report fin 2

Feature Level Fusion for Characterization of Breast Mass using Mammogram and Ultrasound Imaging

CHAPTER I

INTRODUCTION

Breast cancer has become a significant health problem worldwide. In order to prevent the increase of deaths caused by breast cancer, early diagnosis of the disease has been very effective. Detected early, breast cancer is easier to treat, with fewer risks and reduces mortality by 25%[1]. This early detection can be achieved by subjecting women at risk (mainly postmenopausal women) to a mammography every two years, since it takes about five years for a breast tumor to reach 1 mm, two years longer to reach 5mm and one or two years to measure 2 cm, large enough to detect by palpation. Now adays, X-Ray mammography, ultrasound, and magnetic resonance imaging (MRI) are imaging modalities routinely used to screen for breast cancer. It is well known that there is no technology at present, which is capable of curing cancer. But, it is well known that early detection of cancer can aid in recovery and prolong patient life. A major reason for these errors is due to the fact that radiologists depend on visual inspection. During manual screening of a large number of mammograms, radiologists may get easily worn out, missing out vital clues while studying the scans. As yet, there is no definitive literature which focuses on an elaborate discussion on the feature extraction, feature selection and classification methodologies used in breast cancer detection.

Increasing risk of developing breast cancer includes early menarchy, delayed menopause, obesity, infertile mothers, contraceptives, consuming alcohol and certain inherited genetic mutation. Despite advances in other breast imaging modalities, including ultrasound and magnetic resonance imaging, mammography is still a method of choice. However the detection of small malignancies is especially difficult in younger women who tend to present denser breast tissues. Biopsy is applied for the most accurate diagnosis. However, it is an aggressive and high-cost procedure with some risk and causes inconvenience to the patient.

Mammography is the best available inspection facility to detect the symptoms of breast cancer at the early stage and it can disclose information about abnormality, such as masses, microcalcifications, bilateral asymmetry, and architectural distortion. Mammography is the breast image taken with a special X-ray. It uses a low-dose X-ray, high-contrast, and high-resolution film. For the hundreds of mammographic images scanned by a radiologist, only a few are cancerous. While detecting abnormalities, some of them may be missed, as the detection of suspicious and abnormal images is a recurrent mission that causes fatigue and eyestrain. Using enhanced images and segment the suspicious area , extract features , select more accurate features and then classify them into appropriate category are the most important steps that computer aided detection systems should follow. However, due to low contrast and strong noise, digital mammograms are among the most difficult medical images to analyze.

Since the calcification have high attenuation properties and small dense tissues similar to bones, they tend to present low contrast. Thus their visual screening is difficult for physicians. As the above difficulties prevail in the existing methodology of mammographic image

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processing, the improvement of local detail discrimination and removal of noise from the images is a requirement.

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CHAPTER 2

BREAST CANCER

This chapter gives insight into what is cancer, breast cancer, its types, associated signs, diagnostic methods, understanding of these is one of the fundamental requirements to carry out the work.

2.1 Cancer

Uncontrolled multiplication of a group of cells in a particular location of the body is called cancer. Cancer results from a series of molecular events that fundamentally alter the normal properties of cells and the normal control systems that prevent cell overgrowth and invasion to other tissues are disabled. The uncontrolled multiplication of cells forms extra cells which intern may form a mass of tissue called a tumor, tumors are not cancerous always, they can be benign or malignant.

2.1.1 Benign Tumors

These are not cancerous, can be removed and in most cases, they do not appear again. Cells in benign tumors do not spread to other parts of the body.

2.1.2 Malignant Tumors

These are cancerous, can invade nearby tissues and spread to other parts of the body. Among broad categories of cancer types, the breast cancer mainly belongs to the type carcinoma – the cancer that begins in the skin or in tissues that line or cover internal organs. In rare cases breast cancer belongs to the type sarcoma – the cancer that starts in connective tissues such as muscle tissue, fat tissues or blood vessels.

