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Title:
Efficient suspicious region segmentation algorithm for computer aided diagnosis of breast cancer based on tomosynthesis imaging
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Samala, Ravi K
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University of South Florida
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Perona-malik
Anisotropic
3D diffusion
Fuzzy c-means
Spatial fuzzy c-means
Dissertations, Academic -- Electrical Engineering -- Masters -- USF
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Abstract:
ABSTRACT: Computer aided diagnostic tool can aid the radiologist in the early detection of breast cancer. Even though mammography is considered to be the gold standard for breast cancer detection, it is limited by the spatial superposition of tissue. This limitation is the result of a using a two dimensional, (2D), representation of a three dimensional, (3D), structure. The limitation contributes to and results in misclassification of breast cancers. Tomosynthesis is a limited-angle 3D imaging device that overcomes this limitation by representing the breast structure with 3D volumetric data.This research, on tomosynthesis imaging, was a critical module of a larger research endeavor for the detection of breast cancer. Tomosynthesis is an emerging state-of-the-art 3D imaging technology. The purpose of this research was to develop a tomosynthesis based, efficient suspicious region segmentation, procedure for the breast to enhance the detection and diagnosis of breast cancer. The 3D breast volume is constructed to visualize the 3D structure of the breast region. Advanced image processing and analysis algorithms were developed to remove out-of-plane artifacts and increase the Signal Difference to Noise Ratio, (SDNR), of tomosynthetic images. Suspicious regions are extracted from the breast volume using efficient and robust clustering algorithms.A partial differential equation based non-linear diffusion method was modified to include the anisotropic nature of tomosynthesis data in order to filter out the out-of-plane artifacts, which are termed "tomosynthetic noise", and to smooth the in-plane noise. Fuzzy clustering algorithms were modified to include spatial domain information to segment suspicious regions. A significant improvement was observed, both qualitatively and quantitatively, in segmentation of the filtered data over the non-filtered data. The 3D segmentation system is robust enough to be used for statistical analysis of huge databases.
Thesis:
Thesis (M.S.E.E.)--University of South Florida, 2006.
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by Ravi K. Samala.
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Efficient Suspicious Region Segmentation Al gorithm for Computer Aided Diagnosis of Breast Cancer based on Tomosynthesis Imaging by Ravi K. Samala A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering Department of Electrical Engineering College of Engineering University of South Florida Major Professor: Wilfrido A. Moreno, Ph.D. Wei Qian, Ph.D. James Leffew, Ph.D. Date of Approval: October 18, 2006 Keywords: perona-malik, anisotropic, 3D di ffusion, fuzzy c-means, spatial fuzzy c-means Copyright 2006, Ravi K. Samala

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ACKNOWLEDGEMENTS I would like to express my deepest grat itude to, my supervisor, Dr. Xuejun Sun for giving me the opportunity to work with in the Digital Medical Imaging Program, (DMIP), at the Moffitt Research Center, (MRC) Dr. Sun has been a constant guiding force for my research. I would like to express my gratitude to Dr. Wei Qian. Dr. Qian assumed the responsibility for directing my research effo rts during the final phases, which involved the two crucial events of defending my resear ch efforts and the writing of my thesis. I would like to express my sincere thanks to, my major professor, Dr. Moreno for showing his confidence in me right from th e beginning and constant ly reminding me of my goals. It was Dr. Wei Qian’s and Dr. Mo reno’s joint efforts that paved the way for the successful completion of my thesis. Special thanks to Dr. James T. Leffew for volunteering his time and effort to be in my committee and review my thesis. I thank my colleagues. Anand and Vi dhya provided support unselfishly and offered valuable hints. Raghav, Praveen, Ann and Darshan, my friends, provided moral support and were always there for me. I am grateful to Dinesh Divakaran for his encouragement and valuable suggestions th roughout my masters’ studies at USF. Last but certainly not least, I thank my parents and my brothers for constantly encouraging me and reminding me that nothing is impossible to achieve.

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i TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES iv LIST OF ABBREVIATIONS viii ABSTRACT x CHAPTER 1 INTRODUCTION 1 1.1 Motivation 1 1.2 Thesis Goals 3 CHAPTER 2 BREAST CANCER 5 2.1 Anatomy 5 2.2 Breast Cancer Facts 6 2.3 Mammography 8 2.4 Tomosynthesis 9 2.4.1 Acquisition Principal 10 CHAPTER 3 BACKGROUND 14 3.1 Overview of Past Research 14 3.2 Filtering 18 3.3 Segmentation 19 3.4 Proposed Methodology 19 CHAPTER 4 FILTERING 26 4.1 Image Pre-processing 26 4.1.1 Background and Artifact Removal 26 4.1.2 Inversing 29 4.1.3 Histogram Equalization 30 4.2 Perona-Malik, (PM), Anisotropic Filtering 31 4.2.1 Choosing the Value of the Learning Coefficient, ( ) 32 4.2.2 Choosing the Value for K 36 4.2.3 2 Dimensional Diffusion 43 4.2.4 3 Dimensional Diffusion 47

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ii CHAPTER 5 SEGMENTATION 52 5.1 Clustering 52 5.2 Fuzzy Clustering 53 5.3 Cluster Validity Functions 56 5.4 Spatial Fuzzy C-means Clustering 57 5.5 Qualitative Analysis 59 5.6 Quantitative Analysis 64 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS 67 6.1 Conclusions 67 6.2 Recommendations 68 REFERENCES 69

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iii LIST OF TABLES Table 2.1: Probability of Invasive Breast Cancer Within Selected Age Intervals 7 Table 5.1: Variation of the Validity Functions with the Number of Clusters and Type of Clustering 64

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iv LIST OF FIGURES Figure 1.1: Block Diagram of the Effective Suspic ious Region Segmentation 4 Figure 2.1: Anatomy of the Breast 5 Figure 2.2: Anatomy of the Breast with Lobules and Ducts 6 Figure 2.3: A. Standard 2D Left Medi o-Lateral Oblique, (LMLO), View with Obscure Lesion. B. Tomosynthesis Slice with Patient Lesion 10 Figure 2.4: Motion Parallax 11 Figure 2.5: Tomosynthesis Acquisition Pr incipal 12 Figure 3.1: Representative Images of a Spiculated Lesion Using a MRC CAD Method 16 Figure 3.2: Representative Sub-Images of Three Spiculated Lesions with Varying Levels of Subtle and Parenchyma Tissue Density Backgrounds 17 Figure 3.3: Plots of the Diffusion Coeffici ent with Respect to the Ratio of the Gradient and K 21 Figure 3.4: Plots of the Flow Function with Respect to the Ratio of the Gradient and K 21 Figure 4.1: (a) Typical Tomo synthesis Slice (b) Histogram 27 Figure 4.2: Segmentation of the Breast Region Using (a) Canny Edge Detection (b) Fuzzy C-means Clustering (c) Histogram of the Segmented Tomosynthesis Slice of the Breast 28 Figure 4.3: 3D Tomosynthesi s Volume Views (a) Brea st Volume with the Artifacts and Background (b) Breast Volume After Removal of the Artifacts and Background 29 Figure 4.4: (a) Inversed Segmented Tomosynthesi s Breast Slice (b) Histogram 30

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v Figure 4.5: (a) Histogram Equalized Inversed Segmented Tomosynthesis Breast Slice (b) Equalized Histogram 31 Figure 4.6: Images and Normalized Line Profile for the Chosen ROI with the Iterations = 500 and K = 500 32 Figure 4.7: Images and Line Profile of the ROI for = 0.01 33 Figure 4.8: Images and Line Profile of the ROI for = 0.05 33 Figure 4.9: Images and Line Profile of the ROI for = 0.1 34 Figure 4.10: Images and Line Profile of the ROI for = 0.15 34 Figure 4.11: Images and Line Profile of the ROI for = 0.2 35 Figure 4.12: Variation of the SDNR with 36 Figure 4.13: Images and Normalized Line Profile for the Chosen ROI with the Iterations = 50 and L = 0.01 37 Figure 4.14: Images and Normalized Line Profile for the Chosen ROI with the Iterations = 50, L = 0.01 and K = 50 37 Figure 4.15: Images and Normalized Line Profile for the Chosen ROI with the Iterations = 50, L = 0.01 and K = 500 38 Figure 4.16: Tomosynthesis Breast Slice Chosen for the Investigation of the Optimum Value for K 38 Figure 4.17: (a) Filtered Horizontal S lice (b) Variation of SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice; Iterations = 500, L = 0.5, K = 400 39 Figure 4.18: (a) Filtered Horizontal S lice (b) Variation of SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice; Iterations = 500, L = 0.5, K = 500 40 Figure 4.19: (a) Filtered Horizontal S lice (b) Variation of SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice; Iterations = 500, L = 0.5, K = 600 41 Figure 4.20: (a) Filtered Horizontal S lice (b) Variation of SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice; Iterations = 500, L = 0.5, K = 700 42

