ALGORITHMS FOR MAMMOGRAM ANALYSIS
A focus on breast tissue asymmetry
This paper presents a detailed summary of the author’s research in pursuit of a PhD degree entitled "Algorithms for Mammogram Analysis: a focus of breast tissue asymmetry", to October 2004. Extensive references to existing prior work in the field of digital mammography are provided, in addition to unpublished research papers written by the author.
Keywords. mediolateral oblique; mammogram; global segmentation; image processing; image analysis
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It has been suggested that asymmetry in bilateral breast X-ray images may be indicative of early stage cancer. This research project aims to investigate the significance of asymmetric features in such mammogram images with a view to improving the detection and differentiation of malignant masses, microcalcifications and other early indications such as architectural distortions.
Computer Aided Mammography (CAM) generally uses Image Processing techniques on a single digitised mammogram to identify regions of interest (ROIs). These ROIs are generally then used as inputs to a connectionist or evolutionary engine which attempts to classify them as normal or suspect pathology. It must be noted that the job of the CAM system is not to diagnose cancer (i.e. to differentiate benign from malignant). Rather, it is to aid the Radiologist in determining whether the X-ray image presents a disruption in the normal breast pattern and whether such a disruption may present itself as an abnormal process that requires further investigations .
There has been significant research in Computer Aided Mammography, largely focused on the analysis of a mammogram image in isolation, or temporal image registration (the study of images of the same breast imaged over a period of time). This research focuses on the correlation and differential analysis of diagnostic features in contralateral images – studying images of each of a patient’s breasts imaged at the same time, on the same machine, in the same conditions. The left and right breast images will be analysed to determine the normal breast pattern and to identify disruptions using bilateral comparisons. The process will include bilateral registration, asymmetric feature detection and modelling, and the attribution of a significance quotient on each feature. The aim of the research project is to identify and document the potential importance of bilateral comparisons in the diagnosis of early stage carcinoma through the development and application of an automated detection system. [; further references therein].
2. Breast Cancer
Breast cancer, carcinoma of the breast, is a heterogeneous disease, the cause of which is still unknown. It is the most frequently diagnosed malignancy of all non-skin cancers, accounting for 30% of the total cancer cases detected . It is the second most common cancer in women in the world, and in developed countries it is the most common . In the UK, breast cancer accounts for one in three of all cancer cases, with nearly 41,000 new cases diagnosed each year. The lifetime risk for breast cancer in women is one in nine .
The overall mortality rate in breast cancer patients in the UK is, however, in decline – down from 82 deaths per 100,000 population in the 50-64 year age group in 1992 to 60 deaths per 100,000 population in 2002 (the last year for which data is available) . Although breast cancer is not preventable, most medical experts agree that there is a link between early diagnosis and successful treatment of the disease, which therefore increases the chance of recovery and lowers the mortality rate. Screening Mammography can assist in the detection of disease up to two years before they are detectable by external examination, even if the patient has no complaints or symptoms . In the United Kingdom, the government’s Department of Health runs a continuous national breast screening programme , taking regular mammogram x-rays of women aged between 50 and 64 years every three years.
A mammogram is an effective and non-invasive means of examining internal breast tissue using a low dose x-ray system and high contrast, high-resolution film. The breast is placed on a plastic cassette and compressed with a soft plastic paddle. Breast compression is necessary in order to:
- Even out the breast thickness so that all of the tissue can be inspected.
- Spread out the tissue so that overlying breast tissue won’t obscure small abnormalities.
- Enable the use of a lower x-ray dose since a thinner amount of breast tissue is being imaged.
- Hold the breast still in order to eliminate blurring of the image caused by motion.
- Reduce x-ray scatter, which would lead to poor image quality.
The breast is exposed to a small dose of radiation to produce an image of internal tissue. The effective radiation dose from a mammogram is about 0.7 millisieverts (mSv), which is about the same as the average person receives from background radiation in three months. The image of the breast is produced as a result of some of the x-rays being absorbed (attenuation) while others pass through the breast to expose the film. The exposed film is either placed in a developing machine, producing images similar to negatives produced by a 35mm camera, or images are digitally stored on a computer. X-ray mammography’s high-resolution 2D structural representation of a breast is sensitive to scarring and other interference and is therefore quite limited in its applicability to younger women, hormone-replacement therapy (HRT) users and for postoperative assessment.