2.2 Breast Anatomy:

The breast of an adult woman is a milk-producing, tear-shaped gland. The front of the chest wall supports and attached to breast on either side of the sternum by ligaments. Breasts are positioned over the pectoral muscles of the chest wall and attached to chest wall by Cooper‟s ligaments, the fibrous strands.

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Fig 2.1 Breast anatomy.

Breast is mainly composed of glandular, fatty, and fibrous tissues and contains no muscle tissue. A fat layer surrounds the gland and extends throughout the breast, which gives the breast a soft consistency. The mammary glands or milk producing areas lie between the pectoralis major muscle and skin, each breast consist of 15-25 clusters called lobes, with each lobule connected by ducts, that opens into the nipples, which are made up of erectile tissue. The pigmented areas around nipple are called the areola. Size of the breast is primarily decided by heredity and also depends on the existing fat and glandular tissue. Prior to menstruation breasts exhibit cyclical changes, including increased swelling and tenderness. Benign breast changes refer to fibrocystic disease, lumps or masses that are cancerous.

Breast is divided into four different quadrants as shown in fig 3.2, it is important to know quadrants of breast because, the possible chances of breast cancer in different quadrants are different.

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Fig 2.2. Breast quadrant labels.

2.3 Breast Cancer and its stages

Breast cancer is a malignant tumor that starts in the cells or tissues of the breasts. The stages of breast cancer depends on the size of the breast tumors and whether it has spread to lymph nodes or to other parts of the body. Based on these considerations, breast cancer can be divided into following stages:

Stage 0: Abnormal cells are in the walls of breast duct, but not have invaded nearby tissues or spread outside the duct.Stage IA: The lump is smaller than or equal to 2 centimeters and has not spread to the lymph nodes.Stage IB: The tumor is no more than 2 centimeters and cancer cells are found in lymph nodes.Stage IIA: The lump is smaller than 2 centimeters and the cancer has spread to lymph nodes at armpit.Stage IIIA: The tumor is smaller than 5 centimeters and the cancer may have spread to lymph nodes behind breastbone.Stage IIIB: The tumor can be of any size, and it has grown into the walls of chest or the breast skin. The breast may be swollen.Stage IIIC: The cancer has spread to lymph nodes above or below the collarbone.Stage IV: The lump can be of any size, the cancer cells have spread to other parts of the body such as lungs, liver, bones or brain.

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2.4 Types of Breast Cancer

Three are different types of breast cancer, the most commonly observed breast cancer types are:

2.4.1 Ductal Carcinoma In Situ (DCIS)

DCIS is considered as non-invasive or pre-invasive breast cancer, which begins in the lining of the milk ducts. About 1 in 5 new breast cancer cases will be DCIS. Almost all women diagnosed at this stage can be cured.

2.4.2 Lobular Carcinoma

The cancer which begins in the lobules of the breast.

2.4.3 Invasive Ductal Carcinoma (IDC)

The most common type of breast cancer starts in a milk duct of the breast, breaks through the walls of the duct and grows into the fatty tissues of the breast.

2.4.4 Invasive Lobular Carcinoma (ILC)

ILC starts in the milk producing glands, can spread to other parts of the body. ILC may be difficult to detect by a mammogram.

There are many other less common types and special types of breast cancer such as, inflammatory breast cancer, angiosarcoma, adenoid cystic carcinoma etc.

2.5 Signs of breast cancer and their appearances

Breast cancer is detected by identifying either of four signatures associated with breast, its cells and tissues.

2.5.1 Calcifications

Calcifications are tiny deposits of mineral within breast tissue, which appear as small white spots on the films of breast images. There are two types of calcifications:

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Macrocalcifications: Calcifications which are coarse calcium deposits caused by aging of the breast arteries, old injuries or inflammation. These are non-cancerous deposits, about half the women above 50 and 1 of 10 women under 50 have macrocalcifications.