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vi Figure 4.21: Variation of SDNR with Va riation of K 43 Figure 4.22: (a) 4 Adjacent Pixels (b) 8 Adjacent Pixels 44 Figure 4.23: (a) Original ROI (b ) Filtered ROI with 4 point PM Diffusion 44 Figure 4.24: Normalized Line Profile for 4 Point PM Diffusion 45 Figure 4.25: Filtered ROI with 8 Point PM Diffusion 45 Figure 4.26: Normalized Line Profile for 8 Point PM Diffusion 46 Figure 4.27: Quantitative Differe nce for PM Diffusion Using (a) 4 Adjacent Pixels (b) 8 Adjacent Pixels 46 Figure 4.28: (a) 4 In-Plane Pixe ls (b) 8 In-Plane Pixels (c) 8 In-Plane Pixels and 2 In-Dep th Pixels 47 Figure 4.29: (a) Filtered Horizontal Sli ce (b) Variation of the SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice; 2D, [4, 0, 0], Window 48 Figure 4.30: (a) Filtered Horizontal Sli ce (b) Variation of the SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice; 2D, [4, 2, 2], Window 49 Figure 4.31: (a) Filtered Horizontal Sli ce (b) Variation of the SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice; 3D, [8, 0, 0], Window 50 Figure 4.32: (a) Filtered Horizontal Sli ce (b) Variation of the SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice; 3D, [8, 2, 2], Window 51 Figure 5.1: Flow Chart of the Fuzzy C-Means Clustering Algorithm 54 Figure 5.2: FCM of the Tomosynthesis Volume for 3 Clusters (a) In-Plane Tomosynthesis Sli ce (b) Cluster 1 (c) Cluster 2 (d) Cluster 3 55 Figure 5.3: Segmented Tomosynthesis Volume for an In-Plane Slice 56 Figure 5.4: Spatial Function of the SFCM 58

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vii Figure 5.5: (a) FCM (b) SFC M with a 5x5 Window Where p = 1, q = 1 and Clusters = 3 60 Figure 5.6: (a) FCM (b) SFC M with a 5x5 Window Where p = 1, q = 1 and Clusters = 4 60 Figure 5.7: (a) FCM (b) SFC M with a 5x5 Window Where p = 1, q = 1 and Clusters = 5 61 Figure 5.8: 3D Clustering of a Singl e Slice (a) FCM (b) SFCM with a 5x5x3 Window (c) SFCM with a 5x5x5 Window 61 Figure 5.9: (a) FCM Clustered In-Plane Slice, (b) Filtered FCM Clustered In-Plane Slice, (c) Slice Along the In-Depth Di rection of (a) (d) Slice Along the In-Depth Direction of (b) 62 Figure 5.10: (a) FCM Clustered In-Plane Slice, (b) Filtered SFCM Clustered In-Plane Slice, (c) Slice Along the In-Depth Di rection of (a) (d) Slice Along the In-Depth Direction of (b) 63 Figure 5.11: 2D Comparison Between FCM and SFCM for 26 Slices 65 Figure 5.12: Variation Validity Functions Vpc and Vpe for SFCM and FCM Algorithms 66

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viii LIST OF ABBREVIATIONS DBT Digital Breast Tomosynthesis FFDM Full-field Digital Mammography FN False Negative FP False Positive MGH Massachusetts General Hospital BCDDP Breast Cancer Detection Demonstration Project MLM Maximum Likelihood Method PM Perona-Malik FCM Fuzzy C-means Clustering SFCM Spatial Fuzzy C-means Clustering SDNR Signal Difference to Noise Ratio MQSA Mammography Quality Standards Act LMLO Left Medio-Lateral Oblique View DMIP Digital Medical Imaging Program MRC Moffitt Research Center CAD Computer-Aided Diagnosis ACS American Cancer Society NN Neural Networks SAA Shift-and-Add

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ix BP Back Projection PDE Partial Differential Equations CT Computed Tomography

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x EFFICIENT SUSPICIOUS REGION SEGMENTATION ALGORITHM FOR COMPUTER AIDED DIAGNOSIS OF BREAST CANCER BASED ON TOMOSYNTHESIS IMAGING Ravi K. Samala ABSTRACT Computer aided diagnostic tool can aid th e radiologist in the early detection of breast cancer. Even though mammography is considered to be the gold standard for breast cancer detection, it is limited by the spa tial superposition of ti ssue. This limitation is the result of a using a two dimensional, (2D), representati on of a three dimensional, (3D), structure. The limitation contributes to and results in miscla ssification of breast cancers. Tomosynthesis is a limited-angle 3D imaging device that overcomes this limitation by representing the breast structure with 3D volumetric data. This research, on tomosynthesis imaging, was a critical module of a larger research endeavor for the detection of breast cancer. Tomosynthesis is an emerging stateof-the-art 3D imaging technology. The purpos e of this research was to develop a tomosynthesis based, efficient suspicious regi on segmentation, procedure for the breast to enhance the detection and di agnosis of breast cancer. The 3D breast volume is constructed to visualize th e 3D structure of the breast region. Advanced image

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xi processing and analysis algorithms were deve loped to remove out-o f-plane artifacts and increase the Signal Difference to Noise Ra tio, (SDNR), of tomosynthetic images. Suspicious regions are extracted from th e breast volume using efficient and robust clustering algorithms. A partial differential equation based nonlinear diffusion method was modified to include the anisotropic nature of tomosynthesi s data in order to filter out the out-of-plane artifacts, which are termed “tomosynthetic noi se”, and to smooth the in-plane noise. Fuzzy clustering algorithms were modified to include spatial domain information to segment suspicious regions. A significant improvement was observe d, both qualitatively and quantitatively, in segmentati on of the filtered data over th e non-filtered data. The 3D segmentation system is robust enough to be used for statistical analysis of huge databases.

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1 CHAPTER 1 INTRODUCTION Breast cancer is the second leading mort ality cause in the United States, [ACS 2006]. The key to surviving breast cancer is early detection and treatment, [Yankaskas 2001]. It has been estimated that in 2006, 214,640 new cases of invasive breast cancers will be diagnosed, with 212,920 in women and 1,720 in men. Approximately 40,970 women and 460 men are expected to die of breast cancer in the year 2006. Additionally, 61,980 new cases of in-situ breast cancer are expected to occur in women in 2006 in addition to invasive breast cancer, [CFF 2006] Excluding cancer related to skin, breast cancer is considered to be the most common cancer and occurs in approximately one in three women in the United States, [ACS 2006]. Digital Breast Tomosynthesis, (DBT), is expected to overcome the inherent limita tions of Full-Field Digital Mammography, (FFDM), which uses a 2 dimensional projec tion of a 3-dimensional object for early cancer diagnosis. 1.1 Motivation Even though mammography is considered to be the most cost-effective diagnostic method for breast cancer detection, it possess es serious limitations, which arise due to false negative and false positive interpreta tions. The sensitivity of mammography is affected by the overlapping of dense fibr oglandular tissue and parenchyma, which

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2 obscure lesions in dense breasts, [Chan 2005]. The rate of diagnosis of smaller tumors, ( 2.0cm), increased by 2.1% per year from 1988 to 1999 and remained fairly constant. This statistic indica tes the need for the replacement of mammography with a better diagnostic method, which can increase the in cidence of detection of small tumors. False Negative Diagnosis One of the primary reasons for a false negative diagnosis in mammography, which misses breast cancer, is due to the s uper-imposition of normal breast tissue on the cancerous region. Approximately 30% of breast cancers are missed in conventional mammography, [Yankaskas 2001]. False negatives also occur because of the small size of the cancerous growth. False Positive, (FP), Diagnosis False positives result in the classificati on of normal breast tissue as cancerous because of the spatial super-imposition of ti ssue. It was reported by Wu et al, at Massachusetts General Hospital, (MGH), th at approximately 25% of FPs occurs. Additionally, it has been reported that close to threefourths of all post-mammogram biopsy results turn out to be benign lesions by Yankaskas. Super-imposition of normal tissue sometimes causes irregular architectural distortion leading to a false classification of breast cancer. Mammograms do not provide spatial relations hip of structures such as location and depth within the breast region. Howeve r, tomosynthesis does provide the important spatial relationships. Spatial relationships of tissue structur es are important for diagnosis

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3 or analysis of the cancerous region. Afte r 25 years of data collection by the Breast Cancer Detection Demonstration Project (BCDDP), with 280,000 volunteers, it was concluded that mammograms missed 10% of cancers in women younger than 50 and 5% in women older than 50, [Cunningham 1997 ] The false negative rate of mammography is approximately 8-10%, which accounts for the improvements in breast cancer diagnosis standards. Tomosynthesis is the new diagnostic x-ra y imaging system, which overcomes the inherent limitation of mammography. 1.2 Thesis Goals Tomosynthesis slices, obtained from 11 projections over a 50 angle, were reconstructed using the Maximum Li kelihood Method, (MLM), to form 40-60 tomosynthesis slices with 0.1mm x 0.1mm x 1mm resolution along X, Y and Z axes. The Z axis represented the in-depth direction a nd the X and Y axes represented the in-plane resolution. Figure 1.1 presents a block diag ram of the effective suspicious region segmentation.

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4 Reconstruction of Tomosynthesis slices 3D Volumetric Visualization 3D Anisotropic Diffusion Segmentation Image Pre-processing Reconstruction of Tomosynthesis slices 3D Volumetric Visualization 3D Anisotropic Diffusion Segmentation Image Pre-processing Figure 1.1: Block Diagram of Effec tive Suspicious Region Segmentation Perona-Malik anisotropic diffusion was used to filter out the ‘tomosynthetic noise’ or the structured noise. It was also used to smoot h the volumetric image in order to remove noise from the low frequency ra nge. Image pre-processing was performed to remove artifacts and background. In addition, histogram equalizati on and inversion was used to modify the dynamic range and c ontrast of the tomosynthesis volume. Segmentation of suspicious regions was achie ved using robust fuzzy c-means clustering, (FCM), and spatial fuzzy c-means, (SFCM), clustering.

