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Automated detection of microcalcifications in digitized mammogram film images Nesbitt, Daniel 1995

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Automated Detection of Microcalcifications in Digitized Mammogram Film Images By Daniel Nesbitt ~ B.Eng (Electrical Engineering) University of Victoria, Victoria, British Columbia, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Applied Science in THE FACULTY OF GRADUATE STUDIES ELECTRICAL ENGINEERING We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 1995 ©Daniel Nesbitt, 1995 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying for this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of thesis for financial gain shall not be allowed without my written permission. Electrical Engineering The University of British Columbia 2324 Main Mall Vancouver, Canada V6T 1Z4 Date: (O I t £ ABSTRACT Breast cancer is a disease reaching epidemic proportions in North America with a lifetime incidence rate approaching 1 in 10 women. Microcalcifications are the most common and often the only radiological indicator of early breast cancer. Computer Aided Diagnosis (CADx) prompting techniques that alert radiologists to potential microcalcification abnormalities for re-examination have been demonstrated by several research groups to significantly improve the ability of radiologists to detect clustered microcalcifications. Very little research work has been performed to date to evaluate the performance of microcalcification detection techniques on a common set of images under controlled conditions. We have performed such a comparison on two promising methods from the research literature and four novel methods developed as a part of the work for this thesis. Additionally, the performance of these microcalcification detection methods are evaluated against criteria for the task of prompting screening radiologists for microcalcification cluster. As a part of this thesis work, an improved prototype of the Analytical Imaging Mammography (AIM) system was designed and constructed. This system is intended to provide a flexible platform for mammogram film digitization and analysis. Improvements in the ATM system included: (i) novel hardware and software for automatic, computerized focus and camera position control and (ii) a versatile, friendly user interface. The ATM system was used to digitize an extensive database of mammogram film images obtained from the B.C. Cancer Agency covering the full spectrum of mammographic abnormalities. A sub-set of 30 of these images were selected and used to evaluate the performance of the microcalcification detection methods implemented as a part of this thesis. ii TABLE OF CONTENTS Abstract ii Table of Contents iii List of Tables vi List of Figures vii Acknowledgment viii 1. INTRODUCTION 1 1.1 Breast Cancer 1 1.2 X-Ray Mammography....; 1 1.3 Film Digitization 2 1.4 Computer Aided Diagnostics (CADx) 4 1.4.1 Microcalcifications 5 1.5 Survey of Previous Work 7 1.5.1 Kurt Rossmann Laboratories for Radiologic Image Research 8 1.5.2 Research at Other Centers ....9 1.6 Research Goals of this Thesis 14 2. DEVELOPMENT OF THE ANALYTICAL IMAGING MAMMOGRAPHY (AIM) SYSTEM • 17 2.1 Film Digitization System 17 2.2 System Software 19 iii 3. IMAGE DATABASE AND PERFORMANCE ASSESSMENT METHODOLOGY.. 21 3.1 Image Database : 21 3.2 Performance Assessment Methodology 23 3.2.1 Radiologist Truth Data 23 3.2.2 Microcalcification Cluster Evaluation 23 3.2.3 Individual Microcalcification Evaluation 24 4. DENGLER MICROCALCIFICATION DETECTION METHOD 25 4.1 Implementation 25 4.2 Results and Discussion 31 5. KARSSEMEIJER METHOD FOR MICROCALCIFICATION DETECTION 32 5.1 Implementation 32 5.1.1 The Random Field Model 32 5.1.2 The Image Model 34 5.1.2.1 Contrast Feature Map 35 5.1.2.2 Shape Feature Map ..37 5.1.3 Iterative Label Updating 38 5.2 Results and Discussion 44 6. HYBRID METHODS FOR DETECTION OF MICROCALCIFICATIONS 45 6.1 Wavelet Enhancement 46 6.1.1 Theoretical Background 46 6.1.2. Implementation 49 6.2 Local Adaptive Thresholding 53 6.3 False-Positive Suppression 54 6.3.1 Morphological Erosion 54 iv 6.3.2 Localized Contrast Thresholding 55 6.3.3 Combined Local Contrast and Linear Feature Assessment 58 6.4 Results and Discussion 66 6.4.1 Evaluation of the NESB Configuration 67 6.4.2 Evaluation of the NES2 Configuration 68 6.4.3 Evaluation of the NES3 Configuration 69 6.4.4 Evaluation of the NES4 Configuration 70 7. COMPARATIVE PERFORMANCE ASSESSMENT 71 7.1 Microcalcification Cluster Detection Performance 71 7.1.1 Comparison of Results with Other Groups 74 7.2 Microcalcification Detection Performance : 76 8. CONCLUSIONS AND DISCUSSION 79 8.1 Directions for Future Work 80 Bibliography 82 APPENDK A SAMPLE PERFORMANCE EVALUATION SHEET 90 APPENDK B RADIOLOGIST GROUND TRUTH SUMMARY 93 APPENDLX C TRUE-POSITIVE ANALYSIS SUMMARIES 95 APPENDIX D FALSE-POSITIVE ANALYSIS SUMMARIES 102 APPENDIX E RETROSPECTIVE DETECTIONS SUMMARY ; 109 v LIST O F T A B L E S 2.1 MAMMPRO source code modules 20 5.1 Random field model parameters used by Karssemeijer 41 6.1 Least Asymmetric Daubechies 8-tap (LAD8) filter coefficients 50 7.1 Summary of microcalcification cluster detection performance 72 7.2 Microcalcification cluster detection performance with CASE3213 omitted 72 7.3 Retrospective cluster detections summary 74 7.4 Summary of microcalcification detection performance 76 7.5 False-positive microcalcification detections listed by source 77 7.6 Retrospective microcalcification detections summary 78 vi L I S T O F F I G U R E S 1.1 A digitized mammogram containing a subtle microcalcification cluster 6 2.1 Mammogram film digitization system block outline 18 2.2 The MTF of the X-ray screen-film vs. the digitizing camera 18 4.1 Digitized 512x512 region of interest 26 4.2 Blurred version of test image 26 4.3 Test image after background subtraction 28 4.4 Test image following convolution with difference of Gaussians operator 28 4.5 Final output of Dengler method 30 5.1 Digitized 512 x 512 region of interest featuring prominent connective tissue outlines.. 36 5.2 Contrast feature map for the selected test image 36 5.3 Shape feature map for the selected test image 42 5.4 Initial labeling of the test image 42 5.5 Final labeling of the test image after six iterations 43 6.1 One dimensional quadrature mirror filter 50 6.2 Original 512x512 test image 52 6.3 Wavelet enhanced test image 52 6.4 Result of local adaptive thresholding 53 6.5 Eroded version of the wavelet enhanced image 55 6.6 Neighborhoods for local contrast measure 57 6.7 Hough domain geometry 58 6.8 Hough transform of family of co-linear lines through (0.5, 0.5) 62 6.9 Final output after combined local contrast and linear pattern analysis 65 6.10 Block diagram illustrating the step-wise arrangement of the tested methods 66 vii ACKNOWLEDGMENT I would like to thank my research supervisor Dr. Rabab Ward for her help and support throughout my graduate studies at the University of British Columbia. I also owe a great deal of thanks to Dr. Farzin Aghdasi for his supervision and assistance. This project would not be possible without the support of Xillix Technologies Corporation. On an individual basis I am indebted to Xillix Chief Engineer, Mr. Bruno Jaggi P.Eng. and Xillix Chief Scientist, Dr. Branko Palcic. The clinical support of Dr. Jacqueline Morgan-Parkes of the B.C. Cancer Agency has also been invaluable in completing this work. This project has received generous financial support from Xillix Technologies Corp. and a Science Council of B.C. GREAT scholarship. viii Chapter 1 Introduction 1.1 Breast Cancer For women in developed countries, breast cancer is the most frequently diagnosed malignancy and a leading cause of cancer deaths[l]. In Canada, nearly 10% of all women will develop some form of breast cancer during their lifetime. In British Columbia alone over 2,000 women were diagnosed with breast cancer in 1994 and only 50% will be long term survivors[2]. The probability of success in curing breast cancer is directly related to the stage at which it is detected. The earlier the detection, the higher the chances of successful treatment. Breast conserving surgical therapy is only possible at the early stages of the disease. 1.2 X-Ray Mammography Mammography is a common procedure to examine women breast cancers. Several decades of development and the evolution of dedicated x-ray devices for mammography has resulted in the availability of a large choice of sophisticated equipment on the market. The exposure times and dosage have decreased significantly over the past years. An examination with current equipment results in a typical dose of 0.15cGy. Decades of research have resulted in high speed and high contrast films with acceptable spatial resolution for diagnostic use. Typically, the modulation transfer function (MTF) of such a system falls below the visibility limit (~4%) at about 16 cycles/mm [14]. Therefore, in the absence of noise, objects as small as 50 um should be detectable. In spite of these recent advances, many subtle lesions are missed in mammography. This fact has been repeatedly shown in correlated histological-radiological studies [8, 9], Additionally, specimen 1 Chapter 1 - Introduction 2 radiographs of biopsied lesions normally show a larger number of microcalcifications than those visible on the preoperative mammogram. Two factors contribute to this phenomena: noise and system blur. The system blur is due to the finite size of the focal spot, the geometry of the imaging and the point spread function (PSF) of the screen-film receptor. The noise in the system is due to the following four sources: (i) x-ray quantum noise due to the discrete nature of the x-ray photons (ii) fluctuations in the number of light photons emitted from the screen per absorbed x-ray photon (iii) film grain noise due to the spatial fluctuations in number and size of developed film grains (iv) structure noise due to the heterogeneous spatial distribution of the screen phosphor The overall effect of these degradations is that as radiologists search for smaller and smaller microcalcifications, the contrast of the objects decreases and the influence of noise increases. Thus, the presence of smaller microcalcifications is often not detected. In a typical screening mammography setting, less than 6% of all mammograms screened are flagged as containing a visible abnormality requiring further diagnostic evaluation [18]. The overwhelming proportion of screening mammograms viewed by radiologists are completely normal. This makes it very difficult to recognize the more subtle abnormalities over the course of a viewing session. In addition to the high false-negative rate associated with undetected abnormalities, a high false-positive rate is associated with biopsy calls made on the basis of mammographic interpretation. The number of biopsies resulting in malignant diagnosis is typically only between 20-30%. 1.3 Film Digitization A precursor to digital image processing of mammogram images is film digitization. Traditionally digitization at 100 u.m sampling intervals with 8 bit/pixel photometric resolution was deemed adequate for Chapter 1 - Introduction 3 diagnostic use. More recently, however, some researchers are advocating digitization at 50 urn sampling intervals and 12 bits of photometric resolution per pixel [44]. Systems used to date fall into three classes; microdensitometers, linear Charged Coupled Device (CCD) based systems and area CCD based systems. Microdensitometers transmit a narrow beam of light through the x-ray film. The optical density of the film at the illuminated position is estimated by converting the output of a light-sensitive device, which responds to the intensity of the transmitted light, to an optical density value using a calibrated scale. A recent study of these systems for clinical applications concludes that they are generally slow and expensive [19]. Linear CCD based systems sweep a one-dimensional CCD array over an illuminated x-ray film. These devices are limited by the performance of the illumination source and by the relatively long digitization times attributed to the sequential digitization of scan lines. The temporal stability (i.e. flicker) of the illumination source is a limiting factor since scan lines are digitized sequentially. These systems are, however, considerably less expensive than microdensitometers. Area CCD based systems employ a two-dimensional CCD array to digitize an entire image frame at once, thus combining the cost-effectiveness of a CCD based system, while eliminating the sensitivity to illumination instability and long digitization times associated with linear CCD based systems. The images produced by area CCD based systems do contain fixed pattern variations in intensity resulting from spatial variations in the illumination source. Unlike the effects of flicker on linear CCD systems, these can easily be eliminated by background subtraction of a reference image. It should also be noted that several medical imaging manufacturers are beginning to introduce film-less digital radiology systems that will eventually eliminate the need for film digitization. Currently these Chapter 1 - Introduction 4 systems are in limited release and market acceptance is slow due to the high price of these units and unfamiliarity of clinicians with the technology. However, film based radiology will retain its foothold in the diagnostic imaging market for many years to come. 1.4 Computer Aided Diagnostics (CADx) The effectiveness of mammography relies on the ability of a radiologist to detect subtle abnormalities embedded in the complex and highly textured background of normal breast tissue. Not surprisingly, radiologists do sometimes make errors when interpreting mammograms. Such errors can result in the serious consequences of an undetected cancer or the anxiety and extra radiation dosage in the case of a patient who is unnecessarily recalled for further investigation. Unnecessary surgical biopsies are also the frequent result of false-positive interpretations of mammographic findings. The key diagnostic features of mammogram images are microcalcifications, soft-tissue concentrations (masses), and architectural asymmetry between left and right breasts. Studies of eye movements made when searching for abnormalities in other similar radiological applications, such as the examination of lung x-rays for nodules [15], have indicated that visual search patterns made by radiologists are neither consistent nor complete. If the attention of the radiologist can be directed towards those regions of the image that contain mammographic abnormalities, it is likely that the detection of those abnormalities would be improved. There is mounting empirical evidence that this kind of prompting is useful in mammography. For instance, in a study conducted by Hutt et. al. [16], 100 film mammograms accompanied by computer prompting of automatically generated computer prompts were presented to six radiologists in a realistic, clinical setting. It was demonstrated in these experiments that the detection rate of abnormalities was considerably higher than without the prompts. Hutt et. al. noted, however, that prompting techniques are only effective when the false-positive prompting rate was sufficiently low. This is the challenge of Chapter 1 - Introduction 5 Computer Assisted Diagnosis (CADx) techniques; a very high degree of sensitivity is required and must be accompanied by a high degree of specificity. In addition to prompting applications, CADx techniques are also envisioned in risk assessment tasks where the malignant potential of microcalcification abnormalities are assessed. This could be used as a second opinion before sending a patient for biopsy or, more simply, to reduce the number of prompts to re-examine true-positive microcalcification clusters that can be clearly assessed as benign. In order to perform simple prompting, as discussed in the previous paragraph, it is sufficient to identify enough microcalcifications to designate the abnormality a cluster and an accurate segmentation of the constituent microcalcifications is not required. The task of risk assessment of microcalcification clusters, on the other hand, will require a higher rate of individual microcalcification detection and accurate segmentation in order to adequately quantify the spatial distribution of microcalcifications within a cluster. The features of shape and spatial distribution of individual microcalcifications within a cluster provide the majority of diagnostic information for risk assessment. 