Statistical Models of Mammographic           Texture and AppearanceA thesis submitted to the University of Manchester for ...
Contents1 Introduction                                                                     28  1.1   Introduction . . . . ...
CONTENTS                                                               CONTENTS  2.3   Breast cancer . . . . . . . . . . ....
CONTENTS                                                               CONTENTS  3.3   Image enhancement . . . . . . . . ....
CONTENTS                                                               CONTENTS        4.2.1   Dilation and erosion . . . ...
CONTENTS                                                               CONTENTS        4.6.2   Method . . . . . . . . . . ...
CONTENTS                                                               CONTENTS  5.6    Learning from large datasets . . ....
CONTENTS                                                               CONTENTS  6.7   Novelty detection . . . . . . . . ....
CONTENTS                                                               CONTENTS        7.4.3   Method . . . . . . . . . . ...
CONTENTS                                                              CONTENTS        9.2.2   Approaches to modelling the ...
CONTENTS                                                                        11  10.4 Evaluating the detailing model . ...
List of Figures 2.1   Basic anatomy of the normal developed female breast. . . . . . . .         38 2.2   Incidence of bre...
134.6   Rotating the “rectangular” structuring elements. . . . . . . . . . . 1214.7   An “improved” pixel signature from t...
147.4   The circle chord attenuation function. . . . . . . . . . . . . . . . . 2087.5   The sigmoid attenuation function. ...
159.6   The initial and final correspondences for the mammogram shape      model. . . . . . . . . . . . . . . . . . . . . ....
List of Algorithms 1    The non-iterative k-means algorithm. . . . . . . . . . . . . . . . . 143 2    The iterative k-mean...
List of Tables 4.1   Classification results for the two signature types. . . . . . . . . . . 130 7.1   Results for the psyc...
AbstractBreast cancer is the most common cancer in women. Many countries—includingthe UK—offer asymptomatic screening for t...
DeclarationNo portion of the work referred to in the thesis has been submitted in support ofan application for another deg...
Copyright 1. Copyright in text of this thesis rests with the Author. Copies (by any   process) either in full, or of extra...
DedicationThis thesis is dedicated to the memory of Gareth Jones.In addition to being an excellent office mate, Gareth made ...
AcknowledgementsThe author would like to thank the following people:   • My mother, Anne, who has put myself and my brothe...
23• Other members of ISBE, including Tim Cootes, Carole Twining, Sue Astley,  Paul Beatty, Jim Graham, Ian Scott and Tomos...
FundingThe work described in this thesis was supported by the EPSRC as part of theMIAS-IRC project From Medical Images and...
About the AuthorIn holiday time during his A-level studies and first degree, Chris Rose workedfor Kraft Jacobs Suchard on a...
26• C. J. Rose and C. J. Taylor. A Model of Mammographic Appearance. In  British Journal of Radiology Congress Series: Pro...
‘As many truths as men. Occasionally, I glimpse a truer Truth, hiding in im-perfect simulacrums of itself, but as I approa...
Chapter 1Introduction1.1     IntroductionSince work for this thesis began, approximately 64 000 British women have diedfro...
Chapter 1—Breast cancer                                                        29   • An overview of breast cancer.   • An...
Chapter 1—Computer-aided mammography                                           301.3     Computer-aided mammographyResearc...
Chapter 1—Novelty detection                                                       31commercial computer-aided mammography ...
Chapter 1—Generative models                                                      32      significant variation.   • It is o...
Chapter 1—Overview of the thesis                                               33from the model; thus the model must be ge...
Chapter 1—Overview of the thesis                                             34     signature quality, based upon informat...
Chapter 1—Summary                                                              351.7     SummaryThis chapter presented a b...
Chapter 2Breast cancer2.1      IntroductionThis chapter introduces the clinical problem of breast cancer and describes how...
Chapter 2—Anatomy of the breast                                                  372.2      Anatomy of the breastThe main ...
Chapter 2—Anatomy of the breast                                    38Figure 2.1: Basic anatomy of the normal developed fem...
Chapter 2—Breast cancer                                                                       392.3         Breast cancerB...
Chapter 2—Breast cancer                                                        40called telomeres. Part of these sequences...
Chapter 2—Breast cancer                                                          41is synonymous with the phrase malignant...
Chapter 2—Breast cancer                                                         42   • Stage 1        – The tumour is no l...
Chapter 2—Breast cancer                                                                      43Figure 2.2: Incidence of br...
Chapter 2—Breast cancer                                                          44        – Post-menopausal breast densit...
Chapter 2—Breast cancer                                                         452.3.3    PreventionBreast cancer cannot ...
Chapter 2—Breast cancer                                                       46ceptives. Women at very high risk may be o...
Chapter 2—Breast cancer                                                         47UK National Health Service Breast Screen...
Chapter 2—Breast cancer                                                           48£41 600 (assuming other factors do not...
Chapter 2—Breast cancer                                                        49   • Simple mastectomy (or total mastecto...
Chapter 2—Breast cancer                                                         50Trastuzumab (marketed under the name Her...
Chapter 2—Breast imaging                                                         512.4      Breast imagingThis section int...
Chapter 2—Breast imaging                                                      52Figure 2.3: The mediolateral-oblique and c...
Chapter 2—Breast imaging                                                      53tion and the UK National Health Service Br...
Chapter 2—Breast imaging                                                        54Mammograms are most commonly read visual...
Chapter 2—Breast imaging                                                        552.4.2    UltrasonographyUltrasound imagi...
Chapter 2—Breast imaging                                                        56The imparted energy is released as elect...
Chapter 2—Summary                                                                57orientations can be combined to compute...
Chapter 2—Summary                                                            58    now have screening programmes to help d...
Chapter 3Computer-aided mammography3.1     IntroductionThis chapter presents a review of the computer-aided mammography li...
Chapter 3—Computer-aided mammography                                          60   • Research on computer-aided prompting ...
Chapter 3—Image enhancement                                                   61image of the digitised mammogram displayed...
Chapter 3—Image enhancement                                                     62niques use local neighbourhoods, while a...
Chapter 3—Image enhancement                                                    63to be specified more precisely. Wavelets w...
Chapter 3—Image enhancement                                                       64performance of detection algorithms. T...
Chapter 3—Breast segmentation                                                  65mograms. It therefore seems likely that a...
Chapter 3—Breast segmentation                                                  66generally used.Chandrasekhar and Attikiou...
Chapter 3—Breast segmentation                                                    67The approach is sensible because the sk...
Chapter 3—Breast density and risk estimation                                   683.5     Breast density and risk estimatio...
Chapter 3—Breast density and risk estimation                                     69acteristics of mammograms, known as Wol...
Chapter 3—Microcalcification detection                                             70Maximisation (EM) algorithm, was used ...
Chapter 3—Microcalcification detection                                           71is shown in Figure 3.1.Karssemeijer desc...
Chapter 3—Microcalcification detection                                         72Figure 3.1: An example microcalcification c...
Chapter 3—Microcalcification detection                                           73approach is sensible because it acknowle...
Chapter 3—Masses                                                               743.7     MassesMasses are abnormal growths...
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Breast cancer is the most common cancer in women. Many countries—including the UK—offer asymptomatic screening for the disease. The interpretation of mammograms is a visual task and is subject to human error. Computer-aided image interpretation has been proposed as a way of helping radiologists perform this difficult task. Shape and texture features are typically classified into true or false detections of specific signs of breast cancer. This thesis promotes an alternative approach where any deviation from normal appearance is marked as suspicious, automatically including all signs of breast cancer. This approach requires a model of normal mammographic appearance. Statistical models allow deviation from normality to be measured within a rigorous mathematical framework. Generative models make it possible to determine how and why a model is successful or unsuccessful. This thesis presents two generative statistical models. The first treats mammographic appearance as a stationary texture. The second models the appearance of entire mammograms. Psychophysical experiments were used to evaluate synthetic textures and mammograms generated using these models. A novelty detection experiment on real and simulated data shows how the model of local texture may be used to detect abnormal features.