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5 CHAPTER 2 BREAST CANCER 2.1 Anatomy The major anatomical structures of the br east are lobules, ducts, connective tissue, fatty tissue and lymphatic tissue. Lobules are where milk producing glands exist and ducts are passages from lobules to the nipple. Breast cancer, which occurs in lobules, is termed “lobular carcinoma in-situ” and breast ca ncer, which occurs in ducts, is termed “ductal carcinoma in-situ”. Figure 2.1 pictur es the breast and its anatomical features. Figure 2.1: Anatomy of the Breast Source: Massachusetts General Hospital Cancer Resource Room, Boston, MA Breast cancer is classified as benign, in situ or invasive. The classification depends upon the nature and location of the cancer cells. If the abnormality does not grow uncontrollably then it is benign in nature. In-situ breas t cancer is confined within

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6 the lumps or the lobules and has not spread to other areas. Invasive breast cancer is a type that spreads to other areas. Figure 2.2 pictures the areas of the breast where lobular carcinoma and ductal carcinoma originate. Figure 2.2: Anatomy of the Br east with Lobules and Ducts Source: Massachusetts General Hospital Cancer Resource Room, Boston, MA 2.2 Breast Cancer Facts A huge amount of statistical analysis has been perfor med in the area of breast cancer diagnosis. In particular, the relations hip between early diagnos is and survival rate has been analyzed extensively. These analys es have produced critical information. For example: It was estimated that in the year 2005, 211,240 new cases of invasive breast cancers, and an estimated 58,490 cases of in-situ breast cancer would be diagnosed in women. Approximately 40,410 women were expected to die of breast cancer in the y ear 2005, [Imaginis 2006].

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7 The incidence of breast cancer and the asso ciated mortality rate increases with age. Women over the age of 40 are c onsidered to be highly vulnerable and represent potential candidates for fr equent checkup. During 1998 2002, 95% of new cases and 97% of deaths associated with breast cancer occurred in women over the age of 40, [ACS 2006]. The probability of developing invasive breast cancer, within selected age intervals, is presented in Table 2.1[CFF 2006]. Table 2.1: Probability of Invasive Breast Cancer Within Selected Age Intervals Age Interval Percentage Birth – 39 0.48% 40 – 59 4.11% 60 – 69 3.82% 70 – Older 7.13% Birth – Death13.22% Even though men are considered to be at low risk of acquiring breast cancer, approximately 1690 cases of breast cancer were expected to occur in 2005, which was 1% of all breast cancer s in 2005. Approximately 460 men were expected to die of breast cancer in 2005, [ACS 2006]. Between 1975 and 1990 the death rate increased by 0.4% annually. However, between 1990 and 2002, the death rate decr eased by 2.3% annually. The decrease was due to early detection improvement s in the treatment of breast cancer.

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8 2.3 Mammography Mammography is an x-ray imaging device, which uses a rotati ng anode to project x-rays onto the targeted area. Depending upon the density of the tissu e, the absorption of x-rays varies. A detector, which either a screen film or a digital device, is used to capture the x-rays after passing through the target. Regular mammography screening and follo w-up examinations have produced a significant decrease in the mortality due to breast cancer. The principal reason for the death rate decrease is attributed to the ear ly detection of the carcinoma prior to the occurrence of any physical symptoms, [C DC 2005]. With the introduction of mammography from 1980 to 1987, incidence of detection of smaller tumors, ( 2.0cm), more than doubled. During the same time peri od, the incidence of detection of large tumors, ( 3.0cm), decreased by 27%, this was directly related to earlier detection of the cancer. In-situ breast cancer is considered to be the initial stage of the disease. Detection of the cancer at this stage increases the survival rate. Mammography, as a detection mechanism, has proven to be an effec tive tool since its introduction in 1980. Digital mammography, which is also cal led Full field digital mammography, (FFDM), is different from sc reen-film mammography. The scr een used to capture the xrays in the screen-film device is replaced by digital detectors, which convert the x-rays into electrical signals in the FFDM device. The electrical signals, of the FFDM device, are converted and saved in digital format. The digitized data can be viewed on a computer or printed on a similar film as that related to screen-film mammography.

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9 2.4 Tomosynthesis In contrast to Mammography, tomosynthe sis is a 3D x-ray imaging system. Typically tomosynthesis acquire s 11 projection images over a 500 angular range. The imaging system uses an a-Si, (CsI:Tl), flat -panel detector, which possesses an acquisition time of less than 7 seconds. The detector a nd breast positions are fixed during the image acquisition and while the x-ra y source is being rotated. Mammography is the 2D representati on of the 3D breast structure. Tomosynthesis is a 3D, volum etric, representation, which is absent of morphological information. As Dobbins points out, the advantages of tomographic imaging over conventional projection radiogra phy are 3D visualization of anatomical structures and improved contrast of local structures. Breast tissue is extremely dense, which could obscure a lesion on mammography. The existence of this inherent spatial supe rposition of tissue in mammograms increases the difficulty for cancer detection. In most cases the tumor does not have a significant difference in intensity, color or texture from the surrounding tissue to be distinguishable. Thus, a lesion could be well hidden within the normal tissue, [Chen 2003]. Figure 2.3 illustrates the difference between the imager y of a lesion produced by mammography and tomosynthesis.

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10 Figure 2.3: A. Standard 2D Left Medio-Lateral Oblique, (LMLO), View with Obscure Lesion. B Tomosynthesis Slice with Patent Lesion Photo Courtesy of Mercury Com puter Systems Life Sciences. Even though tomosynthesis was introdu ced before Computerized Tomography, it did not attract very much atte ntion. Currently, due to advanc es in x-ray detector devices with respect to large detection area, low noi se and fast acquisition time, tomosynthesis has attracted renewed interest. 2.4.1 Acquisition Principal Tomosynthesis takes advantage of motion pa rallax. Motion parallax produces an apparent shift in the position of an object against a backgroun d as a result of a change in the observer position, [Parallax 2006]. Fi gure 2.4 illustrates the concept of motion parallax.

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11 Figure 2.4: Motion Parallax Viewing from (a) the triangular object a ppears to be in front of the background 1 However, viewing from (b) the object appears to be in front of background 3. The image presented in Figure 2.5 illustr ates the methodology associated with a tomosynthesis imaging device. Instead of 11 x-ray sources only 3 x-ray sources are considered for simplicity. A basic shift-a nd-add reconstruction method is used to reconstruct the image at the plane of interest. (a) (b) View from (a) View from (b) 1 2 3

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12 Figure 2.5: Tomosynthesi s Acquisition Principal Even though the in-plane re solution of the reconstructe d tomosynthesis volume is comparable with that of mammography, the in -depth resolution is low. Thus the volumetric image is anisotropic in nature. According to the Mammography Quality St andards Act, (MQSA), regulations, a single view dose of mammography cannot ex ceed 0.3 rad. The average dose currently used is 1.6 rad. The radiation dose for tomosynt hesis images, at each angle, is equal to or slightly greater than the radiation dose associated w ith standard single-view mammography, [Niklason 1997], [Wu 2003]. The breast is the second most radiosensitive organ in human body, [Rozhkova 2000]. Therefore, radiation dosage level 1 23 Not shifte d Shifted s1 s2 s3 Slice s

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13 is an important parameter, which must be considered, when designing a diagnostic imaging device.

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14 CHAPTER 3 BACKGROUND In the past 15 years, the laboratory at the Moffitt Research Center, (MRC), which is concerned with the Digital Medical Imag ing Program, (DMIP), has developed a series of robust procedures. These procedures have been mainly applied for microcalcification cluster detection and mass detection in digi tal mammograms. Successes associated with the procedures have been demonstrated in many reported clinical evaluations and through the issuance of U.S. Patents, [Qian W. US Patents 1996, 1998a -b, 1999a-b], [Qian, 1993, 1994a-b, 1995a-c, 1996, 1997, 1998a-b, 1999a-b, 2000, 2001, 2002a-b, 2003, 2004 and 2005], [Sun, 2004]. All of research associat ed with the DMIP forms a strong foundation for the tomosynthesis suspicious region segmentation paradigm. 3.1 Overview of Past Research The computer-aided diagnosis, (CAD), of mammography, screen film and digital, has been vigorously studied by Dr. Wei Qian and a large number of other investigators over the past decade. The use of current C AD methods for mass detection, when applied to Retrospective Case Analysis, has been wi dely reported. These methods demonstrate a sensitivity of in the range of 80-90% and an average false positive, (FP), detection rate of (2-4)/image [Petrick 1996, Mendez 1998, Polakowski 1997, Giger 1998]. CAD methods using Retrospective Case studies have proven to be useful for the reduction of the the

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15 variability of reading mammograms when used as a second opinion strategy. The use of current CAD methods for mass detection, when applied to Prospective Case Analysis, have also been studied, Studies of these me thods report a significant drop in sensitivity to less than 70% and a similar FP detection ra te, [Nishikawa 1998]. However, despite the sensitivity reduction, these methods, when appl ied to Prospective Case Analysis, have proven to be useful for detection of missed interval cancers. In past years, despite considerable effort by many researchers, the study of CAD procedures has not been able to produce acceptable levels of both detec tion sensitivity and FP rate for clinical requirements, [Sahiner B., Chan H. P., 1999 and Hadjiiski L. M., 1999]. The drawbacks of CAD methods can be attri buted to the lack of a full optimization mechanism. However, a novel, fully automatic and hi ghly efficient method was developed by the MRC during prior research sponsored by the American Cancer Society, (ACS). The ACS sponsored project was concerned w ith parameter optimization using FROC experiments, which reveals the future of CAD design. The preliminary work on CAD for the dete ction and diagnosis of breast cancer was concerned with the search for optimized so lutions that have more realistic success in clinical trials. These preliminary effo rts focused on iterative and systematic improvements of CAD modules, which em ployed sound signal processing and engineering principles. Dr. Qian, at the MRC, has developed over several years a novel nonlinear, multistage and adaptive filtering algorithm for image noise suppression and artifact reduction. These types of filteri ng capabilities are required for implementation of high order wavelet transforms, which are se nsitive to noise, [Qian 1993 and 1994a]. Dr. Qian has also employed multi-resolution and multi-orientation wavelets for improved