There are many different mammographic views available to image the tissue of a breast. Screening mammography typically involves taking two views of each breast to display as much breast tissue as possible – one from above (craniocaudal view, CC) and one angled view across the breast (mediolateral-oblique, MLO). The MLO view provides a clear image of the upper, outer quadrant of the breast, which is an area that is approximately the same size in most women and where the majority of cancers are found . Further diagnostic mammography may be performed to investigate any suspicious areas seen on the screening mammography form. Typical views for diagnostic mammograms include further CC and MLO imaging and supplemental views tailored to the specific problem, including views from each side – lateromedial (LM) from the side towards the centre of the chest and mediolateral view (ML) from the centre of the chest out, exaggerated craniocaudal, and other special mammography views such as spot compression (also called compression mammogram, spot view, cone views, or focal compression views), magnification view and cleavage view (also called valley view).
Mammogram interpretation is uniquely challenging because of the intrinsically deformable nature of the female breast. The image acquisition process exploits this characteristic to achieve a quality of image by applying significant compression to the breast. This compression can easily introduce sheer and rotation and therefore two mammograms of the same breast taken at an interval can yield quite different images. The appearance of an image may be compromised if there is powder on the breasts, such as antiperspirant or deodorant , or if the patient has undergone breast surgery. Breast implants can also impede accurate mammogram readings because silicone is not transparent on x-rays and can block a clear view of the tissues behind it, especially if the implant has been placed in front of, rather than beneath, the pectoral muscle. However, experienced radiologists can carefully compress the breasts to improve the view without rupturing the implant. The quality of the image is also complicated by the film type and machine configuration parameters such as voltage and exposure, and with X-ray scatter and noise.
Many breast cancer indicators are hard to detect, so radiologists compare the image with views from previous examinations (temporal comparison) if they are available. Approximately 5% of breast screening mammogram results are suspected abnormal and the patient is referred for further investigation in the form of further mammograms, fine needle aspiration, ultrasound, or biopsy. Most of the follow-up tests confirm that no cancer was present and that the original mammogram was a false positive. In the years between 1992 and 2002 for which data is available, the average referral rate is 5.35% but the overall cancer detection rate is just 0.5%.
4. Computer Assisted Detection
The goal of a computer-assisted detection (CADe) system is not to replace or in any way de-skill the radiologist. Nor is it a goal to diagnose any abnormality as malignant, or dismiss it as benign. A diagnosis from a mammogram reading has far reaching effects on the patient and on the health system in terms of resources, and a definitive prognosis is best left to the trained radiologist. A CADe system can, however, help the radiologist to do their job better by acting as a second reader in analysing a mammogram. Double reading has been shown to improve detection of breast cancer by 9–15% . However, as Boggis et al. observe, there is a nationally recognized shortfall in radiologists, specifically in those who are interested and trained in mammographic interpretation .
Machine based second reading can be cost effective if it’s reliable, however the reliability and efficacy of existing systems and methods has come under scrutiny [13-17]. For example, Gur et al.  report that no difference in breast cancer detection and recall rates have been noted between mammograms read with CADe and those interpreted by a single radiologist without CADe . Boggis et al. argue for an evaluation of CADe in a population breast screening programme to determine its effectiveness in increasing cancer detection and its feasibility of implementation .
The breast tissue structure is complex and mammograms contain a number of texture patterns. This complexity makes the analysis a difficult job for trained professional radiologists and a big challenge for automated computer systems. Among the many texture patterns present in any mammogram are a variety of linear structures, such as vessels, ducts, fibrous tissue, skin folds, edges and others, and in abnormal mammograms, linear structures called spicules may also be present. Abnormalities in breast tissue are, in the main, related to linear structures. For example, the significance of microcalcifications located within ducts is greater than those that are not, and spicules are always associated with lesions (called spiculated lesions) . Zwiggelaar et al. have published papers on both the detection  and classification  of linear structures within mammogram images.