Microcalcifications: Tiny specks of calcium in the breast are called microcalcifications. These may appear as alone or in clusters, presence of these do not always mean the

cancer is present. The presence of at least five microcalcifications within a 1 cm3 volume define a cluster, which is considered as cancerous one. Considering the shapes, thin linear, curvilinear and branching shapes suggests malignancy. Fig2.3 (a) and fig2.3 (b) shows view of macrocalcifications and microcalcifications respectively.

(a) (b)

Fig. 2.3 (a) macrocalcifications, (b) microcalcifications

2.5.2 Mass

Masses are areas that look abnormal and they include cysts, the non-cancerous, fluid filled sacs and non-cancerous solid tumors. Masses are also defined as a space occupying lesion. Masses have different density such as fat containing masses, low density isodense and high density masses.

Masses are with different margins like circumscribed, micro lobular, obscured, indistinct and speculated margins and the different shapes associated with mass are round, oval, lobular and irregular shapes. Round and oval shaped masses with smooth and circumscribed margins indicate benign changes. However, a malignant mass usually has a speculated, rough and blurry boundary. Fig 3.4 (a) and fig 3.4 (b) shows circumscribed and speculated masses.

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(a) (b)

Fig 2.4 (a) circumscribed mass with smooth margin, (b) speculated mass with branching margins [1].

2.5.3 Architectural Distortion

Breast Imaging Reporting and Data Systems (BI-RADs) define architectural distortion as “the normal architecture of the breast is distorted with no definite mass visible. This includes speculates radiating from a point and focal retraction or distortion at the edge of the parenchyma, architectural distortion can also be an associated finding”. Architectural distortion is the third most common sign of non-palpable breast cancer, but due to this subtlety and variable presentation, it is very often missed during detection procedure. Architectural distortion accounts for 12% to 45% of breast cancers, the improvement in the detection of architectural distortion could lead to an effective improvement in the prognosis of breast cancer patients.

2.5.4 Bilateral Asymmetry

Humans are considered bilaterally symmetrical, if an individual is exposed to genetic mutations or environmental stresses, the homeostatic mechanisms that maintain symmetry of paired structures tend to breakdown, consequently increased fluctuating asymmetry of paired structures could be an indication of poor health. Bilateral morphological breast asymmetry correlates with the presence of breast cancer. The BI- RADs definition of asymmetry indicates the presence of a greater volume or density of breast tissue without a distinct mass or more prominent ducts, in one breast as compared to the corresponding area in the other breast. The slight asymmetries in distribution of normal parenchyma occurs frequently and that even substantial asymmetry is seen in 3%-5% of totally normal breasts.

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Bilateral asymmetry and architectural distortion are considered as indirect signs of breast cancer. Along with the four signs of breast cancer mentioned above, there are few less observed signs such as single dilated duct, developing density etc.

2.6 Detection and diagnosis of breast cancer: imaging techniques

Detection and diagnosis of breast cancer can be done by various imaging techniques and biopsy, the procedure in which small amount of tissue removed and looked at under a microscope to confirm whether cancer is present. The first step involved is breast imaging. There are various imaging techniques available with their own advantages and limitations, the most common among them are:

2.6.1 Magnetic Resonance Imaging (MRI) Imaging

2.6.1.1 Breast cancer diagnosis with high field MRI (1.5 T)

uses magnetic fields and radio waves to diagnose disease.

Takes about 30 minutes for test.

The main advantage is the contrast between soft tissues in the breast is 10 to 100 times greater than that obtained with X-rays

The main disadvantage of breast MRI is its cost, which is about 5 times that of X- ray mammography.

2.6.1.2 MR guided biopsy with open systems

MRI systems consists of a low-field (0.5 T), very expensive and still in the experimental stage.