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16 feature extraction using the unique propertie s of wavelet transforms. The wavelet transforms were utilized in standard and tr ee-structured forms, which were implemented on filter banks to preserve image details that inherently allow adaptive approaches, [Qian 1997a, b and 1998a, b]. Additionally, single and multistage Neural Networks, (NN), with significantly increased convergence speed, for more efficient classification and use of features, were investigated as input at different NN st ages, [Zheng and Qian, 1994, Qian 2002]. Figure 3.1 presents representative im ages of the results achieved by the application of a MRC CAD method for analyzin g a Spiculated lesion. Figure 3.1: Representative Images of a Spiculated Lesion Using a MRC CAD Method The various images of Figure 3.1 represent: a: A raw image at 180 m, b: Directional features from a directi onal wavelet transform, (DWT), using N=8 directions,

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17 c: segmented image using the multi-resolution tree structured wavelet transform, (TSWT), for enhancement and an adaptive clustering, (AC), module for segmentation of the suspicious area, d: Suspicious areas detected with spic ulations. An obvious lesion is presented, which allows the shape of the mass and the extent of the spiculation to be visually identified. The MRC research has been applied to mass detection, which led to the awarding of five United States patents for Dr. Wei Qian and several journal publications and proceedings, [Qian 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001 and 2002]. Figure 3.2 presents representative results obt ained by applying CAD methods to three Spiculated Lesions with varying levels of subtle and parenchyma tissue density backgrounds. Figure 3.2: Representative Sub-images of Three Spiculated Lesions with Varying Levels of Subtle and Parenchyma Tissue Density Backgrounds

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18 The top row of images in Figure 3.2 presents the raw image data. The bottom row of images in Figure 3.2 presents the segmented lesion with spiculations. 3.2 Filtering Image processing is generally used to enhance the image for human viewing and to process the image for feat ure measurement, [Russ 1995]. The current research was more concerned with image enhancement for feature enhancement. Noise can be introduced at image formation, recording or at the transmission stage. Noise is typically present in the form of shar p transitions in the image. Therefore, image smoothing eliminates noise but also intr oduces blurring, which reduces th e contrast of the tissue in the case of medical images. Image enhancement increases the contrast of the images but does not eliminate noise. Therefore, an idea l filtering process must be employed if both image smoothing and enhancement are to be achieved at the same time. Tomosynthesis is a limited angle image form ation technique. Th erefore, the most basic reconstruction algorithms of “shift-and-add”, (SAA), and “back projection”, (BP), suffer from out-of-plane, (OP), artifacts along the depth axis of the tomosynthesis volume. This is an inhere nt disadvantage of tomosynthe sis reconstruction method. Therefore, objects from other planes ge t superimposed on the plane of interest after getting blurred out, whic h results in lower contrast of the objects in the plane of interest. Several methods have been suggest ed to reduce the impact of this property, [Chakraborty 1984], [Roy 1985], [Badea 1998] [Kim 2005], [Kolitsi 1993]. Badea implemented a wavelet based transformation method to separate noise and in-plane structures and used selective s uppression of unwanted structures.

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19 PM diffusion has been used successfully in medical/non-medical imaging fields for noise reduction, image enhancement a nd segmentation, [Voci 2004], [Gerig 1992]. Gerig discusses the importance of anisotropic filtering of MR I data for reducing the blur of object boundaries and the enhancem ent of fine structural details. 3.3 Segmentation One of the primary reasons why FCM was considered to be better than other clustering methods is that one pixel can belong to different clusters at the same time with different degrees. This featur e can be exploited to increase the sensitivity of the medical diagnostic system. A number of fuzzy c-m eans clustering methods were developed with main emphasis placed on modification of the objective function. The objective function was modified to either intr oduce the spatial information or to use the kernel induced distance metric. FCM with sp atial information is less sens itive to noise, [Chuang 2006]. FCM with a kernel induced di stance metric, for the objective function, is less sensitive to inhomogeneities in spatial intensity, [Zhang 2004]. Wang implemented a feature-weight learning procedure, which depends on a gr adient descent technique to improve the performance of fuzzy c-means clustering. 3.4 Proposed Methodology Depending on the pixel grey level, dire ctly segmenting the suspicious region gives rise to higher FP detecti ons. Filtering the volumetric data for artifacts removal and image enhancement for better suspicious re gion segmentation can be achieved through the use of a Perona-Malik, (PM), Anisotropic Diffusion filter. Image processing based on

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20 partial differential equations. A partial diffe rential equation, (PDE), possess the inherent advantage of being easily extended to highe r dimensions, allow the use of finite difference methods for solution and provide stable solutions, [S uri 2001]. The breast consists of a complex distribution of tissue. Therefore, a linear filter cannot be used for image enhancement or image restoration. Th e anisotropic filter is a non-linear filter, which uses the image gradient as the criter ia for smoothing or enhancing low, medium and high range frequencies. The anisotropic na ture of the volumetric data was considered during the filtering process. The PM anisotropic diffusion is based on a PDE framework. Therefore, the degree of diffusion can be controlled in any dimension and the control process can be extended to higher dimensions. As a result of this pivotal characteristic, PM diffusion was chosen to smooth tomosynthesis images by removing noise and the blurring along the in-depth direction. PM diffusion was al so utilized to enhance images of tissue structures. The use of a Perona-Malik anisotropic diffusion filter encourages intra-region smoothing while inhibiting inter-region smoot hing. PM diffusion satisfies the basic requirement of filtering medical data. These requirements consist of actions to: Preserve object boundaries and detail structures, Remove noise in the regions of homogeneous physical properties. Figure 3.3 presents plots of th e diffusion coefficient with re spect to the ratio of the the Gradient and K.

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21 Figure 3.3: Plots of the Di ffusion Coefficient with Respect to the Ratio of the Gradient and K Figure 3.4 presents plots of the flow function with respect to the ratio of the Gradient and K. Figure 3.4: Plots of the Flow Functi on with Respect to the Ratio of the Gradient and K The plots of Figures 3.3 a nd 3.4 are typical PM Anis otropic Filtering Curves. The process is defined in Equation 1 by: )) ( ) ( ( ) ( t x I t x t x I t (1)

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22 Where, ) ( t x I is the tomosynthesis image, xis the image axis and t refers to the iteration step. The function, ) ( t x, refers to the diffusion function, which is defined as a function of the image gradient by: |) ) ( (| ) ( t x I f t x (2) The diffusion function: 2| ) ( | exp ) ( K t x I t x (3) The parameter, K is defined as the diffusion c onstant and the behavior of the filter depends upon the value of K The value of K determines the amount of smoothing that can be controlled. The flow function is defined as: ) ( ) ( ) (_ _t x I t x t x (4) Hence, )) ( ( ) ( t x t x I t (5)

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23 A 3 dimensional based anisotropic di ffusion equation can be written as: ] ) , ( ) , ( [ ] ) , ( ) , ( [ ] ) , ( ) , ( [ )] , ( [ ) , ( z t z y x I t z y x z y t z y x I t z y x y x t z y x I t z y x x t z y x div t t z y x I (6) In an 8–1–1 diffusion configura tion, 8 pixels are used fr om the in-plane slice, 1 pixel is used from the top slice and 1 pixel is used from the bottom slice. The calculation is defined by: ] 1 1 1 [ ) , ( ) 1 , (bottom top southwest southeast northwest northeast south north west eastz d t t z y x I t z y x I (7) where, is the horizontal or vertical distance be tween the pixels. Diagonal distance is given by: 22 2y x d (8) and the in-depth distance, z depends on the resolution along the in-depth direction. The calculations for the various cardinal and inter-cardinal directions as well as the top

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24 and bottom calculations are defined by Equa tions 10, 11 and 12 respectively. These equations are given by )) , ( ) , 1 ( ( ) , 2 1 ( 1 )) , ( ) , 1 ( ( ) , 2 1 ( 1 )) , ( ) , ,1 ( ( ) , 2 1 ( 1 )) , ( ) , 1 ( ( ) , 2 1 ( 1 t z y x I t z y x I t z y x y t z y x I t z y x I t z y x y t z y x I t z y x I t z y x x t z y x I t z y x I t z y x xsouth north west east (9) )) , ( ) , 1 1 ( ( ) , 2 1 2 1 ( 1 )) , ( ) , 1 1 ( ( ) , 2 1, 2 1 ( 1 )) , ( ) , 1 1 ( ( ) , 2 1 2 1 ( 1 )) , ( ) , 1 1 ( ( ) , 2 1 2 1 ( 1 t z y x I t z y x I t z y x d t z y x I t z y x I t z y x d t z y x I t z y x I t z y x d t z y x It z y x I t z y x dsouthwest southeast northwest northeast (10) )) , ( ) 1 , ( ( ) 2 1 , ( 1 )) , ( ) 1 , ( ( ) 2 1 , ( 1 t z y x I t z y x I t z y x z t z y x I t z y x I t z y x zbottom top (11) Suspicious regions were extracted thr ough fuzzy clustering, which depends on the pixel grey level. Further clustering impr ovement was achieved by introducing a spatial factor. Spatial Fuzzy C-Means, (SFCM), uses information from both the feature and

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25 spectral domains. The use of data from tw o domains provides an ability to achieve a reduction in sensitivity to noise and better clustering.