1.4.1 Microcalcifications Microcalcifications are small deposits of CasfPO^OH in breast tissue. Those of diagnostic importance are generally smaller than 0.5mm. Microcalcifications are considerably more radio-opaque than surrounding soft-tissue resulting in their appearance on the photo-negative x-ray film as bright specks. In order to provide some perspective, Figure 1.1 illustrates a digitized mammogram film image from the Mammographic Image Analysis Society (MIAS) Database [56] with a relatively subtle microcalcification cluster with the region containing the cluster enlarged and contrast stretched. The sampling interval of the inset image corresponds to the sampling interval of the test images shown in later chapters of this thesis. The detection of this microcalcification cluster is made a challenge because of its small size and the poor contrast of the cluster relative to its background in the original digitized image. Figure 1.1 - A digitized mammogram containing a subtle microcalcification cluster Chapter 1 - Introduction 7 Approximately 50% of all breast cancers are associated with microcalcifications [3]. They are the most common radiographic sign of early breast carcinoma and indeed may be the only sign [4]. Microcalcifications are typically smaller than 0.5mm in diameter and vary in size, form and density [5]. A group of at least three microcalcifications within 1 cm2 of breast tissue constitutes a cluster [5, 6]. Approximately 20-30% of clustered microcalcifications are malignant [7]. The number of microcalcifications per square centimeter is the most important parameter [10]. Less than 10 microcalcifications/cm2 is associated with an 82% probability of being benign, while 10 or more microcalcifications/cm2 correlates with a 44% of being malignant. The average distance between the microcalcifications in the cluster is also significant, with a 92% chance of being benign if greater than 1mm and a 52% chance of being malignant if less than 1mm [10]. Biopsy will normally follow the detection of microcalcifications matching any of the above criteria for potential malignancy. Optimally, microcalcifications stand out prominently against their background. Often in practice, however, they are contained within, or superimposed, on concentrations of soft tissue making them difficult to detect by both human observers and by computer assisted techniques. 1.5 Survey of Previous Work In this section, a survey of previous work published in the literature is presented. A special sub-section has been set aside for researchers in digital mammography techniques at the Kurt Rossmann Laboratories for Radiologic Image Research (University of Chicago). This is justified by the volume and consistently high quality of the work performed by this group. In later sections, experimental results obtained as a part of this thesis are compared to the results obtained by Nishikawa et al. [31] as this is the most credible reference containing enough information regarding performance assessment to make comparisons with any degree of confidence. Chapter 1 - Introduction 8 1.5.1 Kurt Rossmann Laboratories for Radiologic Image Research Chan et al. [24, 25, 26, 27, 28, 29] describe a multi-stage, algorithmic approach to the detection of microcalcifications consisting of the sequential steps of difference image enhancement, local adaptive thresholding, region growing and false-positive reduction. Historically, the difference image technique has been implemented in a variety of forms [24, 25, 26, 27, 28, 29]. Most recently Chan et.al [28] have settled on the use of a "box-rim" filter. The box-rim filter is an averaging filter in which the weighting factors in the middle of the convolutional mask are set to zero to exclude the central pixels from averaging [27]. Local adaptive thresholding is then applied to select candidate microcalcification pixels followed by a region growing procedure. The resulting segmented objects are subjected to minimal and maximal size criteria and to a contrast threshold as false-positive elimination. On test image sets Chan et al [27] obtained a true-positive detection rate of 82% with one false-positive cluster per image. Adding the Shift-Invariant Artificial Neural Network (SIANN) post-processing described by Wu et al. [33], Chan et al. [29] reported a true-positive cluster detection rate of 100% for "obvious clusters" with 0.1 false-positive clusters per image, 93% true-positive detection rate for "subtle clusters" with 1 false-positive cluster per image and 87% true-positive rate for "very subtle clusters" with 1.5 false-positive clusters per image. It was not made clear whether full-breast images were processed or if regions of interest containing abnormalities were selected for processing. Nishikawa et al. and Giger et al., colleagues at the Kurt Rossmann Laboratories for Radiologic Image Research (University of Chicago), have focused their efforts on the development of microcalcification detection routines in the format of a "smart" mammography workstation [30, 31, 32, 49]. Full breast mammogram images are digitized using a linear CCD scanner and the breast area is automatically segmented from the rest of the area of the film. Further image processing is confined to the segmented region. A difference image is generated using the method described by Chan et al. [24, 25, 26, 27, 28, 29]. This is followed by global and local grey level thresholding. Morphological erosion is used to eliminate objects too small to be confidently labeled microcalcifications [55]. The features described by Chapter 1 - Introduction 9 Chan [28] characterizing contrast, size and spatial distribution of microcalcifications are processed by traditional feature analysis techniques as a first pass to eliminate false-positive detections. Finally the remaining microcalcification candidates are automatically clustered and the regions of interest containing the cluster candidates are processed by Shift-Invariant Artificial Neural Network (SIANN) as described by Wu et al. [33]. The SIANN accepts the pixels of the region of interest as input data and is trained to discriminate against false individual microcalcifications. The output of the SIANN is also an image of which the intensity at any given coordinate corresponds to likelihood of a true microcalcification present at that coordinate [31]. This output image is thresholded and the number of objects remaining after thresholding is counted. If the number of objects after thresholding is two or more, than a cluster is determined to have been detected [31]. Yoshida et al. [55] designed a microcalcification detection method employing wavelet transform techniques. The wavelet filter used was a Quadrature Mirror Filter (QMF) with 8-tap Least Asymmetric Daubechies (LAD8) coefficients. The raw image data was transformed into the wavelet domain, the data in scales relevant to microcalcifications emphasized and then the data was transformed back into the spatial domain. Local adaptive thresholding of the wavelet enhanced output follows with morphological erosion of objects too small to be confidently labeled as microcalcification. A texture analysis of the resulting output data is performed to reduce the number of false-positive detections. On a test set of 39 mammogram images, a true-positive rate of 85% with a false-positive rate of 5 clusters per image. A modified version of this approach forms the initial stages of the methods developed in Chapter 6. 1.5.2 Research at Other Centers Dengler [44] describes a two-step method for microcalcification detection. First, image data is preprocessed by subtracting a Gaussian blurred image from the raw data. Second the resulting data is convolved with a weighted difference of Gaussian mask formed using knowledge of typical microcalcification sizes and spacings. Dengler also illustrates a method for calculating a data dependent Chapter 1 - Introduction 10 output threshold proportional to the standard deviation of image noise. This method is discussed in-depth in Chapter 4. Karssemeijer [22, 23] employed a stochastic model based on Bayesian decision theory to automatically detect microcalcifications in mammogram images. The images were preprocessed using an iso-precision scale [21] on which the absolute error of the pixel values due to film noise is equal over the entire range of pixel values. This preprocessing was intended to improve the performance of feature detection algorithms over regions of high optical density. Features for pattern recognition were derived from local contrast and shape. The shape features were found to be of help in distinguishing microcalcifications from background tissue. The fact that microcalcifications often occur in clusters was integrated into the detection scheme by only indicating the detection of faint microcalcifications which occur in the neighborhood of other, more distinct microcalcifications. This method is discussed in-depth in Chapter 5. Davies and Dance [37, 38] developed a multi-stage microcalcification detection algorithm involving local thresholding, individual microcalcification false-positive suppression and automatic clustering of the surviving microcalcification objects. The local thresholding involves the grey level histogram analysis of overlapping sub-regions. The idea is that each pixel is a member of five equal sized sub-regions located on a displaced grid, each with its own threshold. The grey level histogram in each sub-region is smoothed until a unimodal or bimodal distribution is obtained. If the histogram is bimodal, the threshold is taken as the grey level index corresponding to the "valley" between the two modes. If the histogram is unimodal, the threshold is interpolated from adjacent sub-regions with bimodal histograms. A pixel is accepted as foreground data if the pixel is above a pre-determined number of sub-region thresholds. The false-positive reduction is accomplished by computing the area, a compactness shape feature and the average edge strength for each candidate microcalcification. The remaining objects are accepted as microcalcifications and are automatically clustered. Davies and Dance reported a 100% true-positive rate with an accompanying false-positive rate of 0.1 false-positives per image on a test set of 50 images. Chapter 1 - Introduction 11 Aghdasi [13] implemented a locally adaptive greyscale technique for automated microcalcification detection with a thresholding technique modeled after the sub-region method described by Davies and Dance [37, 38]. The mammogram image was subdivided into 100 square sub-regions and grey level histograms for each level were calculated. The grey level histograms were smoothed using a three tap FIR averaging filter until the processed histogram contained two or fewer modes. The position of the "valley" between modes is used to calculate the local threshold for microcalcification detection and segmentation in that subregion. Unimodal distributions are supplemented with information from neighboring regions in order to select an appropriate threshold level. A two step method is employed. On the first pass, objects are labeled and their boundaries determined. On the second pass, thresholds for objects spanning subregions are matched and then segmentation of all objects is invoked. Alternatively, Aghdasi [13] describes an approach for the detection of microcalcifications based on the identification of seed pixels using the Roberts gradient operator. Region growing techniques based on a local threshold established from the grey levels of pixels surrounding the seed pixel in the direction of steepest gradient descent are used to grow the seed pixels into a relatively accurate segmentation of the microcalcification objects. Aghdasi tested these two approaches on a test set of 68 images. The final segmented objects are subjected to a maximal size test. He found that false-positive objects tend to grow into unreasonably large objects which can be eliminated on this simple criterion. Unfortunately, the results were given in terms of per pixel segmentation accuracy instead of microcalcification detection rates which precludes meaningful comparison with the other methods discussed. Aghdasi also implemented a neural network assisted microcalcification segmentation using a modified Hopfield neural network architecture [13]. Each neuron in the network is assigned to a single pixel in the image and each neuron is connected locally to a small, pre-defined neighborhood. In this implementation the network dynamics favor the formation of compact regions and lead to a stable output corresponding to binarized microcalcification masks. A second neural network, a classical three layer perception with error backpropagation for training, is used to flag valid microcalcification masks generated by the first network. Chapter 1 - Introduction 12 The approach was tested on a database of 68 images. Aghdasi [13] reported that near perfect segmentation on a per image basis could be obtained using this approach but a number of network parameters had to be tuned to the characteristics of each test image to obtain a reasonable level of performance. Fam [36, 37] has implemented a multi-pass process for detecting and segmenting microcalcifications. On the first pass, all microcalcifications within a given acceptable, double grey level threshold range are identified as potential members of a microcalcification object. On a second pass, region growing is employed to find connected pixels within a statistically defined grey level deviation from the seed pixel. In this way the pixels that comprise microcalcifications are identified. The third pass involves acceptance testing of valid microcalcifications based on shape and gradient features. On the final pass, accepted valid microcalcifications are grouped into clusters and cluster features such as number of microcalcifications and spatial density are calculated. Fam [36] tested this method on a set 40 digitized mammograms and achieved 100% true-positive cluster detection rate with two false-positive cluster detections for the entire data set. Zhao [39, 40] documents a rule-based morphological feature extraction method for the detection of microcalcifications. A local adaptive thresholding scheme is first used to identify candidate microcalcifications. The binarized image is then operated on by size specific morphological filters. The remaining objects are then classified on the features of member pixel connectivity in the binarized image and statistical measurements of the intensity characteristics of a small region of the original image data containing the candidate object. Zhao presented only qualitative descriptions of the results of the application of this method to a handful of test images. Bankman et al. [42, 43] describe an algorithm for microcalcification detection based on feature extraction from 3-D contour plots of grey level intensity values. Iso-contour lines are first found in the image contour map. Regions less than 2mm enclosed by iso-contour lines are thought to compose the Chapter 1 - Introduction 13 "microstructure" of the images of which most microcalcifications were found to be a subset. Five features are extracted from regions of the contour map less than 2mm2, contained within iso-intensity contours: departure, prominence, steepness, distinctness, and compactness. These features are meant to correspond to visual cues as indicated the separability of the iso-contour bounded regions in terms of intensity and spacing. The five features are examined for each iso-intensity contour enclosed region using a Bayesian feature classifier to separate microcalcifications from false-positive detections. Bankman et al. [42] indicated a true-positive detection rate of 100% with 0.22 false-positive clusters on a small test set of 9 mammogram images. Qian et al. [46] compared three methods of multi-scale image decomposition for the detection of microcalcifications: (i) preprocessing with a Tree-Structured Nonlinear Filter (TSF) and microcalcification extraction using a 2 channel Tree-Structured Wavelet Transform (TSWT); (ii) preprocessing with a TSF and microcalcification extraction with a 3 channel Quadrature Mirror Filter (QMF) and (iii) preprocessing with an Adaptive Order Statistic Filter (ASOF). The three methods were found to all demonstrate a similar level of performance with 100% true-positive detection rate and 0.1-0.2 false-positive clusters per image. Method (iii) proved to retain the greatest amount of image detail. Barman and Granlund [45] describe a wavelet based, hierarchical feature extraction method for microcalcification detection. The initial step involves the generation of a low-pass pyramidal representation of the image