5. Breast tissue asymmetry
In general, the human body is bilaterally symmetrical. However, when the width, height or volume of bilaterally paired structures, such as ears, fingers or breasts is compared, most individuals will demonstrate a small deviation from perfect symmetry. These minor degrees of asymmetry are called fluctuating asymmetry (FA). The mean FA of breasts is much higher than most other structures  as it is recognised that breast volume changes across the menstrual cycle. Internal asymmetry within breast tissue, however, is less common and until recently any asymmetric breast tissue, and in particular an increasing area of asymmetric tissue, was regarded as a mammographic sign of malignancy . Asymmetry between contralateral breasts is an important sign used by radiologists to diagnose breast cancer [22, 23], however recent thought is that asymmetric breast tissue is nearly always regarded as benign [21, 24]. This may explain the lack of published research in the area of bilateral mammogram analysis, noted by Sallam and Bowyer .
Despite these specific claims, confusion and dismissal of the significance of asymmetric tissue in the detection of malignancy, it is accepted that bilateral asymmetry may still prove to have potential for improving the detection of early signs by CADe systems, and further research is required. The tissue asymmetry in itself may not be a significant factor, but contralateral comparison of the width and direction/orientation [2, 23], local curvature and branching points of linear structures are often used by radiologists when comparing mammograms , and such comparison could add value to a CADe system. Specifically, the vasculature of the breast is generally symmetrical in size and distribution and an asymmetrically large vein may indicate abnormality . Research continues into the correlation of asymmetry and malignancy, using various modalities, including in mammograms [22, 23, 27], MR images  and infrared Thermograms [29, 30]. Externally, breast asymmetry is generally regarded as not being a risk factor for breast cancer, although there is contradictory evidence here too. In , Scutt et al. conclude from their study that external breast asymmetry may be a valuable factor in considering women with an increased risk of developing breast cancer, but acknowledge other studies that support and contradict their conclusions.
Asymmetry can be measured as statistics of directional distribution of tissue in the fibro-glandular disc, spatial-geometric moments of the fibro-glandular disc . BI-RADS  includes separate definitions for asymmetric tissue, focal asymmetric density, masses with ill-defined borders, and masses with obscured borders. 
6. Test Images
To achieve the clarity and quality required for examination and diagnosis, digital mammogram images are very high resolution, typically 4096 x 4096 pixels, with a colour depth of up to 16 bits per pixel. This resolution and colour depth inevitably results in very large image files and places a great demand on the storage capacity requirements for digital analysis systems; 4096 x 4096 x 2 = 32Mb per image.
There are a limited number of mammogram databases that have been made publicly available and have become popular with researchers. Some of these databases are no longer available as they have been superseded by others. Perhaps one of the first was Nico Karssemeijer's Nijmegen Database from the National Expert and Training Centre for Breast Cancer Screening and the Department of Radiology at the University of Nijmegen in the Netherlands. This database was removed from the University of South Florida server on 31/03/2000 in favour of the Digital Database for Screening Mammography (DDSM). See http://marathon.csee.usf.edu/Mammography/OtherResources.html#NIJMEGEN and http://marathon.csee.usf.edu/Mammography/Database.html for details of these respective databases.
The Lawrence Livermore National Laboratories (LLNL) together with University of California at San Fransisco (UCSF) Radiology Dept. has developed a 12 volume CD library, the UCSF/LLNL Digital Mammogram Library. The library contains 198 films from 50 patients (4 views per patient, but only 2 views from one mastectomy case) digitized to 35 microns, with 12 bit grey scale. Each image is therefore 50Mb in size. The library is available for $100 via http://marathon.csee.usf.edu/Mammography/OtherResources.html.
The Mammographic Image Analysis Society (MIAS) is an organisation of UK research groups interested in the understanding of mammograms. MIAS produce a database  containing 322 images representing bilateral mammogram images of 161 subjects aged 50-65. All images are in the mediolateral oblique view, the view used in the UK Breast Screening Programme  with the image taken diagonally across the breast (see Figure 1). The films have been digitised using a Joyce-Loebl scanning microdensitometer to 50µm × 50µm resolution with a linear grey-scale response in the optical density range 0–3.2 OD . The images have been reviewed by a consultant radiologist to identify abnormalities and provide truth data supplied with the database. The database is classified by tissue density to contain fatty (106 images), fatty-glandular (104 images) and dense-glandular (112 images) and divides into 204 images without abnormality, 15 images with ill-defined masses and 103 with abnormalities – malignant and benign – consisting of calcifications (25 images), circumscribed masses (20 images), spiculated masses (21 images), architectural distortions (20 images) and tissue asymmetry (17 images).