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26 CHAPTER 4 FILTERING Tomosynthesis is a limited-range 3D imagi ng modality system, which is different from a complete 3D imaging system such as Computed Tomography. Tomosynthesis possesses a limited angular range. Therefore, a slice at a particular fo cal point of interest is constructed by blurring out-of-plane struct ures and keeping the in-plane structures intact along the in-depth direc tion of the volumetric data. The out-of-plane artifacts are inherent and must be removed before segm entation to avoid false positive detections. 4.1 Image Pre-processing The objective of image pre-processing is to remove unwanted artifacts and enhance the image for further image processing. Image pre-processing is applied prior to filtering the tomosynthesis data for blurring and noise removal. 4.1.1 Background and Artifact Removal Tomosynthesis results in 14-bit, grey le vel, images. The dynamic range of the image encompasses (0 – (214 – 1)) or (0 – 16,383). However, a limited dynamic grey level range is used for the breast region. The limited dynamic range for the breast region is necessary due to the presen ce of artifact and background re gions, which result in lower

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27 contrast. Figure 4.1, presents a typical tomo synthesis slice with image, artifacts, background and breast region along with the histogram spread. 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 x 104 0 1 2 3 4 5 6 x 104 Histogram of Original Tomosynthesis Slice Pixel Intensities Max = 16383 Min = 4478 Artifact Background Breast region (a) (b) Figure 4.1: (a) Typical Tomosynthesis Slice (b) Histogram Two edge-detection methods were used to extract the breast region, which is the region of interest. The canny edge dete ction method combines Gaussian smoothing, gradient calculation and a non-maximum suppr ession technique followed by hysteresis to detect the breast region edge. The other e dge detection method utilized was fuzzy cmeans, (FCM), clustering. In FCM the numbe r of clusters was chosen as a function of the histogram spread. Figure 4.2 presents a comparison of both edge-detection methods. FCM clustering provided a better classification of the breast region than the canny edge detection method.

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28 (a) (b) 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 0 0.5 1 1.5 2 2.5 x 104 Histogram of breast segmented Tomosynthesis Slice Pixel Intensities Max = 8813 Min = 4478 (c) Figure 4.2: Segmentation of the Breast Region Using (a) Canny Edge Detection (b) Fuzzy C-means Clustering (c) Histogram of the Segmented Tomosynthesis Slice of the Breast In order to emphasize the a dvantages of tomosynthesis imaging it is useful to observe the 3D tomosynthesis volume before and after breast segmentation. Figure 4.3 presents the 3D tomosynthesis volume before and after breast segmentation

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29 (a) (b) Figure 4.3: 3D Tomosy nthesis Volume Views (a) Breast Volume with Artifacts and Background (b) Breast Volume After Removal of the Artifacts and Background 4.1.2 Inversing The objective of inversing the image is to shift the histogram of the image to the right side, which is in the direction of a higher dynamic range. Figure 4.4 presents an image of the inversed segmented breast sli ce and the resulting histogram. A comparison of Figures 4.2 and 4.4 clearly depicts the move ment of the histogram to a higher dynamic range.

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30 7500 8000 8500 9000 9500 10000 10500 11000 11500 12000 0 0.5 1 1.5 2 2.5 x 104 Histogram of inversed breast segmented Tomosynthesis Slice Pixel Intensities Max = 11905 Min = 7570 (a) (b) Figure 4.4: (a) Inversed Segmen ted Tomosynthesis Breast Slice (b) Histogram 4.1.3 Histogram Equalization Histogram equalization enhances the contra st of the tissue structure and aids in improved segmentation. In the inversed image the pixel range was (7,570 – 11,905). The actual image pixel range was (0 – 16383) which encompassed the entire available dynamic range of the 14 bit image. Figure 4.5 presents the inversed, equalized histogram, segmented breast s lice and equalized histogram.

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31 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 0 500 1000 1500 2000 2500 Histogram of inversed histogram equalized breast segmented Tomosynthesis slice Pixel Intesities Max = 16383 Min = 1 (a) (b) Figure 4.5: (a) Histogram E qualized Inversed Segmented Tomosynthesis Breast Slice (b) Equalized Histogram A comparison of Figure 4.4(a) and Figure 4.5(a) reveals that, after equalization, the structural detail can be seen more clearly. 4.2 Perona-Malik, (PM), Anisotropic Filtering It was pointed out in section 3.4 that PM diffusion can be extended to higher dimensions. In addition, the anisotropic nature of the data can be incl uded in the filtering process. Different 2D and 3D windows were te sted to compare and establish an efficient window to remove out-of-plane artifacts. Experiments with the various windows were required in order to establish appropriate values for the K parameter and the learning coefficient,

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324.2.1 Choosing the Value of the Learning Coefficient, () The stability of the filter and the rate at which diffusion is performed is controlled by the learning coefficient, ( ). In order to evaluate the best suitable value, for the learning coefficient, for tomosynthesis data filtering was perfor med on a phantom while the value of K and the number of iterations wa s held constant. The images and the line profile for the chosen Region of Intere st, (ROI), is presented in Figure 4.6. Original ROI 20 40 60 80 20 40 60 Original Background ROI 20 40 60 80 20 40 60 Cropped Original ROI 20 40 60 80 2 4 6 8 10 0 20 40 60 80 -1 -0.5 0 0.5 Normalized Line Profile Pixels -->Normalized Contrast --> Figure 4.6: Images and Normalized Line Profile for the Chosen ROI with the Iterations = 500 and K = 500 The value of K and the number of itera tions was maintained at 500. The value chosen for the learning coefficient was vari ed. The values chosen for the learning coefficient were 0.01, 0.05, 0.1, 0.15 and 0.2. Four, (4), adjacent pixels were chosen in the filtering process. In order to construc t the line-profil e, the average background pixel intensity was subtracted from the ROI, [Wu 2004]. Ten consecutive rows, with 60 pixels per row, were averaged. The profile was th en divided by the number of pixels. The

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33 results for the images and line profile of the ROI for the various values of the learning coefficient are presented in Figures 4.7, 4.8, 4.9, 4.10 and 4.11. Filtered ROI 20 40 60 80 20 40 60 Filtered Background ROI 20 40 60 80 20 40 60 Cropped Filtered ROI 20 40 60 80 2 4 6 8 10 0 20 40 60 80 -0.5 0 0.5 Normalized Line Profile Iter=500, K=500, L=0.01 Pixels -->Normalized Contrast --> Figure 4.7: Images and Line Profile of the ROI for = 0.01 Filtered ROI 20 40 60 80 20 40 60 Filtered Background ROI 20 40 60 80 20 40 60 Cropped Filtered ROI 20 40 60 80 2 4 6 8 10 0 20 40 60 80 -0.4 -0.2 0 0.2 0.4 Normalized Line Profile Iter=500, K=500, L=0.05 Pixels -->Normalized Contrast --> Figure 4.8: Images and Line Profile of the ROI for = 0.05

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34 Filtered ROI 20 40 60 80 20 40 60 Filtered Background ROI 20 40 60 80 20 40 60 Cropped Filtered ROI 20 40 60 80 2 4 6 8 10 0 20 40 60 80 -0.4 -0.2 0 0.2 0.4 Normalized Line Profile Iter=500, K=500, L=0.1 Pixels -->Normalized Contrast --> Figure 4.9: Images and Line Profile of the ROI for = 0.1 Filtered ROI 20 40 60 80 20 40 60 Filtered Background ROI 20 40 60 80 20 40 60 Cropped Filtered ROI 20 40 60 80 2 4 6 8 10 0 20 40 60 80 -0.4 -0.2 0 0.2 0.4 Normalized Line Profile Iter=500, K=500, L=0.15 Pixels -->Normalized Contrast --> Figure 4.10: Images and Line Profile of the ROI for = 0.15

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35 Filtered ROI 20 40 60 80 20 40 60 Filtered Background ROI 20 40 60 80 20 40 60 Cropped Filtered ROI 20 40 60 80 2 4 6 8 10 0 20 40 60 80 -0.2 0 0.2 0.4 0.6 Normalized Line Profile Iter=500, K=500, L=0.2 Pixels -->Normalized Contrast --> Figure 4.11: Images and Line Profile of the ROI for = 0.2 A learning curve value for of 0.05 yielded the largest normalized contrast range. This result is displayed in Figure 4.8. The Signal Difference to Noise Ratio, (SDNR), which was introduced by Wu, yields a measure for the ability to detect a feature in the reconstructed plane. The inplane resolution of a tomosynthesis slice can be evaluated using the SDNR. The SDNR is evaluated in Equation 1 by: BG BG featureSDNR (1)

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36 where, feature is the average pixel intensity of the feature, BG is the average intensity of the background region and BG is the standard deviat ion of the background pixel intensity. Figure 4.12 presents a histogram of the variation of the SDNR with respect to 0 0.05 0.1 0.15 0.2 0.25 0 5 10 15 20 25 30 35 40 LambdaSDNRVariation of SDNR with Lambda (PM1 (exp), K = 500, Iter =500) Figure 4.12: Variation of the SDNR with The best SDNR was achieved with a value for the learning coefficient of 0.05. Qualitatively, from Figures 4.6 – 4.11, and quantitatively, from Figure 4.12, the best value for the learning coefficient was 0.05. When = 0.05, better contrast was observed between the sphere and the backgrou nd and the highest SDNR was achieved. 4.2.2 Choosing the Value for K The magnitude of the flow function is highe st when the image gradient is close to the value of K. Therefore, it is important when choosing the optimum value of K, to choose a value that corresponds closely to the gradient values of the out-of-plane

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37 artifacts. Both tomosynthesis phantom and brea st data were used to evaluate the value of K. The results for the phantom data inve stigations are presented in Figures 4.13 – 4.15. Original ROI for Normalized Line profile 20 40 60 80 20 40 60 Original Background ROI for Normalized Line profil e 20 40 60 20 40 60 80 Cropped Original ROI for Normalized Line profile 20 40 60 80 2 4 6 8 10 0 20 40 60 80 -0.5 0 0.5 Line Profile Pixels -->Normalized Contrast --> Figure 4.13: Images and Normalized Line Profile for the Chosen ROI with the Iterations = 50 and L = 0.01 ROI for Normalized Line profile 20 40 60 80 20 40 60 Background ROI for Normalized Line profile 20 40 60 20 40 60 80 Cropped ROI for Normalized Line profile 20 40 60 80 2 4 6 8 10 0 20 40 60 80 -0.5 0 0.5 Line Profile Iter = 50, K = 50, L = 0.01 Pixels -->Normalized Contrast --> Figure 4.14: Images and Normalized Line Profile for the Chosen ROI with the Iterations = 50, L = 0.01 and K = 50