data. Next, the low-pass, multi-scale data is convolved with a bank of four quadrature filter pairs to effect a wavelet transform. Numeric features generated from wavelet coefficients are calculated that relate information regarding the orientation, Fourier phase and energy of the underlying image data. Points in the feature maps corresponding to feature values typical of microcalcifications are correlated across adjacent scales to gain confidence in the significance of the response of the features to the image data. The points classified as microcalcifications are mapped back to their spatial coordinates. Test results were not provided. Chapter 1 - Introduction 14 1.6 Research Goals of this Thesis Computer Aided Diagnosis (CADx) prompting techniques that alert radiologists to potential microcalcification abnormalities for re-examination have been demonstrated by several research groups to significantly improve the ability of radiologists to detect clustered microcalcifications. Very little research work has been performed to date to evaluate the performance of microcalcification detection techniques on a common set of images under controlled conditions. We set out to perform such a comparison on two promising methods from the research literature and four novel methods developed as a part of the work for this thesis. Additionally, the performance of these microcalcification detection methods are evaluated against criteria for the task of prompting screening radiologists for microcalcification cluster. The setting of adequate performance criteria for the task of microcalcification detection is made difficult by the complications involved in making comparisons with work being performed at other institutions around the world. Comparisons are made extremely difficult by the wide variations in the selection and size of the image database, the digitization method, the overall quality control of the film image generation and the performance assessment methodology used. In examining the performance of the methods implemented in this thesis, the author decided to make the level of performance required to significantly improve the performance of radiologists in a screening mammography setting the minimum level of acceptable performance. In particular, this improvement in performance would be achieved through computer generated prompts indicating areas to be examined by screening radiologists for clustered microcalcifications. The first step towards achieving this goal in microcalcification cluster prompting is the detection of the individual microcalcifications that comprise the microcalcification clusters. In a prompting application, this is followed by computerized clustering of individual microcalcifications and the generation of prompts to alert radiologists to the position of Chapter 1 - Introduction 15 potential abnormalities. The prompts usually take the form of a circle or square on the display monitor around the suspect region. In this thesis, only the detection of individual microcalcifications that comprise clusters is implemented. Automated clustering and prompt generation are left as future work. The question that must be addressed within the scope of this work is; what level of true-positive and false-positive microcalcification detection rate must be achieved to significantly improve the performance of screening radiologists? Chan et al. [28] examined the ability of prompting techniques to improve the performance of radiologists in the task of detecting clustered microcalcifications. Two levels of accuracy of microcalcification detection were used to generate prompts. Level 1 accuracy provided a true-positive microcalcification cluster detection rate of 87% and a false-positive rate of 4 clusters per image. Level 2 accuracy provided an 87% true-positive detection rate and a false-positive rate of 1 cluster per image. The level of performance of both level 1 and level 2 detection schemes alone were both poorer than the performance of the radiologists alone. However, when the detection schemes were used to generate prompts for microcalcification clusters the performance of the radiologists increased by a margin that was found to be statistically significant. The performance of the radiologists studied was found to be superior with level 2 accuracy (1 false-positive per image) prompting than it was at level 1 accuracy (4 false-positives per image), but the difference was found to be not statistically significant. Hutt et al. [16] conducted an experiment similar to that conducted by Chan et al. [28]. Prompting was generated from automated microcalcification detection at three levels of accuracy: level 1(89% true-positive rate with 0.5 false-positive clusters per image), level 2 (89% true-positive rate with 2.4 false-positive clusters per image) and level 3 (60% true-positive rate with 2.4 false-positive clusters per image). The test images were selected so that only one prompt was present per image. The performance of radiologists was found to be significantly improved for prompting at level 1 accuracy relative to the standard, unprompted performance of the radiologists. Neither prompts generated at level 2 accuracy, nor Chapter 1 - Introduction 16 prompts generated at level 3 accuracy significantly improved the ability of radiologists to detect the presence of clustered microcalcifications in the set of test images. In this experiment, the effect of the false-positive rate is even more pronounced. In a second experiment conducted by Hutt et al. [16] the effect of multiple prompts on test images was evaluated. In this experiment a large variety of mammographic abnormalities were present including clustered microcalcifcations and mass lesions. The combined performance of the microcalcification cluster and mass detection methods used to generate the prompts had a true-positive detection rate of 68% with a false-positive detection rate of 1.1 abnormality per image. Again, even though the sensitivity of the prompt generators was quite low compared to that of the screening radiologists, a statistically significant improvement in the performance of each of the six radiologists involved in the experiment was demonstrated. Clearly, it is not possible to define precise acceptability criteria for microcalcification detection rates based on these results. However, it should be reasonable to set minimums for true-positive and false-positive performance for microcalcification detection intended to be used in prompting applications. For the purpose of this thesis work, a true-positive microcalcification cluster detection rate of 80% or greater and a false-positive rate of 1.5 false-positive cluster or less per image will be considered as acceptability limits for this task. Chapter 2 Development Of The Analytical Imaging Mammography (AIM) System 2.1 Film Digitization System The construction of a revised prototype of a film digitization system, originally designed by Aghdasi, has been completed by the author. This system employs the Microlmager™ 1400 camera designed and manufactured at Xillix Technologies Corp. This camera uses a Kodak KAF-1400 two-dimensional CCD detector. The KAF-1400 is capable of capturing 1320 x 1035 pixels with square sensor elements of 6.8 um per side. Up to six frames per second can be acquired with variable integration times. The CCD output is digitized to 12 bits, 8 of which can be displayed at any given time on the system display. The output is displayed on a 1280 x 1024 pixel high resolution gray scale monitor. The camera is mounted on a motorized vertical belt drive allowing sub-millimeter positioning to provide continuously variable spatial sampling intervals from 187 um down to 48 um. A computer controlled focus drive is mounted on a standard 35mm camera lens to provide automated focusing. Focusing is controlled using a novel predictive focus mechanism whereby the appropriate focus setting is spline interpolated from a look-up table of calibrated focus positions. A block diagram of the system is shown in Figure 2.1. The vertical drive system is powered by a Compumotor OEM-83-135, NEMA size 34, 3-stack stepper motor and is controlled by a Compumotor OEM650X driver/indexer. The focus drive is mounted on a modified Nikkon Nikkor 35mm f/2.8 lens in a rim-drive configuration. Custom machining of focus drive gears and mount was performed by AcuSaw Ltd. (Vancouver) under the supervision of the author. The focus drive is powered by an Portescap P310 stepper motor and is also controlled by a Compumotor OEM650X driver/indexer. The two OEM650X units are interfaced in a "daisy chain" configuration to the system computer via an RS-232 serial interface. 17 Chapter 2 - Development of the Analytical Imaging Mammography (AIM) System 18 X-Y Stage Figure 2.1 - Mammogram film digitization system block outline Two sources of image degradation are incurred in the digitization process; image blur and noise. The degree of blur generated by the system is characterized by the Modulation Transfer Function (MTF) of the system. The MTF curve for the digitization system was characterized on an earlier prototype digitization system and this curve is plotted versus the curve for the x-ray imaging system screen-film combination in Figure 2.2 [11]. M o d u l a t i o n T r a n s f e r F u n c t i o n s 1.0 0.9 0.8 - • 0.7 "\ \ o MTF of the Digitizino, Camera ' x MTF of the Screen Film -0.6 - 1 \-_ u. g 0.5 \ o\ 0.4 0.3 \ c \ \ °a %> 0.2 - \ 0.1 \ n n 0 8 15 ' 24 . 32 40 48 55 54 72 80 r reque'ncy (Cyc l e s / m m j Figure 2.2 - The MTF of the X-ray screen-film vs. the digitizing camera Chapter 2 - Development of the Analytical Imaging Mammography (AIM) System 19 Two types of noise are present in the digitized images using a two-dimensional scanner: (i) fixed pattern noise such as optical shading and aberrations (ii) random noise of optical and electronic origin The random noise was measured to have a standard deviation of 1% [12]. The fixed pattern noise can be corrected (decalibrated). Applying this method to the full image, the noise standard deviation can be reduced to 1.3% [12]. Furthermore, averaging 25 frames per image reduces this figure to a standard deviation of 0.5 gray levels at mid-range [12]. This low level of noise was found to be independent of the integration time or the size of the image and is primarily due to arithmetic round-off errors. After correction for both kinds of noise a 1.4 megabyte image with maximum background variation of ±2 gray levels can be obtained [12]. 2.2 System Software The system software was written on a PC platform supporting OS/2 V2.1. The current software package developed to date is called MAMMPRO. MAMMPRO provides a user friendly graphical user interface for use by clinicians. A great deal of effort has been made to create an intuitive user interface making extensive use of mouse driven control with drop-down menus, list-boxes and icon buttons consistent in operation with other applications typical of a windowing environment. The user interface allows the user to control the film digitization system, perform image enhancement functions and apply software routines for the automated detection of mammographic abnormalities. A number of modules were written containing groupings of routines arranged by function. Approximately 15,000 lines of C code were written as a part of thesis related software development. The MAMMPRO source code modules are listed in Table 2.1 with the appropriate supported operations. Chapter 2 - Development of the Analytical Imaging Mammography (AIM) System 20 MAMMUF User Interface Control MAMMSYS Hardware interfacing: image filing, display hardware control, camera control, camera positional/focus control MAMMANYL Image Filtering: spatial convolutional filters (Gaussian, Laplacian of Gaussian, Difference of Gaussian), wavelet filters, global and local adaptive thresholding MAMMENHC Image enhancement routines: contrast stretching, histogram equalization, gradient operators (Sobel, Kirsch, Prewitt) MAMMFEAT Microcalcification feature evaluation: local adaptive contrast feature, linear pattern feature calculation (Hough transform based), feature classifier (Mahalanobis distance assessment) MAMMORPH Morphological operators: erosion, dilation, opening, conditional thickening MAMMCALC Microcalcification candidate management MAMMKARS Karssemeijer microcalcification detection routines: markovian image analysis, point-wise contrast and linear pattern feature calculation MAMMRSTR Image restoration algorithms (in development) MAMMNNET Shift-invariant neural network (in development) Table 2.1 - MAMMPRO source code modules Chapter 3 Image Database And Performance Assessment Methodology 3.1 Image Database Two sources of test images were considered for use in the experimental verification of the techniques described in this thesis; films provided by Dr. Jacqueline Morgan-Parkes of the B.C. Cancer Agency and digitized images provided by the Mammographic Image Analysis Society (MIAS) of the Royal Marsden Hospital, London, England. In the fall of 1994, 45 cases featuring good examples of a large variety of microcalcification abnormalities were provided by Dr. Morgan-Parkes for our use. Each case consisted of three films: a cranio-caudal (CC) projection, a medio-lateral oblique (MLO) projection and an additional radiological magnification. Each of the 45 cases was accompanied by biopsy outcome. The region of interest containing the microcalcification abnormality in each film was digitized at both 48 \xm and 100 um sampling intervals with 8 bits/pixel using the system described in Chapter 2. A copy of the MIAS database images was sent to us in the summer of 1995. The MIAS database consists of 322 full-breast, digitized images. Of these, 25 feature microcalcification abnormalities. Each of the images in the database was digitized to a spatial resolution of 50 um with a Joyce-Loebl microdensitometer. The photometric characterization of the microdensitometer used specifies a linear response in the optical density range of 0.0 to 3.2 with 8 bits per pixel [56], Although the photometric resolution of these images is comparable to those digitized by the system used by our group, since the entire film was digitized, a wider range of optical densities must be discerned by the digitization system as compared to our own test images restricted only to the region of interest containing the abnormality. As a 21 Chapter 3 - Image Database and Performance Assessment Methodology 22 result, the quantization of film optical density is considerably more coarse for a typical region of interest in the MIAS images as compared to those obtained from our digitization system. Consequently, the decision was made to use only the images obtained from our own digitization system in the experiments for this thesis. With some additional work to re-calibrate the microcalcification detection routines, it might be possible to also use the MIAS images. For the purpose of the experiments for this thesis 30, 512 x 512 pixel test images were selected from the digitized images from the 45 cases provided by Dr. Morgan-Parkes. The size of the test images was chosen according to two constraints: (i) the amount of data storage space available for the output of the detection algorithms (ii) the ability to display the raw digitized image and the resulting output alongside each other for the sake of easy evaluation on a 1280 xl024 pixel display The 30 test images were evaluated by Dr. Morgan-Parkes to produce ground truth data for the evaluation of the detection algorithms. A detailed analysis of the test set ground truth data is provided in Appendix B. The 30 test images contained a total of 42 microcalcification clusters. These clusters were roughly classified into three conspiquity categories: obvious, subtle and very subtle. The conspiquity of a cluster is determined by the size of its constituent microcalcifications, the spatial extent of the cluster and the local contrast of the cluster relative to its background. Obvious clusters are those that are immediately apparent to the viewer and would be very unlikely to be missed. Subtle clusters are those that were relatively difficult to see and would be occasionally overlooked. Very subtle clusters are those that are very difficult to perceive against background tissue and would often be overlooked. Of the 42 clusters present in the test images 18 were designated obvious, 10 subtle and 14 very subtle. There were a total of 511 microcalcifications present in the test images. This number includes the microcalcifications contained in clusters and those appearing in relative isolation within the region of interest. Chapter 3 - Image Database and Performance Assessment Methodology 23 3.2 Performance Assessment Methodology 3.2.1 Radiologist Truth Data The raw digitized images were presented first and the microcalcification clusters were counted. A cluster was counted in the raw images following typical radiological criteria of at least three microcalcifications within an area corresponding to an area roughly 0.5 cm on the original film. The clusters were also categorized by conspiquity into three groups: obvious, subtle and very subtle as discussed in the previous section. Following the evaluation of clusters, the number of microcalcifications present in the raw image were counted. This total included those microcalcifications occurring within clusters and those appearing in relative isolation. 