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Statistical Models of Mammographic Texture and Appearance

  1. 1. Statistical Models of Mammographic Texture and AppearanceA thesis submitted to the University of Manchester for thedegree of Doctor of Philosophy in the Faculty of Medical and Human Sciences 2005 Christopher J. Rose School of Medicine 1
  2. 2. Contents1 Introduction 28 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.2 Breast cancer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.3 Computer-aided mammography . . . . . . . . . . . . . . . . . . . 30 1.4 Novelty detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1.5 Generative models . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.6 Overview of the thesis . . . . . . . . . . . . . . . . . . . . . . . . 33 1.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 Breast cancer 36 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2 Anatomy of the breast . . . . . . . . . . . . . . . . . . . . . . . . 37 2
  3. 3. CONTENTS CONTENTS 2.3 Breast cancer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.3.1 What is breast cancer? . . . . . . . . . . . . . . . . . . . . 39 2.3.2 Predictive factors . . . . . . . . . . . . . . . . . . . . . . . 42 2.3.3 Prevention . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.3.4 Clinical detection . . . . . . . . . . . . . . . . . . . . . . . 46 2.3.5 Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.3.6 Survival . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.4 Breast imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.4.1 X-ray mammography . . . . . . . . . . . . . . . . . . . . . 51 2.4.2 Ultrasonography . . . . . . . . . . . . . . . . . . . . . . . 55 2.4.3 Magnetic resonance imaging . . . . . . . . . . . . . . . . . 55 2.4.4 Computed tomography . . . . . . . . . . . . . . . . . . . . 56 2.4.5 Thermography . . . . . . . . . . . . . . . . . . . . . . . . 57 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573 Computer-aided mammography 59 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.2 Computer-aided mammography . . . . . . . . . . . . . . . . . . . 60 3
  4. 4. CONTENTS CONTENTS 3.3 Image enhancement . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.4 Breast segmentation . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.5 Breast density and risk estimation . . . . . . . . . . . . . . . . . . 68 3.6 Microcalcification detection . . . . . . . . . . . . . . . . . . . . . 70 3.7 Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.8 Spiculated lesions . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.9 Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.10 Clinical decision support . . . . . . . . . . . . . . . . . . . . . . . 85 3.11 Evaluation of computer-based methods . . . . . . . . . . . . . . . 86 3.12 Image databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.13 Commercial systems . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.14 Prompting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.15 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.16 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054 Scale-orientation pixel signatures 107 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 4.2 Mathematical morphology . . . . . . . . . . . . . . . . . . . . . . 108 4
  5. 5. CONTENTS CONTENTS 4.2.1 Dilation and erosion . . . . . . . . . . . . . . . . . . . . . 109 4.2.2 Opening and closing . . . . . . . . . . . . . . . . . . . . . 110 4.2.3 M- and N-filters . . . . . . . . . . . . . . . . . . . . . . . . 111 4.3 Pixel signatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.3.1 Local scale-orientation descriptors . . . . . . . . . . . . . . 112 4.3.2 Constructing pixel signatures . . . . . . . . . . . . . . . . 113 4.3.3 Metric properties . . . . . . . . . . . . . . . . . . . . . . . 115 4.4 Analysis of the current implementation . . . . . . . . . . . . . . . 116 4.4.1 Structuring element length . . . . . . . . . . . . . . . . . . 116 4.4.2 Local coverage . . . . . . . . . . . . . . . . . . . . . . . . . 117 4.5 An information theoretic measure of signature quality . . . . . . . 122 4.5.1 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.5.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 4.5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 4.6 Classification-based evaluation . . . . . . . . . . . . . . . . . . . . 128 4.6.1 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 5
  6. 6. CONTENTS CONTENTS 4.6.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 4.6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 4.6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1315 Modelling distributions with mixtures of Gaussians 133 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 5.3 Density estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 136 5.4 Gaussian mixture models . . . . . . . . . . . . . . . . . . . . . . . 140 5.4.1 Learning the parameters . . . . . . . . . . . . . . . . . . . 141 5.4.2 The k-means clustering algorithm . . . . . . . . . . . . . . 142 5.4.3 The Expectation Maximisation algorithm for Gaussian mix- tures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 5.5 Useful properties of multivariate normal distributions . . . . . . . 151 5.5.1 Marginal distributions . . . . . . . . . . . . . . . . . . . . 151 5.5.2 Conditional distributions . . . . . . . . . . . . . . . . . . . 153 5.5.3 Sampling from a Gaussian mixture model . . . . . . . . . 160 6
  7. 7. CONTENTS CONTENTS 5.6 Learning from large datasets . . . . . . . . . . . . . . . . . . . . . 161 5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1646 Modelling mammographic texture for image synthesis and anal- ysis 166 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 6.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 6.3 Non-parametric sampling for texture synthesis . . . . . . . . . . . 170 6.4 A generative parametric model of texture . . . . . . . . . . . . . . 172 6.5 Generating synthetic textures . . . . . . . . . . . . . . . . . . . . 174 6.5.1 Pixel-wise texture synthesis . . . . . . . . . . . . . . . . . 174 6.5.2 Patch-wise texture synthesis . . . . . . . . . . . . . . . . . 174 6.5.3 The advantages and disadvantages of a parametric statisti- cal approach . . . . . . . . . . . . . . . . . . . . . . . . . . 177 6.6 Some texture models and synthetic textures . . . . . . . . . . . . 178 6.6.1 A model of fractal mammographic texture . . . . . . . . . 178 6.6.2 A model of real mammographic texture . . . . . . . . . . . 179 6.6.3 The quality of the synthetic textures . . . . . . . . . . . . 182 6.6.4 Time and space requirements of the parametric method . . 185 7
  8. 8. CONTENTS CONTENTS 6.7 Novelty detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 6.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1897 Evaluating the texture model 190 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 7.2 Psychophysical evaluation of synthetic textures . . . . . . . . . . 191 7.2.1 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 7.2.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 7.2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 7.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 7.3 Initial validation of the novelty detection method . . . . . . . . . 197 7.3.1 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 7.3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 7.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 7.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 7.4 Evaluation of novelty detection performance . . . . . . . . . . . . 200 7.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 200 7.4.2 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 8
  9. 9. CONTENTS CONTENTS 7.4.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 7.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 7.4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2208 GMMs in principal components spaces and low-dimensional tex- ture models 222 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 8.2 Dimensionality reduction . . . . . . . . . . . . . . . . . . . . . . . 223 8.3 Gaussian mixtures in principal components spaces . . . . . . . . . 224 8.3.1 A numerical issue . . . . . . . . . . . . . . . . . . . . . . . 227 8.4 Texture synthesis in principal components spaces . . . . . . . . . 228 8.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2319 A generative statistical model of entire mammograms 233 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 9.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 9.2.1 Why are mammograms hard to model? . . . . . . . . . . . 234 9
  10. 10. CONTENTS CONTENTS 9.2.2 Approaches to modelling the appearance of entire mammo- grams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 9.3 Modelling and synthesising entire mammograms . . . . . . . . . . 242 9.3.1 Breast shape and the correspondence problem . . . . . . . 243 9.3.2 Approximate appearance . . . . . . . . . . . . . . . . . . . 249 9.3.3 Detailed appearance . . . . . . . . . . . . . . . . . . . . . 254 9.3.4 Generating synthetic mammograms . . . . . . . . . . . . . 256 9.4 Example synthetic mammograms . . . . . . . . . . . . . . . . . . 257 9.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25810 Evaluating the synthetic mammograms 261 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 10.2 Qualitative evaluation by a mammography expert . . . . . . . . . 262 10.3 A quantitative psychophysical evaluation . . . . . . . . . . . . . . 263 10.3.1 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 10.3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 10.3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 10.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 10
  11. 11. CONTENTS 11 10.4 Evaluating the detailing model . . . . . . . . . . . . . . . . . . . . 265 10.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26911 Summary and conclusions 271 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 11.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 11.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 11.4 Final statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279A The expectation maximisation algorithm 280 A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 A.2 The algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 A.3 Proof of convergence . . . . . . . . . . . . . . . . . . . . . . . . . 282
  12. 12. List of Figures 2.1 Basic anatomy of the normal developed female breast. . . . . . . . 38 2.2 Incidence of breast cancer in England. . . . . . . . . . . . . . . . 43 2.3 The mediolateral-oblique and cranio-caudal views. . . . . . . . . . 52 3.1 An example microcalcification cluster. . . . . . . . . . . . . . . . 72 3.2 An example circumscribed mass. . . . . . . . . . . . . . . . . . . . 75 3.3 An example spiculated lesion. . . . . . . . . . . . . . . . . . . . . 79 4.1 Dilation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.2 A sieved mammographic image. . . . . . . . . . . . . . . . . . . . 112 4.3 Example pixel signatures. . . . . . . . . . . . . . . . . . . . . . . 114 4.4 An illustration of the two limitations of the existing implementation.118 4.5 Incremental approximations of the bow tie structuring element. . 119 12
  13. 13. 134.6 Rotating the “rectangular” structuring elements. . . . . . . . . . . 1214.7 An “improved” pixel signature from the centre of a Gaussian blob. 1224.8 Regions of increased Shannon entropy. . . . . . . . . . . . . . . . 1274.9 An example region of interest and its groundtruth. . . . . . . . . 1295.1 An illustration of the expectation maximisation algorithm. . . . . 1495.2 A two-dimensional distribution marginalised over one dimension. . 1525.3 A conditional distribution. . . . . . . . . . . . . . . . . . . . . . . 1545.4 The divide-and-conquer clustering algorithm. . . . . . . . . . . . . 1636.1 Unconditional samples from the fractal model. . . . . . . . . . . . 1806.2 Fractal training and synthetic textures. . . . . . . . . . . . . . . . 1816.3 Unconditional samples from the real mammographic texture model. 1826.4 Real training and synthetic textures. . . . . . . . . . . . . . . . . 1836.5 Examples of synthesis failure using patch-wise synthesis with a model of real mammographic appearance. . . . . . . . . . . . . . 1857.1 A screenshot of one of the trials. . . . . . . . . . . . . . . . . . . . 1957.2 Fractal and scrambled textures. . . . . . . . . . . . . . . . . . . . 1987.3 ROC curve for texture discrimination. . . . . . . . . . . . . . . . 199
