miss-classifiedin figure 4.13 have a larger classification weight, as represented by their size.

Figure 4.15: Illustration of the third learner of the AdaBoost. As it can be seen, the patterns miss classified both infigure 4.13 or 4.14 have larger weights than the others.

In each step, after the computation, the weights are normalized. This means that if the patterns were

miss-classified, their weights increased.

N∑i=1

w(t+1)i = 1. (4.17)

After AdaBoost is trained, it is used for classifying the test and/or the validation set. Let’s consider Z

to be a set without labels, in which C is the label vector output by the AdaBoost. C is computed through

a fusion of the outputs of the several weak learners as presented in equation 4.18, where α(t) = log 1β(t) .

C(Zi) =

1, ifT∑t=1

α(t)h(t)(Zi) >12

T∑t=1

α(t)

0, otherwise

(4.18)

To sum up, the final classifier of the AdaBoost is a weighted combination of the outputs of the weak

learners, in which α(t) represent the weight associated to each one. Notice that the term to the right,12

T∑t=1

α(t), represents the situation where 50% of the learners classified pattern Zi as 1 and the other 50

57

as 0, hence, if the term on the left overcomes this value, the pattern is classified as 1, otherwise, as 0.

The pseudo-code in algorithm 4.2 enhances the order of each step mentioned.

Algorithm 4.2: AdaBoostData: Given x to be the training dataset, y to be the label vector and Z to be unclassified dataResult: Vector C is the label vector of Z, output by the AdaBoost classifier

Initialization of weights according to the label, where wxc= 1

2Nc, where xc represents a pattern

of class c and Nc is the number of patterns in such a class;for t −→ T do

Normalize the weighs by w(t)i ←

w(t)i∑

jw

(t)j

;

Select h(t), f, θ and p by minimizing ε(t) = minf,θ,p

N∑i=1

w(t)i |h(xi, f, θ, p)− di|

Updates the weights with w(t+1)i = w(t)β

(1− |h(t)

i −yi|)

(t)

Compute the final weighted classification using

C(Zi) =

1, ifT∑t=1

α(t)h(t)(Zi, f(t), θ(t), p(t)) < 1

2

T∑t=1

α(t)

0, otherwise

In this thesis, a third experiment is done using an AdaBoost Ensemble. Opposite to the experiment

presented in section 4.2.1, instead of 3 classifiers, 300 are used (100 for each type), each using, for

training, 80% of the total training data obtained using bootstrap sampling with replacement [42]. The

schema for this experiment is as presented in figure 4.16.

Figure 4.16: Schema of the classifier used in the AdaBoost Ensemble experiment.

58

In order for it to be compared with the other experiments, algorithm 3 presents the pseudo-code of

the AdaBoost Ensemble experiment.

Algorithm 4.3: Pseudo-code of the algorithm used in the AdaBoost Ensemble experiment.Data: Dataset off all patterns (and their features)Result: Label vector C, the accuracy, true positive and true negative

for kfold = 1−→ 10 do%Stage 1for loop = 1:3:300 do

train←− Sample 80% of the data ;Ensemble(loop)←− Ensemble trained with morphological features;Ensemble(loop+1)←− Ensemble trained with intensity features;Ensemble(loop+2)←− Ensemble trained with texture features;

CMat←− Compute confusion matrix for each of the classifier (to be used by the fusiontechnique);

OutputEnsemble(loop)←− classify validation set with Ensemble(loop);OutputEnsemble(loop+1)←− classify validation set with Ensemble(loop+2);OutputEnsemble(loop+2)←− classify validation set with Ensemble(loop+3);

OutputsS1←− Naive Bayes fusion off all 300 outputs;

%Stage 2;for loop:1:3:300 do

train←− Sample 80% of the patterns which are masses ;Ensemble(loop)←− Ensemble trained with morphological features;Ensemble(loop+1)←− Ensemble trained with intensity features;Ensemble(loop+2)←− Ensemble trained with texture features;

CMat←− Compute confusion matrix for each of the classifier (to be used by the fusiontechnique);

if pattern classified as mass in stage 1 thenOutputEnsemble(loop)←− classify validation set with Ensemble(loop);OutputEnsemble(loop+1)←− classify validation set with Ensemble(loop+1);OutputEnsemble(loop+2)←− classify validation set with Ensemble(loop+2);

OutputsS2←− Naive Bayes fusion off all three outputs;Final Output←− OutputsS2;

elseFinal Output←− OutputsS1;

Compute the accuracy for this fold using Final Output and Label.