3.2.2 Microcalcification Cluster Evaluation Following the collection of truth data, the output of the computerized detection process was then displayed alongside the raw image and the clusters identified in the raw image were correlated with those appearing in the output image. The number of true-positive clusters was assessed. A cluster was considered to be successfully detected if at least two microcalcifications within it were detected. False-positive clusters were also counted and the predominant source of each of the false-positive cluster detections was classed roughly into glandular tissue, connective tissue and film defect sources. A separate count was made of those clusters that were determined to be present in the raw image retrospectively given the output image but that were not originally perceived as microcalcification clusters in the initial truth data. These retrospective detections are very important since they represent microcalcification abnormalities that would otherwise have been overlooked. Chapter 3 - Image Database and Performance Assessment Methodology 24 3.2.3 Individual Microcalcification Evaluation Following the assessment of cluster detection performance, individual microcalcification detection was examined. The microcalcifications appearing in the output image were correlated with those counted in the raw image data. Those appearing in the output image that could be matched with microcalcifications in the raw input image were counted as true-positive detections. Those that appeared in the output image that were found in retrospect to correspond to true microcalcifications in the input image were tabulated separately as retrospective microcalcification detections. The remaining detections in the output image were assessed as false-positive microcalcification detections. These were classed, as with the clusters, into three groups, glandular tissue, connective tissue and film-defect generated false-positive detections. The form used to record the performance assessment data is presented in Appendix A. Chapter 4 Dengler Microcalcification Detection Method Dengler et al. [44] proposed a method for the detection of microcalcifications involving the application of a weighted difference of Gaussians filter for noise-invariant and size specific labeling criteria. In designing this method, Dengler et al. suggested that an algorithm for automatically detecting microcalcifications should have the following properties. (i) It should be insensitive to low frequency background intensity variations. (ii) It should be adaptive to the noise level within a given neighborhood. (iii) It should be respond best to objects of a given size without being too specific. These criteria were used as guidelines to construct the microcalcification detection algorithm described in this chapter. 4.1 Implementation In Figure 4.1, a 512 x 512 region of interest containing a microcalcification cluster is shown which will be used to demonstrate the various stages of the Dengler algorithm. The first step is to make the detection process independent of the background grey level. This is accomplished through the use of a broadband high-pass filter which is realized by subtracting a low-pass filtered version of I(x, y) from the original image I(x, y). The low-pass version of I(x, y) is generated using a Gaussian filter G of width Q-Q as described below [44] Ij(x,y)=I(x,y)-G*I(x, y) 25 Figure 4.2 Blurred version of test image Chapter 4 - Dengler Microcalcification Detection Method 27 The size aa is chosen to be larger than the maximal expected size of the spots. Figure 4.2 shows the blurred region of interest. Here <JQ = 4 pixels was chosen, which means that the spatial variations at a scale larger than this are attenuated. With 20 pixels/mm this corresponds to a spatial standard deviation 1 of 0.2 mm, which covers objects of up to 0.5mm. Therefore, the maximal sensitivity is concentrated on small objects. Dengler et al. indicated that the exact choice of this parameter is not critical within a factor of 2 [44]. The low-pass filtering operation was performed in floating-point arithmetic with a Gaussian mask size of 13x13 giving a mask width of 3cro.. This was found to be a good compromise of computational complexity and finite width Gaussian mask truncation efTects. The observation Uiat the microcalcifications are brighter relative to the background leads to the decision to discard the negative part of the filtered image I\ (x, y). Thus, the following operation is applied to the difference image [44], I2 (x, y) = max(0, Ij (x, y)) This operation results in the suppression of the soft-tissue background data whereas the small structures such as microcalcifications are retained in the image data. Figure 4.3 illustrates the appearance of the region of interest after background subtraction. A noticeable enhancement of microcalcifications in the images is noted. The next step makes use of the knowledge of the approximate size of the microcalcifications. It also requires knowledge of the typical minimum distance between microcalcifications. Again, a precise measurements of the spacing are not required. The basic idea is that the grey level average within a microcalcification should be significantly larger than the average around a microcalcification. A simple way to measure the difference of these averages is a difference of Gaussians operation with a positive kernel of width a+ reflecting the expected spot size, and a negative kernel of width a. reflecting the expected distance to neighboring microcalcifications. A positive kernel size of cx+ = 4 pixels and a negative kernel size of cr. = 8 pixels were used. Chapter 4 - Dengler Micrccalcification Detection Method 28 Figure 4.3 - Test image after background subtraction Figure 4.4 - Test image following convolution with difference of Gaussians operator Chapter 4 - Dengler Microcalcification Detection Method 29 In order to be independent of the local noise level, a method is used that is adaptive to the local variations of grey levels. The idea is to give the two Gaussian convolution kernels different weights. The positive kernel is assigned a weight w smaller than 1 with [44], I4(x,y) = (wG+ - G-)*I2 The first decision criterion for a microcalcification pixel is [44] h(x,y)>0 This means that for a spot to be detected, the local average defined by the kernel of size cr+ has to be larger by a factor of 1/w than the local average defined be a kernel of size cr. This criterion assumes a non-negative signal, which is assured by the forced condition of positive data. The important point of this criterion is that it is invariant with respect to the scale of I2. This means that a low contrast microcalcification in a homogeneous background is detected equally well as a high contrast spot in an area of high noise level. In other words, the threshold depends on the contrast ratio between the center part of the detector and the peripheral part. The low-pass filtering operation was performed in floating-point arithmetic with a difference of Gaussian mask size of 16x16 giving a mask width of 4cr+. Again, this was found to be a good compromise of computational complexity and finite width mask truncation effects. The result of convolving the test image with the difference of Gaussians operator described above is demonstrated in Figure 4.4. A threshold T is established, which is related to the film granularity and measurement noise. Below this absolute threshold T, any signal is considered to be unreliable. When both criteria are combined, the final decision criterion is [44] U(x,y)>T Chapter 4 - Dengler Microcalcification Detection Method 30 In order to produce an adaptive, data dependent threshold, the threshold T is estimated from the image itself as k times the global standard deviation of noise in image I4. Thus, the values of the parameters w and k are the same for all images, but the threshold T depends on the standard deviation which is determined by a two-step estimation process. First the standard deviation of the whole image I4(x, y) is taken. The standard deviation is then recalculated using only those values less than 2.5 times the initially calculated standard deviation. This is a simplified way of a robust estimation of the standard deviation of the image noise [44]. The final threshold is determined in such a way that by human judgment no microcalcification is missed. This is consistent with the condition of k = 3, indicating a nice agreement between objective statistical criteria and subjective human judgment. Figure 4.5 shows the final output of the Dengler method for the test image. Figure 4.5 - Final output of Dengler method The parameter w is the single most important parameter for establishing the sensitivity of this detection scheme. The effect of the w parameter is to set the minimum contrast level for the detection of a Chapter 4 - Dengler Microcalcification Detection Method 31 microcalcification. In experiments with varying w, large changes in the sensitivity of the detection scheme were observed for small variations in w. The value of w is chosen with the emphasis on avoiding missing a microcalcification. Dengler et al. suggested a value of w = 0.8 as the optimal choice [44]. In the trials performed for this thesis, a value of w = 0.76 was found to produce the optimal trade off of true-positive detection rate vs. false-positive detection rate. 4.2 Results and Discussion The results of the application of the Dengler detection method are detailed in Appendices C, D and E on the pages with "DENG" as the algorithm type. The application of this method to the set of test images resulted in the detection of 36 of the 42 true clusters for a true-positive cluster detection rate of 86%. There were 3 false-positive clusters detected giving a false-positive rate of 0.10 false-positive cluster per image or 0.08 false-positive clusters per true-positive cluster detection. All of the false-positive clusters were detected on one image (CASE3213) and were generated by connective tissue outlines. Of the 511 true microcalcifications, 311 were successfully detected for a true-positive microcalcification detection rate of 61%. There were 133 false-positive microcalcifications detected giving a false-positive microcalcification detection rate of 4.4 false-positive detections per image or 0.43 false-positive microcalcification detections per true-positive detection. Of the false-positive microcalcification detections 44% were generated by glandular tissue and 55% were generated by connective tissue. It should be noted that 30% of the false-positive microcalcification detections were generated by CASE3213. Additionally, this method resulted in 8 retrospective microcalcifications cluster detections and 33 retrospective microcalcification detections. Chapter 5 Karssemeijer Method For Microcalcification Detection Karssemeijer [22, 23] has reported on a stochastic model for microcalcification detection in mammogram images based on Bayesian decision theory. Labeling of the image is performed by a deterministic relaxation scheme in which both image data, as represented by two parameter images, and a priori knowledge of typical patterns in the image data are considered simultaneously. The two parameter images are designed to be representative of local contrast and shape. A shape feature was found to be necessary to distinguish thin patches of connective tissue from microcalcifications. A random field models contextual relations between pixel labels. Long range interaction is used to weight label decisions to increase the sensitivity of the detection of microcalcifications occurring in clusters. This ensures that faint objects are only interpreted as microcalcifications if they are in the neighborhood of others that can be confidently labeled as microcalcifications. 5.1 Implementation 5.1.1 The Random Field Model Random field models provide iterative rules for updating pixel labels in a process of local competition and cooperation. In this approach, a segmentation X is estimated by iteratively assigning pixel labels x, with a maximum a posteriori probability given the data Y. Given a prior distribution p(X) the posterior distribution of X given Y is [22] p(X\Y)KP(Y\X)p(X) (5.1) 32 Chapter 5 - Karssemeijer Method for Microcalcification Detection 33 A Markov random field (MRF) is used as a model for p(X). A Markov random field relates the local dependence of individual pixel labels x, on the labels in the surrounding neighborhood x§j.. The probability distribution of a MRF has the following form [22] p(X) = ±exp[-U{X)] (5.2) where U(X) is known as the energy function and Z is a normalizing constant. If only pairwise interaction is considered, the energy function takes on the following form [22] N tfW = E4(*,)+£*,.,(*,,*,) («) '=1 <<•>» where Afej) represents the external field and fi/jfx,-, xj) represents the interaction parameters with summation over all neighboring pairs in the neighborhood 5/ with N equal to the number of sites in 8i. The interaction parameters Btj are assumed to be independent of relative position of pairs within the neighborhood 8/'. The external field Afe,) is assumed to be zero. Using this model, the conditional probability of a label to occur at a site within the neighborhood 5/ is derived to be [22] p(xt =k\xs) oc exp n=l (5.4) The number of neighbors in 8; labeled as n is denoted g,(w) and K is the number of classes. These probabilities are used to iteratively update the pixel labels to obtain progressively better estimations of the "true" segmentation X. The pixel labels are iteratively updated using a method called Iterative Conditional Modes (ICM) whereby pixel labels are updated by choosing the most probable label x. given the latest estimate of labeling of the image pixels Xt and the image data Y [22]. Chapter 5 - Karssemeijer Method for Microcalcification Detection 34 ( AV x. = max p x. -k\Y,Xi (5.5) The iterative updating of labels will continue until the labeling of image data converges to achieve a minimization of the posterior distribution P(X\Y). By applying Bayes' relation and the Markov property the labeling probability to be maximized can be written as [22] The success of this method depends heavily on a reasonably accurate initial labeling of image data. Typically an initial labeling is obtained by maximizing the data term [23] without considering the interactions of neighboring sites. 5.1.2 The Image Model Karssemeijer established four label classes; microcalcification, connective tissue, background and film defects (e.g. scratches and film emulsion defects) [22, 23]. Microcalcifications are distinguished mainly on the basis of local contrast. Connective tissue pixels typically have local contrast values comparable but slightly lower than those of microcalcifications thus, some measure of a linear shape feature must be used to cue the presence of connective tissue pixels. Background pixels generally have low local contrast and are usually not a part of a linear shaped pattern. Film defect pixels have extremely high local contrast and may or may not be a part of a linear shaped pattern. It is reasonable, therefore, that these four classes should be distinguishable on the basis of the information by combining the cues of local contrast and p[xt = k\Y,X, ) a p{Y\xt = h,Xt )p[xt = k\xs) (5.6) (5.7) Chapter 5 - Karssemeijer Method for Microcalcification Detection 35 linear shaped patterns. A test image is shown in Figure 5.1 in its raw, unprocessed form. The prominent connective tissue objects are noteworthy and the attention of the reader is directed towards these features in successive images. 