2.6.2 Digital Imaging

In digital imaging, the digital image is formed when a detector absorbs the X-rays and converts them to an electrical signal corresponding to each pixel. When images are digitally acquired and displayed, film is eliminated. There are several imaging techniques under this category, the most common and most used are

2.6.2.1 Full Field Digital Mammography

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Mammography is a specific type of imaging that uses a low-dose X-ray system to examine the breast and is currently the most effective method for detection of breast cancer before it becomes clinically palpable.

Mammography offers high quality images at a low radiation dose and is currently the only widely accepted method used for routine breast cancer screening.

Digital mammography is potentially advantageous over film mammography such as it has wider dynamic range, lower noise, improved contrast and lower X-ray dose.

screening mammography generally consists of four views, with two views of each breasts: the Cranio- Caudal (CC) view and the Medio Lateral Oblique (MLO) view. Fig2.5 (a) and fig2.5 (b) shows CC and MLO views of breast respectively.

(a) (b)

Fig 2.5 (a) Cranio-Caudal (CC) (b) Medio Lateral Oblique (MLO) views of mammograms [21].

2.6.2.2 Tomosysnthesis

In this method multiple images are acquired as the X-ray tube is moved in an arc above the stationary breast and digital detector.

The total reduction dose required for imaging the entire breast being approximately equal to the dose used for a single film-screen mammogram.

The method is benefited for women with radiographically dense breasts.

The less used and uncommon digital imaging techniques involves stereotactic imaging, single energy X-ray technique and 3D digital reconstruction.

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2.2.3 Ultra Sound (US) Imaging

Involves identification of pathological vascularization in the breast with Doppler imaging.

More accurately map the extent of tumor within breast than possible with mammography.

Contrast imaging method among the various methods under ultra sound imaging is more beneficial.

Involves less cost than MRI. Usually done in combination with mammography.

The other less common imaging techniques involves nuclear imaging, Positron Emission Tomography (PET) imaging, sestamibi imaging, bioelectric imaging, optical diffusion imaging.

2.7 Statistics

2.7.1 Statistics based on age group

Figure below shows percentage distribution of breast cancer among different age group.

Fig 2.6 percentage of breast cancer among different age groups .

2.7.2 Statistics based on different quadrants of breast

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The percentage distribution of possible occurrence of breast cancer at different quadrants of breast is as show in fig 2.7.

Fig 2.7 percentage of breast cancer associated with different quadrants of breast

2.7.3 Gender wise and 2014 statistics

In 2014, the new cases involve 232,670 among female and 2360 among male. In 2014, numbers of deaths are 40,000 among female and 430 among male. about 1 in 8 women in United States will develop invasive breast cancer during their

lifetime.

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CHAPTER III

CONCEPTUAL DESIGN

It is well known that there is no technology at present, which is capable of curing cancer. But, early detection of breast cancer can aid in recovery and also prolong patient life. A major reason for errors in reading mammograms is due to the fact that radiologists depend on visual inspection. During manual screening of a large number of mammograms, radiologists may get easily worn out, missing out vital clues while studying the scans. As yet, there are very less efficient models of CAD which incorporates feature extraction, feature selection and classification methodologies used in breast cancer detection. As double reading of mammograms and diagnosis by imaging techniques other than mammography, such as MRI, are expensive, the costs incurred is very high for the patients, the project proposes the development of Computer-Aided Detection(CAD) and diagnosis method, by developing efficient algorithms for early identification of breast masses with low cost mammography & ultrasound images.

3.1 Proposed SystemWe propose to preprocess the mammogram image, segment the suspicious mass region and extract features before classifying it into benign or malignant. We use Contrast Limited Adaptive Histogram Equalization(CLAHE) method for preprocessing the mammogram image before extracting the lesion. Support vector machine (SVM) classifiers are used to classify the fused features.