Research for this project was performed using the freely available MIAS MiniMammographic database. This dataset contains the same images as the full database, reduced to a 200µm resolution and padded/clipped so that all the images are 1024 × 1024 pixels. The author recognised the importance of validating the research algorithms using realistic resolution images from the full MIAS database.
6.1 Image Preparation
Before a mammogram can be analysed for internal tissue detail such as the presence of any carcinoma indicators, the raw mammographic image must undergo some pre-processing to eliminate noise and other artefacts and to identify the significant breast region, which can then be the focus of detailed processing.
6.1.1 Image Orientation
To analyse a bilateral pair of mammogram images, a CADe system must first be able to distinguish the left from the right. The system is not concerned with the origin of the breast in relation to the patient, but the orientation of the breast within the image. Identification is therefore based on the position of the nipple within the image, and not whether the mammogram is from the left or right side of the patient. However, this information is important to the radiologist, especially in the case of detection and need for further investigation. The CADe system must therefore report results with respect to the original image so the radiologist has the required information. This initial image orientation problem is generally omitted from the registration procedure and left to the operator to provide the x-ray images in the order and orientation that the software system requires. In a fully automated system, this is an unacceptable burden on the system operator. .
6.1.2 Hierarchical Mammogram Segmentation
Image segmentation describes a process in which an image is decomposed into smaller, significant constituent parts known as segmented objects. Hierarchical segmentation is an iterative procedure that recursively decomposes an image into ever smaller and significant objects. The accurate segmentation of a mammogram to identify the breast area is an important pre-processing step in mammogram analysis , and a two-phase segmentation is a common approach. The image is initially segmented to isolate the breast area from the background, and this area is then further segmented into regions of interest for detailed analysis.
22.214.171.124 Global Segmentation
Global segmentation is applied to the entire image and is used to separate the breast region from the non-breast (background) region. The background generally consists of a film label to identify the image, noise and other artefacts such as scratches or unexposed areas of film. Segmentation of these two regions will occur along the breast boundary, also known as the breast contour or skin-air interface. This boundary contains significant information relating to differences between the deformations of two contralateral mammograms and is the source of information for relating the position of the nipple relative to the skin . Accurate identification of this boundary is therefore important in bilateral comparisons as it identifies the region used in the registration of the images. The non-uniform deformation of the breast during the acquisition of a mediolateral oblique (MLO) mammogram yields a weaker contrast along the breast boundary at the axilla. This region is the area where compression is reduced due to the closer proximity to the rigid chest wall. The contour on the mammogram image in this region will fade and the boundary of the breast may not be visible at all.
The simplest technique for achieving global segmentation of an image is thresholding. The intensity of each pixel in the image is compared to a predefined threshold value, and set to zero intensity (black) if it is lower, or full intensity (white) if it is greater. Mammogram segmentation methods often rely on thresholding the image at a fixed  or dynamically calculated intensity value. Many methods for finding an appropriate threshold value have been proposed. In the frequency domain, a threshold value can be extrapolated from the first peak in a smoothed histogram of the image  or the first valley after the first peak in the intensity histogram of the original image  or a median filtered image . Others [39-41] simply refer to a peak detection algorithm without qualification. Wirth and Stapinski  used a dual threshold technique to obtain an estimate of the breast contour, establishing an initial threshold intensity value using the unimodal thresholding technique from Rosin . Alternatively, inspecting the spatial image using a point-dependent technique  can yield an intensity threshold value by comparing the difference between neighbouring pixels .
Global thresholding alone is inadequate for identifying an accurate skin boundary, however, because background noise appears at similar grey scale intensities as subcutaneous tissue. This is a recognised limitation of global thresholding, and other researchers have investigated contour tracing [11, 34, 46] as an alternative technique and Suckling et al.  introduced a neural network to assist contour tracing. Ojala et al.  used a dynamically calculated binary threshold followed by morphological smoothing to produce an initial estimate of the breast area, and then experimented with three alternative methods of Fourier transform, snake and B-spline curves to enhance the rippled boundary to restore the shape of the breast skin. In a recent paper , Wirth et al. proposed a segmentation technique to remove high-intensity artefacts using morphological reconstruction , a method founded on the concept of geodesic transformations. While this method will eliminate the bright non-breast features that are easily visible on the image – such as the film clip – it will fail in segmenting the skin-air boundary because background noise and scratches are generally low intensity, especially on skin boundary.