5.1.2.1 Contrast Feature Map The local contrast measure as defined by Karssemeijer is quite straightforward. The pixel value at site / in an image is denoted by .y, and the local contrast is defined as [22, 23] c,=y,-yZy, (5.8) The neighborhood Si is defined as a square area of 9 x 9 pixels with the site ; at the middle of this area. In practice this method of obtaining a point-wise contrast feature was found to be extremely noisy. In lieu of this definition, the following definition of point-wise contrast was substituted by the author. c t = y t - & — (5.9) n The results obtained using this methodology were found to be far more satisfying than those obtained in the initial attempt. Figure 5.2 below illustrates the contrast map for the chosen test image. Karssemeijer described a preprocessing stage involving rescaling of the image data using an iso-precision criteria [21]. This was not implemented here. This might account for the poor results obtained for the definition of point-wise contrast suggested by Karssemeijer. Chapter 5 - Karssemeijer Method for Microcalcification Detection 36 * • Figure 5.1 - Digitized 512 x 512 region of interest featuring prominent connective tissue outlines Figure 5.2 - Contrast feature map for the selected test image Chapter 5 - Karssemeijer Method for Microcalcification Detection 37 5.1.2.2 Shape Feature Map The calculation of the shape feature 0, employs a method inspired by the Hough transform, a frequently used tool for searching for straight lines in image processing tasks. The direction <p and magnitude r of the gradient are calculated, forming an (r, <p) table. The values of a horizontal, Gx(i), and vertical, Gy(i), oriented Sobel 3x3 gradient operators are combined to calculate r and <p as follows A histogram of gradient directions, incremented by the gradient magnitudes, is generated from the values in the (r, <p) table greater than a fixed value T. This fixed threshold is used to reduce the influence of image noise. A value of T = 20.0 was used for all of the experimental runs for this thesis. A coordinate transform is applied to the gradient direction histogram, J[<p), to achieve directional independence of the shape feature This involves translating the least occurring gradient direction to <p. = 0 using a circular shift of the data. This is followed by a circular shift of the f(<p) data to translate the mean value to <p = n. The shape parameter is then calculated as [22] r = Gx(i)2 + Gy(i)2 (5.10) <p = arctan(Gy(/) / Gx{i)) (5.11) in (5.12) o with <pb = 7t/2 on the interval [0, %) and tpi, = 3n/2 on the interval [n, 2n). The shape feature map for the selected test image is illustrated in Figure 5.3. The reader's attention is drawn to the response of this feature map in the areas corresponding to connective tissue outlines. Chapter 5 - Karssemeijer Method for Microcalcification Detection 38 5.1.3 Iterative Label Updating For the purpose of the study conducted for this thesis, the class defined by Karssemeijer as "other", which corresponds to film defects was eliminated. The assumption is that the "other" class objects will be captured by the microcalcification class because of their high contrast levels. The three remaining pixel classes of microcalcification, connective tissue, and background were assigned the labels of k = 1, 2, and 3 respectively. As discussed in the introductory section above we seek to maximize the probability x, = max k at each iteration. By describing the previous equation in terms of the contrast and shape features c, and 6t we obtain [23] p(xt = k\Y, Xi ) oc f(ct, 0t |x. = k, X , )/?(*,. = k\xs) (5.14) The influence of neighboring labels is limited to the term p(xt = k\ xs ) using the approximation [16] f(citet\x, = kX) = /M,.|x,. = k) (5.i5) Karssemeijer gave no explicit definition of the calculation of f{ci,9i\xi = k}. Since Karssemeijer found that the distributions of the feature values per class were approximately Gaussian it was decided to use the Mahalanobis distance measurement. The Mahalanobis distance measurement gives an estimate of the distance of a feature vector distance from a class mean vector in units of class standard deviation [51]. k\Y,X (5.13) Chapter 5 - Karssemeijer Method for Microcalcification Detection 39 The Mahalanobis distance is calculated from f(ci,Gi\xi=k) = dk= ( i - m j K - ; ( x - r a t ) (5.16) where x is the vector of feature values of the pixel being examined where x = (x l 5 x 2 ) is the vector of the class feature means K t is the class covariance matrix The class statistics and covariance matrices were obtained by generating contrast and linear feature maps for a subset of the test images and pixels, selected by inspection as belonging to each of the classes, were referenced back by their coordinates to their respective feature values. Approximately 100 feature pairs were obtained for each of the three classes. Class statistics were obtained from the sets of feature pairs for each classes using a statistical analysis software package. The xi values correspond to the contrast feature and X2 values to the linear pattern feature. The class statistics obtained were as follows: Class 1 (Microcalcifications) m u = 47.82 m u = 155.99 649.94 211.46 211.46 1021.18 Class 2 (Connective Tissue) m 2 1 = 20.17 m 2 2 = 176.21 K 2 = 77.81 86.75 86.75 1397.56 Chapter 5 - Karssemeijer Method for Microcalcification Detection 40 Class 3 (Background) m 3 ; 1 = 0.524 m 3 ) 2 = 93.319 31.70 17.53 17.53 1326.33 Karssemeijer also assumed conditional independence of c, and citing experimental results to verify this claim. The interaction term p(xf = k\xa^ defines the likelihood of combinations of spatial configurations of labels (e.g. a microcalcification pixel adjacent to another microcalcification pixel is a likely occurrence, a microcalcification pixel adjacent to a film defect pixel is a much less likely occurrence). The interaction term is modeled as follows [23] in which A,-(Q defines the long range interaction of calcification patterns from the set of pixels labeled as microcalcification, C, as [23] where Sj(C) = 1 fory'eC and zero otherwise, fry) is a function of the distance between the sites /' and j. The constant hmax sets an upper limit to the effect of long range interaction. The function g(m) represents the number of pixels in the 3 x 3 neighborhood of /. The interaction constants a(k) and /?(k, m) adjust the a priori likelihood of spatial arrangements of labels. The per class values of a(k) and fflk, m) as suggested by Karssemeijer are listed in Table 5.1 below [23]. p{xi=k\x) oc exp -a(k) + /(kXh, (C) - h0) - p(k, m)g{m) (5.17) (5.18) Chapter 5 - Karssemeijer Method for Microcalcification Detection 41 k a(k) Mk,l) B{k,2) 0(k, 3) /KM) 1 7.0 0.05 0.5 0.0 2.0 2.0 2 4.0 0.0 1.5 2.0 0.0 0.0 3 0.0 0.0 0.0 0.5 1.5 0.0 Table 5.1 - Random field model parameters used by Karssemeijer These random field parameters suggested by Karssemeijer were used as a starting point in finding optimal settings. The value of cx(l) on the initial labeling iteration was decreased to tx(l) = 3.5 and then set to a (1) = 5.0 for successive iterations. This was found to be helpful in detecting the more faint microcalcifications since faint microcalcifications not labeled as such on the initial iteration are not likely to labeled correctly upon iteration. The initial labeling is shown in Figure 5.4. The value of y(l) was set to y(l) = 0.05 and y(2) = y(3) = 0.0. The values of P(l) used were 0.3 times the values listed in Table 5.1. As suggested by Karssemeijer, the labeling was iterated six times to produce the final output. The final output of the Karssemeijer method is shown in Figure 5.5. Chapter 5 - Karssemeijer Method for Microcalcification Detection 42 Figure S.4 - Initial labeling of the test image Chapter 5 - Karssemeijer Method for Microcalcification Detection 43 Figure 5.5 - Final labeling of the test image after six iterations Chapter 5 - Karssemeijer Method for Microcalcification Detection 44 S.2 Results and Discussion The results for the application of Karssemeijer's detection method are detailed in Appendices C, D and E on the pages with "KARS" as the algorithm type. The application of this method to the set of test images resulted in the detection of 29 of the 42 true clusters for a true-positive cluster detection rate of 69%. There were no false-positive clusters detected Of the 511 true microcalcifications, 290 were successfully detected for a true-positive microcalcification detection rate of 57%. There were 28 false-positive microcalcifications detected giving a false-positive microcalcification detection rate of 0.93 false-positive detections per image or 0.10 false-positive microcalcification detections per true-positive detection. Of the false-positive microcalcification detections 86% were generated by glandular tissue, 7% were generated by connective tissue and 7% were generated by film-defects. The reduction in the proportion of false-positive microcalcifications resulting from connective tissue sources is noteworthy and can be attributed to the incorporation of the shape feature map in this approach. The resulting low true-positive and false-positive rates would indicate that the sensitivity of this detection method should be increased by varying the random field model parameters. Many attempts were made to better optimize these settings but interdependency of the model parameters and the sensitivity of the model to small changes in the parameter valued made this extremely difficult. This method resulted in 4 retrospective cluster detections and 5 retrospective microcalcification detections. Chapter 6 Hybrid Methods for the Detection of Microcalcifications The objective of the work in this chapter is to develop hybrid methods of microcalcification detection by combining the most successful portions of the other work implemented with some original innovations. Methods for wavelet enhancement of objects occurring at scales characteristic of microcalcifications, local adaptive thresholding of the enhanced image as directed by local estimates of image noise and false-positive object suppression were developed. Three false-positive suppression methods were examined: morphological erosion, local adaptive contrast thresholding and linear pattern feature analysis. The wavelet enhancement process is modeled after the method described by Yoshida [55]. The published work by Yoshida described the wavelet filter implemented in the work but did not describe how the image data was manipulated in the wavelet domain. The work described in this thesis describing scaling of image data in the wavelet domain is original work. Yoshida also discusses a local adaptive thresholding in very vague terms. The method of global, data dependent thresholding from estimates of image noise as described by Dengler [44] was adapted for use as a local adaptive thresholding method. The morphological erosion processing was modeled after that described by Nishikawa et al. [30], however, the choice of structuring elements was different than those used in the above mentioned work. The local adaptive contrast thresholding method and linear pattern feature calculation are novel aspects of this thesis. 45 Chapter 6 - Hybrid Methods for Microcalcification Detection 46 6.1 Wavelet Enhancement 6.1.1 Theoretical Background Wavelet theory has emerged in recent years as an integrating theoretical framework for most of the work done in signal processing since the 1960's in many related topics such as multi-resolution signal analysis and sub-band filtering. The well known Fourier transform of the form x(f)=)x{ty^dt - C O is clearly limited in its practical application by the infinite time record required for accurate frequency analysis and the implicit assumption of signal stationarity. For non-stationary signals and finite time records, alternate tools are required One well known alternative is the Short-Time Fourier Transform (STFT) of the form derived by Gabor [54] STFT(T,f) = \x(t)g(t-T)e-2«tdt The STFT transforms a signal into a two-dimensional, time-frequency representation in terms of "instantaneous frequency". The STFT resolves the frequency content of a signal within a time record windowed by g(r). Chapter 6 - Hybrid Methods for Microcalcification Detection 47 The ability of the above defined STFT to discriminate between two pure sinusoids can be determined by the measure [54] where Af is the necessary separation in frequency of two sinusoids for successful discrimination. Similarly, the analogous separation in time is defined as [54] Since resolution in time and frequency cannot be arbitrarily small their product can at best meet a lower bound defined as [54] which is the mathematical expression of the well known uncertainty principle. This is also known as the time-bandwidth product. This statement implies that time resolution must be traded for frequency resolution and vice versa. Another indirect implication of this approach is that once a window function g(t) has been chosen for the STFT its respective time-frequency resolutions are also fixed for the entire time-frequency plane. Gabor in his research showed that a Gaussian window results in the lower bound of this expression. AtAf > — An The multiresolution approach of wavelet theory allows the time and frequency resolutions to vary by assigning Af to be proportional to / or [54] Chapter 6 - Hybrid Methods for Microcalcification Detection 48 where c is a constant. As a result, time resolution can be made arbitrarily good at high frequencies and frequency resolution can be made arbitrarily good at low frequencies. This approach will work best with signals composed of low frequency signals with long durations and high frequency components of short duration. This is often a property of signals encountered in practical application of these techniques. The Continuous Wavelet Transform (CWT) exploits this property with the added twist that all impulse responses of the filter bank used are scaled and translated versions of a prototype or "mother" wavelet h(t). Another equally valid perspective is to view the set of scaled and translated versions of h(t) as basis functions. The CWT is defined as [54] Wavelet analysis results in a set of wavelet coefficients which indicate the degree of similarity of the signal x(t) to the chosen basis function or, in other words, a generalized signal x(t) can be decomposed into a set of scaled wavelets of the same shape. The inverse CWT exists and can be formulated as [54] where c is dependent only on the form of h(t). Reconstruction is contingent on the necessary and sufficient condition of [54] dadt ^h{t)dt = 0 Chapter 6 - Hybrid Methods for Microcalcification Detection 49 Optimally, microcalcifications stand out prominently against their background. Often in practice, however, they are contained within or superimposed on concentrations of soft tissue. As a result, there is a need to improve the signal-to-noise ratio of microcalcifications relative to the non-stationary background image data. Wavelet techniques find great utility due to their ability to localize scale-space information and, with appropriate filter coefficients, to reconstruct image data through the inverse wavelet transform. 