Average the accuracy

59

4.2.3 Fusion Techniques

In order to combine the outputs of the three classifiers which use different types of features (morpho-

logical, intensity and texture) and of the classifiers which use only a sample of the training data (instead

of the whole set), three combing techniques can be used: Majority Vote, Weighted Majority Vote and

Naive Bayes combination [38].

The first one, Majority Vote, as the name implies, is simply to pick the class which is output by the

majority of the classifiers. Given that there are binary classes in this work, let’s map the classes as

presented in equation 4.19 or 4.20.

ostage1 =

1, if mass

0, if healthy(4.19)

or

ostage2 =

1, if mass malignant

0, if mass benign(4.20)

Given this, in order to combine the outputs via a majority vote technique, one must simply average

them and choose the closest class. For example, let’s say that there are K classifiers, in this example,

k ∈ 1, 2, 3 and that o1 = 0, o2 = 1, o3 = 1. Then, by averaging, one obtains,

oexample =1

K

K∑k=1

ok = 0.666 (4.21)

Given that the value is bigger than 0.5, this pattern would be classified as a mass.

The second method, Weighted Majority Vote, uses the accuracy of each classifier and computes a

weight function based on it. This way, the classifiers have more power to make the final decision, if they

perform better. The weighted function is computed, as seen in equation 4.22, where, acck represents

the accuracy of each classifier k. For convenience, this function is normalized, as seen in equation 4.23.

b(k) = logacck

1− acck(4.22)

K∑k=1

b(k) = 1 (4.23)

Given binary classes, one must simply multiply the weight of each classifier by its output, as in

equation 4.24, for each pattern.

ocomb =

K∑k=1

bk × ok (4.24)

Using the same example as before, where o1 = 0, o2 = 1, o3 = 1, 4, let’s say that b1 = 0.58, b2 =

4in which the pattern is classified as a mass according to the Majority Vote technique

60

0.21, b3 = 0.21, then, the combined output would be

ocomb = (0.58× 0) + (0.21× 1) + (0.21× 0) = 0.42 (4.25)

In which case, the pattern would be considered healthy tissue and not a mass.

The third combining method, Naive Bayes Combination, as the name implies, computes the combi-

natorial output using the Bayes rule. This method assumes independence between the classifiers and

its added value is that it computes the posterior probability of a pattern to be of a certain class, given the

output of the classifier. This probability is described in equation 4.26.

P (di = c|o) =P (di = c)P (o|di = c)

P (o)(4.26)

where P (di = c|o) is the probability of the correct label di to be of class c knowing the output vector

o, P (di = c) is the probability of the correct label di to be of class c, P (o|di = c) is the probability of

output vector o to happen, knowing that di = c and P (o) is the probability of the output vector o to

happen. Given the assumption of independence between the classifiers, the equivalence present in

equation 4.27 can be stated.

P (o|di = c) = P (o1, o2, ..., oK |di = c) =

K∏k=1

P (ok|di = c) (4.27)

Hence, one can say that,

P (di = c|o) =P (di = c)

∏Kk=1 P (ok|di = c)

P (o)(4.28)

and given that the denominator is independent from the class, one classifies a pattern as class c by

saying class c is the value that maximizes equation 4.29:

P (di = c|o) ∝

(P (di = c)

K∏k=1

P (ok|di = c)

)(4.29)

All the elements of equation 4.29 can be computed from the dataset or from the confusion matrix of

each classifier, by estimating the prior probability of class c (P (di = c)) as Nc/N , which is the number of

patterns belonging to class c over the number of total patterns and by computing the posterior probability

from the confusion matrix as described in equation 4.30, where the (c, s)th entry of matrix cm is the

number of elements in the dataset whose true class is c and are classified as s.