In , Saha et al. consider the first peak in the intensity histogram as the mean background intensity and observed the symmetry of the intensities surrounding the peak. In the paper, the standard deviation of background intensities is computed as the root-mean-squared distance of the intensities and is used along with the mean intensity to compute an object-feature-based affinity. The background is eventually subtracted from the original image to yield a segmented breast region.
Méndez et al.  detected the skin boundary using an algorithm that calculates the gradient on a dynamically thresholded smoothed mammogram image. The pre-processed image is divided into three regions that determine the direction of a tracking process that uses the gradient of nine preceding pixels to detect the border pixels. A pixel (x, y) is assumed to belong to the border if the grey-scale value, f(x, y), of the nine previous pixels satisfies the condition:
f(x1, y1) < f(x2, y2) < ... < f(x7, y7) = f(x8, y8) = f(x9, y9) = f(x, y)
Outside of the mammogram segmentation domain, other low contrast image segmentation techniques have been used, such as statistical segmentation [51, 52] where images are modelled as realisations of random fields and statistically optimal estimation techniques such as minimum mean squared error, maximum likelihood and maximum a posteriori estimations are used to classify pixels. Torres et al.  describes a technique using clustering algorithms and the well-known Hough Transform [54, 55] together to segment and eliminate false contours (in underwater multi-spectral images) claiming it to be robust with respect to noise and low contrast between background and foreground. Vitulano et al.  look to Gestalt theory and neurophysiologic theory in an attempt to mimic the human eye’s mechanism of homogenising the object and the background by minimising variations in them, and ultimately enhancing the edges at the transition from one to the other. Although an interesting technique, this is unlikely to be successful when applied to mammogram skin boundary identification due to the low contrast between the subcutaneous fat and background noise.
126.96.36.199 Local Segmentation
Local segmentation is used to delineate regions contained within the breast area such as the pectoral muscle and fibro-glandular tissue and fatty tissue.
188.8.131.52 Pectoral muscle segmentation
The pectoral muscle, pectoralis major or simply pectoralis, is seen in a mediolateral oblique mammogram image as a triangular area of relatively stable intensity in the top corner. The edge should be visible to the level of the nipple and should appear slightly convex. The pectoralis minor is also shown in some MLO mammograms  and appears as a very bright triangular region in the top corner of the pectoralis major region. The presence of a pectoralis minor can complicate the algorithm to segment the pectoral muscle, as the mammogram appears to have two definable pectoral muscle candidates, and the algorithm must detect and select the most appropriate. In craniocaudal images, the pectoralis major can be seen as a crescent of increased intensity on the vertical edge, but is generally visible in only 30 - 40% of images . The pectoralis minor is not seen in CC mammograms.
Literature relating to the identification and segmentation of the pectoral muscle is limited. Among the published works addressing the problem, a common assumption is that the pectoralis boundary is adequately modelled using a straight line approximation. Karssemeijer observes that this line will lie between 45 and 90 degrees if the chest side is on the left of the image or between 90 and 135 degrees if the chest side is on the right, and applies a Hough Transform to identify the boundary line and segment the pectoralis . Alyward et al.  assume that the boundary will intercept the top of the image before crossing the breast’s edge and apply a gradient magnitude traversal algorithm and claims parallel results with Karssemeijer . Ferrari et al., however, note that the hypothesis of a straight line for the representation of the pectoral muscle is not always correct, and may impose limitations on subsequent stages of image analysis .
The pectoralis major consists of pixels in a grey-scale range similar to that of fibro-glandular tissue [11, 57]. Pre-processing the image to remove this area can therefore increase the accuracy of intensity based processing algorithms. Sallam  uses a thresholding technique and morphological filtering followed by a connected-component process to segment the pectoral muscle. Karssemeijer , however, presented an alternative method specific to MLO images using the prior knowledge of the orientation of the image and the representation of the pectoral muscle. The centre of mass of the region of interest (the globally segmented breast region) is calculated, M = (xm, ym), and a straight-line approximation of y = ½x + c is drawn through M. All pixels above this line are selected into a region of interest for further processing. A Sobel edge detection operator  is applied, followed by a Hough Transformation [54, 55] to detect a straight line. The pectoral muscle boundary is found by selecting an appropriate peak in the Hough space, and back-projecting it onto the original image .