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38 ROI for Normalized Line profile 20 40 60 80 20 40 60 Background ROI for Normalized Line profile 20 40 60 20 40 60 80 Cropped ROI for Normalized Line profile 20 40 60 80 2 4 6 8 10 0 20 40 60 80 -0.4 -0.2 0 0.2 0.4 Line Profile Iter = 50, K = 500, L = 0.01 Pixels -->Normalized Contrast --> Figure 4.15: Images and Normalized Line Profile for the Chosen ROI with the Iterations = 50, L = 0.01 and K = 500 Based on the data presented in Figures 4.13 – 4.15 the best value for K is 500. The results for the breast data investiga tions are presented in Figures 4.16 – 4.20 Cropped Original Tomosynthesis slice SDNR of Original = 1.1924 50 100 150 200 20 40 60 80 100 120 140 160 180 200 Figure 4.16: Tomosynthesis Br east Slice Chosen for the Investigation of the Optimum Value for K

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39 SDNR of filtered slice = 1.5649 pm1 (exp), (4), Iter = 1000, K1 = 400, L = 0.5 50 100 150 200 20 40 60 80 100 120 140 160 180 200 0 100 200 300 400 500 600 700 800 900 1000 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 Variation of SDNR PM1 (exp) (4 0 0), Iter = 1000, K1 = 400, L = 0.5 Iterations --->SDNR (a) (b) (c) (d) Figure 4.17: (a) Filtered Horizontal Slice (b) Variation of SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice Iterations = 500, L = 0.5, K = 400 10 20 30 40 50 50 100 150 200 10 20 30 40 50 50 100 150 200

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40 SDNR of filtered slice = 1.6127 pm1 (exp), (4), Iter = 1000, K1 = 500, L = 0.5 50 100 150 200 20 40 60 80 100 120 140 160 180 200 0 100 200 300 400 500 600 700 800 900 1000 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 Variation of SDNR PM1 (exp) (4 0 0), Iter = 1000, K1 = 500, L = 0.5 Iterations --->SDNR (a) (b) (c) (d) Figure 4.18: (a) Filtered Horizontal Slice (b) Variation of SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice Iterations = 500, L = 0.5, K = 500 10 20 30 40 50 50 100 150 200 10 20 30 40 50 50 100 150 200

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41 SDNR of filtered slice = 1.4628 pm1 (exp), (4), Iter = 1000, K1 = 600, L = 0.5 50 100 150 200 20 40 60 80 100 120 140 160 180 200 0 100 200 300 400 500 600 700 800 900 1000 1.25 1.3 1.35 1.4 1.45 1.5 Variation of SDNR PM1 (exp) (4 0 0), Iter = 1000, K1 = 600, L = 0.5 Iterations --->SDNR (a) (b) (c) (d) Figure 4.19: (a) Filtered Horizontal Slice (b) Variation of SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice Iterations = 500, L = 0.5, K = 600 10 20 30 40 50 50 100 150 200 10 20 30 40 50 50 100 150 200

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42 SDNR of filtered slice = 1.4164 pm1 (exp), (4), Iter = 1000, K1 = 700, L = 0.5 50 100 150 200 20 40 60 80 100 120 140 160 180 200 0 100 200 300 400 500 600 700 800 900 1000 1.26 1.28 1.3 1.32 1.34 1.36 1.38 1.4 1.42 Variation of SDNR PM1 (exp) (4 0 0), Iter = 1000, K1 = 700, L = 0.5 Iterations --->SDNR (a) (b) (c) (d) Figure 4.20: (a) Filtered Horizontal Slice (b) Variation of SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice Iterations = 500, L = 0.5, K = 700 A value for K of 500 yielded the largest SDNR. This result is displayed in Figure 4.18. An additional check was performed, during the investigation of the optimum value for K, by constructing a histogram of the vari ation of the SDNR with respect to a variation in K. The results are presented in Figure 4.21. 10 20 30 40 50 50 100 150 200 10 20 30 40 50 50 100 150 200

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43 0 400 500 600 700 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 KSDNRVariation of SDNR with K Figure 4.21: Variation of SD NR with Variation of K Qualitatively the optimum value for K was found in Figure 4.18 to be 500. Quantitatively the highest SDNR was achieved for K = 500 as displayed in Figure 4.21. Additionally, qualitatively the out-of-plane artif acts were best eliminated for K = 500 for both in-plane and in-depth images. 4.2.3 2D Diffusion In the 2D diffusion case, only pixels in the in-plane direction are considered during the filtering process. Two different windows, which consisted of 4 and 8 adjacent pixels, were considered for comparison. Th ese 2D windows are depicted in Figure 4.22.

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44 (a) (b) Figure 4.22: (a) 4 Adjacent Pixels (b) 8 Adjacent Pixels Pixels from the north, south, east and west directions were considered in the 4 adjacent pixels window. Pixels from north east, northwest, sout heast and southwest directions were considered in the 8 adjacen t pixels window. An ROI was chosen for the 4 and 8 adjacent pixel analysis comparison. In each case the region wa s filtered with PM diffusion and the normalized line profile constructed. The results of the analysis for the wi ndow containing 4 adjacent pixels are presented in Figures 4.23 and 4.24. Figure 4.23 presents the images before and after filtering and the associated line profiles. Original ROI 20 40 60 80 20 40 60 Original Background ROI 20 40 60 80 20 40 60 Cropped Original ROI 20 40 60 80 2 4 6 8 10 0 20 40 60 80 -1 -0.5 0 0.5 Normalized Line Profile Pixels -->Normalized Contrast --> Filtered ROI PM(4) 20 40 60 80 20 40 60 Filtered Background ROI 20 40 60 80 20 40 60 Cropped Filtered ROI 20 40 60 80 2 4 6 8 10 0 20 40 60 80 -0.5 0 0.5 Normalized Line Profile Iter=60, K=500, L=0.05 Pixels -->Normalized Contrast --> (a) (b) Figure 4.23: (a) Original ROI (b) Filt ered ROI with 4 point PM Diffusion

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45 Figure 4.24 presents the data, in a compar ison format, for the normalized original and filtered line profiles. The smoothing effect of the PM diffusion is clearly displayed in Figure 4.24. 0 10 20 30 40 50 60 70 80 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0 3 Pixels -->Normalized Contrast --> SDNR of Original = 1.7011 SDNR of Filtered = 18.7531 Original Normalized line profile Filtered Normalized line profile Figure 4.24: Normalized Line Profile for 4 Point PM Diffusion The results of the analysis for the wi ndow containing 8 adjacent pixels are presented in Figures 4.25 and 4.26. Figure 4.25 only presents the images after filtering and the associated line profiles since the ROI did not change. Filtered ROI PM(8) 20 40 60 80 20 40 60 Filtered Background ROI 20 40 60 80 20 40 60 Cropped Filtered ROI 20 40 60 80 2 4 6 8 10 0 20 40 60 80 -0.5 0 0.5 Normalized Line Profile Iter=60, K=500, L=0.05 Pixels -->Normalized Contrast --> Figure 4.25: Filtered ROI with 8 Point PM Diffusion

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46 Figure 4.26 presents the data, in a compar ison format, for the normalized original and filtered line profiles for the window c ontaining 8 adjacent pixels. The smoothing effect of the PM diffusion is clearly displayed in Figure 4.26. 0 10 20 30 40 50 60 70 80 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0 3 Pixels -->Normalized Contrast --> SDNR of Original = 1.7011 SDNR of Filtered = 52.1563 Original Normalized line profile Filtered Normalized line profile Figure 4.26: Normalized Line Profile for 8 Point PM Diffusion A comparison of the SDNRs achieved as a function of the number of iterations is for the 4 and 8 adjacent pixel windows is presented in Figure 4.27. 0 50 100 150 200 250 300 350 400 450 500 0 10 20 30 40 50 60 Variation of SDNR PM(4) PM1 (exp), Iter = 500, K1 = 500, L = 0.05 IterationsSDNR MAX SDNR = (144, 52.373) 0 50 100 150 200 250 300 350 400 450 500 0 10 20 30 40 50 60 Variation of SDNR PM(8) PM1 (exp), Iter = 500, K1 = 500, L = 0.05 IterationsSDNR MAX SDNR = (60, 52.1563) (a) (b) Figure 4.27: Quantitative Difference for PM Diffusion Using (a) 4 Adjacent Pixels (b) 8 Adjacent Pixels

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47 Figure 4.27 demonstrates the relative simila rity of the SDNR for both windows. The maximum SDNR achieved for the PM di ffusion of the window containing 4 adjacent pixels occurred later than the highest SDNR achieved for the PM diffusion of the window containing 8 adjacent pixels. Therefore, the 8 adjacent pixel window was used to achieve a faster PM diffusion solution. 4.2.4 3D Diffusion Instead of only considering pixels in the in-plane dire ction, pixels from the indepth direction were also used in the filte ring process. Diagrams for pixel selection involving in-plane and in-plane combined with in-depth pixels are presented in Figure 4.28. (a) (b) (c) Figure 4.28: (a) 4 In-Plane Pi xels (b) 8 In-Plane Pixels (c) 8 In-Plane Pixels and 2 In-Depth Pixels Four different windows were compared. Two of the windows were 2D based, ([4,0,0], [8,0,0]). The other two were 3D ba sed, ([4,2,2], [8,2,2]). The horizontal slice, vertical slice and the varia tion of the SDNR w ith iterations are presented for each N E W S N E W S NE NW SE SW N E W S NE NW SE SW T B