  14. 14. 147.4 The circle chord attenuation function. . . . . . . . . . . . . . . . . 2087.5 The sigmoid attenuation function. . . . . . . . . . . . . . . . . . . 2087.6 Examples of simulated masses using the three methods. . . . . . . 2097.7 Example log-likelihood image and ROC curve for simulated micro- calcifications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2117.8 Example log-likelihood image and ROC curve for a simulated mass. 2127.9 ROC curve for simulated masses and microcalcifications (combined).2137.10 Example log-likelihood image and ROC curve for a real microcal- cification cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2157.11 ROC curve for real masses. . . . . . . . . . . . . . . . . . . . . . . 2167.12 ROC curve for real microcalcifications and masses (combined). . . 2178.1 Synthesis using a principal components model. . . . . . . . . . . . 2299.1 Examples of mammographic variation. . . . . . . . . . . . . . . . 2359.2 Overview of the Active Appearance Model. . . . . . . . . . . . . . 2409.3 Samples from two shape models, illustrating the need for good correspondences. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2449.4 Values of the Kotcheff and Taylor objective function. . . . . . . . 2469.5 Values of the MDL objective function. . . . . . . . . . . . . . . . 247
  15. 15. 159.6 The initial and final correspondences for the mammogram shape model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2489.7 Block diagram for the steerable pyramid decomposition. . . . . . . 2529.8 The coefficients in the top three levels of a steerable pyramid de- composition of a mammogram. . . . . . . . . . . . . . . . . . . . 2539.9 Synthetic mammograms generated using the model. . . . . . . . . 2599.10 Real and synthetic mammograms. . . . . . . . . . . . . . . . . . . 26010.1 Contributions of detailing coefficients to real and synthetic mam- mograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
  16. 16. List of Algorithms 1 The non-iterative k-means algorithm. . . . . . . . . . . . . . . . . 143 2 The iterative k-means algorithm. . . . . . . . . . . . . . . . . . . 143 3 The EM algorithm for fitting a GMM with two components to one-dimensional data. . . . . . . . . . . . . . . . . . . . . . . . . . 148 4 The EM algorithm for fitting a GMM with multiple components to multivariate data. . . . . . . . . . . . . . . . . . . . . . . . . . 150 5 Efros and Leung’s texture synthesis algorithm. . . . . . . . . . . . 171 6 Pixel-wise texture synthesis with a Gaussian mixture model of local textural appearance. . . . . . . . . . . . . . . . . . . . . . . . . . 175 7 Patch-wise texture synthesis with a Gaussian mixture model of local textural appearance. . . . . . . . . . . . . . . . . . . . . . . 176 8 Fractal mammographic texture algorithm. . . . . . . . . . . . . . 179 9 Novelty detection using a Gaussian mixture model of texture. . . 188 10 Simulating microcalcification clusters. . . . . . . . . . . . . . . . . 206 11 Generating a synthetic mammogram . . . . . . . . . . . . . . . . 256 16
  17. 17. List of Tables 4.1 Classification results for the two signature types. . . . . . . . . . . 130 7.1 Results for the psychophysical experiment. . . . . . . . . . . . . . 196 17
  18. 18. AbstractBreast cancer is the most common cancer in women. Many countries—includingthe UK—offer asymptomatic screening for the disease. The interpretation ofmammograms is a visual task and is subject to human error. Computer-aidedimage interpretation has been proposed as a way of helping radiologists performthis difficult task. Shape and texture features are typically classified into trueor false detections of specific signs of breast cancer. This thesis promotes analternative approach where any deviation from normal appearance is marked assuspicious, automatically including all signs of breast cancer. This approach re-quires a model of normal mammographic appearance. Statistical models allowdeviation from normality to be measured within a rigorous mathematical frame-work. Generative models make it possible to determine how and why a model issuccessful or unsuccessful. This thesis presents two generative statistical models.The first treats mammographic appearance as a stationary texture. The sec-ond models the appearance of entire mammograms. Psychophysical experimentswere used to evaluate synthetic textures and mammograms generated using thesemodels. A novelty detection experiment on real and simulated data shows howthe model of local texture may be used to detect abnormal features. 18
  19. 19. DeclarationNo portion of the work referred to in the thesis has been submitted in support ofan application for another degree or qualification of this or any other universityor other institute of learning. 19
  20. 20. Copyright 1. Copyright in text of this thesis rests with the Author. Copies (by any process) either in full, or of extracts, may be made only in accordance with instructions given by the Author and lodged in the John Rylands University Library of Manchester. Details may be obtained from the Librarian. This page must form part of any such copies made. Further copies (by any process) of copies made in accordance with such instructions may not be made without the permission (in writing) of the Author. 2. The ownership of any intellectual property rights which may be described in this thesis is vested in the University of Manchester, subject to any prior agreement to the contrary, and may not be made available for use by third parties without the written permission of the University, which will prescribe the terms and conditions of any such agreement. 3. Further information on the conditions under which disclosures and ex- ploitation may take place is available from the Head of School of School of Medicine. 20
  21. 21. DedicationThis thesis is dedicated to the memory of Gareth Jones.In addition to being an excellent office mate, Gareth made a substantial contri-bution to my PhD research. With his dry sense of humour, willingness to helpand pragmatic perfectionism—and despite his admirable unwillingness to bendto the stupidity of others—he motivated me to learn how to prepare documentsusing the L TEX typesetting system, contributed to discussions on mathematical Amatters, helped me with various aspects of MATLAB and UNIX, and radicallyaltered my view of computers and programming. It is a pleasure to have knownhim, and I wish I had known him better.Friday 21 November 2003. 21
  22. 22. AcknowledgementsThe author would like to thank the following people: • My mother, Anne, who has put myself and my brothers first in everything she has done. • My girlfriend, Chris, for uncountable reasons. • My PhD supervisor, Prof. Chris Taylor OBE, who is patient, supportive, giving and hard-working. • Anthony Holmes, for his generosity in getting me started. • Special thanks go to Andrew Bentley, who employed a spotty teenage geek and taught him electronics and computer programming. This thesis would not exist without his support—thank you! Thanks also to Richard, David, Keith and Martin for all their assistance. • My friends, for their support over the last few years: Stuart, Rick, Rob, Jimi, Elios, Alan, Caroline, Harpreet, Karen, Ruth and Siˆn. a • My office mates: Gareth, Craig, Mike, Kaiyan, Basma, Tamader, John and Rob. 22
  23. 23. 23• Other members of ISBE, including Tim Cootes, Carole Twining, Sue Astley, Paul Beatty, Jim Graham, Ian Scott and Tomos Williams, for their help at various times during my time as a PhD student.• The ISBE information technology support team for keeping things ticking.• Alexandre Nasrallah for proof-reading some of the chapters in this thesis.
  24. 24. FundingThe work described in this thesis was supported by the EPSRC as part of theMIAS-IRC project From Medical Images and Signals to Clinical Information (EP-SRC GR/N14248/01 and UK Medical Research Council Grant No. D2025/31). 24
  25. 25. About the AuthorIn holiday time during his A-level studies and first degree, Chris Rose workedfor Kraft Jacobs Suchard on a range of electronic and software projects. Hegraduated from The University of Manchester in 1999 with a 2.1 BEng (Hons)degree in Electronic Systems Engineering. He then worked for a small softwarehouse where he developed software and produced training materials for Ericsson.In 2000, he returned to The University of Manchester to begin a PhD in theDivision of Imaging Science and Biomedical Engineering, under the supervisionof Prof. Chris Taylor OBE. During this period he published the following papersrelated to the work in this thesis. • C. J. Rose and C. J. Taylor. An Improved Method of Computing Scale- Orientation Signatures. In Medical Image Understanding and Analysis, pages 5–8, July 2001 • C. J. Rose and C. J. Taylor. A Statistical Model of Texture for Medical Im- age Synthesis and Analysis. In Medical Image Understanding and Analysis, pages 1–4, July 2003 25
  26. 26. 26• C. J. Rose and C. J. Taylor. A Model of Mammographic Appearance. In British Journal of Radiology Congress Series: Proceedings of UK Radiolog- ical Congress 2004, pages 34–35, Manchester, United Kingdom, June 2004• C. J. Rose and C. J. Taylor. A Statistical Model of Mammographic Ap- pearance for Synthesis and Analysis. In International Workshop on Digital Mammography, 2004. (Accepted, pending.)• C. J. Rose and C. J. Taylor. A Generative Statistical Model of Mammo- graphic Appearance. In D. Rueckert, J. Hajnal, and G.-Z. Yang, editors, Medical Image Understanding and Analysis 2004, pages 89–92, Imperial College London, UK, September 2004• C. J. Rose and C. J. Taylor. A Holistic Approach to the Detection of Abnormalities in Mammograms. In British Journal of Radiology Congress Series: Proceedings of UK Radiological Congress 2005, page 29, Manchester, United Kingdom, June 2005• A. S. Holmes, C. J. Rose, and C. J. Taylor. Measuring Similarity between Pixel Signatures. Image and Vision Computing, 20(5–6):331–340, April 2002• A. S. Holmes, C. J. Rose, and C. J. Taylor. Transforming Pixel Signa- tures into an Improved Metric Space. Image and Vision Computing, 20(9– 10):701–707, August 2002
  27. 27. ‘As many truths as men. Occasionally, I glimpse a truer Truth, hiding in im-perfect simulacrums of itself, but as I approach, it bestirs itself and moves deeperinto the thorny swamp of dissent.’ From Cloud Atlas by David Mitchell. 27
  28. 28. Chapter 1Introduction1.1 IntroductionSince work for this thesis began, approximately 64 000 British women have diedfrom breast cancer [24]. Computer-aided X-ray mammography has been pro-posed as a way to help radiologists detect breast cancer at an early stage. Thisthesis describes work on generative statistical models of normal mammographicappearance. The ultimate aim of this strand of research is to be able to detectbreast cancer as a deviation from normal appearance. The generative propertyenables insight into what has been modelled successfully and where improvementis needed. Two generative statistical models of mammographic appearance aredescribed.This chapter presents a brief overview of the main subjects and motivations ofthis thesis. The chapter presents: 28
  29. 29. Chapter 1—Breast cancer 29 • An overview of breast cancer. • An overview of computer-aided mammography. • A description of novelty detection, the approach to breast cancer detection that motivates this thesis. • A description of generative models, and an explanation of why this property is vital to developing accurate models. • An overview of the organisation of the thesis.1.2 Breast cancerApproximately 11 500 women die from breast cancer each year in England andWales and it is the most common cancer in women (both in the UK and world-wide) [82]. It is possible to detect breast cancer at an early stage using X-raymammography; treatments are available and survival rates are good [82]. The UKNational Health Service Breast Screening Programme (NHSBSP) was initiated in1988 as a result of the Forrest report [66], published in 1987. All asymptomaticwomen aged 50–69 are invited for X-ray mammographic screening every threeyears. Radiologists visually inspect these X-ray images for signs of breast cancerand other problems. A more detailed background to breast cancer and screeningis presented in Chapter 2.