P (ok|di = c) =cmk(c, s)

Nc(4.30)

61

The final expression to compute the combinatorial label can be found in equation 4.31 and 4.32.

P (di = c|o) ∝NcN

∏Kk=1 cmk(c, s)

NKc

∝1

NK−1c

K∏k=1

cmk(c, s) (4.31)

ocomb = argmax (P (di = c|o))c

(4.32)

62

5Experimental Results

Contents

5.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.2 Pre-Processing and Segmentation Results . . . . . . . . . . . . . . . . . . . . . . . . 66

5.3 Classification Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.4 Comparison of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

63

64

5.1 Data

The database used for this work was compiled by South Florida University and is called Digital

Database for Screening Mammography(DDSM) [43] [44]. It is composed of 1950 lesion-free mammo-

grams, 836 mammograms containing malignant masses and 399 containing benign ones, as displayed

in figure 5.1. In DDSM, the lesions are previously labelled by physicians and confirmed via a biopsy. A

certain error in this database has to be assumed, for although each exam might have been reviewed

by other experts, the sensitivity of a doctor is lower than 93% [45], when locating lesions, in this type of

exam. This means that there might be masses that are present in the images but that are not accounted

for. There are also several exams with microcalcification clusters, which were not used, for these type of

lesions fall outside of the scope of this thesis.

Figure 5.1: Histogram of the 3 classes of exams contained in DDSM database.

One obstacle when using this database is the fact that the files are compressed in ljpeg format

(lossless jpeg). This format is not widely known, therefore, there is a need to convert them to a format

readable by MATLAB2016a (or other applications). Along with the database, a C source code is available

to convert the images from .ljpeg to .pgm. This last format is not commonly recognized by a standard

image viewer, but it can be written to other formats in order to be viewed. In this thesis, a virtual machine

with Ubunto as an operating system is used to run the C code to convert the files to .pgm. The total

size of files is around 220Gb, so a total of 1 day of computation time is required to convert the entire

65

database.

The contents of DDSM database are originated from two locations: Massachusetts General Hospital

(MGH) and Wake Forest University School of Medicine (WFUSM). Although the race of each patient is

not specified per exam, table 5.1 presents the race breakdown of the female patient population of both

medical facilities.

Table 5.1: The female population at MGH and WFUSM by race

Race MGH (%) WFUSM (%)Asian 2.06 0.20Black 4.12 20.40Spanish (origin) 6.55 1.80American Indian 0.00 0.10Other 0.75 0.10Unknown 30.34 0.30White 56.18 77.00

So far, no study has found a direct connection between breast cancer and race, but it is important to

be aware that the exams presented in this database are, in majority, from white women.

5.2 Pre-Processing and Segmentation Results

This section describes the results of the bilateral filter and segmentation method presented in section

3.2. The bilateral filter built in this work is custom built, according to the literature, as described in section

3.1. The filter is used with a window of analysis of 81 × 81 pixels, a standard deviation of 20 pixels (for

the spatial distance filter) and a standard deviation of 12% of the maximum value of the image (for the

intensity based filter).

The effects of this filter can be seen in figures 5.2(a) to 5.4(b), where its influence over the segmen-

tation stage is exemplified. The effects of the bilateral filter can be divided into three categories: the filter

improves the final result, the filter has no influence and the use of the filter outputs a worse result. The

segmentation algorithm (SBF) is provided by the writers of literature [33] and adapted to this experiment.

For these experiments, the segmentation algorithm used a total of 32 orientation points.

The best case scenario, where the bilateral filter reduces the number of false positives, is presented

in figures 5.2(a) and 5.2(b). The figures exemplify a case of a patient’s breast with cancer (seen in blue).

The segmentation algorithm starts by considering 9 regions to be ROI, none of which is the correct

lesion, whereas if the image is filtered, only 3 ROIs are considered (including the correct one). This is a

proof that the use of the bilateral filter reduces the number of false positives.

Other cases occur as well, where the bilateral filter does not influence the final result, by not reducing

the number of ROIs, as is presented in figures 5.3(a) and 5.3(b).