184.108.40.206 Texture segmentation
There are three modes of analysis of a mammogram for detecting abnormality indicators: breast background texture, linear image structures such as spicules, vessels and ducts, and two-dimensional structures such as masses and microcalcifications. Texture analysis of breast tissue regions as they are presented in the image can be sensitive to noise and natural variation in breast tissue structure. Zwiggelaar , and again with Blot in , reasons that separating the background texture from the image structures can improve texture classification, and they present statistical modelling techniques for background texture extraction.
Identification of the FGT region is also important as this region contains the ductal paths which are associated with high incidence of cancer. Once identified, mammographic parenchyma tissue can be classified into a number of grades, such as those proposed by Wolfe , that are used by radiologists for the assessment of risk in mammographic images . In a 1998 paper, Bakic et al. claims that as much as 99% of all breast cancers originate in the ductal networks . Indicators can be shown as microcalcifications within or surrounding the ducts, or in bilateral asymmetric duct sizes that can show signs of disease.
7 Mammogram Registration
In obtaining a mammogram image, the breast is compressed between two plates parallel to the image plane. Registration of two mammograms taken of the same breast at different times (a temporal pair)  or of a left and right breast of a subject taken at the same time (a bilateral pair)  must account for the two-dimensional projection of three-dimensional deformations which occur largely due to changes in position and pressure applied to the breast during the procedure . It is therefore difficult to remove deformations that have caused changes in the 3D relationship of anatomical tissue structures . Most of the literature focuses on registration of temporal MLO images, and there are few recent papers on the research of bilateral MLO images, or correspondence between different mammogram views. Highnam et al. recognised the benefit of two-view breast screening  and describe an algorithm matching features in craniocaudal and mediolateral oblique mammograms.
Registration of segmented mammogram images first requires the identification of reference points in each of the contralateral images. The nipple is the only external anatomical feature of the breast, therefore locating its position is important to provide a specific reference point. However, the procedure is difficult, and good techniques are scarce. Ideally, the nipple will be in profile in an MLO image , however, it may not be visible at all, or it may be rotated into an unusual orientation as a consequence of the deformable non-rigid nature of the breast. Behrenbruch et al.  sampled the breast outline and approximated its shape with a cubic spline curve parameterised along the breast boundary, enabling the boundary curvature to be calculated at any point along its length. The nipple position can then be determined by the largest change in curvature along the boundary between the axilla and the rib cage. Olsén et al. note a relationship between the perpendicular distance from a straight line estimate of the pectoral muscle to the skin boundary and the nipple position. The authors show that assuming the nipple to lie on the skin boundary at a position where the boundary is farthest from the pectoral muscle yields a good approximation in the images available in the MIAS database . An alternative technique was presented by Méndez et al.  working with craniocaudal mammogram images rotated 45° and 135° clockwise for right and left images respectively such that the rise of the breast contour increased along the y-axis with the bottom edge of the image along the original chest side. The authors suggested three algorithms for selecting the nipple position, assuming the nipple to be located at (1) the maximum height of the breast border to be the nipple position, (2) the maximum of the gradient across the median-top section of the breast, or (3) the maximum of the second derivative across the median-top section of the breast.