Fig. 3.1: Process Flow

3.2 Implementation

The proposed algorithms are mainly developed using MATLAB 2013a, LabVIEW 2013 and Vision Assistant (2013). MATLAB is a high performance language for technical computing. It integrates computation, visualization and programming environment. MATLAB has sophisticated data structures, contains built-in editing and debugging tools, and supports object-

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oriented programming. MATLAB is an interactive system whose basic data element is an array which does not need dimensioning. In this work, image processing toolbox is used implement segmentation, Contrast Limited Adaptive Histogram Equalization(CLAHE), and image arithmetic parts of proposed algorithms. Scripts to obtain GUI and other techniques such as Gaussian pyramid, log transformation, canny edge detection, morphological operations, dimension measurements etc., the LabVIEW Vision Assistant is used.

Fig. 3.2: Overview of the system

The mammogram images when wavelet transformed, can be experimented with various techniques such as Singular Value Decomposition(SVD), Identification of Chebyshev moments, log Polar transform & Binary PSO.

The objective is to enable Computer Aided Detection and to provide statistical analysis of parameters such as

Entropy Correlation Information Measure Variance PSNR Sum of Variance

Also, a modeling of the process is to be performed merged with Support Vector machine/Learning machine.

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Fig. 3.3: Detailed Block Diagram

3.3 Dual Modality

We can characterize the breast mass as malignant or benign by investigating the features retrieved from dual modalities: Mammograms and Ultrasound.

We consider the features such as: Spiculated feature. Acoustic shadowing. Elliptical shape feature. Entropy and standard deviation for discrimination.

We plan to use three well-known normalization methods: Min-Max (MM) Z-score (ZS) Tanh (TH)

3.4 Preprocessing & Segmentation Outputs

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Fig3.4 : Ultrasound and Preprocessing Outputs

The proposed dual modality system combines the structural and functional behavioural trait of mammogram and ultrasound modalities as shown in Fig 3. We have extracted texture features and directional features from mammograms using Gabor filters, gradient orientation and phase portraits. Using angle of curvature method and intensity based method functional features like acoustic shadow and shape features are retrieved from ultrasound. As Mammogram and Ultrasound are independent modalities, we need to normalize the features. Feature Normalization is done using Z-score, Min-Max and Tanh (TH) methods for feature level fusion. Support vector machine (SVM) classifiers are used to classify the fused features.

Ultrasound (US) is an important adjunct to mammography in breast cancer detection as it doubles the rate of detection in dense breasts and also does dynamic analysis of moving structures in breast. Architectural distortions and spiculated masses with Architectural distortions on mammography are considered to be one of the most indicators of breast cancer. But recently AD and AD with spiculated mass has been detected via ultrasonography also. Distortion refers to presence of radiating structure concentrated at a point. The features we have considered are discriminative and effective in characterizing the mass in ultrasound images. Using a single feature as parameter to discriminate is always a tradeoff between the sensitivity and specificity. The tradeoff is due to that each feature parameter is mainly related to its nature. So we have considered the features like spiculated feature, acoustic shadowing, elliptical shape feature, entropy and standard deviation for discrimination.

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Fig 3.5: Different techniques for Preprocessing

The features retrieved from mammogram are structural features and that from ultrasound are functional features and they are dissimilar in terms of dimension. For fusion of features we needed coherent dataset from both modalities which belong to a same person. Data set was created by collecting and getting the ground truth marked images from expert radiologists trained with those kinds of images. All images in our dataset contained only one abnormality (AD with

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spiculated mass). As discussed in previous sections both modalities will output a collection of features. The fusion process fuses this collection of features into a single feature set.

Feature level fusion is a medium level fusion strategy which performs well, if the features are homogenous. If the features are heterogeneous, then it requires normalization to convert them into a range that makes them more similar. We have used three well-known normalization methods:

Min-Max (MM) Z-score (ZS) Tanh (TH)

Support vector machines (SVM) are a learning tool based on modern statistical learning method that classifies binary classes. SVM has been shown to perform better than many other classification algorithms due to several reasons:

SVM has good capacity of generalization. SVM is highly robust and work well with images. The theory of SVM is well defined and has a very good base of mathematics and

statistics. Over training problem is less compared to other neural network classifiers.