66

Lastly, the final case that occurs is where the application of the bilateral filter has a negative impact

and the real lesion is not detected as a ROI. This implies that the use of the bilateral filter, in some

cases, reduces the accuracy of the whole system. Such a case is presented in figures 5.4(a) and 5.4(b).

(a) Unfiltered image (b) Filtered image

Figure 5.2: Effect of filtering on the segmentation of a breast image with a malignant lesion a) without the bilateralfilter b) with the bilateral filter. In this figure, it can be seen the output of the segmentation in green andthe ground truth in blue.

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(a) Unfiltered image (b) Filtered image

Figure 5.3: Effect of filtering on the segmentation of a breast image with a malignant lesion a) without the bilateralfilter b) with the bilateral filter. In this case, the filter had no effect on the segmentation output.

(a) Unfiltered image (b) Filtered image

Figure 5.4: Effect of filtering on the segmentation of a breast image with a malignant lesion a) without the bilateralfilter b) with the bilateral filter. In this case, the segmentation algorithm does not locate the correct ROIin the filtered image.

This filter influences the final FP value, reducing the number of ROIs found in 20%. The system can

be parametrized for a smaller FP with the trade-off of reducing the TP rate, for some lesions would not

be detected in the segmentation stage.

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After the segmentation algorithm is applied, the features mentioned in section 4.1 are extracted in

order to build a feature dataset, with three possible labels: healthy tissue, benign mass and malignant

mass.

5.3 Classification Results

5.3.1 Single Model Decision Tree Experiment

As mentioned in section 4.2.1, a first experiment is done using only one DT. This experiment was

done to be compared with the others, for given that the AdaBoost classifier is built with single-node deci-

sion trees, a single decision tree is the simplest form of this type of classifier. This tree is computed with

MATLAB2016a’s built-in function and pruned as much as possible, without increasing the classification

error, using 10-fold cross-validation. Pruning is used in order to avoid over-fitting the tree, by growing

it too large. Figures 5.5(a) and 5.5(b) exemplify the same tree (not pruned and pruned, respectively),

where it is possible to see that the tree’s size is reduced. After training and cross-validating the tree, the

confusion matrix present in table 5.2 represents the output of this classifier, which obtained an average1

accuracy of 82%.

(a) Decision tree (b) Pruned Decision Tree

Figure 5.5: DT a) not pruned, b) pruned, with three possible outputs: 0,1 and 2 or healthy tissue, malignant massand benign mass.

1Average of the 10 cross-validation folds

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Table 5.2: Confusion matrix of the decision tree presented in the Single Model Decision Tree experiment. Thismodel obtained a classification rate of 82%.

Output Labels

Healthy Tissue Benign Mass Malignant Mass

Target Class

Healthy Tissue 1760 83 107

Benign Mass 136 189 125

Malignant Mass 134 56 595

DDSM is not a balanced database, as seen in section 5.1. This means that some classes of patterns

are more present in the dataset than others, which will affect the results when using a DT. This type of

classifier has an unstable behaviour when used with unbalanced datasets, which privileges the patterns

which are most common (and the reverse for the uncommon ones).

In tables 5.2 and 5.3 can be observed that this model performs better when classifying healthy tissues

and performs significantly worse when classifying benign masses, which are the most common class

of patterns and the most rare, respectively. This is the result of the unstable behaviour from the DT

mentioned earlier.

Table 5.3: Table presenting the per class accuracy results of the Single Model Decision Tree experiment.

Accuracy of the Single Model Decision Tree

General 0.82

Malignant 0.80

Benign 0.47

Healthy Tissue 0.91

5.3.2 Decision Tree Ensemble Experiment

In this experiment, a two stage hypothesis was tested as presented in section 4.2.1. It is composed

of 6 DTs, grown with a stopping criteria of 16 splits. In each tree, only a specific set of features is used

as training set: morphological, intensity based or texture ones. This experiment is tested using 10 fold

cross-validation technique and the trees are also pruned. The confusion matrix for this experiment can

be seen in table 5.4 and its accuracy is 82%.