6.1.2. Implementation The basic outline of the method employed is to perform a forward wavelet transform, emphasize data in certain scales relative to the other scales and then perform an inverse wavelet transform to reconstruct the enhanced image. The wavelet filter used is a two-dimensional, tree-structured quadrature mirror filter with the 8-tap, Least-Asymmetric Daubechies (LAD8) coefficient set [53]. The one-dimensional case is modeled in Figure 6.1. The h{ri) filters are high-pass filters generating "detailed" image data and the g(n) are low-pass filters generating "smoothed" data. The h(n) and g(n) coefficients are related by [54] h(L-\-ri) = {-\fg(ri) where L is the number of filter coefficients. The circled operator in Figure 6.1 represents sub-sampling by a factor of two. Cascaded pairs of h(ri) and g{ri) filters result in an octave-by-octave decomposition of image data. Chapter 6 - Hybrid Methods for Microcalcification Detection 50 Figure 6.1 - One dimensional quadrature mirror filter Yoshida et. al. demonstrated that LAD filters are especially useful for enhancing microcalcifications. Amongst the varying length LAD coefficient sets the LAD8 set produced the best performance when evaluated as a part of a Free Receiver Operating Characteristic (FROC) study with the various LAD coefficient sets as the free variable [55]. The LAD8 coefficients are listed in Table 6.1 [53] n h(n) 0 -7.5765714790e-2 1 -2.9635527646e-2 2 4.97618866763e-l 3 8.03738751809e-l 4 2.97857795606e-l 5 -9.92195435772e-2 6 -1.26039672623e-2 7 3.22231006041e-2 Table 6.1 - Least Asymmetric Daubechies 8-tap (LAD8) Filter Coefficients Chapter 6 - Hybrid Methods for Microcalcification Detection 51 The result of the wavelet transform operation is the generation of a multi-scale pyramidal representation of the image data. The data for the octaves corresponding to the first four octaves (smallest scale data) are scaled with a factor of 0.5 for octave #1, 1.0 for octave #2, 1.0 for octave #3 and 0.5 for octave #4. Data from the remaining octaves are zeroed. The effect of this procedure is analogous to the operation of a band-pass filter. After the data has been scaled in the wavelet domain, an inverse wavelet transform is performed to obtain the enhanced image in the spatial domain. An untouched 512 x 512 test image is shown in Figure 6.2 and the wavelet enhanced version is shown in Figure 6.3. Chapter 6 -Hybrid Methods for Microcalcification Detection 52 Figure 6.3 - Wavelet enhanced test image Chapter 6 - Hybrid Methods for Microcalcification Detection 53 6.2 Local Adaptive Thresholding Local adaptive thresholding is performed on non-overlapping, tiled 64 x 64 pixel regions across the entire enhanced image. The threshold value in each 64 x 64 region is proportional to estimations of image noise using a method as proposed by Dengler et. al. [44] The threshold is established in a two-pass approach. On the first pass, the standard deviation a r of the 64 x 64 region is calculated. A value / is calculated as t = 2.5 * a r The region's standard deviation is then calculated for pixels less than t. This gives a good estimate of the standard deviation of noise, an, in the image region. Figure 6.4 - Result of local adaptive thresholding Chapter 6 - Hybrid Methods for Microcalcification Detection 54 The local adaptive threshold is then established to be T = T c o n s t * CT„. A binarized version p \x, y) of the 64 x 64 regionp(x, y) is created with p'(x, y) = 255 for p(x, y) > T and p \x, y) = 0 otherwise. This procedure is repeated for the entire region forming a collection on non-overlapping tiled 64 x 64 pixel regions. The resulting binarized image is denoted P'(x, y). The thresholded output is shown in Figure 6.4. 6.3 False-Positive Suppression At the completion of the local adaptive thresholding step, there are numerous small false-positive objects which passed through the thresholding process. These are mostly generated by the presence of prominent, structured background data from glandular and connective tissue outlines. Three methods were implemented to reduce the number of false-positive detections; one based on morphological erosion for eliminating objects too small to be confidently assessed as microcalcifications, one based on a measure of local contrast and one based on combining features of local contrast and linear pattern resemblance. 6.3.1 Morphological Erosion A set of four 3x3 structuring elements are used with a traditional binary erosion operator to suppress small objects in the binarized image. The structuring elements are applied in parallel, centered over each image pixel in the binarized image P'(x, y) successively. The resulting image is denoted P"(x, y). This method is modeled after that described by Nishikawa [30], however, the choice of structuring elements is different. The structuring elements used are 0 10 0 10 Si = 110 S2 = 0 11 000 000 Chapter 6 - Hybr id Methods for Microcalcification Detection 55 0 0 0 0 0 0 S3 = 0 1 1 S 4 = 1 1 0 0 1 0 0 1 0 Figure 6.5 - Eroded version of the wavelet enhanced image 6.3.2 Localized Contrast Thresholding It was found that many false-positive objects could be discriminated from true-positive objects on the basis of local contrast only. The weakness of contrast measures implemented by all other known research groups is the dependency on a fixed neighborhood for the evaluation of contrast. This is a severe limitation when objects are closely spaced as fixed neighborhoods will often overlap, thereby reducing the effectiveness of any such contrast measure. Thus, die first task is to determine appropriate neighborhoods for the calculation of the local contrast measure. This is achieved by a morphological operation known as conditional thickening. The second is to calculate the contrast of objects relative to their neighborhoods. The operation CTHICKENING of X relative to Y with pairs of structuring elements (A/y, Ma) is defined by Dengler et. al. as [44] Chapter 6 - Hybrid Methods for Microcalcification Detection 56 (M, , MI2 )CTHICKENING XY = F n j l u ((MAERO X) n {MU2ERO JT)) ) where ERO is the traditional binary erosion operator. Jf is the initial binarized image data and Y = X DIAL B where DIAL is the traditional binary dilation operator with structuring element B. In this case, B is a disc 13 pixels in diameter On a square grid the Mj,i structuring elements are defined as 111 000 A / u = 0 0 0 M2,\ = 0 0 1 000 ' 0 11 and all 90° rotations of these structuring elements. The MU2 structuring elements are defined as 000 0 10 M u = 0 1 0 M 2 ; 2 = 110 111 ' 000 and all 90° rotations of these structuring elements. The CTfflCKENING operator is applied iteratively as E = u , , u ( M u , M,. 2 )CTHICKENING X Y with X = E, until E does not change with successive iterations. For the initial iteration X is the initial binarized image data. Chapter 6 - Hybrid Methods for Microcalcification Detection 57 The effect of the iterative CTHICKENING operation is to grow the boundaries of the objects in X towards the boundaries of the dilated objects in Y until the boundaries in Y are reached, or objects are separated by a line of only one pixel width. In this manner, the local neighborhoods for each object are found such that distinct objects at the beginning of the operation remain distinct throughout the conditional thickening procedure. Figure 6.6 shows the neighborhoods for the microcalcification candidates in the test image. The mean gray level of pixels originally labeled as belonging to a particular microcalcification is calculated. Next, the mean gray level of the pixels in the neighborhood as defined by the iterative conditional thickening operation is found. Microcalcification candidate objects are retained according to the following rule 'f I H R - H M l/mv^Tct then ACCEPT candidate object else REJECT candidate object where UM is the mean value of pixels of the microcalcification candidate object and UR is the mean value of pixels in the surrounding neighborhood. Figure 6.6 - Neighborhoods for local contrast measure Chapter. 6 - Hybrid Methods for Microcalcification Detection 58 6.3.3 Combined Local Contrast and Linear Feature Assessment The majority of the false-positive objects surviving the local contrast thresholding procedure are found to be generated by prominent wisps of connective tissue. On a localized scale, portions of connective tissue outlines can have similar contrast properties as true-positive objects, thus, there exists a need to eliminate the false-positive objects generated by connective tissue by quantifying the likelihood of a given object lying along the outline of connective tissue. This is similar to what Karssemeijer developed as a part of his work. The weakness of Karssemeijer's approach to this problem was that his linear feature calculation was based on a small neighborhood of 9 x 9 pixels around any given point. As a result, this feature does not adequately integrate the local and more global information available in the image to operate with acceptable accuracy. With this in mind, a linear feature for the evaluation of microcalcification candidate objects was developed with the aim of exploiting a larger neighborhood around the objects. The method implemented is based on a version of the Hough transform similar to the version described by O'Gorman and Clowes [50]. On a discretized grid the Hough transform geometry can be described as in Figure 6.7 [52] H(m,n) Figure 6.7 - Hough domain geometry Chapter 6 - Hybrid Methods for Microcalcification Detection 59 with %k = k-1/2 and.y, = J + 1/2 - j. The Hough array, H(m, n), consists of cells of the quantized variables pm and 6n. As defined above it follows that r\ r m r n <0<n 2 " where Pmax = [ * * +yf] The following algorithm for the computation of the O'Gorman and Clowes version of the Hough transform is described by Pratt [52] as follows: 1. Initialize the Hough array, H(m, n) to zero 2. Given the raw image data F(j, k), generate a first-order derivative edge gradient array G(j, k) and an edge gradient angle array y(i, j) as follows: 3. For each (j, k) for which GO, k) > T, where T is the edge detector threshold value, compute PO> k)= xk c o s{ o(J>k)} + y}- ®n{ k)} where 6=W + — 2 for y/< <j) 6-w 2 for y/> (/> Chapter 6 - Hybrid Methods for Microcalcification Detection 60 with tan \yj and 3TZ: n w = y + — for -n <y < 2 2 n n K W = y + — for <y < — 2 2 ^ 2 W = V for — <Y<7T 2 2 4. The quantized m and n indices are calculated from m ( ^ m a x - ^ ^ - l ) 2p max M n •• N • 2n N 5. The Hough array is incremented as H(m,n) = H(m,n) + G(j,k) Chapter 6 - Hybrid Methods for Microcalcification Detection 61 The intent here is to attempt to detect if a microcalcification candidate is actually a portion of a connective tissue outline with sufficiently high local contrast so as to be misclassified as a true-positive detection on the basis of local contrast alone. The approach is to produce a numeric feature proportional to the likelihood that a candidate is a false-positive generated by a portion of connective tissue using data from the O'Gorman and Clowes implementation of the Hough transform. A region of interest of 128x128 pixels centered on the coordinate of the microcalcification centroid is used as the basis for the linear feature evaluation. Since the region of interest for each feature calculation is centered over the microcalcification candidate, it is sufficient to examine the Hough transform data corresponding to the family of co-radial lines passing through the center of the region of interest. The Hough transform space parameterization is as follows p = xcost9 + ^ sint9 For co-radial lines passing through the center of the region of interest, there exists a common point for all such lines. With the above described geometry, (0.5, 0.5) is a common point for all co-radial lines. By substituting this point for x and y in the Hough space parameterization expression we can obtain a closed form description of the coordinates in Hough space corresponding to the family of co-radial lines passing through the common point (0.5, 0.5). 2p = cos#-r-sin# .'. 4p2 = cos2 0 + 2cos0sin0 + sin 2 6 :. 4p2 = 2 cos <9 sin 0+1 .-. 4yo 2=sin20 + l Chapter 6 - Hybrid Methods for Microcalcification Detection 62 from the above equation we can obtain an2c9+1 and Figure 6.8 - Hough transform of family of co-linear lines through (0.5, 0.5) From Figure 6.8 it is clear that the Hough transform data of a family of co-linear lines lies along the outline of a single sinusoid. Thus, the trajectory of this sinusoid in Hough space is given by the pair of equations above, solved for p and# The linear feature implemented here is calculated by comparing the magnitude of the Hough transform data along the sinusoidal trajectory described by the p-0 relationship above to the magnitude off of this trajectory. Additionally, however, die connective tissue outlines are generally four to five pixels wide with Chapter 6 - Hybrid Methods for Microcalcification Detection 63 a 48 ]xm sampling interval and non-circular microcalcification candidate shapes can cause the centroid of the object can lead to the centroid coordinates being several pixels of center of the connective tissue outline. These two factors both contribute to the strongest Sobel operator gradient response being somewhat off-center. In Hough transform space, this equates to a shift in the p direction off of the sinusoidal trajectory that would be obtained for co-radial lines under ideal conditions. The linear feature is calculated by calculating the sum of the values in Hough transform space along the trajectory described above and the points in a buffer zone a small distance off of the trajectory in the +/-p direction for the reasons just expressed. After initial experimentation with the linear feature calculation in conjunction with the local contrast measure it was found that too many true-positive microcalcification candidates were eliminated by sequentially thresholding objects on the basis of local contrast and then by a linear feature measure. Obviously, some manner of weighting the two features simultaneously would have to be used. The Mahalanobis distance measure as applied to the two-dimensional feature space defined by the local contrast and linear features was used in this application. The Mahalanobis distance is calculated from where x is the vector of feature values of the microcalcification candidate being examined mk is the vector of the class feature means K k is the class covariance matrix The class statistics and covariance matrices were obtained by calculating the two features for all microcalcification candidates surviving the local adaptive thresholding and morphological erosion stages of the processing sequence. Each candidate object was determined to belong to one of the classes of Chapter 6 - Hybrid Methods for Microcalcification Detection 64 microcalcification, connective tissue outline and background by visual evaluation of the raw digitized image at the location of the detected microcalcification candidate object. Approximately 50 example feature pairs were obtained for each of the three classes. Class statistics were obtained from the sets of feature pairs for each classes using a statistical analysis software package. The xj values correspond to contrast values and X2 values to linear pattern feature values. The class statistics obtained were as follows: Class 1 (Microcalcifications) m u = 0.31 m 1 ; 2 = 60.31 9.85e-3 -1.82e-l -1.82e-l 1.58e + 3 Class 2 (Connective Tissue) Class 3 (Background) m2ji=0.21 m2 2 = 188.53 6.86e-3 -4.96<?-2 -4.96e-2 1.59e+3 m 3 ; 1 = 0.16 m3;2 = 55.90 K 3 = 2.64e-3 -2.2\e-l -2.2le-\ 1.32e + 3 Microcalcification candidates are classified based on their feature pairs on the basis of Mahalanobis distance. The microcalcification candidate is assigned to the class corresponding to the smallest distance measure of the three possible classes. Figure 6.9 shows the final output after candidates deemed not to be microcalcification have been eliminated. Chapter 6 - Hybrid Methods for Microcalcification Detection 65 Figure 6.9 - Final output after combined local contrast and linear pattern analysis Chapter 6 - Hybrid Methods for Microcalcification Detection 66 6.4 Results and Discussion In order to assess the performance of these methods, four combinations of the various techniques described above were implemented and evaluated with the test image set. Figure 6.10 illustrates the stepwise arrangement of these four configurations henceforth denoted NESB, NES2, NES3 and NES4. NESB NES2 NES3 NES4 INPUT INPUT INPUT INPUT Wavelet Enhancement Local Adaptive Thresholding Wavelet Enhancement Local Adaptive Thresholding 1 Eros ion Wavelet Enhancement Local Adaptive Thresholding 1 Erosion Local Contrast Thresholding T 1 Contrast Stretching > Wavelet Enhancement i Local Adaptive Thresholding Erosion Feature Classifier T OUTPUT OUTPUT OUTPUT OUTPUT Figure 6.10 - Block diagram illustrating the step-wise arrangement of the tested methods Chapter 6 - Hybrid Methods for Microcalcification Detection 67 6.4.1 Evaluation of the NESB Configuration The NESB configuration consists of only the wavelet enhancement process as discussed in Section 6.1 and the local adaptive thresholding process described in Section 6.2. Since no further false-positive reduction techniques were applied after the thresholding step a relatively high value of T c o n s t = 8.5 was used to prevent an overwhelming number of false-positive detections to result from the application of these techniques. The results for the application of NESB detection method are detailed in Appendices C, D, and E on the pages with "NESB" as the algorithm type. The application of this method to the set of test images resulted in the detection of 39 of the 42 true clusters for a true-positive cluster detection rate of 93%. There were 10 false-positive clusters detected giving a false-positive rate of 0.33 false-positive cluster per image or 0.26 false-positive clusters per true-positive cluster detection. Of the 10 false-positive cluster detections, 3 were attributed to regions of prominent glandular tissue and 7 were generated by connective tissue outlines. CASE3213 was responsible for 4 of the 10 false-positive cluster detections. Of the 511 true microcalcifications, 363 were successfully detected for a true-positive microcalcification detection rate of 71%. There were 162 