  30. 30. Chapter 1—Computer-aided mammography 301.3 Computer-aided mammographyResearch into the use of computers to detect breast cancer in mammograms hasbeen underway for about thirty years. In the most common approach, a com-puter automatically analyses a digitised mammogram and attempts to locatesigns of cancer. Detections are displayed to clinicians as prompts on a computerscreen or paper printout. Computer-aided mammography research has maturedto the point where, in 1998, the US Food and Drug Administration (FDA) gavepre-market approval to the ImageChecker system, developed by R2 TechnologyIncorporated. Three other systems have since been given FDA approval. How-ever, results from research into the effectiveness of these systems in the clinicalenvironment are mixed. A large prospective study recently showed that expertscreening radiologist performance in one academic practice was not improved bythe use of a computer-aided mammography system [76] (see Section 3.14 for amore detailed discussion). Other studies have indicated that such systems canhelp radiologists detect breast cancer earlier [8]. Psychophysical experimentsthat have studied the effect of the false prompt rate (i.e. incorrect detections ofcancer) on radiologist performance indicate that the number of true and falseprompts must be approximately equal if radiologist performance is to be im-proved [95]. Only 5% of screening mammograms have any form of abnormality.This suggests that a target rate should be approximately 0.0125 false positivesper image (see Chapter 3). Commercial systems operate at much higher falsepositive rates. For example, R2 Technology Incorporated claim that version 8.0of their ImageChecker algorithm achieves ‘1.5 false positive marks per normalcase at the 91 percent sensitivity level’ [149]. This perhaps explains why the
  31. 31. Chapter 1—Novelty detection 31commercial computer-aided mammography systems do not appear to improveradiologist performance. Research is needed to determine how computer-aidedmammography systems can be improved and how the false positive rate can bereduced to the target level. It is likely that much more sophisticated approacheswill be required. This thesis investigates one such approach, which is describedbriefly in the next section.1.4 Novelty detectionBreast cancer, as imaged in mammograms, can manifest itself in a number ofdifferent ways. Masses appear as “blob”-like features, microcalcifications appearas very small specks, architectural distortions subtly change the appearance ofthe breast tissue and spiculated masses have radiating linear structures. Each ofthese can be extremely subtle. Current computer-aided mammography methodstypically target only microcalcifications and masses (including spiculated masses),and treat each type of abnormality separately. A common approach is to locatecandidate abnormalities (often using ad hoc methods), compute measurements ofshape and texture (called features) and then use a classifier to classify the featuresinto clinically meaningful classes (e.g. malignant or benign). The approach has anumber of drawbacks: • Different features and classifiers are required for each type of abnormality. • The features and classifiers implicitly and incompletely model the appear- ance of normal and breast cancer tissue. These tissue types are subject to
  32. 32. Chapter 1—Generative models 32 significant variation. • It is often difficult to justify why a particular measure of texture or shape is better than another and what it actually represents. • The use of ad hoc methods risks the accidental adoption of assumptions about the data.The approach advocated in this thesis is novelty detection, which is motivatedby the fact that signs indicative of breast cancer are not found in pathology-freemammograms. If deviation from normality could be detected, then all types ofabnormality would automatically be detectable. This approach requires a modelof what normal mammograms look like. Mammograms vary dramatically, bothbetween women and between screening sessions, so such a model must be able tocope with this variability. Statistical models capture variability and are suited tonovelty detection problems because deviation from normality can be measured ina meaningful way within a rigorous mathematical framework. Abnormal mam-mograms are relatively rare in the screening environment, so there is much moredata with which to train a model of normality than there is to train a classifierthat has an “abnormal” class.1.5 Generative modelsIf novelty detection is to be used, then the underlying model must be able to“legally” represent any pathology-free instance and be unable to legally representabnormal instances. The only way to verify this is to be able to generate instances
  33. 33. Chapter 1—Overview of the thesis 33from the model; thus the model must be generative. Further, generative modelsmake it relatively easy to visualise what has been modelled successfully and whathas not. The generative property makes progress towards a model that accuratelyexplains mammographic appearance tractable. The aim of the research presentedin this thesis was to develop and evaluate generative statistical models of normalmammographic appearance with the ultimate aim of being able to detect breastcancer via novelty detection. Two models have been developed and evaluated.The first assumes that mammograms are textures and neglects the shape of thebreast and the spatial variability in mammographic texture. The model allowssynthetic textures to be generated and can be used in an analytical mode toperform novelty detection. The second is a generative statistical model of entiremammograms and addresses many of the problems associated with modellingmammographic appearance.1.6 Overview of the thesis • Chapter 2 presents background information on breast cancer, the clinical problem and the various imaging modalities that are used to diagnose the disease. • Chapter 3 presents a review of the computer-aided mammography litera- ture. • Chapter 4 describes work on improving the way that scale-orientation pixel signatures (a type of texture feature) are computed. A measure of
  34. 34. Chapter 1—Overview of the thesis 34 signature quality, based upon information theory, is developed and a simple classification experiment is presented. • Chapter 5 presents background information on the multivariate normal distribution and the Gaussian mixture model. These models are used ex- tensively in this thesis. • Chapter 6 presents Efros and Leung’s algorithm for texture synthesis and develops the method into a parametric statistical model of texture that can be used in both generative and analytical modes. Synthetic textures are presented. • Chapter 7 presents a psychophysical evaluation of synthetic mammo- graphic textures produced by the model developed in Chapter 6. A novelty detection experiment using simulated and real data is presented. • Chapter 8 presents an investigation into how Gaussian mixture models (and hence the class of texture model presented in Chapter 6) may be learned in low-dimensional principal components spaces. Texture synthesis and analysis using such models is discussed. • Chapter 9 describes a generative statistical model of entire mammograms and shows how synthetic mammograms may be generated. • Chapter 10 presents three evaluations of the synthetic mammograms gen- erated using the model of entire mammograms. • Chapter 11 summarises the work presented in the thesis.
  35. 35. Chapter 1—Summary 351.7 SummaryThis chapter presented a brief overview of the subjects, motivations and structureof this thesis. The next chapter presents an introduction to breast cancer andthe imaging modalities used to detect the disease.
  36. 36. Chapter 2Breast cancer2.1 IntroductionThis chapter introduces the clinical problem of breast cancer and describes howmedical imaging is used to detect the disease. The chapter discusses: • The anatomy of the breast. • Breast cancer and its risk factors, prevention, detection, treatment and survival. • The various medical imaging modalities used to detect breast cancer, par- ticularly X-ray mammography. 36
  37. 37. Chapter 2—Anatomy of the breast 372.2 Anatomy of the breastThe main purpose of the female breast is to produce and deliver milk to offspring.Additionally, breasts are a secondary sexual characteristic and serve to indicatesexual maturity. A brief description of the basic anatomy of the breast follows,but the interested reader is directed to [172] for a comprehensive descriptionwithin the context of mammography.The breast itself is a modified sweat gland and is composed of several structures,illustrated in Figure 2.1. Above the ribcage is the pectoral muscle. At the frontof the breast, and externally visible, is the nipple. Milk is produced in lobes anddelivered to the nipple by ducts. These are collectively referred to as parenchymalor glandular tissue; they are the functional structures of the breast, as opposed tobeing connective or supporting tissues. The areola exposes glands that lubricatethe nipple during breastfeeding. Circular radiating muscles behind the areolacause the nipple to become erect upon tactile stimulation, facilitating suckling.The lymphatic system is responsible for protecting the body from infection frommicroorganisms and antigens. This is achieved by transporting the microorgan-isms and antigens to the lymph nodes where they are dealt with by the body’scellular immune system. Blood is transported to and from the breast by the vas-culature. Blood delivers oxygen and nutrients and removes waste products. Thestructure of breast is supported by Cooper’s ligaments and also contains adipose(fatty) tissue, neither of which are shown in Figure 2.1.
  38. 38. Chapter 2—Anatomy of the breast 38Figure 2.1: Basic anatomy of the normal developed female breast.Key:A Pectoral muscleB VasculatureC LobeD DuctE Lymph node and lymphatic systemF NippleG Areola
  39. 39. Chapter 2—Breast cancer 392.3 Breast cancerBreast cancer is almost exclusively a disease that affects women: 11 491 womenand 82 men died from breast cancer in England and Wales in 2002 [82]. We willnow briefly examine the background to the disease.2.3.1 What is breast cancer?We will now briefly discuss the cellular basis of cancer1 . Our bodies are composedof cells, which typically carry all of the genetic information required to determinehow we will grow. Cancer is an umbrella term for a group of diseases that causecells in the body to reproduce in an uncontrolled manner.Cells have several abilities, one of which is reproduction. Reproduction is achievedvia cell division. At each cell division, the genetic material contained within themother cell is copied to the daughter cells via a robust mechanism. This robustmechanism can detect errors in the genetic material contained within the cell andcan instruct the cell to “commit suicide” via programmed cell death (PCD)2 toprevent the erroneous information from being propagated.Recent cancer research has suggested that an enzyme called telomerase [77] playsan important role. At each normal cell division, genetic material at the endsof the chromosomes is lost. To prevent useful genetic material from being de-stroyed, the ends of chromosomes have redundant repeating genetic sequences 1 The interested reader is directed to [36] for background material on cellular biology 2 PCD is also referred to as apoptosis.