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48 window considered in Figures 4.29 – 4.32. The extracted vert ical slice was 200x52, where 52 equals the number of slices. The value for K was chosen to be 500 and the learning coefficient was chosen to be 0.5 in order to achieve a faster solution. SDNR of filtered slice = 1.6358 pm1 (exp), (4), Iter = 2000, K1 = 500, L = 0.5 50 100 150 200 20 40 60 80 1 00 1 20 1 40 1 60 1 80 2 00 0 200 400 600 800 1000 1200 1400 1600 1800 2000 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 Variation of SDNR PM1 (exp) (4 0 0), Iter = 2000, K1 = 500, L = 0.5 Iterations --->SDNR (a) (b) (c) (d) Figure 4.29: (a) Filtered Horiz ontal Slice (b) Variation of the SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice 2D, [4, 0, 0], Window 10 20 30 40 50 50 100 150 200 10 20 30 40 50 50 100 150 200

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49 SDNR of filtered slice = 1.7788 pm1 (exp), (4 2 2), Iter = 2000, K1 = 500, L = 0.5 50 100 150 200 20 40 60 80 1 00 1 20 1 40 1 60 1 80 2 00 0 200 400 600 800 1000 1200 1400 1600 1800 2000 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 Variation of S DNR PM1 (exp ) (4 2 2), Iter = 2000, K1 = 500, L = 0.5 Iterations --->SDNR (a) (b) (c) (d) Figure 4.30: (a) Filtered Horiz ontal Slice (b) Variation of the SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice 2D, [4, 2, 2], Window 10 20 30 40 50 50 100 150 200 10 20 30 40 50 50 100 150 200

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50 SDNR of filtered slice = 6.1736 pm1 (exp), (8 0 0), Iter = 2000, K1 = 500, L = 0.5 50 100 150 20 0 20 40 60 80 1 00 1 20 1 40 1 60 1 80 2 00 0 500 1000 1500 2000 1 2 3 4 5 6 7 Variation of SDNR PM1 (exp) (8 0 0), Iter = 2000, K1 = 500, L = 0.5 Iterations --->SDNR (a) (b) (c) (d) Figure 4.31: (a) Filtered Horiz ontal Slice (b) Variation of the SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice 3D, [8, 0, 0], Window 10 20 30 40 50 50 100 150 200 10 20 30 40 50 50 100 150 200

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51 SDNR of filtered slice = 4.2367 50 100 150 200 20 40 60 80 1 00 1 20 1 40 1 60 1 80 2 00 0 200 400 600 800 1000 1200 1400 1600 1800 2000 1 1.5 2 2.5 3 3.5 4 4.5 Variation of S DNR PM1 (exp ) (8 2 2), Iter = 2000, K1 = 500, L = 0.5 Iterations --->SDNR (a) (b) (c) (d) Figure 4.32: (a) Filtered Horiz ontal Slice (b) Variation of the SDNR with Iterations (c) Original Vertical Slice (d) Filtered Image of the Original Vertical Slice 3D, [8, 2, 2], Window The data from the four windows, clearly indicates that th e [4, 2, 2] window yielded the best results with respect to removal of out-of-plane artifacts. In addition, it is also clear that the in-plane SDNR for the [4, 2, 2] window was less than the in-plane SDNR for the [8, 0, 0] or [8, 2, 2] windows. The SDNR only provides image quality along the in-plane direction rather than th e in-depth direction. However, the main objective of the anisotropic diffusion was rem oval of out-of-plane artifacts. Therefore, the [4, 2, 2] window was chosen as the proper window for the filtering. 10 20 30 40 50 50 100 150 200 10 20 30 40 50 50 100 150 200

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52 CHAPTER 5 SEGMENTATION After image pre-processing th e next important step is detection of suspicious regions. Lesions associated w ith a tomosynthetic image appear more isolated than they would in a comparable mammographic image. This phenomenon is the result of less overlaying of the parenchyma tissue in the tomosynthesis procedure. Segmentation of suspicious regions is achieved through clus tering, which consists of a procedure for finding a structure within the unlabelled data. 5.1 Clustering Clustering is defined as finding a structur e in unlabelled data, [Tutorial 2006]. Clustering is considered to be an unsuper vised problem since the process lacks any a priori input. Clustering is also defined as a collection of objects, which can be placed, according to their correspondence to a descriptiv e concept, into groups or clusters. There is no absolute measure, which can be applie d to determine the best clustering method. The best measure will vary as a function of the criteria established by the specific need to design a clustering procedure. Therefore, the effectiveness of the clustering method depends on the definition created by the crit erion. The different types of clustering algorithms are:

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53 Exclusive clustering, Overlapping clustering, Hierarchical clustering, Probabilistic clustering. 5.2 Fuzzy Clustering Developed by Dunn in 1973 and modified by Bezdek in 1981, fuzzy clustering is a very popular overlapping clustering algorithm. Fuzzy clustering is used extensively for image segmentation in medical field due to th e sensitivity associated with assigning each data value to different clusters with closely associated degrees of sensitivity. An image can be represented in various feature spaces. The FCM algorithm classifies the image by grouping similar data po ints in the feature domain into clusters. The clustering is achieved iteratively by maxi mizing the cost function that is dependent on the distance of the pixels to the cluste rs centers in the feature domain, [Chuang 2006]. Figure 5.1 presents a flow chart for the FCM algorithm.

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54 Figure 5.1: Flow Chart of the Fu zzy C-Means Clustering Algorithm Figure 5.2(a) presents an unfiltered tomosynthesis image of an in-plane slice. Images (b), (c) and (d) present the results of the application of the FCM algorithm for three clusters. The lesion of interest lies in the southeast region at approximate horizontal and vertical coordinates of (165, 170). The presence, configuration and extent of the lesion has been dramatically enhanced by the application of the FCM algorithm.

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55 Original Slice 50 100 150 200 20 40 60 80 100 120 140 160 180 200 0 2000 4000 6000 8000 1000 0 1200 0 1400 0 1600 0 Cluster 1 50 100 150 200 20 40 60 80 100 120 140 160 180 200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (a) (b) Cluster 2 50 100 150 200 20 40 60 80 100 120 140 160 180 200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Cluster 3 50 100 150 200 20 40 60 80 100 120 140 160 180 200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 (c) (d) Figure 5.2: FCM of the Tomosynt hesis Volume for 3 Clusters (a) In-Plane Tomosynthesis Slice (b) Cluster 1 (c) Cluster 2 (d) Cluster 3 Figure 5.3 presents a segmentation of the sa me in-plane slice presented in Figure 5.2. It is clear that segmenta tion, by itself, does not provide the results that are possible with filtering and provides another example of the need for filtering.

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56 Segmented slice 50 100 150 200 20 40 60 80 100 120 140 160 180 200 0 2000 4000 6000 8000 1000 0 1200 0 1400 0 1600 0 Figure 5.3: Segmented Tomosynthesis Volume for an In-Plane Slice 5.3 Cluster Validity Functions Cluster validity functions are used to evaluate the performa nce of clustering. There are two important types of validity f unctions, [Wang 2004]. One type is based on the fuzzy partition of the sample set and the other type is based on the geometric structure of the sample set. The functions representing the validity functions based on a fuzzy partition are labeled Vpc and Vpe. Less fuzziness of the partitio n indicates better performance. The validity functions for a fu zzy partition are defined by: n u Vc i ij n j pc 1 2 1 (1) c i ij ij n j peu u n V1 1log 1 (2)

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57 The optimal partition should generate a maximum for Vpc and a minimum for Vpe. The geometric structure of the sample set indicates that the sample s within a particular cluster should exhibit more compactness and sample s within different clusters should be separate. The functions representing the vali dity functions based on a geometric partition are labeled Vfs and Vxb [Xie 1991]. The validity functions for a geometric partition are defined by: n j i i j ij c i fsv v v X u V1 2 2 2 1 (3) 2 1 2 2 1min *k i k i n j i j ij c i xbv v n v X u V (4) Minimum values for Vfs and Vxb infer good clustering. 5.4 Spatial Fuzzy C-means Clustering A conventional FCM algorithm does not fully utilize the spatial information in the image. SFCM incorporates spatial information into the objective function for clustering. The advantages of SFCM over conventional FC M are reduction of spurious blobs, noisy spots are removed and the procedure is less sensitive to noise. [Chuang 2006]. The pixels on an image are highly correlated, which means that the pixels in the immediate neighborhood possess nearly the same feature data. Ther efore, the spatial

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58 relationship of neighboring pixe ls is an important charac teristic that can be of considerable aid in image segmentation. The standard FCM procedure, wrongly cla ssifies a noisy pixel due to its abnormal feature data. The SFCM technique incorporat es spatial information and the membership weighing of each cluster is altered after th e cluster distribution in the neighborhood is considered. The SFCM reduces the effect of noise consider ably and biases the algorithm toward homogeneous clustering. Figure 5.4 pr esents the functions related to SFCM. Figure 5.4: Spatial Function of the SFCM The spatial function is given by: where NB(xj) represents a square window centered on pixel xj in the spatial domain. The spatial function hij represents the probability that the pixel xj belong to ith cluster. The spatial function of a pixel, for a cluster, is large if the major ity of its neighborhood ) (ix NB k kj iju hSpatial function where, NB(xi) represents a square window centered on pixel xi c k q ik p ik q ij p ij ijh u h u u1 'Spatial function incorporated into membership function ) (ix NB k kj iju h

