Breast Tissue Classification Based on Application of Gabor Filter, PCA and SVM

Breast Tissue Classification Based on Application of Gabor Filter, PCA and SVM

Pravin S. Hajare, Vaibhav V. Dixit

Department of E&Tc Engineering, Pune University, Pune, M.S., India.

Assistant Professor, Department of E&Tc Engineering, Pune University, Pune, M.S., India.

Abstract

Breast cancer is the most common cancer in women. In detection of breast cancer, the prominent tool, image processing is used. This experiment focuses towards the identification of relevant, representative and more important, discriminate image features for analysis of medical images. The original images of dimensions 1024×1024 are taken as an input for further processing from MIAS database. Then Gabor filter is used to extract intensity features and the patches of size 140 X

140 are obtained to recognize whether the mammogram image is normal benign or malign. Then these patches are down sampled to size of 30 X 30 pixels. These are large dimensions so further applied to Principal Component Analysis (PCA) to reduce data dimensionality. The PCA converts 30 X 30 patches into 10 Eigen vectors. Finally, the extracted features are classified using the proximal support vector machines as classifier. The Gabor filter used here is with orientations of 0, /4, 3/4, and /2 and also with all orientations. Also, two different frequencies (low frequency and high frequency) of Gabor filters are used. Thus, one image is passed through 12 Gabor filters as 3 frequencies of each are taken. Finally, the recognition rate of all orientations and different frequencies are calculated and compared. The Gabor filter with low frequency and all orientation gives the highest recognition rate of 84.375%.

1. Introduction

   Mammography is at present the best available technique for early detection of breast cancer. In mammographic images early signs of breast cancer, such as bilateral asymmetry, can be revealed. Bilateral asymmetry is asymmetry of the breast parenchyma between corresponding regions in left and right breast. The most common breast abnormalities that may indicate breast cancer are masses and calcifications. Early detection and treatment are considered as the most promising approaches to reduce breast cancer mortality. Mammogram image is considered as the most reliable, low cost, and highly sensitive technique

   for detecting small lesions. One of the main points that should be taken under serious consideration when implementing a robust classifier for recognizing breast tissue is the selection of the appropriate features that describes and highlight the differences between the abnormal and the normal tissue in an ample way. Feature extraction is an important factor that directly affects the classification result in mammogram classification. Most systems extract features to detect and classify the abnormality as benign or malignant from the textures. A particular image type is given by mammographic images that are typically X-ray captures of breast region displaying points with high intensities density that are suspected of being potential tumors. Early diagnostic and screening is crucial for having a appearing in the mammogram images could indicate a potential presence of a benign or malignant tumor.

2. Database (MIAS)

   The experimentation is done with the database images taken from Mammographic Image Analysis Society (MIAS), which contains 322 samples belonging to three different categories as normal, benign and malign. The database consists of 208 normal images, 63 benign and 51 malign cases, which are considered abnormal [13]. These database images are of 1024 x 1024 pixel size and having background information like breast contour, therefore the pre- processing of these images is required. To obtain region of interest, 140 × 140 patches are extracted from mammogram images as shown in figure 1. The database is with two different sets. First set is having 80% database images of whole database with known classes, normal, benign and malign. Whereas the second set is with 20% database images which are the test images and are having unknown classes. This experiment uses 258 training images and 64 testing images from mammogram database which are with all the classes, normal, benign and malign.

   With,

   (3)

   (4)

   Figure 1 Patches of 140 X140 pixels extracted from Mammographic images.

   To reduce the computations during the further processing the images are down sampled to the size of 30×30 pixels. The patches from image are extracted based on the intensity variations. The affected area is with light intensity. Also, the database provides the information of all three classes, normal, benign and malign.

3. Feature Extraction

   In order to provide accurate recognition, feature patterns must be extracted. Only the significant features must be encoded. In this experimentation, the method used to extract the intensity features is the Gabor filter with low and high frequencies and also with four different orientations. Three low frequencies and three high frequencies with four orientations give 12 combinations of Gabor filter. Thus, the mammographic image is passed through 12 Gabor filters and magnitudes of all are represented.

   3.1 Gabor Wavelets

   A 2-D Gabor function is a Gaussian modulated by a sinusoid. It is a non orthogonal wavelet. Gabor filters exhibits the properties as the elementary functions are suitable for modelling simple cells in visual cortex [12] and gives optimal joint resolution in both space and frequency, suggesting simultaneously analysis in both domains. The definition of complex Gabor filter is defined as the product of a Gaussian kernel with a complex sinusoid. A 2D Gabor wavelet transform is defined as the convolution of the image I (z).

   (1)

   with a family of Gabor filters:

   (2)

   Where, z = x, y and k is characteristic wave vector:

   The results obtained by extracting the features with Gabor filters are as shown in figure 2 and 3. Fig. 2 shows the magnitude response of features with low frequency Gabor filter bank (v=2, 3, 4 and µ=0, /4, /2, 3/4) whereas fig. 4 shows the magnitude response of high frequency filter bank (v=0, 1, 2 and µ=0, /4, /2, 3/4).