A first analysis to be done is that this schema performs (in general) the same way as the single

decision tree presented in section 5.3.1. An interesting aspect that can be observed through tables 5.4

and 5.5 is the influence of the fusion technique. Note that, for both types of mass and all classes put

together, the output results is always improved when using the fusion of the 3 model than when using

each model in separate. With it, it can also be observed that the effect of the data being unbalanced

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is attenuated with the fusion technique, increasing the per class accuracy for the less common class

(benign mass) and decreasing for other two. An analysis on the relationship between each model can

also be retrieved, where it can be noted that the morphological features model performs best (compared

to the other models). Table 5.5 displays these relationships.

Table 5.4: Confusion matrix of the classifier presented in the Decision Tree Ensemble Experiment. The final classi-fier obtained a classification rate of 82%.

Output Labels

Healthy Tissue Benign Mass Malignant Mass

Target ClassHealthy Tissue 1763 99 88

Benign Mass 99 255 96

Malignant Mass 105 80 600

Table 5.5: Table presenting the accuracies per class and per model obtained from the results of the Decision TreeEnsemble Experiment.

Morphological Feat. Intensity Feat Texture Feat Classifier ensemble

General 0.80 0.73 0.71 0.82

Malignant 0.62 0.42 0.43 0.77

Benign 0.41 0.45 0.18 0.57

Healthy Tissue 0.97 0.92 0.94 0.90

Table 5.6: Confusion matrix of the morphological, intensity and texture features model presented in the DecisionTree Ensemble Experiment. Each model obtained a classification rate of 80%, 73% and 71%, respec-tively.

Output Labels

Healthy Tissue Benign Mass Malignant Mass

Target Class - Morphological featuresHealthy Tissue 1879 43 28

Benign Mass 193 183 74

Malignant Mass 211 87 487

Target Class - Intensity featuresHealthy Tissue 1801 112 37

Benign Mass 193 202 55

Malignant Mass 249 207 329

Target Class- Texture featuresHealthy Tissue 1834 75 41

Benign Mass 292 84 74

Malignant Mass 331 122 332

In order to comprehend the relationship between each model and each class, one can observe the

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confusion matrix of each of them, presented in table 5.6. In this matrix, the effect of the unbalanced

data can be observed by the amount of patterns miss classified as healthy tissue. In the limit, the

morphological features and the texture features models classify patterns corresponding to the benign

classes more often as healthy tissues, than as benign masses themselves.

5.3.3 AdaBoost Ensemble Experiment

The third and last experiment is an optimized/modified version of the second one. In this case,

AdaBoost replaces the DTs in the classifier ensemble. 600 AdaBoost were trained, in which each had

a maximum of 10 learners. The input of each classifier was 80% of the total training set, obtained using

bootstrap sampling with replacement. Table 5.7 presents the confusion matrix of the final classifier. With

it, significant improvements can be spotted, when comparing this AdaBoost Ensemble experiment with

Decision Tree Ensemble experiment: the correct labels for benign masses and healthy tissue increased.

Also, these settings reduce, in a great deal, the number of patterns miss classified as mass (both benign

and malignant).

Table 5.7: Confusion matrix of the AdaBoost Ensemble Experiment classifier. This model obtained a classificationrate of 85%.

Output LabelsHealthy Tissue Benign Mass Malignant Mass

Target ClassHealthy Tissue 1863 59 28Benign Mass 113 269 68

Malignant Mass 81 153 551

Table 5.8 allows us to analyse the relationship between models and classes. It can be observed that

using AdaBoost improves the results of the final classifier for all 3 features models, and, consequently,

for the general accuracy as well. When using AdaBoost, the fusion technique does not always increase

the result of the classifier ensemble, when comparing to each model in separate, for the effect of the

unbalanced data is contradicted in the AdaBoost itself, in the weight pattern attribution (see section

4.2.2). Given this, the fusion technique outputs a better result than any of the models, when the per

class accuracy is low and might not increase the general accuracy if the per class accuracy is high.

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Table 5.8: Table presenting the accuracies per class and per model obtained from the results of the AdaBoostEnsemble Experiment classifier.