Thus we have used SVM classifiers to classify the fused feature vector. Implementation is done using MATLAB. For experimentation we have randomly partitioned the dataset training and testing data with the proportion of 70% and 30% respectively. We have used receiver operating characteristic curve (ROC) to evaluate the performance. FROC graphically represents the true positive rate as a function of false positives rate.

In this study information from multiple modalities such as mammogram and ultrasound was used to classify the breast mass as benign or malignant. The features retrieved from mammogram are spiculation feature and denseness texture feature and that from ultrasound are spiculation feature, shape feature and shadowing feature. From both modalities we have retrieved some additional features like: standard deviation, entropy and homogeneity. Both modalities supply complementary information which is helpful in discriminating benign from malignant mass.

Results show that the multimodal fusion improves the performance to classify breast mass more accurately. Accuracy can still be improved if standard dataset is made available for fusion. Comparative study in ultrasound methods can be made more accurate if standard dataset is available. Research towards multimodality in breast cancer analysis is very less. We can work in different directions of multimodality to improve the sensitivity rate in detecting breast cancer as early as possible.

Multimodality information system provides complementary information to radiologists and has a great benefit for diagnosis and therapy. Radiologists in a normal follow-up face lot of difficulties

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in interpreting mammograms or ultrasonograms due to which more than half of breast biopsies turn out to be negative. Thus it is desirable to have an alternative approach as a second line of defence. Towards that we have embarked on developing a dual modality model which fuses the features retrieved from mammogram and ultrasound.

Any of the single modality used to analyse breast cancer is not rich enough to capture all classification information available in the image. Thus in normal medical diagnoses, images from different modalities are used to get a complete picture or information of abnormality. For example mammogram provides textural and morphological information where as ultrasound images give functional and metabolic information. Hence most of the limitations imposed by unimodal systems can be overcome by including multiple sources of information. Images from different modalities may be taken at different time, different resolutions and may be from different viewpoints so it is very difficult to simply overlay different images from different modalities to fuse the information. Integration of information in multimodality can occur at feature level or at decision level. Feature level methods combine several feature sets into a single fused one which is then used by any conventional classifier. Decision level fusion combines several classifiers resulting in strong final classifier.

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Fig 3.6: Different Techniques for Image Segmentation

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CHAPTER IV

RESULT ANALYSIS

4.1 Histogram EqualizationThe idea behind Histogram Equalization is that we try to evenly distribute the occurrence of pixel intensities so that the entire range of intensities is used more fully. We are trying to give each pixel intensity equal opportunity; thus, equalization. Especially for images with a wide range of values with detail clustered around a few intensities, histograms will improve the contrast in the image.

In MATLAB, the function to perform Histogram Equalization is histeq(I).

An image lacks contrast when there are no sharp differences between black and white. Brightness refers to the overall lightness or darkness of an image.

To change the contrast or brightness of an image, the Adjust Contrast tool performs contrast stretching. In this process, pixel values below a specified value are displayed as black, pixel values above a specified value are displayed as white, and pixel values in between these two values are displayed as shades of gray. The result is a linear mapping of a subset of pixel values to the entire range of grays, from black to white, producing an image of higher contrast.

Fig 4.1 : Contrast Adjustment between pixels

The Histogram Equalization algorithm enhances the contrast of images by transforming the values in an intensity image so that the histogram of the output image is approximately flat. See the picture below.