  40. 40. Chapter 2—Breast cancer 40called telomeres. Part of these sequences are lost at each cell division, but thegenetic information specific to the organism is preserved. If telomeres becometoo short, or are deleted entirely, the body interprets the genetic sequence asbeing broken. In this situation, the cell can be instructed to perform PCD, orreparative mechanisms can be employed. These reparative mechanisms can intro-duce genetic mutations. Cancer cells are “immortal” in that they do not respondto PCD instructions. Telomerase—an enzyme that builds new telomeres—is ex-pressed in approximately 90% of cancers, and the telomeres in cancer cells do notshorten. It is believed that telomerase may be the reason why cancer cells areimmortal. Cancer cells divide rapidly until they are forcefully destroyed (e.g. bymedical intervention or the death of the host organism). Cancer cells are there-fore genetically abnormal, but the exact genetic nature of cancer is not yet fullyunderstood.Cancers are named after their originating organ (i.e. breast cancer originates inthe breast and is composed of pathological breast tissue). Cancer cells can breakaway from their original location and travel through the vascular or lymphaticsystems. These cells may lodge to form secondary cancers in other parts of thebody. This process is called metastasis. The new cancer is named after theoriginating tissue and new location, for example secondary breast cancer of thebrain. Breast cancer generally develops in the ducts (ductal cancer), but mayalso develop in the lobes (lobular cancer).The terms cancer and tumour are not synonymous. A tumour may be benign ormalignant. Benign tumours are abnormal growths, but do not grow uncontrol-lably or metastasise, and are not necessarily life-threatening. The word cancer
  41. 41. Chapter 2—Breast cancer 41is synonymous with the phrase malignant tumour. Benign tumours can becomemalignant, but malignant tumours do not become benign. Cancer is caused by anumber of factors that can act individually or in combination [5]. These include: • External factors, e.g. exposure to: – Chemicals—particularly tobacco use – Infectious organisms – Radiation • Internal factors, e.g. : – Inherited and metabolic genetic mutations – Hormones – Immunity responsesBreast cancers can be described as being in situ (i.e. they have not spread fromtheir originating duct or lobule), and are often cured [4]. Alternatively, breastcancers can be described as being invasive or infiltrating (i.e. they have brokeninto the surrounding fatty tissue of the breast). The severity of an invasive breastcancer is related to the stage of the disease, which describes how far it has spread(e.g. it is confined to the breast, or surrounding tissue, or has metastasised todistant organs). The following terms are often used to describe the stage of thedisease [37]:
  42. 42. Chapter 2—Breast cancer 42 • Stage 1 – The tumour is no larger than 2 cm in diameter. – The lymph nodes in the armpit are unaffected. – The cancer has not metastasised. • Stage 2 – The tumour is between 2 cm and 5 cm in diameter, and/or the cancer has spread to the lymph nodes under the armpit. – The cancer has not spread elsewhere in the body. • Stage 3 – The tumour is larger than 5 cm in diameter. – The cancer has spread to the lymph nodes under the armpit. – The cancer has not spread elsewhere in the body. • Stage 4 – The tumour may be any size. – The lymph nodes in the armpit are often affected. – The cancer has spread to other parts of the body.2.3.2 Predictive factorsThe risk of developing breast cancer increases with age, as Figure 2.2 illustrates.In the USA, 95% of new cases and 96% of breast cancer deaths in the period
  43. 43. Chapter 2—Breast cancer 43Figure 2.2: Incidence of breast cancer in England.The incidence of breast cancer in English women in 2001 per 100 000 populationas a function of age. Linear interpolation is used between data points. Source ofdata: National Statistics [21].1996–2000 occurred in women aged 40 and older [4].Risk factors can be grouped by relative risk3 [4]: • Relative risk > 4.0 – Inherited genetic mutations (particularly BRCA1 and/or BRCA2). – Two or more first-degree relatives4 diagnosed with breast cancer at an early age. 3 Relative risk is defined as the ratio of the probability of the disease in the group exposedto the risk, to the probability of the disease in a control group. 4 A first-degree relative is a mother, father, sister, brother, daughter or son
  44. 44. Chapter 2—Breast cancer 44 – Post-menopausal breast density. • Relative risk > 2.0 and ≤ 4.0 – One first-degree relative with breast cancer. – High dose of radiation to the chest. – High post-menopausal bone density. • Relative risk > 1.0 and ≤ 2.0 – Late age at first full-term pregnancy (> 30 years). – Early menarche (< 12 years). – Late menopause (> 55 years). – No full-term pregnancies. – Recent oral contraceptive use. – Recent and long-term hormone replacement therapy. – Tall. – High socioeconomic status. – Post-menopausal obesity.Tobacco use is not necessarily linked to breast cancer. Some studies have shownthat smoking is not associated with the disease, while others have indicated alink [43]. Effects due to smoking are confounded by alcohol use, which correlateswith both tobacco use and increased breast cancer risk. Alcohol is the dietaryfactor most consistently associated with increased breast cancer risk [4] and breastcancer risk increases by about 7% per alcoholic drink consumed per day [112].
  45. 45. Chapter 2—Breast cancer 452.3.3 PreventionBreast cancer cannot be prevented due to the environmental and inherited riskfactors. However it should be possible to reduce the incidence of cancers that canbe attributed to lifestyle factors via behavioural modification.One of the most important lifestyle changes that can be made is the managementof alcohol consumption: even moderate alcohol use is associated with increasedbreast cancer risk [4]. Moderate alcohol consumption has a cardio-protectiveeffect, so advice on alcohol consumption must consider more than just breastcancer risk [182]. Women who are not known to have an increased risk of breastcancer are advised to adopt a healthy lifestyle by limiting alcohol, avoiding to-bacco use and by maintaining a healthy weight through regular exercise and adiet that is low in fats and high in fruit and vegetables. However, this adviceis not specific to breast cancer, and instead considers evidence for all commondiseases [182]. Women who are known to have an increased risk of breast cancershould be advised accordingly.There is debate within the clinical community about how women should be ad-vised regarding tobacco use and its effect on breast cancer risk. Some favourhonest advice that states that the balance of evidence shows no or little increasedrisk, while others favour advice that emphasises the evidence that indicates thatthere is an increased risk in some circumstances, and that women should be dis-couraged from smoking because of other associated risks (e.g. lung cancer) [43].General practitioners should consider the risk of breast cancer when prescrib-ing hormonal medications such as hormone replacement therapy or oral contra-
  46. 46. Chapter 2—Breast cancer 46ceptives. Women at very high risk may be offered prophylactic mastectomy ortreatment with a drug such as Tamoxifen [4].2.3.4 Clinical detectionBreast cancer is most successfully treated at an early stage and it has been rec-ommended for the past 30 years or so that women perform regular breast self-examination (BSE). In recent years this advice has been challenged. A Canadianmeta-analysis failed to find evidence that BSE reduces breast cancer mortality,but found that BSE results in more benign breast biopsies and increased patientdistress [12]. The study recommended that women should not be taught BSE, butthe author stresses the difference between BSE and breast self-awareness, and en-courages the latter [118]. An American study found that women who had benignbiopsies after performing BSE tended to perform BSE less frequently as a result[13]. Advice on BSE and breast self-awareness needs to informed by evidence ofthe risks of increased biopsy rate and distress with the potential benefits. TheAmerican Cancer Society currently recommends that women optionally performmonthly BSE [4].Some countries have implemented national screening programmes—where womenare invited for asymptomatic X-ray imaging of the breast (mammography) todetect cancer at an early stage. The International Breast Cancer Screening Net-work currently has 27 member countries who have pilot or established nationalor subnational screening programmes [101]. These members are predominantlydeveloped countries in North America, Western Europe and the Far East. The
  47. 47. Chapter 2—Breast cancer 47UK National Health Service Breast Screening Programme (NHSBSP) was initi-ated in 1988 as a result of the Forrest report [66]. Women between the ages of50 and 70 (formerly 65) are invited for screening every three years. Women nowhave two views of each of their breasts imaged at each screening session, resultingin 13% more breast cancers being detected in 2002/3 compared with the previ-ous 12 months when a single view was used [133]. A 14 year follow-up of theEdinburgh randomised trial of breast screening, published in 1999, showed thatbreast screening reduced breast cancer mortality by 13% [2]; the NHSBSP an-nual review for 2004 [133] claims that mortality dropped by 30% in the precedingdecade, though this success cannot be attributed to breast screening alone.The benefits of asymptomatic breast screening are disputed and some argue thatscreening may even be detrimental to the health of women. Gøtzsche and Olsenargue that there is no reliable evidence that screening mammography reducesmortality and that screening may result in distress and unnecessarily aggressivetreatment [73, 136]. However, their conclusions are largely based upon meta-analyses which debunk studies that show that screening has a positive effect,rather than upon data that show that screening has a negative effect. Anothercriticism of screening mammography is economic. While the cost per womanscreened is low (approximately £40 [134] in the UK), another picture emergeswhen one looks at the cost per life saved. The UK NHSBSP currently costsapproximately £52M per year and is estimated to save approximately 300 livesper year [134]. This equates to an approximate average cost of £173 300 perlife saved. By the year 2010, it is estimated that the NHSBSP will save 1 250lives per year; this will bring the cost per life saved down to approximately
  48. 48. Chapter 2—Breast cancer 48£41 600 (assuming other factors do not change). In 1995, the cost per life savedby the Ontario, Canada screening programme was estimated to be £558 000,based upon the cost of a single mammography examination and the estimatednumber of women who would need to be screened in order for one life to be saved[186]. Variation in the cost of screening can be attributed to the environmentand manner in which screening and treatment are implemented. It is a matterfor those responsible for public health policy to determine the best use of availableresources given the evidence for and against screening mammography.Molecular tests are now available that can detect some of the BRCA geneticmutations [4] and these may be used routinely in the future. Consideration isbeing given to a UK-wide programme to use magnetic resonance imaging to screenpre-menopausal women at high genetic risk of breast cancer [28].2.3.5 TreatmentTreatment for breast cancer is dependent upon several factors: the stage of dis-ease and its biological characteristics, patient age and the risks and benefits asdetermined by clinicians and the patient [4]. Surgery to remove the canceroustissue is common, and the type of surgery is chosen to balance the need to re-move the cancer with the disfigurement that the surgery will cause. Surgery mayinvolve (in order of increasing disfigurement): • Lumpectomy—which can be employed when the cancer is localised—involves removing the “lump” and a border of “normal” tissue which is checked to ensure that all cancerous tissue has been removed.
  49. 49. Chapter 2—Breast cancer 49 • Simple mastectomy (or total mastectomy) involves the removal of the entire breast. • Modified radical mastectomy involves the removal of the entire breast and underarm lymph nodes. • Radical mastectomy involves the removal of the breast, underarm lymph nodes and chest wall muscle. This type of surgery is now used less frequently as less disfiguring approaches have proved to be effective [4].Surgery is often used alongside chemotherapy, hormone therapy, biologic (alsocalled immune and antibody) therapy or radiotherapy. Chemotherapy, hormoneand biologic therapies are systemic treatments in that they are applied to theentire body—rather than a specific organ—with the intention of killing cancercells that may have metastasised.Chemotherapy is a drug treatment that kills rapidly dividing cells. This includescancer cells as well as some types of normal cells, such as blood and hair cells.Chemotherapy, in combination with surgery, has been shown to deliver five yearsurvival rates of between 50% and 70% [25]Hormone therapy attempts to prevent the growth of metastasised cancer cellsby blocking the effects of hormones (such as oestrogen) that can promote theirgrowth. An anti-oestrogen drug called Tamoxifen has been used successfully,but recent research shows that the aromatase inhibitor anastrozole significantlyincreases disease-free survival over five years compared to Tamoxifen [75].