Morphological Feat. Intensity Feat Texture Feat Classifier ensemble

General 0.84 0.76 0.75 0.85

Malignant 0.74 0.59 0.62 0.70

Benign 0.46 0.27 0.20 0.60

Healthy Tissue 0.97 0.94 0.92 0.96

As explain in section 4.2.2, each AdaBoost contains 10 learners, each with a corresponding weight

that is posteriorly used when computing the label of the AdaBoost. This type of classifier works in a

coarse-to-fine manner, so, for the first learner, the classification weights associated to the patterns is

uniform, which means that the first learners will have the highest weights associate to them, as seen in

figure 5.6(a). Equally, the same happens with the learners, broken down by model, as seen in figure

5.6(b). In section 4.2.2 it is proven that the weights of each leaner are proportional to the learner’s

classification rate and such can be observed by the information contained in table 5.8 and figure 5.6(b),

where it can be seen that the model which uses morphological features has both the highest weights

and highest accuracy.

(a) Total average of the weights of the learners (b) Average of the weights of the learners by model

Figure 5.6: Relative weights of the learners of the AdaBoost classifier a) in total b) by model.

5.4 Comparison of Results

In order to compare the results of the three experiments, the results can be seen from two different

perspectives:

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• A mathematical perspective, where we compare the classification results for the three classes,

independently of what they mean, as reported in section 5.3.

• A commercial/medical perspective, where we analyse and compare only the accuracy of the

classifier in distinguishing healthy tissue from masses (output of stage 1). Given this, it is consid-

ered irrelevant the distinction between benign mass and malignant mass, since both information

should be reported to the doctor.

The first analysis to be done is to compare the three experiments as presented in section 5.3. This

way it is possible to identify the settings which would output the best results, from a mathematical point

of view. Table 5.9 contains the general and per class accuracies of the three experiments. Here, one

can observe that the settings from AdaBoost Ensemble experiment output the best results in general,

when classifying benign lesions or healthy tissue, behaving the worse for malignant lesions.

Table 5.9: Table for comparison of general accuracies and per class accuracy of the three experiments

Single Model Decision Tree Decision Tree Ensemble AdaBoost EnsembleACC General 0.82 0.82 0.85

ACC Malignant 0.80 0.77 0.70ACC Benign 0.47 0.57 0.60

ACC Healthy Tissue 0.91 0.90 0.96

A second analysis is done, considering the commercial/medical perspective. Let’s look at the fact that

this CAD system deals with a diagnosis problem, where it can be said that if the CAD miss classifies

a benign mass as a malignant one, it is not the same as mistaking a malignant mass for a healthy

tissue. With this assumption, it is possible to adapt the classifier to reality and real life environments

by considering only two classes (healthy tissue or mass), in order for the output of the classifier to be

studied under a different perspective.

Table 5.10 presents the confusion matrix off all three experiments, where the patterns labelled as

”benign mass” or ”malignant mass” were simply labelled as ”mass”. The data provided by this table sup-

ports the fact that the settings of the AdaBoost Ensemble experiment perform better when appropriating

the CAD system to real life, considering only two classes. Although these settings performed worse for

malignant class, when joining both lesions as one single class, the AdaBoost based classifier ensemble

outperforms the other two, achieving higher classification rates for both classes.

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Table 5.10: Confusion matrix for all three experiments, considering only two masses.

Output LabelsHealthy Tissue Mass

Target Class - Single Mode Decision Tree Healthy Tissue 1745 205TP = 0.79 — FP = 0.11 — ACC = 0.85 Mass 266 969

Target Class - Decision Tree Ensemble Healthy Tissue 1763 187TP = 0.84 — FP = 0.09 — ACC = 0.88 Mass 204 1031

Target Class - AdaBoost Ensemble Healthy Tissue 1863 87TP = 0.84 — FP = 0.04 — ACC = 0.91 Mass 194 1041

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6Conclusions and Future Work

77

78

This thesis presents a Computer Aided Diagnosis (CAD) system that identifies lesions in mammo-

graphies. The system is built to filter and segment images in order to find regions of interest (ROIs) to

later classify them into healthy tissue, benign mass or malignant mass.