false-positive microcalcifications detected giving a false-positive microcalcification detection rate of 5.4 false-positive detections per image or 0.45 false-positive microcalcification detections per true-positive detection. Of the false-positive microcalcification detections 38% were generated by glandular tissue, 59% were generated by connective tissue and 3% were attributed to film defects. This method resulted in 8 retrospective cluster detections and 87 retrospective microcalcification detections. Chapter 6 - Hybrid Methods for Microcalcification Detection 68 6.4.2 Evaluation of the NES2 Configuration The NES2 configuration consists of wavelet enhancement, local adaptive thresholding and morphological erosion as discussed in Sections 6.2 and 6.3.1. The threshold multiplier constant was set to T c o n s t = 8.5. The results for the application of NES2 detection method are detailed in Appendices C, D and E on the pages with "NES2" as the algorithm type. The application of this method to the set of test images resulted in the detection of 28 of the 42 true clusters for a true-positive cluster detection rate of 67%. There were 6 false-positive clusters detected giving a false-positive rate of 0.20 false-positive cluster per image or 0.21 false-positive clusters per true-positive cluster detection. Of the 6 false-positive cluster detections, 1 was attributed to regions of prominent glandular tissue and 5 were generated by connective tissue outlines. CASE3213 was responsible for 4 of the 5 false-positive clusters. Of the 511 true microcalcifications, 209 were successfully detected for a true-positive microcalcification detection rate of 41%. There were 35 false-positive microcalcifications detected giving a false-positive microcalcification detection rate of 1.2 false-positive detections per image or 0.17 false-positive microcalcification detections per true-positive detection. Of the false-positive microcalcification detections 9% were generated by glandular tissue, 89% were generated by connective tissue and 2% were attributed to film defects. CASE3213 was responsible for 57% of the false-positive microcalcifications. This method resulted in 6 retrospective cluster detections and 18 retrospective microcalcification detections. Chapter 6 - Hybrid Methods for Microcalcification Detection 69 6.4.3 Evaluation of the N E S 3 Configuration The NES3 configuration consists of wavelet enhancement, local adaptive thresholding, morphological erosion and local adaptive contrast thresholding. The threshold multiplier constant was set to T c o n s t = 7.5. The local adaptive contrast threshold was set to T c s t = 0.18. The results for the application of NES3 detection method are detailed in Appendices C, D and E on the pages with "NES3" as the algorithm type. The application of this method to the set of test images resulted in the detection of 33 of the 42 true clusters for a true-positive cluster detection rate of 79%. There were 4 false-positive clusters detected giving a false-positive rate of 0.13 false-positive cluster per image or 0.12 false-positive clusters per true-positive cluster detection. Of the 4 false-positive cluster detections, 1 was attributed to regions of prominent glandular tissue and 3 were generated by connective tissue outlines. CASE3213 was responsible for 3 of the 4 false-positive clusters. Of the 511 true microcalcifications, 235 were successfully detected for a true-positive microcalcification detection rate of 46%. There were 29 false-positive microcalcifications detected giving a false-positive microcalcification detection rate of 0.97 false-positive detections per image or 0.12 false-positive microcalcification detections per true-positive detection. Of the false-positive microcalcification detections 14% were generated by glandular tissue, 83% were generated by connective tissue and 3% were attributed to film defects. CASE3213 was responsible for 48% of the false-positive microcalcifications. This method resulted in 6 retrospective cluster detections and 13 retrospective microcalcification detections. Chapter 6 - Hybrid Methods for Microcalcification Detection 70 6.4.4 Evaluation of the NES4 Configuration The NES4 configuration consists of wavelet enhancement, local adaptive thresholding, morphological erosion and combined local contrast and linear feature assessment. The threshold multiplier constant was set to T c o n s t = 7.0. The class statistics listed in Section 6.3.3 were used to generate Mahalanobis distance measurements for feature vector classification. A preprocessing stage involving a contrast stretching operation was added in hope of better optimizing the false-positive discriminating potential of the local adaptive contrast feature. The results for the application of NES4 detection method are detailed in Appendices C, D and E on the pages with "NES4" as the algorithm type. The application of this method to the set of test images resulted in the detection of 33 of the 42 true clusters for a true-positive cluster detection rate of 79%. This was the same true-positive cluster detection rate as NES3. The same false-positive cluster detection statistics were also the same as NES3 with 4 false-positive clusters detected giving a false-positive rate of 0.13 false-positive cluster per image or 0.12 false-positive clusters per true-positive cluster detection. All of the 4 false-positive clusters were generated by connective tissue. CASE3213 was responsible for 3 of the 4 false-positive clusters. Of the 511 true microcalcifications, 234 were successfully detected for a true-positive microcalcification detection rate of 46%. There were 42 false-positive microcalcifications detected giving a false-positive microcalcification detection rate of 1.4 false-positive detections per image or 0.18 false-positive microcalcification detections per true-positive detection. Of the false-positive microcalcification detections 21% were generated by glandular tissue and 79% were generated by connective tissue. CASE3213 was responsible for 40% of the false-positive microcalcifications. This method resulted in 5 retrospective cluster detections and 19 retrospective microcalcification detections. Chapter 7 Comparative Performance Assessment 7.1 Microcalcification Cluster Detection Performance As was stated in Section 1.6 of this thesis, the goal of this work is to produce methods for microcalcification cluster detection adequate for the task of microcalcification cluster prompting. This level of performance was established as meeting or exceeding the mimmum performance bounds of 80% (or greater) true-positive microcalcification cluster detection with 1.5 (or less) false-positive cluster detections per image. Table 7.1 below summarizes the microcalcification cluster detection performance for the six methods examined. As was noted in earlier sections detailing the results for the individual detection schemes, CASE3213 was an extremely difficult case, often accounting for more than 1/2 of the false-positive detections per method. It seems reasonable then to eliminate the output for this image as "outlier" data so that this one case does not overly influence the results. Table 7.2 shows the performance data with CASE3213 results omitted from consideration. The definition of a single image is a difficult one. All test images used in the experiments conducted for this thesis were 512x512 pixel images digitized at a 48 um sampling interval. This corresponds to a region roughly 6.25 cm in area. A standard mammogram film size is 8" x 10" or 20.3 cm x 25.4 cm 2 which amounts to an area of 516 cm . As an approximation, the area of a mammogram film corresponding to the breast parenchyma, which is the only area that need be examined for the presence of microcalcifications, could be estimated to be 1/4 of the area of a mammogram film on average. The rest of the film area is occupied by empty space and the image of the chest wall etc. Therefore, the 512 x 512 71 Chapter 7 - Comparative Performance Assessment 72 test images correspond roughly to 4 * 6.25cm2 / 516cm2 = 1/20 of the film area requiring processing for the detection of microcalcification abnormalities. A reasonable estimate of the false-positive detection data extrapolated for full-breast processing can then be obtained by multiplying the false-positive detection rates by a factor of 20. The area corrected false-positive rates are also shown in Table 7.2. True-Positive Rate False-Positive Rate (FP / image) DENG 86% 0.10 KARS 69% 0.00 NESB 93% 0.33 NES2 67% 0.20 NES3 79% 0.13 NES4 79% 0.13 Table 7.1 - Summary of microcalcification cluster detection performance True-Positive Rate False-Positive Rate (F.P. / image) Area Corrected False-Positive Rate (F.P. / image) DENG 85%> 0.00 0.00 KARS 71% 0.00 0.00 NESB 93% 0.20 4.00 NES2 66% 0.07 1.40 NES3 78%o 0.03 0.60 NES4 78%o 0.03 0.60 Table 7.2 - Microcalcification cluster detection performance with CASE3213 omitted Chapter 7 - Comparative Performance Assessment 73 Of the methods implemented for this thesis the DENG algorithm demonstrated the best over-all performance with a true-positive cluster detection rate of 85% with 0.0 false-positives per image with CASE3213 omitted from the data analysis. The weakness of the DENG method is that is responds most strongly to objects roughly circular in profile and will tend to miss microcalcifications which are more linear in shape. This is unfortunate since many malignant microcalcification formations have this linear appearance. The DENG method also tends generate a "rounded-out" inaccurate segmentation of the microcalcifications. This is not important for cluster detection but if the output of the detection algorithm is carried forward for risk-assessment the segmented shape of the detected microcalcifications will have to be corrected with further processing. Clearly the DENG method surpasses the minimum criteria set for supporting the task of cluster prompt generation. The NES3 and NES4 methods also performed well giving true-positive cluster detection rates of 78%. The area corrected false-positive rate was 0.60 for both methods. The NES3 and NES4 methods have the advantage that they produce relatively good segmentation in their detection output and have a less pronounced shape detection bias as the DENG algorithm. The NES3 and NES4 methods provided a true-detection rate slightly lower than the mimmum criteria for a successful cluster prompt generator. However, the true-positive performance is close enough to this limit that additional optimization of these methods could provide acceptable performance. The KARS algorithm produced an all-round lower performance. Great difficulty was experienced in setting random field model parameter values that gave good results for the entire test image set. The iso-precision scaling that Karssemeijer [21] documented might improve the performance of this method. The KARS method gave results considerably lower than the minimum criteria for successful cluster prompt generation. The NESB method produced the highest true-positive detection rate but also had the highest false-positive detection rate. If used with more advanced false-positive suppression techniques, such it could prove to be Chapter 7 - Comparative Performance Assessment 74 a valuable tool in generating a method with overall high-sensitivity. The true-positive rate for the NESB method was significantly better than the minimum level of performance for cluster prompt generation. Unfortunately, the false-positive cluster detection rate is far too high for this application. Retrospective Clusters DENG 8 KARS 4 NESB 8 NES2 6 NES3 6 NES4 5 Table 7.3 - Retrospective cluster detections summary Table 7.3 provides a summary of retrospective cluster detections. These retrospective detections are of particular importance because they emphasize the ability of CADx prompting techniques to catch a significant number of subtle cancers that would otherwise go unnoticed. 7.1.1 Comparison of Results with Other Groups Comparison of these results to those published by other groups is made extremely difficult by the wide variations in the selection and size of the image database, the digitization method and performance assessment methodology. A group at the Kurt Rossmann Laboratories for Radiologic Image Research at the University of Chicago has emerged as the world leader in clinically viable CADx techniques for the automated detection of Chapter 7 - Comparative Performance Assessment 75 microcalcification abnormalities and mass lesions [24, 25, 26, 27, 28, 29]. The methods developed by this group have undergone a greater degree of clinical verification than any other group in the world. As such, their published results will be used as a comparison for the results obtained for this thesis work. The University of Chicago group performs CADx examination of full-breast images. Standard 8"xl0" films are digitized at a 0.1mm pixel size to produce a 2048 x 2580 pixel image [31]. An automated segmentation method isolates imaged breast tissue from the rest of the film. Further processing is applied only to this segmented region. On the basis of this information approximate comparisons can be made with the true-positive rates and area-corrected false-positive rates in Table 7.2. The University of Chicago group reported on a study conducted on a database of 78 mammograms containing a total of 41 microcalcification clusters. The method they used for their study is as discussed in the introductory section of this thesis. The published results indicate a true-positive microcalcification cluster detection rate of 85.4% with a corresponding false-positive detection rate of 0.5 clusters per image [31]. From the area corrected false-positive cluster detection rates in Table 7.2 it can be seen that the DENG method provides a true-positive detection rate just slightly lower than that demonstrated by Nishikawa et al. [31] but with a false-positive detection rate of 0.0 false-positive clusters per image. Obviously a false-positive detection of 0.0 false-positives per image is unrealistic and a study conducted on a larger set of images would undoubtedly result in a non-zero false-positive detection rate. However, in the absence of evidence to the contrary we will assume the false-positive rate of the DENG method is lower than that reported by Nishikawa et al [31]. The NES3 and NES4 methods show true-positive rates approximately 5% lower than the results from the University of Chicago group. The area-corrected false-positive rates are slightly higher that that for the University of Chicago. Chapter 7 - Comparative Performance Assessment 76 In the end, the strongest statement that can realistically be made here is that the DENG, NES3 and NES4 methods offer similar performance characteristics as those of the method developed by Nishikawa et al. at the University of Chicago. 