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59 belongs to the same cluster. The spatial f unction is incorporated into the membership function as: where p and q are parameters used to control the relative importance of both the membership functions. In a homogeneous regi on, the spatial functi on adds extra strength to the membership function and the clustering result remains unchanged. In the case of a noisy pixel, the spatia l function reduces the we ighting of a noisy clus ter by the labels of its neighborhood pixels. Therefor e, misclassified pixels from noisy regions or spurious blobs can be easily corrected. The SFCM algorithm consists of a two-pa ss process during each iteration. The first pass is the same as the conventiona l FCM algorithm in orde r to calculate the membership function in the feature domain. During the second pass, the membership information of each pixel is mapped to the spectral domain and the spatial function is computed. The SFCM algorithm pr oceeds with the new membership that is incorporated by the spatial function. 5.5 Qualitative Analysis Domain knowledge of the tomosynthetic data is used to calc ulate the number of clusters. Three cases are considered with 3, 4 and 5 numbers of clusters. It can be inferred from Figure 5.6 that after 4 clusters th e increase in the numbers of clusters does c k q ik p ik q ij p ij ijh u h u u1 '

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60 not contribute to the enhancement of the pres ence of the lesion. In fact, the increase to five clusters degraded the cap ability to definitively define the presence of the lesion Case #1: Number of clusters = 3 (a) (b) Figure 5.5: (a) FCM (b) SFCM with a 5x5 Window Where p = 1, q = 1 and Clusters = 3 Case #2: Number of clusters = 4 (a) (b) Figure 5.6: (a) FCM (b) SFCM with a 5x5 Window Where p = 1, q = 1 and Clusters = 4 Case #3: Number of clusters = 5

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61 (a) (b) Figure 5.7: (a) FCM (b) SFCM with a 5x5 Window Where p = 1, q = 1 and Clusters = 5 3D clustering involves the use of a 3D window in case of SFCM. Two windows, with dimensions of 5x5x3 and 5x5x5 were used to perform the qualitative comparison. The 5x5x5 window was less sensitive to out-ofplane artifacts when compared to the 5x5x3 window. Hence the 5x5x5 window was the window used for the SFCM algorithm. Figure 5.8 presents the results of the 3D cluste ring experiment for different window sizes. (a) (b) (c) Figure 5.8: 3D Clustering of a Single Slice (a) FCM (b) SFCM with a 5x5x3 Window (c) SFCM with a 5x5x5 Window A comparison between fuzzy and spatial fu zzy clustering of the original volume and the filtered volume are pr esented in Figures 5.9 and 5.10.

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62 (a) (b) (c) (d) Figure 5.9: (a) FCM Clustered In-Plane Slice (b) Filtered FCM Clustered In-Plane Slice (c) Slice Along the In-Depth Direction of (a) (d) Slice Along the In-Depth Direction of (b)

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63 (a) (b) (c) (d) Figure 5.10: (a) FCM Clustered In-Plane Slice (b) Filtered SFCM Clustered In-Plane Slice (c) Slice Along the In-Depth Direction of (a) (d) Slice Along the In-Depth Direction of (b) The SFCM algorithm provided a better clas sification when compared to the FCM algorithm for both the original volume and the filtered volume.

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645.6 Quantitative Analysis The validity functions Vpc and Vpe were used to evaluate the performance difference between the FCM and the SFCM algorithms for 26 slices. The SFCM algorithm utilized a 5x5x5 window size. Table 5.1 presents the data for the validity functions associated with fuzzy and geometric clustering for the FCM and the SFCM algorithms. The data are consistent with the theory. The data demonstrate the superiority of the SFCM algorithm over the FCM algorithm. Table 5.1: Variation of the Validity Functions with the Nu mber of Clusters and the Type of Clustering Number of Clusters Vpc Vpe Vxb With b/g Without b/g With b/g Without b/g With b/g Without b/g 3 FCM 0.97361 0.90005 0.01942 0.07357 0.01688 0.02111 3 SFCM 0.98294 0.93537 0.01211 0.04586 0.01858 0.02327 4 FCM 0.97162 0.89249 0.02116 0.08017 0.01672 0.01576 4 SFCM 0.98122 0.92885 0.01337 0.05065 0.18842 0.17772 5 FCM 0.97053 0.88884 0.02214 0.08388 0.01669 0.01261 5 SFCM 0.97973 0.9232 0.01448 0.05485 0.01891 0.01429 Figure 5.11 presents a graphical compar ison of the validity functions. The functions were compared on both original a nd filtered slices and for both algorithms. The results are consistent with theory and confirm the superiority of the SFCM algorithm over the FCM algorithm. The results presente d in Figure 5.11 correspond to the presence of background effects in the left graphs and the absence of background effects in the right graphs for each validity function presented. Table 5.1 data and the graphs of Figure 5.11

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65 indicate a distortion in the Vxb validity function since it should provide the least minimums when compared to Vpe. The SFCM algorithm works on the spatial domain. Therefore, the compactness of the clusters in the feature domain get distorted, which results in an abnormal variation of Vxb for both the FCM and SFCM algorithms. 0 5 10 15 20 25 30 0.85 0.9 0.95 1 Vpc with background SFCM FCM 0 5 10 15 20 25 30 0.85 0.9 0.95 1 Vpc SFCM FCM 0 5 10 15 20 25 30 0.01 0.015 0.02 0.025 0.03 Vpe with background SFCM FCM 0 5 10 15 20 25 30 0.04 0.06 0.08 0.1 Vpe SFCM FCM 0 5 10 15 20 25 30 0.02 0.04 0.06 0.08 Vxb with background SFCM FCM 0 5 10 15 20 25 30 0.01 0.02 0.03 0.04 Vxb SFCM FCM Figure 5.11: 2D Comparison Between FCM and SFCM for 26 Slices A quantitative histogram comparison of the validity function for fuzzy clustering is presented in Figure 5.12. The histogram also demonstrates the superiority of the spatial fuzzy clustering of filtered volume over spatial fuzzy clustering of unfiltered and fuzzy clustering of filtered and unfiltered volumes.

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66 1 4 7 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Variation of Vpc and Vpe for different cases Different casesVpe and Vpc Vpc Vpe FCM of Original SFCM of Original FCM of Filtered SFCM of Filtered Figure 5.12: Variation Validity Functions Vp c and Vpe for SFCM and FCM Algorithms

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67 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS 6.1 Conclusions Image pre-processing was performed to remove the background region and unwanted artifacts, which occur during image acquisition. The segmented breast volume was inversed and the histogram equalized in order to improve the contrast and to effectively use the available dynamic range of the image. Filtering, required values to be established for two critical parameters K and The K and parameters are unique to tomosynthesis data and were calculated using phantom tomosynthesis and breast tomosynthesis volumes. The SDNR and line pr ofiles were used to derive an effective conclusion for both the parameters. 2D an isotropic diffusion was implemented with different windows in order to determine an optimum window for in-plane filtering. Similarly, 3D anisotropic diffusion was used with different windows to remove the outof-plane artifacts and incr ease the SDNR parameter. Fuzzy C-means and Spatial Fuzzy C-means clustering methods were implemented in order to segment the suspicious regions When employing the Spatial FCM algorithm, the anisotropic nature of the tomosynt hetic data was incl uded by modifying the multiplying parameter of the window, which was used. Comparison between the FCM and the SFCM algorithms was performed qualitatively using the visual representation of tomosynthesis horizontal and vertical slices and quantitatively using validity functions

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68 such as the partition coeffici ent, the partition entropy and th e Xie Beni functions. In addition, a comparison of clustering between filtered and non-filtered tomosynthesis volumes was presented. 6.2 Recommendations Classification of suspicious region by extending the 2D BIRADS system for 3D volumetric tomosynthesis data will be the next critical module for computer aided diagnosis of breast cancer. Application of contemporary pa ttern recognition algorithms, such as the support vector machine, (SVM), to enhance procedures that differentiate between abnormal breast lesions and normal breast tissues and further classify the abnormal objects as malignant or benign lesions should prove to be ex tremely beneficial. The essential requirement for a good classi fication analysis is a huge database. Therefore, acquiring data will play an important role in the success of diagnostic analysis. Since the existing module, which was the object of this research, was tested on a small database, it needs to be enhanced and, possibl y, modified for a huge database set in order to be confidently used as a versatile tool for diagnosis. The existing evaluation methods for good classification techniques are ROC and FROC curves which are based on 2D data. They need to be modified for analysis of 3D tomosynthesis classification.

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Efficient suspicious region segmentation algorithm for computer aided diagnosis of breast cancer based on tomosynthesis imaging
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ABSTRACT: Computer aided diagnostic tool can aid the radiologist in the early detection of breast cancer. Even though mammography is considered to be the gold standard for breast cancer detection, it is limited by the spatial superposition of tissue. This limitation is the result of a using a two dimensional, (2D), representation of a three dimensional, (3D), structure. The limitation contributes to and results in misclassification of breast cancers. Tomosynthesis is a limited-angle 3D imaging device that overcomes this limitation by representing the breast structure with 3D volumetric data.This research, on tomosynthesis imaging, was a critical module of a larger research endeavor for the detection of breast cancer. Tomosynthesis is an emerging state-of-the-art 3D imaging technology. The purpose of this research was to develop a tomosynthesis based, efficient suspicious region segmentation, procedure for the breast to enhance the detection and diagnosis of breast cancer. The 3D breast volume is constructed to visualize the 3D structure of the breast region. Advanced image processing and analysis algorithms were developed to remove out-of-plane artifacts and increase the Signal Difference to Noise Ratio, (SDNR), of tomosynthetic images. Suspicious regions are extracted from the breast volume using efficient and robust clustering algorithms.A partial differential equation based non-linear diffusion method was modified to include the anisotropic nature of tomosynthesis data in order to filter out the out-of-plane artifacts, which are termed "tomosynthetic noise", and to smooth the in-plane noise. Fuzzy clustering algorithms were modified to include spatial domain information to segment suspicious regions. A significant improvement was observed, both qualitatively and quantitatively, in segmentation of the filtered data over the non-filtered data. The 3D segmentation system is robust enough to be used for statistical analysis of huge databases.
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