  50. 50. Chapter 2—Breast cancer 50Trastuzumab (marketed under the name Herceptin) is a biologic therapy thattargets cancer cells which produce an excess of a protein called HER2. Whencombined with chemotherapy, trastuzumab treatment can reduce the relativerisk of mortality by 20%, but can increase the risk of heart failure [119].In contrast to the systemic treatments, radiotherapy (also called radiation ther-apy) is targeted at specific locations. High energy radiation is focused on areas ofthe body affected with cancer (such as the breast, chest wall or underarm area).Alternatively, small radiation sources, called pellets, can be implanted into thecancer. There is no significant difference in survival between women who havesmall breast tumours removed by lumpectomy compared to those who also re-ceive radiotherapy, but women who receive radiotherapy have a reduced risk oftheir cancer returning and therefore require less additional treatment [64].2.3.6 SurvivalThe one and five year survival rates for English women diagnosed with breastcancer between 1993 and 2000 were 92.6% and 75.9% respectively [148]. Forcomparison, in the same period the mean one and five year survival rates inboth sexes for lung cancer—the second most common cancer in women and mostcommon cancer in men—were 21.6% and 5.5% respectively. In the USA, thefive year survival rate for women with breast cancer is 87% [4]. There is also anassociation between low socioeconomic status, poor access to medical care andadditional illness and low survival rates [4].
  51. 51. Chapter 2—Breast imaging 512.4 Breast imagingThis section introduces X-ray mammography—the most common form of clinicalimaging used to detect breast cancer—and briefly discusses the other imagingmodalities that may be used.2.4.1 X-ray mammographyX-rays were discovered by Wilhelm Conrad R¨ntgen in 1895, who was awarded othe first Nobel prize for physics for his discovery. X-rays are high-frequencyelectromagnetic radiation (30 PHz–60 EHz) and are useful in diagnostic imagingbecause the dense tissues in the body are more likely to absorb X-rays (i.e. theyare radio-opaque) while the soft tissues are less likely to absorb X-rays (i.e. theyare radiolucent). X-rays are formed by accelerating electrons from a heated cath-ode filament towards an anode. The interaction of the high energy electrons withthe anode emits radiation in the X-ray spectrum. This radiation is then directedtowards the patient.X-rays are detected using photographic film or digitally (e.g. using a charge-coupled device). By placing a body part between the X-ray source and detector,it is possible to form an image that spatially describes the X-ray absorption ofthe body part. This image will be a two-dimensional projection of the three-dimensional structure.X-rays were first used to investigate breast cancer almost a hundred years ago[160]. An X-ray mammogram is obtained by imaging the breast compressed
  52. 52. Chapter 2—Breast imaging 52Figure 2.3: The mediolateral-oblique and cranio-caudal views.The diagram illustrates the directions of compression used in the mediolateral-oblique (MLO) and cranio-caudal (CC) views. The MLO view is illustrated onthe left in blue and the CC view is illustrated on the right in red.between two parallel radiolucent plates. Different directions of compression allowclinicians to view the three-dimensional structure of the breast in more than oneway. This allows ambiguities caused by occlusion or other perspective effects tobe minimised. Two common views are the cranio-caudal view (CC—“head totail”) and the mediolateral-oblique view (MLO; where the compression is angledapproximately 45◦ to the CC view). These are illustrated in Figure 2.3.X-ray mammography is the imaging modality of choice for breast cancer investiga-
  53. 53. Chapter 2—Breast imaging 53tion and the UK National Health Service Breast Screening Programme generateshundreds of thousands of mammograms each year [133]. X-ray mammographyis favoured because of its high resolution (required to image microcalcifications)and low cost (approximately £40 per woman screened [134]).Fully digital systems are increasing in quality and popularity. The advantages offully digital systems may include: • Direct digital image acquisition. • Increased sensitivity compared to film-based methods, permitting lower ra- diation dosage. • Immediate image display and enhancement. • Improved archival and transmission possibilities (including remote image analysis by human or computer).It is expected that fully digital mammography will soon supersede film-basedmammography. Fully digital mammography is likely to benefit the computer-aided mammography research community, as the digitisation step required forfilm-based mammography is an impediment to the collection of useful imagedata.Although X-ray mammography remains the most useful imaging modality forbreast cancer, it is dependent upon the use of radiation, which itself can causecancer. It is likely that some cancers are caused by the screening programme.Efforts are made to monitor and minimise radiation dose.
  54. 54. Chapter 2—Breast imaging 54Mammograms are most commonly read visually as X-ray films, although com-mercial computer-aided mammography and digital systems are being used—particularly in the USA (see Section 3.13 for a discussion of commercial sys-tems). In the screening environment, dedicated viewing stations are loaded witha batch of mammograms. The mammograms are positioned so that left andright breasts—and CC and MLO views, if both are available—can be compareddirectly. Radiologists use strategies to try and ensure that ‘danger zones’ are al-ways examined. In the UK screening environment, it is typical that a radiologistwill take an average of 30 s to read each patient’s mammograms. Radiologistsrecord their assessments and difficult cases are likely to be discussed with col-leagues. If double reading is used—where two radiologists independently readeach mammogram—a protocol will be followed to combine the assessments ofeach radiologist.Women for whom screening indicates abnormality are recalled for further investi-gation such as a magnification X-ray or ultrasound. The diagnosis of breast cancermay be confirmed by analysing a tissue sample extracted by biopsy. Because theinterpretation of mammograms is a difficult task and is subject to human error,biopsies are sometimes performed on women who do not have cancer. The recallprocess is traumatic and biopsy—like any surgery—causes discomfort and worry.The benign biopsy rate in 2002/3 was 1.20 per 100 000 women screened [133].The benign biopsy rate has improved with advances in diagnostic technique.The radiological signs of breast cancer are described in Chapter 3; example imagesare given for the most common indicative signs.
  55. 55. Chapter 2—Breast imaging 552.4.2 UltrasonographyUltrasound imaging works by sending high-frequency sound pulses into the tissuesof a patient using an array of transceivers that is placed on the patient’s skin.When these sounds encounter tissue interfaces, some of the sound is reflected backto the array. The distances from the skin surface to the tissue interfaces are thencomputed based upon the time between the pulses being sent and received andthe speed of the sound wave. One-dimensional transceiver arrays produce imageslices, while two-dimensional arrays produce volumes. These are presented tothe ultrasonographer on a computer display. Ultrasound images are generated inreal-time and are useful in breast cancer investigation when a suspicious featurehas been identified by X-ray mammography or when a patient has reported withsymptoms [63]. It is particularly useful for differentiating between cysts (whichare benign) and malignant masses.2.4.3 Magnetic resonance imagingThe human body is composed largely of water, which in turn is composed largelyof hydrogen. A hydrogen atom has an unpaired proton, and so has a non-zeronuclear spin. In magnetic resonance imaging (MRI), the patient is placed in astrong uniform magnetic field (usually between 0.23T and 3.0T). This forces thespins of the protons in the hydrogen atoms to align with the field. Almost allprotons will be paired, in that each member of a pair will be oriented at 180◦ tothe other, but some will not. A radio frequency pulse can temporarily deflect theunpaired protons.
  56. 56. Chapter 2—Breast imaging 56The imparted energy is released as electromagnetic radiation as the spins realignwith the field. The realignment signal is characteristic of tissue type and canbe measured. By applying an additional graduated magnetic field it is possibleto localise the signals, since their frequency is related to their position in thegraduated field. The received signals are recorded in a frequency space calledK-space. An inverse Fourier transform is applied to form the correspondingspatial volumetric data. Voxel values represent tissue type and hence the patient’sanatomy.The spatial resolution of current clinical MRI systems is not as good as that of X-ray mammography, so microcalcifications cannot be imaged. However, MRI hasseveral advantages over X-ray imaging: patients are exposed to little radiation,three-dimensional data can be acquired and contrast agents can be used. Un-fortunately, MRI is currently too expensive for routine asymptomatic screeningfor breast cancer, but may be useful for screening younger women whose familyhistory and/or genetic status suggest that are at increased risk of breast cancer[28].2.4.4 Computed tomographyIn computed tomography (CT), an X-ray source is rotated around the patient’smajor axis. Whereas the beam of a conventional X-ray can be considered to beconical (i.e. 3-D), CT typically uses a “triangular” beam (i.e. a very thin cone).The attenuation of the beam as it passes through the patient is recorded by anX-ray detector positioned opposite to the source. The attenuation data from all
  57. 57. Chapter 2—Summary 57orientations can be combined to compute a 2-D image “slice”, where each locationin the slice represents the X-ray attenuation of the tissue to which it corresponds.By slowly passing the patient through the rotating mechanism, 3-D data can beacquired. Although it is possible to use CT for breast imaging, it is rarely usedto diagnose breast cancer [117]. The technique can be useful for surgical planningand to assess the patient’s response to treatment.2.4.5 ThermographyAdvanced cancers promote angiogenesis—the development of a blood supply tothe tumour. Regions containing more blood are hotter than others, and this heatmay be detectable on the skin surface. Thermography is an imaging techniquethat forms maps of the emission of infrared radiation [117]. These maps enableclinicians to look for asymmetries in the heat patterns on the breasts that mayresult from angiogenesis or the enhanced metabolic processes that occur in atumour. Compared to X-ray mammography, thermography lacks specificity andresolution.2.5 SummaryThis chapter presented an introduction to breast cancer and the imaging modal-ities used to detect the disease. In summary: • Breast cancer is a significant public health issue. While many countries
  58. 58. Chapter 2—Summary 58 now have screening programmes to help detect the disease at an early and treatable stage, the image interpretation task is performed visually and is subject to human error. • X-ray mammography is the most useful imaging modality because of the high image quality and low cost. X-ray mammography allows the anatomy of the breast to be imaged at very high resolution, allowing very small indicative signs of breast cancer—such as microcalcifications—to be seen. • X-ray mammography does have some drawbacks (e.g. the use of radiation, 2-D projection of the 3-D structure, potential for poor patient positioning, potential for poor film exposure and development). • Other imaging modalities have their uses in detecting and diagnosing breast cancer, but X-ray mammography for screening is unlikely to be replaced by any of the currently available imaging techniques.