7.2 Microcalcification Detection Performance The detection performance for microcalcifications was also assessed. Although the performance of microcalcification detection is less important than cluster detection, the microcalcification detection performance gives an idea of the potential of the methods for risk assessment tasks. The higher the microcalcification detection rate is, the more complete the detection of all of the microcalcifications in a given cluster. The microcalcification detection data also gives a better review of the effectiveness of false-positive reduction methods. The microcalcification detection performance is summarized in Table 7.4. The trend in the performance is similar to that for cluster detection. False-positive rates in Table 7.4 were not area corrected as only the relative performance need be examined in this case. True-Positive Rate False-Positive Rate (F.P. / image) DENG 61% 4.43 KARS 57% 0.93 NESB 71% 5.40 NES2 41% 1.17 NES3 46% 0.97 NES4 46% 1.40 Table 7.4 - Summary of microcalcification detection performance Chapter 7 - Comparative Performance Assessment 77 In Table 7.5 the false-positive microcalcifications are listed by source and the contribution by source is detailed in brackets. From the table it can be concluded that the addition of the false-positive reduction methods in NES2 with morphological erosion, NES3 with morphological erosion and local adaptive contrast thresholding that the false-positive detection rate also decreased. In NES4, however, the false-detection rate climbed. One would also have expected the false-positive related to connective tissue sources to also decrease, this did not occur. From the data in Table 7.2 and Table 7.4 that the morphological erosion and local adaptive contrast thresholding schemes are successful in reducing the number of false-positive detections but also reduce the sensitivity of the detection scheme a considerable amount. From the results for NES4, it would seem that linear pattern feature was not effective in reducing the number of false-positive detections as it was intended to do. FALSE-POSITIVE DISTRIBUTION Glandular Tissue Connective Tissue Film Defects DENG 59 (44%) 73 (55%) 1 (1%) KARS 24 (86%) 2 (7%) 2 (7%) NESB 61 (38%) 94 (58%) 7 (4%) NES2 3 (9%) 31 (86%) 1 (3%) NES3 4(14%) 24 (83%) 1 (3%) NES4 9 (21%) 33 (79%) 0 (0%) Table 7.5 - False-positive microcalcification detections listed by source Chapter 7 - Comparative Performance Assessment 78 Retrospective Microcalcifications DENG 33 KARS 5 NESB 87 NES2 18 NES3 13 NES4 19 Table 7.6 - Retrospective microcalcification detections summary Table 7.6 shows the number of retrospective microcalcification detections by method. Again, the trend in sensitivity is consistent with the results for cluster and microcalcification detections. Chapter 8 Conclusions And Discussion As a part of this thesis work, an improved prototype of the Analytical Imaging Mammography (ATM) system originally developed by Aghdasi was designed and constructed. This system is intended to provide a flexible platform for mammogram film digitization and analysis. Improvements in the AIM system included: (i) novel hardware and software for automatic, computerized focus and camera position control and (ii) a versatile, friendly user interface. The new prototype was found to perform extremely well and was used extensively in the digitization and analysis of mammogram film images for this thesis work. Two methods from the research literature for the detection of microcalcifications were implemented. In addition, four novel methods developed for the task of detecting microcalcification clusters were designed and implemented. Criteria for the performance of microcalcification detection techniques in the application of generating prompts to alert radiologists to potential microcalcification clusters were established as 80% (or greater) true-positive cluster detection rate and a 1.5 (or less) false-positive detection rate. The performance of the two microcalcification detection methods from the literature and the four novel methods were tested on a set of 30 test images and evaluated against criteria for the task of prompting screening radiologists for microcalcification clusters. The microcalcification method described by Dengler et al. [44] was found to provide the best performance with an 85% true-positive microcalcification detection rate and a 0.0 false-positive cluster per image detection rate. This performance was well above that established for adequate performance in the task of prompt generation. Two of the novel methods for microcalcification detection, NES3 and NES4, were found to be very close to the minimum criteria for generating prompts for microcalcification clusters with true-positive detection rates of 79% and false-positive detection rates of 0.6 clusters per image. The false-79 Chapter 8 - Conclusions and Discussion 80 positive rates for all methods are corrected to estimate their performance for full-breast image analysis as opposed to processing regions of interest as was performed in the experiments here. The weakness of the method described by Dengler et al. is that is responds most strongly to objects roughly circular in profile and will tend to miss microcalcifications which are more linear in shape. This is unfortunate since many malignant microcalcification formations have this linear appearance. The four novel methods have the advantage that they have a less pronounced shape detection bias than the Dengler algorithm. From the results obtained, it can be concluded that the novel methods developed as a part of this work for false-positive detection reduction do reduce the number of false-positive detections but also reduce the true-positive rates of the detection methods by an unacceptable margin. The number of retrospective microcalcification cluster detections obtained from the application of all the tested methods for automated microcalcification detection emphasize the potential of CADx prompting techniques to detect a significant number of cancers that would otherwise be missed. 8.1 Directions for Future Work The experimental results confirm the ability of signal extraction techniques to demonstrate a high level of true-positive detection in the task of microcalcification detection. They also demonstrate the difficulty of obtaining the corresponding level of false-positive detection required to implement a clinically useful system to prompt radiologists to examine potential microcalcification abnormalities. The challenge is to find techniques that effectively reduce the false-positive microcalcification detection rate while not dramatically lowering the sensitivity of the technique. Chapter 8 - Conclusions and Discussion 81 More study is required to assess and improve the performance of the local adaptive contrast measure. A lower contrast threshold value would most likely improve the performance of this feature. A Receiver Operating Characteristic study should be performed to find the best contrast threshold for the use of this feature. The framework of the Mahalanobis distance feature classifier could easily be expanded to accommodate a larger set of features. Other features that might prove valuable in this application should be investigated. Nishikawa et al. [31] demonstrated tremendous improvement in terms of false-positive reduction using a shift-invariant neural network for post-processing of the output of their microcalcification detection routines. Some initial work was performed in this area by the author to implement a similar scheme, more work in this area could produce significant results. 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APPENDIX A SAMPLE PERFORMANCE EVALUATION SHEET 90 Automated Microcalcification Detection Assessment TEST IMAGE RADIOLOGIST GROUND TRUTH # of clusters Cluster conspiquity rating: obvious subtle very subtle # of microcalcifications TRUE-POSITIVE DETECTIONS DENG KARS NESB NES2 NES3 NES4 # of clusters # of microcalcifications RE-VISIT DETECTIONS DENG KARS NESB NES2 NES3 NES4 # of clusters # of microcalcifications 91 FALSE-POSITIVE DETECTIONS DENG KARS NESB NES2 NES3 NES4 # of clusters Sources: Glandular Tissue Connective Tissue Film Defects # of microcalcifications Sources: Glandular Tissue Connective Tissue Film Defects A P P E N D I X B R A D I O L O G I S T G R O U N D T R U T H S U M M A R Y 93 AUTOMATED MICROCALCIF CATION DETECTION ASSESSMENT Radiologist Ground Truth CONSP QUITY RATING CASE# # OF CLUSTERS Obvious Subtle V. Subtle # OF MICF tOCALCIF CATIONS 0123 1 1 9 0313 1 1 6 0413 1 1 8 0423 1 1 5 0523 4 1 3 27 0613 1 1 5 0623 2 2 11 0823 2 1 1 10 0913 1 1 26 0923 1 1 18 1513 1 1 20 1523 1 1 16 2213 1 1 42, 2413 1 1 31 2423 1 1 26 2723 2 1 1 29 2913 2 2 27 2923 3 . . . . . . 1 1 1 22 3013 1 1 19 3123 1 1 11 3213 1 1 17 3323 1 1 8 3513 1 1 15 3623 1 1 10 3723 2 12 3913 1 1 18 4023 1 1 16 4123 1 1 7 4313 2 1 1 1? 4323 2 1 1 23 . TOTALS 42 18 10 14 511 94 APPENDIX C TRUE-POSITIVE ANALYSIS SUMMARIES 95 AUTOMATED MICROCALCIFICATION DETECTION ASSESSMENT True-Positive Analysis: DENG CLUS TERS MICROCAL CIFICATIONS CASE# TRUTH DATA #DETECTED TRUTH DATA #DETECTED 0123 1 1 9 3 0313 1 1 6 4 0413 1 1 8 4 0423 1 1 5 2 0523 4 27, 17 0613 1 1 5 3 0623 2 11 5 0823 2 1 10 7 0913 1 1 26 16 0923 1 1 18 14 1513 1 1 20 13 1523 1 1 16 10 2213 1 1 42 19 2413 1 1 31 21 2423 1 1 26 16 2723 2 0 29 2 2913 2 2 27 25 2923 3 3 22 21 3013 1 1 19 15 3123 1 1 11 9 3213 1 1 17 9 3323 1 8 2 3513 1 1 15 11 3623 1 1 10 7 3723 1 12 6 3913 1 1 18 4 4023 1 1 16 12 4123 1 1 7 4 4313 2 2 17 14 4323 2 2 23 16 TOTALS 42 36 511 311 96 AUTOMATED MICROCALCIFICATION DETECTION ASSESSMENT True-Positive Analysis: KARS CLUS TERS MICROCAL CIFICATIONS CASE# TRUTH DATA # DETECTED TRUTH DATA # DETECTED 0123 1 1 9 9 0313 1 1 6 4 0413 1 1 8 8 0423 1 1 5 6 0523 4 27 8 0613 1 1 5 2 0623 2 11 8 0823 2 1 10 6 0913 1 1 26 12 0923 1 1 18 6 1513 1 1 20 14 1523 1 1 16 12 2213 1 1 42 19 2413 1 31 2 2423 1 1 26 20 2723 2 1 29 10 2913 2 27 25 2923 3 22 12 3013 1 1 19 15 3123 1 1 11 3 3213 1 17 3 3323 1 1 8 3 3513 1 1 15 . 15 3623 1 1 10 10 3723 2 12 10 3913 1 0 18 3 4023 1 0 16 2 4123 1 1 7 12 . 4313 2 • 2. 17 8 4323 2 2 23 23 TOTALS 42 29 511 290 97 AUTOMATED MICROCALCIFICATION DETECTION ASSESSMENT True-Positive Analysis: NESB CLUS TERS MICROCAL CIFICATIONS CASE# TRUTH DATA # DETECTED TRUTH DATA # DETECTED 0123 1 1 9 4 0313 1 1 6 6 0413 1 1 8 5 0423 1 1 5 3 0523 4 3 27 22 0613 1 1 5 3 0623 2 2 11 8 0823 2 2 10 8 0913 1 1 26 24 0923 1 1 18 16 1513 1 1 20 14 1523 1 1 16 11 2213 1 1 42 27 2413 1 1 31 13 2423 1 1 26 15 2723 2 1 29 17 2913 2 • 2 27 21 2923 3 3 22 22 3013 1 0 19 12 3123 1 1 11 11 3213 1 1 17 11 3323 1 1 8 5 3513 1 1 15 13 3623 1 1 10 9 3723 12 8 3913 1 1 18 8 4023 1 1 16 12 4123 1 1 7 7 4313 2 2 17 12 4323 2 2 23 16 TOTALS 42 39 511 363 98 AUTOMATED MICROCALCIFICATION DETECTION ASSESSMENT True-Positive Analysis: NES2 CLUS TERS MICROCAL CIFICATIONS CASE # TRUTH DATA # DETECTED TRUTH DATA # DETECTED 0123 1 1 9 3 0313 1 1 6 4 0413 1 1 8 2 0423 1 1 5 2 0523 4 27 11 0613 1 1 5 2 0623 2 1 11 4 0823 2 10 7 0913 1 1 26 10 0923 1 1 18 5 1513 1 1 20 10 1523 1 1 16 8 2213 1 42 9 2413 1 31 8 2423 1 1 26 10 2723 2 1 29 9 2913 2 27 16 2923 3 1 22 14 . 3013 1 19 6 3123 1 1 11 6 3213 1 1 17 11 3323 1 8 1 3513 1 1 15 7 3623 1 1 10 8 3723 1 12 5 3913 1 0 18 2 4023 1 0 16 9 4123 1 .1 7 4 4313 2 2 17 9 4323 2 0 23 7 TOTALS 42 28 511 209 J 99 AUTOMATED MICROCALCIFICATION DETECTION ASSESSMENT True-Positive Analysis: NES3 CLUS TERS MICROCAL CIFICATIONS C A S E # TRUTH DATA # DETECTED TRUTH DATA # DETECTED 0123 1 1 9 4 0313 1 1 6 4 0413 1 1 8 • • • 4 0423 1 1 5 2 0523 4 3 27 11 0613 1 1 5 2 0623 2 2 11 7 0823 2 1 10 6 0913 1 1 26 12 0923 1 1 ,18 8 1513 1 .1: 20 14 1523 1 • ' 1 16 10 2213 1 1 42 10 2413 . 1 . 0 31 11 2423 1 1 26 11 2723 2 1 29 4 2913 2 2 27 16 2923 3 2 22 17 3013 1 0 19 7 3123 1 1 11 5 3213 1 1 17 8 3323 1 0 8 1 3513 1 1 15 8 3623 1 1 10 8 3723 2 12 9 3913 1 0 18 1 4023 1 0 16 9 4123 1 1 7 4 4313 2 2 17 10 4323 2 2 23 12 TOTALS 42 33 511 235 100 AUTOMATED MICROCALCIFICATION DETECTION ASSESSMENT True-Positive Analysis: NES4 CLUS TERS MICROCAL CIFICATIONS CASE# TRUTH DATA #DETECTED TRUTH DATA # DETECTED 0123 1 1 9 4 0313 1 1 . 6 5 0413 1 1 8 4 0423 1 1 5 2 0523 4 3 27 11 0613 1 1 5 2 0623 2 2 11 7 0823 2 1 10 4 P913 1 1 26 :. 11 0923 1 1 18 7 1513 1 1 20 13 1523 1 1 16 10 2213 1 1 42 12 2413 1 0 31 10 2423 1 1 26 11 • 2723 2 1 29 7 2913 2 2 27 14 2923 3 2 22 16 3013 1 0 19 7 3123 1 1 11 6 3213 1 1 17 9 3323 1 0 8 1 3513 1 1 , 15 9 3623 ' 1 1 10 7 3723 2 12 , 9 3913 1 0 18 1 4023 1 0 16 8 4123 1 1 7 5 4313 2 2 17 10 4323 2 2 23 12 TOTALS 42 33 511 234 101 APPENDIX D FALSE-POSITIVE ANALYSIS SUMMARIES 102 AUTOMATED MICROCALCIFICATION DETECTION ASSESSMENT False-Positive Analysis: DENG CLUSTERS MICROCALCIFICATIONS CASE # t Glandular Connective Film Defects Glandular Connective Film Defects 0123 0 0 0 0 0 0 0313 0 0 0 0 0 0 0413 0 0 0 0 0 0 0423 0 0 0 0 0 0 0523 0 0 0 0 2 0 0613 0 0 0 0 0 0 0623 0 0 0 0 0 0 0823 0 0 0 0 0 0 0913 0 0 0 1 4 0 0923 0 0 0 0 0 0 1513 0 0 0 1 0 0 1523 0 0 0 0 . 0 0 2213 0 0 0 0 0 0 2413 0 0 0 5 0 0 2423 0 0 0 4 • 2 0 2723 0 0 0 0 0 0 2913 0 0 0 7 1 0 2923 0 0 0 0 3 0 3013 0 0 0 27 0 0 3123 0 0 0 5 4 0 3213 0 3 0 0 40 0 3323 0 0 0 0 0 0 3513 0 0 0 6 7 0 3623 0 0 p 0 0 0 3723 0 0 0 0 3 0 3913 0 0 0 0 1 0 4023 0 0 0 2 0 0 4123 0 0 0 0 1 0 4313 0 0 0 0 4 0 4323 0 0 0 1 1 1 TOTALS 0 3 0 59 73 1 GRAND TOTALS 3 133 103 AUTOMATED MICROCALCIFICATION DETECTION ASSESSMENT False-Positive Analysis: KARS CLUSTERS MICF IOCALCIFICATIONS CASE # Glandular Connective Film Defects Glandular . Connective Film Defects 0123 .0 0 0 0 0 0 0313 0 0 0 0 0. 0 0413 0 0 0 0 0 0 0423 0 0 0 0 0 1 0523 0 0 0 0 0 0 0613 0 0 0 0 0 0 0623 0 0 0 0 0 0 0823 0 0 0 0 0 0 0913 0 0 0 0 1 0 0923 0 0 0 0 0 0 1513 0 0 0 0 0 0 1523 0 0 0 0 1. 0 2213 0 0 . 0 0 0 0 2413 0 0 0 0 0 0 2423 0 0 0 0 0 0 2723 0 0 0 0 0 0 2913 0 0 0 0 0 0 2923 0. 0 0 0 0 0 3013 0 0 0 0 0 0 3123 0 0 0 0 0 0 3213 0 0 0 0 0 0 3323 0 0 0 0 0 0 3513 0 0 0 24 0 0 3623 0 0 0 0 0 0 3723 0 0 0 0 0 0 3913 0 0 0 0 0 0 4023 0 0 0 0 0 0 4123 0 0 0 0 0 0 4313 0 0 0 0 0 0 4323 0 0 0 0 0 1 TOTALS 0 0 0 24 2 2 GRAND TOTALS 0 28 104 AUTOMA1 fED MICROCALCIFICATION DETECTION ASSESSMENT False-Pos itive Analysis: NESB CLUSTERS MICROCALCIFICAT ONS CASE # Glandular Connective Film Defects Glandular Connective Film Defects 0123 0 0 0 0 0 0 0313 0 .0 0 9 8 0 0413 0 0 0 0 8 0 0423 0 0 0 0 0 1 0523 0 0 0 0 2 0 0613 0 0 0 0 0 0 0623 0 0 0 0 0 0 0823 0 0 o. 2 2 0 0913 0 0 0 4 7 0 0923 0 o 0 0 0 . 0 1513 0 0 0 1 1 0 1523 0 0 0 5 0 0 2213 0 0 0 1 0 0 2413 1 0 0 7 2 0 2423 0 0 0 0 0 0 2723 0 0 0 0 0 0 2913 0 0 0 8 1 0 2923 2 o 0 6 5 0 3013 0 0 0 16 0 0 3123 o 1 0 1 3 0 3213 0 4 0 0 20 0 3323 0 0 0 0 0 0 3513 0 2 0 0 12 0 3623 0 0 0 0 0 0 3723 0 0 0 0 9 0 3913 o 0 0 0 3 0 4023 0 0 0 0 7 0 4123 0 0 0 0 .4 0 4313 0 0 o 0 0 0 4323 0 0 0 1 2 4 TOTALS 3 7 0 61 96 5 GRAND TOTALS 10 162 105 AUTOMATED MICROCALCIFICATION DETECTION ASSESSMENT False-Positive Analysis: NES2 CLUSTERS MICF IOCALCIFICATIONS CASE# Glandular Connective Film Defects Glandular Connective Film Defects 0123 0 0 0 0 0 0 0313 0 0 0 0 0 0 0413 0 0 0 0 1 0 0423 0 0 0 0 0 1 0523 0 0 0 o 2 0 0613 0 0 0 0 0 0 0623 0 0 0 0 0 0 0823 0 0 0 0 0 0 0913 0 1 0 1 2 0 0923 0 0 0 0 0 0 1513 o 0 0 1 0 0 1523 0 0 0 0. 0 0 2213 0 0 o 0 0 0 2413 0 0 0 0 0 0 2423 0 CL 0 0 0 0 2723 0 0 0 0 0 0 2913 . 0 0 0 0 1 0 2923 1 0 0 0 3 0 3013 0 0 0 0 0 0 3123 o 0 0 0 0 0 3213 0 4 0 o 20 0 3323 0 0 0 o 0 0 3513 0 0 0 0 0 0 3623 0 0 0 0 0 0 3723 0 0 0 0 0 0 3913 0 0 0 0 0 0 4023 0 0 0 0 2 0 4123 0 0 0 0 0 0 4313 0 0 0 0 0 0 4323 0 0 0 1 0 0 TOTALS 1 5 0 3 31 1 GRAND TOTALS 6 35 106 AUTOMATED MICROCALCIFICATION DETECTION ASSESSMENT False-Positive Analysis: NES3 CLUSTERS MICF tOCALCIFICATIONS CASE # Glandular Connective Film Defects Glandular Connective Film Defects 0123 0 0 0 0 0 0 0313 0 0 0 0 0 0 0413 0 0 0 0 0 0 0423 0 0 0 0 0 1 0523 0 0 0 0 2 0 0613 0 0 0 0 0 0 0623 0 0 0 0 0 0 0823 0 0 0 0 0 0 0913 0 0 0 0 2 0 0923 0 0 0 0 0 0 1513 0 0 0 0 0 0 1523 0 0 0 1 0 0 2213 0 0 0 0 0 0 2413 0 0 0 0 0 0 2423 0 0 0 0 0 0 2723 0 0 0 0 0 0 2913 0 0 0 0 0 0 2923 1 0 0 0 3 0 3013 0 0 0 2 0 0 3123 0 0 0 0 0 0 3213 0 3 0 0 14 0 3323 0 0 0 0 0 0 3513 0 0 0 0 3 0 3623 0 0 0 0 0 0 3723 0 0 0 0 0 0 3913 0 0 0 0 0 0 4023 0 0 0 1 0 0 4123 0 0 0 0 0 0 4313 0 0 0 0 0 0 4323 0 0 0 0 0 0 TOTALS 1 3 0 4 24 1 GRAND TOTALS 4 29 107 AUTOMA1 fED MICROCALCIFICATION DETECTION ASSESSMENT False-Pos itive Analysis: NES4 CLUSTERS MICF tOCALCIFICAT ONS CASE# Glandular Connective Film Defects Glandular Connective Film Defects 0123 0 0 0 0 0 0 0313 0 0 0 0 0 0 0413 0 0 0 0 0 0 0423 0 0 0 0 0 0 0523 0 0 0 0 2 0 0613 0 0 0 0 0 0 0623 0 0 0 0 0 0 0823 0 0 0 0 0 0 0913 0 0 0 0 1 0 0923 0 0 0 0 0 0 1513 0 0 0 1 0 0 1523 0 0 0 1 0 0 2213 0 0 0 0 0 0 2413 0 0 0 1 0 0 2423 0 0 0 0 0 0 2723 0 0 0 0 0 0 2913 0 0 0 0 0 0 2923 0 0 0 0 0 0 3013 0 0 0 2 0 0 3123 0 1 0 3 0 0 3213 0 3 0 0 17 0 3323 0 0 0 0 0 0 3513 0 0 0 0 5 0 3623 0 0 0 1 0 0 3723 0 0 0 0 4 0 3913 0 0 0 0 0 0 4023 0 0 0 0 1 0 4123 0 0 0 0 1 0 4313 0 0 0 0 0 0 4323 0 0 0 0 2 0 TOTALS 0 4 0 9 33 0 GRAND TOTALS 4 42 108 APPENDIX E R E T R O S P E C T I V E DETECTIONS S U M M A R Y 109 AUTOMATED MICROCALCIFICATION DEI fECTION ASSESSME NT Retrospective Detection Analysis CLUS TERS C A S E # DENG KARS NESB NES2 NES3 NES4 0123 0 0 0 0 0 0 0313 0 0 0 0 0 0 0413 0 0 0 0 0 0 0423 0 0 0 0 0 0 0523 0 0 0 0 0 0 0613 0 0 0 0 0 0 0623 0 0 0 0 0 0 0823 0 0 1 1 0 0 0913 0 0 0 0. 0 0 0923 0 0 3 0 1 0 1513 0 0 0 0 0 0 1523 0 0 0 0 0 0 2213 0 0 0 0 0 0 2413 1 0 1 0. 0 0 2423 1 1 0 0 1 1 2723 0 0 0 0 0 0 2913 3 1 1 2 2 1 2923 1 1 0 1 1 1 3013 0 1 1 1 1 1 3123 0 0 0 0 0 0 3213 0 0 0 0 0 0 3323 0 0 0 0 0 0 3513 1 0 0 0 0 0 3623 0 0 0 0 0 0 3723 0 0 0 0 0 0 3913 0 0 0 0 0 0 4023 1 0 1 1 0 1 4123 0 0 0 0 0 0 4313 0 0 0 0 0 0 4323 0 0 0 0 0 0 TOTALS 8 4 8 6 6 5 MICROCALCIFICATIONS C A S E # DENG KARS NESB NES2 NES3 NES4 Ol 23 1 1 1 0 0 0 0313 1 0 3 1 1 1 0413 0 1 3 0 0 1 0423 0 0 1 0 0 1 0523 3 0 5 0 1 1 0613 0 2 1 0 0 0 0623 1 0 3 1 1 1 0823 0 0 4 1 0 0 110 0913 3 0 5 1 0 1 0923 0 0 3 0 0 0 1513 3 0 2 0 2 2 1523 1 0 1 0 0 0 2213 0 0 0 0 0 0 2413 3 0 2 1 0 0 2423 0 0 2 0 0 1 2723 0 0 2 0 0 . 0 2913 2 0 6 0 0 0 2923 0 0 2 1 0 0 3013 4 0 0 1 2 2 3123 0 0 7 0 1 1 3213 4 0 6 6 .1 1 3323 0 0 2 1 1 1 3513 4 0 6 1 2 1 3623 0 0 7 0 , 0 0 3723 2 0 4 0 1 2 3913 0 0 3 1 0 0 4023 0 0 0 0 0 0 4123 0 0 1 1 0 0 4313 0 0 0 0 0 0 4323 1 1 5 1 0 2 TOTALS 33 5 87 18 13 19 111 

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