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Fig4.2 : An example of Histogram Stretching

A histogram is a graphical representation of the distribution of data. It is an estimate of the probability distribution of a continuous variable (quantitative variable) and was first introduced by Karl Pearson.[11] To construct a histogram, the first step is to "bin" the range of values—that is, divide the entire range of values into a series of small intervals—and then count how many values fall into each interval. A rectangle is drawn with height proportional to the count and width equal to the bin size, so that rectangles abut each other. A histogram may also be normalized displaying relative frequencies. It then shows the proportion of cases that fall into each of several categories, with the sum of the heights equaling 1. The bins are usually specified as consecutive, non-overlapping intervals of a variable. The bins (intervals) must be adjacent, and usually equal size.[12] The rectangles of a histogram are drawn so that they touch each other to indicate that the original variable is continuous.

4.2 Contrast Limited Adaptive Histogram EqualizationWhile performing AHE if the region being processed has a relatively small intensity range then the noise in that region gets more enhanced. It can also cause some kind of artifacts to appear on those regions. To limit the appearance of such artifacts and noise, a modification of AHE called Contrast Limited AHE can be used. The amount of contrast enhancement for some intensity is directly proportional to the slope of the CDF function at that intensity level. Hence contrast enhancement can be limited by limiting the slope of the CDF. The slope of CDF at a bin location is determined by the height of the histogram for that bin. Therefore if we limit the height of the histogram to a certain level we can limit the slope of the CDF and hence the amount of contrast enhancement.

The only difference between regular AHE and CLAHE is that there is one extra step to clip the histogram before the computation of its CDF as the mapping function is performed.

Following is the overview of the algorithm for this function:1. Calculate a grid size based on the maximum dimension of the image. The minimum grid

size is 32 pixels square.

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2. If a window size is not specified chose the grid size as the default window size.

3. Identify grid points on the image, starting from top-left corner. Each grid point is separated by grid size pixels.

4. For each grid point calculate the histogram of the region around it, having area equal to window size and centered at the grid point.

5. If a clipping level is specified clip the histogram computed above to that level and then use the new histogram to calculate the CDF.

6. After calculating the mappings for each grid point, repeat steps 6 to 8 for each pixel in the input image.

7. For each pixel find the four closest neighboring grid points that surround that pixel.

8. Using the intensity value of the pixel as an index, find its mapping at the four grid points based on their cdfs.

9. Interpolate among these values to get the mapping at the current pixel location. Map this intensity to the range [min:max) and put it in the output image.

Clipping the histogram itself is not quite straight forward because the excess after clipping has to be redistributed among the other bins, which might increase the level of the clipped histogram. Hence the clipping should be performed at a level lower than the specified clip level so that after redistribution the maximum histogram level is equal to the clip level.

The below diagram shows the preprocessing output of the input mammogram image. We observe that the preprocessed image clearly shows the masses visible which can now be sent for segmentation.

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Fig 4.3 : CLAHE method preprocessing output

Fuzzy C-Means Clustering

Fuzzy c-means (FCM) is a method of clustering which allows one piece of data to belong to two or more clusters. This method (developed by Dunn in 1973 and improved by Bezdek in 1981) is frequently used in pattern recognition. It is based on minimization of the following objective function:

where m is any real number greater than 1, uij is the degree of membership of xi in the cluster j, xi is the ith of d-dimensional measured data, cj is the d-dimension center of the cluster, and ||*|| is any norm expressing the similarity between any measured data and the center.

Fuzzy partitioning is carried out through an iterative optimization of the objective function shown above, with the update of membership uij and the cluster centers cj by:

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This iteration will stop when where is a termination criterion between 0 and 1, whereas kare the iteration steps. This procedure converges to a local minimum or a saddle point of Jm. The algorithm is composed of the following steps:

1. Initialize U=[uij] matrix, U(0)

2. At k-step: calculate the centers vectors C(k)=[cj] with U(k)

3. Update U(k) , U(k+1)

4. If || U(k+1) - U(k)||< then STOP; otherwise return to step 2.

Fuzzy C-means (FCM) algorithm is one of the most popular fuzzy clustering methods widely used in various tasks of pattern recognition, data mining, image processing, gene expression data Recognition etc. Modifying and generalizing the FCM algorithm is a prevailing research stream in fuzzy clustering in recent decades.