This work uses several steps to locate and identify each lesion. It uses a bilateral filter to pre-process

the image, which enhances the edges of objects within it. This filter can be computationally heavy, for it

computes both the spatial distance between the pixels and their intensity difference. The bilateral filter

uses these two measurements and smooths the inside and the outside of the objects, removing noise

and irrelevant information, without losing the edges.

After preprocessing, probable regions of being a lesion (ROIs) are identified and segmented. This is

based on the gradients of the image, for the ROIs are located by finding the local maxima of convergence

of such gradients. In this work, Sliding Band Filter (SBF) is used for this step. This algorithm takes into

account a radius range, in order to reduce the possibilities of the search and decreases, in a great

deal, the number of false positives, for it provides the possibility to consider only certain regions as

ROIs, instead of assuming every possible location. By using the bilateral filter, prior to this segmentation

algorithm, the number of false positives is reduced in 20%.

After the ROIs have been segmented, different information about each ROI can be extracted. In this

work, morphological, intensity-based and texture information is analysed.

This information is used to classify each ROI into healthy tissue, benign or malignant mass. In this

work, different classifier ensembles have been tested to classify such ROIs. The first experiment is a

Single Model Decision Tree, with all features available. This set-up outputs a maximum accuracy of

82% and, in these conditions, it has a higher per class accuracy for healthy tissues. The classifier

ensemble of the second experiment, Decision Tree Ensemble, uses a 2-stage schema and combines 3

classifiers per stage, where the first classifies the ROIs into healthy tissue or lesion and the second, in

benign mass or malignant one. This experiment results in a classifier with an accuracy of 82%, which

is similar to the Single Model Decision Tree. This points to the conclusion that this model might be

using the ”weaknesses” of its settings without using the ”strengths”: it divides the dataset by features

(which reduces the number of features available for the classifier) (weakness) but it combines only three

models, which it not enough to leverage on the fusion technique used to combine the outputs of each of

them (strength).

The third one also uses a 2-stage classifier, but this time, it uses 300 classifiers, instead of just

3, where in each is input an 80% sample of the data, instead of the whole set. This means that not

all classifiers will output the same results. With these settings, a general classification rate of 85% is

achieved. As shown in section 5.4, when considering benign masses and malignant masses to be one

class, it is also the settings of the AdaBoost Ensemble experiment the ones which output the best results.

79

As seen, when using the CAD present in this thesis, the results of a diagnosis would improve, in

general. Nevertheless, many other hypothesis can be studied and some modifications can be done to

this work that might improve its performance. One analysis to further be done is the influence of the

parameters of the initial stages in the final classification. The minimum and maximum radius of the

lesions considered in the bilateral filter and segmentation algorithm or the thresholds of this last one,

were chosen based on their visual results and in the amount of ROIs found and their location. This can

be perfected if a system is built to analyse the direct influence of these parameters (at the beginning of

the stream) in the output of the final classifier. Another subject where this work can be improved is in

the analysis of the lesions themselves. Given that it falls out its scope, this thesis leaves much room

for exploring the different kinds of malignant and benign masses and for introducing expert medical

knowledge about their physical aspects or typical locations in order to optimize the segmentation and/or

classification algorithms. An extended possibility of this aspect is to introduce several other classes,

where instead of simply malignant or benign lesions, the system can be searching for micro invasive1,

ductal invasive1, lobular invasive1 lesions, etc. This creates the possibility to optimize the procedures to

find each particular class, according to its characteristics.

The study for using the CAD for its final purpose, where it is more significant to detect the malignancy

of a lesion, than to exclude healthy tissue, can be further continued by exploring the cost of classification

between classes of the classifiers. As mentioned in section 5.4, the best settings presented in this work

achieved TP and FP rate values of 84% and 4%, respectively. This FP value is low enough for a further

research to increment the TP value (and consequently, increment the FP value), in order to explorer the

best settings, not just in terms of accuracy, but in terms of appropriating the system to its final use.

All the suggestions made above, aim to bring the work on CAD systems closer to reality and real life

environments.

1Examples of different types of malignant tumours

80

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