In many papers [2, 63, 64, 67], Wirth et al. have described non-rigid registration of mammograms using a non-rigid-body transformation to “approximately model the inherent nonlinear deformable behavior associated with images of the breast” . In , the authors combine rigid and non-rigid registration methods using a hierarchical technique that begins with a global transformation followed by a series of localised transformations using mutual information – also known as relative entropy – an intensity-based similarity-measure quantifying the degree of similarity between two images using the corresponding pixel intensity values and a cost-function [64, 67]. Rueckert et al. applied a similar technique for 3D non-rigid registration of contrast enhanced MR breast images [68, 69], based on free-form deformations (FFDs) using B-splines and normalised mutual information as a voxel-similarity measure. Local registration with respect to linear features is discussed in [18-20, 26, 70], where the authors describe methods of extracting linear features such as vessels and ducts, and registering the structures across temporal images to track their development and change over time. Sallam et al.  described a method of deformable registration through the application of warping techniques in the image domain. In fact, the authors treat one mammogram as a warped image of the other, and describe the function to be applied as an un-warping function. After initial segmentation, the process is performed in two stages. First, control points around the boundary are defined and an initial un-warping function is calculated using corresponding points. Second, features are identified in the first image and matched to the second using the initial deformation and a final un-warping function is calculated using corresponding features sampled from matched feature points along the breast outline and within the breast region.
In corresponding bilateral images of deformable objects, such as mammograms, referencing the features can prove difficult because of the intrinsic nonlinear movement of internal structures. This movement is sensitive to the positioning of the patient and the pressure applied externally to the breast. The movement is nonlinear as the deformability of the breast is greater at the nipple than at the point of connectivity to the torso at the axilla and the rib cage. Georgsson  derived a dynamic referencing system that he calls anatomic coordinates that can be used to reference features within the deformable breast area. The coordinate system is dynamically positioned relative to a straight line approximation of the pectoral muscle and its perpendicular. Measurements can be recorded within this coordinate system to accurately position features of the breast tissue without any geometrical transformations of the image.
8 Mammogram Modelling
Recognising the limitations of image processing techniques alone to perform the registration of a pair of mammograms, several papers have been published that pursue alternative techniques. Aylward et al., for example, proposed a mixture modelling technique  whereby the image background and pectoral muscle are modelled in a geometric component and the breast area is modelled statistically. Sajda et al.  developed a class of multi-scale probabilistic network models for images, which they call Hierarchical Image Probability (HIP) models. HIP was shown to reduce the number of false positive results from a CADe system, without any loss in sensitivity.
Predictably, modelling is better documented in the three dimensional Magnetic Resonance Imaging domain. Sciarretta et al.  researched the applicability of Finite Element Modelling (FEM), a numerical method based on continuum mechanics principles and primarily used in the analysis of rigid structures, for use in soft tissue applications. Schnabel et al. later used FEM to validate non-rigid registration using biomechanical modelling of tissue properties [73, 74] and Tanner et al.  furthered the work of Rueckert et al.  by considering the underlying material properties of the different tissue types within the breast. Azar et al. had in fact developed a “deformable finite element model of the breast” [75, 76] in 1999, pre-dating the research of Sciarretta et al.
One group of researchers at the University of Oxford have been particularly active in the research of mammogram modelling methods. Highnam et al. have published a series of papers since the early 1990s in their development of a physics-model-based method of calibrating the mammographic imaging process, called hint . The system provides a means of obtaining a quantitative measure of the breast tissue at each pixel representing the thickness of ‘interesting’ (non-fat) tissue. A hint representation of a mammogram contains the hint value at each pixel rather than the traditional grey scale x-ray resultant value, and can be regarded as a surface that conveys information about the anatomy of the breast.
Achieving an accurate representation of non-fat tissue at each pixel in the image is complex because of the relatively poor quality of the mammogram image. Mammograms have a poor signal-to-noise ratio, typically three to four grey levels in intensity, for three reasons: (1) the images contain complex textures, (2) the x-ray process produces scattered photon radiation and (3) there is compromise between the radiation dose and the image quality. In , the authors present a means of calculating the scatter component and describe a method of removing that scatter component from an image in . Other papers [65, 80-85] describe the various aspects of the modelling process in detail, and present applications that are based on, and extend, the model such as its use in the analysis of microcalcifications , and others have recently begun to use hint in their research [61, 86-88].
The hint representation model has been so successful that it is now developed by a commercial company, Mirada Solutions Ltd. and has been given a new name, Standard Mammogram Form™, abbreviated to SMF.
9 Feature Analysis and Classification
Breast density is the percentage of breast volume involved by fibro-glandular densities . The most commonly used mammographic classification of the breast parenchyma is the Wolfe classification  which has four main categories: Breast consisting almost entirely of tissue with fat density are designated N1. Breasts with a prominent duct pattern in no more than 25% of the breast are classified as P1 and as P2 if more than 25% is involved. Breast dominated by more or less homogenous areas with the density of fibro-glandular tissue are classified as DY. Mammographic density is an important predictor of future breast cancer risk , and there is some data that suggests that women with P2 and DY pattern breasts are at a slightly increased risk of developing the disease, although other studies contradict this .