  59. 59. Chapter 3Computer-aided mammography3.1 IntroductionThis chapter presents a review of the computer-aided mammography literature.The chapter reviews: • Image pre-processing. • Automatic prediction of breast cancer risk. • The appearance of common signs of breast cancer and approaches to their detection by computer. • Methods of evaluating computer-aided mammography systems. • Common image databases. • Available commercial systems. 59
  60. 60. Chapter 3—Computer-aided mammography 60 • Research on computer-aided prompting of radiologists.We discuss the typical approach to computer-aided mammography and the prob-lems associated with it. We propose how this problem might be solved.3.2 Computer-aided mammographyAlthough screening mammography has been shown to reduce breast cancer mor-tality [133, 2], it suffers from some problems that computer vision systems mightbe able to solve, for example: • Double reading improves cancer detection rate [57], but it cannot always be performed in the screening environment due to human resource or economic limitations. Computer vision systems could act as a second reader. • The interpretation of mammograms is a difficult task and human error does occur [97]. Computer vision systems could deliver a guaranteed minimum quality of screening and potentially catch some of the errors made by radi- ologists. • Cancer is detected in less than 1% of women screened [133]. A computer vision system that could accurately dismiss mammograms that were normal could dramatically reduce radiologist workload.The most commonly proposed approach to computer-aided mammography isprompting, in which a computer system automatically analyses a digitised mam-mogram and places prompts on a representation of the mammogram—e.g. an
  61. 61. Chapter 3—Image enhancement 61image of the digitised mammogram displayed on screen or a paper printout—toindicate the presence and location of possible signs of abnormality. A radiol-ogist would then consider these prompts alongside their own interpretation ofmammograms. Prompting is discussed further in Section 3.14. The following re-view of computer-aided mammography research generally assumes the promptingapproach, but other paradigms are also discussed.3.3 Image enhancementImage enhancement describes approaches that change the characteristics of im-ages to make them more amenable to other tasks (e.g. inspection by humans orfurther processing by computer). This includes noise suppression or equalisation,image magnification, grey-level manipulation (e.g. brightness and contrast im-provement) and feature enhancement or suppression. Generic image enhancementtechniques are well-established and are routinely used within more sophisticatedalgorithms.A commonly-used algorithm is histogram equalisation [168]. Histogram equali-sation attempts to modify the grey-level values in an input image such that thehistogram of those values matches a specified histogram, which is often flat. Ifa flat target histogram is specified, the result will be an image that uses theentire range of grey-levels, with increased contrast near maxima in the originalhistogram, and decreased contrast near minima. A possible problem with theapproach is that the image is modified based upon global image statistics, whichmight not be appropriate in local contexts. Local histogram modification tech-
  62. 62. Chapter 3—Image enhancement 62niques use local neighbourhoods, while adaptive histogram modification methodsuse local contextual information [168].Averaging filters replace pixel values with the average of those within a localneighbourhood. Using the mean tends to blur edges (as it is essentially a low-pass filter) while using the median does not. Bick et al. used median filtering toremove noise spikes [15, 168]. Lai et al. used a modified median filter where theset of pixels considered by the filter was restricted to exclude those that were toodissimilar to the pixel that the filter was centred on [116]. The approach achievedbetter edge preservation compared to the standard median filter. Such methodsare “coarse” in that they rarely have any model of the domain in which theyoperate (e.g. such filters might mistake film noise for small microcalcificationsbecause they have no “knowledge” about those two classes of image feature).Zwiggelaar et al. used a directional recursive median filter to construct mam-mographic feature descriptors [192] (see Section 3.8 and Chapter 4 for a moredetailed description of such descriptors).Grey-level values can be manipulated via the Fourier domain. For example,image smoothing can be used in an attempt to suppress noise by attenuatinghigh-frequency components [168]. However, methods that operate only in theFourier domain lack spatial information, and so important context may not beavailable. Wavelets address this problem as they can be used to describe imagesin terms of both space and frequency, and are commonly used in mammography.Wavelet analysis was used by Qian et al. [147] to enhance microcalcifications byselectively reconstructing a subset of the wavelet sub-band images. Comparedto Fourier methods, wavelets allow the characteristics of the signal(s) of interest
  63. 63. Chapter 3—Image enhancement 63to be specified more precisely. Wavelets were used in place of ad hoc texturefeatures by Campanini et al. [35] and used to statistically model mammographictexture by Sajda et al. [159] (see Section 3.7 for a more detailed discussion ofthese methods).In contrast to the frequency-based methods such as Fourier and wavelet analy-sis, mathematical morphology analyses images based upon the shape of imagefeatures. It can be used to remove image features of a given shape and size(e.g. Dengler et al. considered microcalcification candidates [55]). A possibleproblem with mathematical morphology is that a specification of shape is re-quired: image features that vary dramatically in shape may require very manysuch specifications, leading to implementation issues. A detailed discussion ofmathematical morphology can be found in Chapter 4.Noise equalisation is important because machine learning systems are under-pinned by statistical methods which often implicitly assume that the noise hasparticular characteristics. By equalising the noise, the properties of the imagedata are likely to be more closely matched to the assumptions made by the al-gorithms that operate on that data. Image noise in digitised mammograms maybe considered to vary as a function of grey-level pixel value [106, 166]. Smithet al. used a radiopaque step-wedge phantom to estimate this relationship in orderto correct the non-uniformity [166], but a phantom is likely to be a nuisance in ascreening environment. Karssemeijer and Veldkamp described noise equalisationtransforms where the noise is estimated from the image itself—rather than from aradiological phantom—using the standard deviation of local contrasts [106, 180].It was demonstrated that equalising the noise using the approach improved the
  64. 64. Chapter 3—Image enhancement 64performance of detection algorithms. This is likely to be due to the explanationgiven above.Highnam and Brady [88, 86] proposed a physics-based model of the mammo-graphic image acquisition process to convert digital mammograms to an imagerepresentation they call hint . In the hint representation pixel values represent thethickness of the “interesting” (non-fat) tissue. The technique relies upon knowingseveral parameters that describe the X-ray imaging process, such as the thicknessof the compressed breast, tube voltage, film type and exposure time. By modellingthe imaging process, the appearance under a set of “standard” imaging conditionscan be predicted, leading to the Standard Mammogram Form (SMF) [88]. It isnot always practical to measure the various imaging parameters during routinescreening and radiologists do not train with such standardised mammograms. Itseems likely that working with mammograms where pixel values represent tangi-ble quantities will lead to better detection algorithms, but digital mammogramsare not widely available in hint form. One of the goals of the eDiaMoND projectwas to make such data available to researchers (see Section 3.12) [23].The identification of curvilinear structures is useful in detecting and classifyingspiculated lesions (see Section 3.8). Cerneaz and Brady developed a physics-basedmodel that was used to model the expected attenuation of curvilinear structures[39]. The authors assumed that such structures are elliptical in cross-section andso would appear to have strong second derivative components in the image. Thesecond derivative was used to enhance candidate pixels and a skeletonisation al-gorithm [168] was used in further processing. Physics-based models would haveto be extremely complex and specific to properly explain the appearance of mam-
  65. 65. Chapter 3—Breast segmentation 65mograms. It therefore seems likely that approaches based upon image data itselfhave more potential. Most research on digital mammography has used this latterapproach.3.4 Breast segmentationThe identification of the breast border is a common task in digital mammog-raphy and the development of reliable automatic methods is important. Suchinformation is required to limit the search for abnormalities to the breast area(particularly when algorithms are computationally expensive), or so that someform of breast shape analysis can be performed (see Chapter 9 for an example).Locating the breast border is a non-trivial task due to the variation both betweenwomen and inherent to the X-ray acquisition process.Grey-level thresholding is a common approach to breast segmentation. Twothresholds are generally sought. The first discards pixels with low grey-levels,assuming them to belong to non-breast radiolucent objects (such as air). Thesecond discards pixels with high grey-levels, assuming them to belong to non-breast radiopaque objects (such as film markers). The selection of these thresh-olds is generally non-trivial, and other information such as shape is often alsoused. Byng et al. determined these thresholds manually [33]. They can also bedetermined by analysing the shape of the image histogram [42]. Although thresh-olding can provide an initial estimate of the boundary, the approach is generallyconfounded by features such as film markers, and much more sophisticated ap-proaches that have some model of what the segmented image should look like are
  66. 66. Chapter 3—Breast segmentation 66generally used.Chandrasekhar and Attikiouzel analysed the shape of the cumulative grey-levelimage histogram to identify a characteristic ‘knee’ which represents the bound-ary between background and breast tissue [42]. Adaptive thresholding yielded aninitial segmentation which was then modelled by polynomials. This segmentationwas subtracted from the original image and the result was thresholded, resultingin a binary image describing the breast and non-breast regions. Morphologicaloperations were used to remove artifacts arising from film scratches. An imple-mentation of Chandrasekhar and Attikiouzel’s algorithm was subjectively goodenough to approximately limit the operation of detection algorithms to the breastregion, but was not good enough to allow the shape of entire mammograms to bemodelled in the work described in Chapter 9.Lou et al. [121] quantised mammograms using k-means clustering and inspectedhorizontal slices through the quantised images to determine the direction of adecrease in pixel value. The direction was used to estimate the left-right orien-tation of the breast. Pixel values on the skin-air border were found to lay in oneof three quantised pixel values. This information was used to generate an initialestimate of the breast border. Actual mammogram pixel values were sampledalong normals to the initial estimate. Pixels values along normals to the breastborder will decrease from values associated with the edge of the breast to thoseassociated with the non-breast region. Linear models of pixel value as a func-tion of distance along the normals were used to refine the estimate of the breastborder. A rule-based search was then used to further refine the breast border.Finally, a B-spline was used to link and smooth the located breast border points.