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Fig4.4 : Multicluster display output

•Choose a number of clusters

•Assign randomly to each point coefficients for being in the clusters

•Repeat until the algorithm has converged (that is, the coefficients' change between two iterations is no more than ε, the given sensitivity threshold)

•Compute the centroid for each cluster, using the formula

above

•For each point, compute its coefficients of being in the clusters, using the formula above

Fig 4.5 :Cluster outputs

K-means clustering

Clustering is the process of partitioning a group of data points into a small number of clusters. For instance, the items in a supermarket are clustered in categories (butter, cheese and milk are grouped in dairy products). Of course this is a qualitative kind of partitioning. A quantitative approach would be to measure certain features of the products, say percentage of milk and others, and products with high percentage of milk would be grouped together. In general, we have n data points xi,i=1...n that have to be partitioned in k clusters. The goal is to assign a cluster to each data point. K-means is a clustering method that aims to find the positions μi,i=1...k of the clusters that minimize the distance from the data points to the cluster. K-means clustering solves

argminc∑i=1k∑x∈cid(x,μi)=argminc∑i=1k∑x∈ci∥x−μi∥22

where ci is the set of points that belong to cluster i. The K-means clustering uses the square of the Euclidean distance d(x,μi)=∥x−μi∥22. This problem is not trivial (in fact it is NP-hard), so the

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K-means algorithm only hopes to find the global minimum, possibly getting stuck in a different solution.

K-means algorithm

The Lloyd's algorithm, mostly known as k-means algorithm, is used to solve the k-means clustering problem and works as follows. First, decide the number of clusters k. Then:

1. Initialize the center of the clusters μi= some value ,i=1,...,k

2. Attribute the closest cluster to each data point ci={j:d(xj,μi)≤d(xj,μl),l≠i,j=1,...,n}

3. Set the position of each cluster to the mean of all data points belonging to that cluster μi=1|ci|∑j∈cixj,∀i4. Repeat steps 2-3 until convergence

Notation |c|= number of elements in c

The algorithm eventually converges to a point, although it is not necessarily the minimum of the sum of squares. That is because the problem is non-convex and the algorithm is just a heuristic, converging to a local minimum. The algorithm stops when the assignments do not change from one iteration to the next.

Deciding the number of clusters

The number of clusters should match the data. An incorrect choice of the number of clusters will invalidate the whole process. An empirical way to find the best number of clusters is to try K-means clustering with different number of clusters and measure the resulting sum of squares.

Initializing the position of the clusters

It is really up to you! Here are some common methods:

Forgy: set the positions of the k clusters to k observations chosen randomly from the dataset.

Random partition: assign a cluster randomly to each observation and compute means as in step 3.

Since the algorithm stops in a local minimum, the initial position of the clusters is very important.

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CHAPTER VI

CONCLUSION

Mammography and Ultrasound are the best available inspection facility to detect the onslaught of breast cancer at the early stage. It can disclose information about abnormality, such as masses, microcalcifications, bilateral asymmetry, and architectural distortion. For the hundreds of mammographic images scanned by a radiologist, only a few are cancerous. While detecting abnormalities, some of them may be missed due to human error, as the detection of suspicious and abnormal images is a recurrent mission that causes fatigue and eyestrain. Using CAD to enhance images, segment & extract the suspicious area, more accurate features can be viewed. Furthermore, they can be classified into appropriate category are the most important steps that computer aided detection systems can contribute leading to significant reduce in the false diagnosis of Breast Cancer.

The early detection of Breast Cancer based on image processing techniques is reliable and can prove to be an important investigative tool in the clinical evaluation of detection of cancer in early stages

Dept. of IT, DSCE


REFERENCES

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