Breast tissue classification research has been published in recent years. In 2002, Blot et al. investigated the classification of parenchyma patterns  and Bovis et al. presented a method of classification of breast density . Petroudi et al. recognised that the intensities of the mammogram do not indicate the actual volume of the breast regions , and develop a density measure based on a normalised representation .
Poorly defined masses can be an important sign of malignancy in a mammogram and will generally show as regions with uniform grey scale intensity . Detection of these masses has received some attention in the literature with researchers using techniques such as neural networks , rank nearest neighbour classification , mutual information [64, 67] and relative image intensity  for finding a mass with defined borders within the texture of the breast tissue. In , Distasi et al. describe a hierarchical entropy method which they use for texture indexing into an image database – and demonstrate its effectiveness in searching for mammogram images that are similar to a given sample. A general review of the image processing techniques effective in mammogram analysis is provided in .
10 Incomplete research aims
10.1 Bilateral registration
Registration of two images is a process of alignment such that the objects in each of the images cover the same area and in an ideal situation the subtraction of one image from the other would yield an empty (all black) image (see section 2.3). Breasts are intrinsically deformable and naturally asymmetric, and the registration of two mammogram images is therefore a complex procedure. Non-rigid registration techniques have been designed to attempt to morph breast images into a common shape to achieve registration, but generally focusing on the registration of temporal mammograms where the difference in the subject is limited to change in imaging procedure (compression and positioning) and the natural breast change in the patient. Bilateral mammogram registration is a less well-documented research area.
The analysis of mammogram images is sensitive to the intensity of each pixel. The image acquisition process of X-ray imaging and digitisation are imprecise methods and significant noise can be present on the final digital image. Morphing and rotation of an image introduces variances that will further reduce the precise definition of sensitive image data. In light of this, it is my belief that the image domain registration procedures are fundamentally flawed in their approach and will damage the image to an extent that after full registration is complete, a degree of significant image information will have been irretrievably lost. As an alternative method, I propose to use a data modelling process to register images in an abstract domain without modification of the source image data. All subsequent contralateral image analysis and comparison will be performed in the abstract domain with registration information available along with the precise original image data. With such a technique, the accuracy of the procedure should be directly related to the quality of the source X-ray image and not sensitive to the quality of implementation of algorithms that modify the image, such as rotation and morphing.
10.2 Local segmentation
Section 220.127.116.11 describes in detail the principles of local segmentation applied to mammogram analysis. This research will pull knowledge from existing literature to locally segment the mammograms in isolation of the contralateral image. It has become apparent during the background reading and literature review that bilateral comparison and analysis will not aid local segmentation as the position and compression of the breast is individual for each image acquisition. The local segmentation performed in this research will eliminate the pectoral muscle using a straight line approximation [11, 40], despite the observations made by Ferrari et al. .
10.3 Texture analysis
The interesting tissue in the breast is the fibro-glandular tissue, the appearance of which indicates many linear structures running through the tissue. Zwiggelaar et al. have published a number of papers on the analysis of linear structures in mammogram images [18-20, 59]. The authors define linear structures as eight-connected pixels terminated by end points or separated by junctions, nodes or crossings. The papers investigate the identification and extraction, analysis and classification of linear structures, all in the context of a single mammogram image. I believe that the attributes of linear structures in contralateral breast images will be a significant factor in the comparison of bilateral mammograms, for example in the detection of architectural distortions or an asymmetrically large vein that may indicate abnormality . It will be during the texture analysis stage of the project that the abstract mammogram model will be designed and implemented to construct a database of potentially significant textural regions in each of the contralateral mammograms, avoiding the need to apply any destructive image processing algorithms to the original image data.
10.4 Feature asymmetry analysis and classification
Once a mammogram model is fully populated for a particular pair of contralateral images, the regions of interest contained in the model will be analysed and classified. This work is likely to involve some machine learning process which can adapt the classification based upon experience of previous analysis and results.
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