  67. 67. Chapter 3—Breast segmentation 67The approach is sensible because the skin-air border should be relatively easy tomodel. However, a common confounding feature is the placement of film markers.These would pose an occlusion problem to methods that do not also use a modelof legal breast shape.The active shape model (ASM) [48] has been used in a number of medical and non-medical applications. An ASM models the statistical variation of shape associatedwith a particular class of object and uses a statistical model of pixel values alongnormals to the shape boundary to legally deform the model to fit to an objectin an image. Smith et al. used an ASM to locate the breast outline [165]. TheASM can therefore be viewed as a generalisation of the approach proposed byLou et al. [121]. The two main problems with the ASM are that it does not useall the image information in its search strategy and it requires an initialisationthat is already a good approximation to the final solution. The former wasrectified by the Active Appearance Model [47]. A better approach to breastborder segmentation might be to build a low resolution appearance model (similarto that described in Chapter 9) and then search over the model parameters to findthose that best describe a low resolution version of the mammogram in question.This would provide a low resolution estimate of the boundary. The estimatecould then be refined at high resolution using a model of the skin-air boundarytransition. Refinements could be propagated upwards to the low resolution modelwhere illegal (unlikely) refinements could be rejected.
  68. 68. Chapter 3—Breast density and risk estimation 683.5 Breast density and risk estimationPost-menopausal breast density is a high risk factor for breast cancer [4]. Also,because cancer develops from dense (glandular) tissue it may be masked in mam-mograms by normal dense tissue. Automatic assessment of the density of breastsand the risk associated with that density may be helpful to radiologists, particu-larly as automated methods can provide stable independent measurements, whilethere will be inherent variability in assessments made by humans.Byng et al. proposed a simple interactive approach where users of their systemselected grey-level thresholds to segment the breast region and dense tissue [33].The proportion of dense to total area was used as a measure of breast density. Theapproach is reasonable because the mammographic brightness indicates density,but it seem that a similar approach using the calibrated hint measure wouldbe more stable. Additionally, the manual selection of thresholds will introducevariation between and within users; a fully automated system could avoid suchproblems.Taylor et al. investigated sorting mammograms into fatty and dense sets usinga multi-resolution non-overlapping tile-based method. A number of statisticaland texture measures, computed for each tile, were evaluated and local skewnesswas found to best discriminate between the classes [175]. The reader is hereafterreferred to Section 3.15 for a discussion of ad hoc texture descriptors.Wolfe proposed that parenchymal patterns are related to breast cancer risk [185]and developed a radiological lexicon for describing the dense and fatty char-
  69. 69. Chapter 3—Breast density and risk estimation 69acteristics of mammograms, known as Wolfe grades. The relationship betweenparenchymal pattern and breast cancer risk has been confirmed by Boyd et al. [22]and van Gils et al. [178]. Tahoces et al. statistically modelled various texture de-scriptors to predict Wolfe grades [173].Caldwell et al. used fractal dimension—a measure of the complexity of a self-affine object—with mammographic images (considered as surfaces) to measuretextural characteristics. They classified mammograms by Wolfe grade, basedupon average fractal dimension and the difference between that average and thefractal dimension of a region near the nipple [34].Karssemeijer divided the breast into radial regions so that the distances to theskin line were approximately equal. Grey-level histograms were computed foreach region and the mean standard deviation and skewness were used to classifymammograms by Wolfe grade using a k-nearest neighbour classifier [107]. Thesuccess of the method can probably be attributed to the statistical characterisa-tion of the appearance of the mammograms.Zhou et al. used a rule-based method that classified mammograms according toprototypical characteristics in their grey-level histograms. This classification wasused to automatically select a threshold with which to segment the dense tissue.The proportion of dense to total breast area was then computed [189]. Detectinga well-understood feature in a 1-D function (the histogram) can be reasonablyeasy, although the approach is dependent upon the stability of these histogramcharacteristics.A Gaussian mixture model of texture descriptors, learned using the Expectation-
  70. 70. Chapter 3—Microcalcification detection 70Maximisation (EM) algorithm, was used by Zwiggelaar et al. to segment mammo-grams into six tissue classes [193]. The area of dense tissue—as segmented by themodel—as a proportion of total area was used in a k-nearest neighbour frameworkto classify mammograms into one of five density classes. Although learning thedistribution of texture features allows a principled statistical approach to be used,it is not clear that the clustering produced by the EM algorithm would necessarilycorrespond to a clustering that an expert might produce. Further, the EM algo-rithm aims to find the best fit of a model of a probability density function to thedata, rather than to partition the data (as Algorithm 3 in Chapter 5 explains, inthe EM algorithm every data point belongs to every model component, so thereis no actual partitioning). Dedicated clustering methods might have been moreappropriate. Gaussian mixture models are discussed in some detail in Chapter 5and a proof of the convergence property of the EM algorithm is presented inAppendix A.3.6 Microcalcification detectionMicrocalcifications are tiny (approximately 500 µm) specks of calcium. A clusterof microcalcifications can indicate the presence of an early cancer. Microcalci-fications can sometimes be detected easily as they can be much brighter thanthe surrounding tissue. However, small microcalcifications may appear to bevery similar to film or digitisation noise. Scratches on the mammographic filmcan sometimes be mistaken for bright microcalcifications, particularly by auto-mated methods. A mammogram containing an obvious microcalcification cluster
  71. 71. Chapter 3—Microcalcification detection 71is shown in Figure 3.1.Karssemeijer describes an iterative scheme for updating pixel labels, based uponthree local image descriptors (local contrast at two spatial resolutions and an es-timate of local orientation). Pre-processing was used to achieve noise equalisationusing information from a radiological phantom. A Markov random field modelwas used to model the spatial constraints between four pixel classes (background,microcalcifications, lines or edges, and film emulsion errors) and a final labellingwas achieved via iteration [105]. Local methods are appropriate for individualmicrocalcification detection because of their small size, but are inappropriate forcluster detection. Detecting clusters of microcalcifications is important becausetheir form contains important information about the cause of the cluster (e.g. ma-lignancy). In addition, it can be difficult to determine when Markov random fieldmodels have converged.Veldkamp et al. [179] classified microcalcification clusters as being malignant orbenign by estimating the likelihood of them being malignant. Individual micro-calcifications were detected using Karssemeijer’s method. Discs were then centredon each microcalcification and the boundaries of the intersection of the discs werecomputed. Microcalcifications were clustered according to which boundary theywere located within. The procedure was performed for both mediolateral-obliqueand cranio-caudal views, and correspondences were determined between clustersin each view. Features used for classification included the relative location of thecluster in the breast, measures of calcification distribution within the cluster andshape features. The likelihood of malignancy was computed as the ratio of thenumber of malignant to benign neighbours in the k-nearest neighbourhood. The
  72. 72. Chapter 3—Microcalcification detection 72Figure 3.1: An example microcalcification cluster.The location of the microcalcification cluster is indicated by the red circle. Thebottom left image shows a magnification of the cluster; the bottom right imageshows a histogram equalised version of the magnified cluster. Source: The mam-mographic image analysis society digital mammogram database [171].
  73. 73. Chapter 3—Microcalcification detection 73approach is sensible because it acknowledges that it is the clusters that are im-portant, includes information about the form of clusters and delivers a statisticalmeasure of the likelihood of malignancy.Bocchi et al. [18] designed a matched filter to enhance microcalcifications by as-suming a Gaussian model of microcalcifications and a fractal model of mammo-graphic background. A region growing algorithm was used to segment candidatemicrocalcification clusters and to describe the location of each candidate micro-calcification. An artificial neural network was used to discriminate between mi-crocalcifications and artifacts of the filtering stage. Segmented regions were char-acterised by fractal descriptors and these were used in a second artificial neuralnetwork to identify true clusters. The underlying assumptions of the approach—a Gaussian model of microcalcifications and a fractal model of mammographicbackground—while being reasonable models, are not true. A more realistic modelof these image features may have improved their results.False positive elimination was addressed by Ema et al. who used edge gradientsat signal-perimeter pixels to eliminate features such as noise or other artifacts[61]. Zhang et al. used a “shift-invariant” artificial neural network to segmentcandidate microcalcifications [188]. The size and “linearity” of candidate micro-calcifications were analysed to reject false positives due to vessels. Both of thesemethods implicitly attempt to model the neighbourhood around true microcalci-fications and direct modelling of that neighbourhood—such as that described inChapter 6—might be more appropriate.
  74. 74. Chapter 3—Masses 743.7 MassesMasses are abnormal growths and may be malignant or benign. Masses may ap-pear to be localised bright regions, but are often very similar in appearance to,and may be obscured by, normal glandular tissue. Detection and discriminationof masses can be difficult even for expert mammography radiologists. Malignantmasses are often characterised by linear features radiating from the mass, calledspicules, and we discuss methods for detecting and assessing spiculation in Sec-tion 3.8. A mammogram containing an obvious circumscribed mass is shown inFigure 3.2.A common approach to the detection and classification of masses is to determinecandidate mass regions and then compute descriptors for the region designedto allow discrimination between true and false detections. The problems thatresearch addresses is how candidate mass locations are found, which featuresshould be extracted and how they should be combined to yield a classification.Karssemeijer and te Brake compared two methods for segmenting masses [177].The first grew a region from a seed location, expanding the region if neighbour-ing pixels were above a certain threshold. The region growing was repeated usinga number of thresholds and the “best” region was selected using a maximumlikelihood method that considered the distribution of pixel grey-levels inside andoutside the region. The second method was a dynamic contour defined by a setof connected vertices, similar to the method proposed by Kass et al. [111]. Thevertices were accelerated towards the mass boundary using internal and externalforces. The internal forces served to encourage compactness and circularity of the

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