   Figure 2. Magnitude of Gabor representation for one MIAS sample convolved with 12 Gabor filters Low frequency, v=2, 3, 4 and µ=0, /4, /2, 3/4

   Figure 3. Magnitude of Gabor representation for one MIAS sample convolved with 12 Gabor filters High frequency, v=0, 1, 2 and µ=0, /4, /2, 3/4

4. Principal Component Analysis

   PCA involves the calculation of the Eigen value decomposition of a data covariance matrix or singular value decomposition of a data matrix, usually after mean centering the data for each attribute. The results of a PCA are usually discussed in terms of component

   scores and loadings. PCA is the simplest of the true eigenvector-based multivariate analyses. Often, its operation can be thought of as revealing the internal structure of the data in a way which best explains the variance in the data. If a multivariate dataset is visualized as a set of coordinates in a high-dimensional data space, PCA supplies the user with a lower- dimensional picture, a "shadow" of this object when viewed from its most informative viewpoint. PCA is closely related to factor analysis; indeed, some statistical packages deliberately conflate the two techniques. True factor analysis makes different assumptions about the underlying structure and solves eigenvectors of a slightly different matrix. PCA is mathematically defined as an orthogonal linear transformation that transfors the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinate the second greatest variance on the second coordinate, and so on [4]. PCA is theoretically the optimum transform for given data in least square terms. For a data matrix, XT, with zero empirical mean (the empirical mean of the distribution has been subtracted from the data set), where each row represents a different repetition of the experiment, and each column gives the results from a particular probe.

   Given a set of points in Euclidean space, the first principal component (the eigenvector with the largest Eigen value) corresponds to a line that passes through the mean and minimizes sum squared error with those points. The second principal component corresponds to the same concept after all correlation with the first principal component has been subtracted out from the points. Each Eigen value indicates the portion of the variance that is correlated with each eigenvector. Thus, the sum of all the Eigen values is equal to the sum squared distance of the points with their mean divided by the number of dimensions. PCA essentially rotates the set of points around their mean in order to align with the first few principal components. This moves as much of the variance as possible (using a linear transformation) into the first few dimensions. The values in the remaining dimensions, therefore, tend to be highly correlated and may be dropped with minimal loss of information. In this way, the PCA is used in this experiment for dimensionality reduction. Fig. 4 shows 10 Eigen images resulted from PCA. Thus, the 30 X 30 down sampled image is applied to PCA and total 900 dimensions are represented with 10 Eigen vectors.

   Figure 4. Each row depicts 10 Eigen images obtained by applying PCA for the Matrix Xkc and columns contain concatenated Gabor convolution results corresponding to 4 orientations and 3 frequencies (low frequency range).

5. Support Vector Machine

   Support vector machines (SVMs) are a set of related supervised learning methods that analyze data and recognize patterns, used for classification and regression analysis. The standard SVM is a non- probabilistic binary linear classifier, i.e. it predicts, for each given input, which of two possible classes the input is a member of. Since an SVM is a classifier, then given a set of training examples, each marked as belonging to one of two categories, an SVM training algorithm builds a model that predicts whether a new example falls into one category or the other. Intuitively, an SVM model is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible. New examples are then mapped into that same space and predicted to belong to a category based on which side of the gap they fall on.

   Multiclass SVM aims to assign labels to instances by using support vector machines, where the labels are drawn from a finite set of several elements [10]. The dominating approach for doing so is to reduce the single multiclass problem into multiple binary classification problems. Each of the problems yields a binary classifier, which is assumed to produce an output function that gives relatively large values for examples from the positive class and relatively small values for examples belonging to the negative class. Two common methods to build such binary classifiers are where each classifier distinguishes between (i) one of the labels to the rest (one-versus-all) or (ii) between every pair of classes (one-versus-one). Classification of new instances for one-versus-all case is done by a

   winner-takes-all strategy, in which the classifier with the highest output function assigns the class (it is important that the output functions be calibrated to produce comparable scores). For the one-versus-one approach, classification is done by a max-wins voting strategy, in which every classifier assigns the instance to one of the two classes, then the vote for the assigned class is increased by one vote, and finally the class with most votes determines the instance classification.

   Here, in this experiment the SVM is trained with the images from training dataset whose classes are known. Total 258 training images are taken from dataset. Dataset has 64 testing images which are classified with SVM as benign, normal or malign. The figure 5 shows the classification result for one sample testing image.

   Figure 5. Classification result obtained by using proximal support vector machine.

   Features	Frequency range	Orientation	Recognition Rate (%)
   Gabor filter and PCA	Low frequency range	0	65.62
   		/4	67.18
   		/2	68.75
   		3/4	64.06
   		All	84.375
   Gabor filter and PCA	High frequency range	0	65.62
   		/4	64.06
   		/2	71.87
   		3/4	64.06
   		All	68.75

   Table 1. Recognition Rate for Different combinations of Gabor and PCA with different orientations.

6. Conclusion

The system works on two filter banks, low frequency and high frequency. Initially, the patches of 140 x 140 are extracted from mammographic images. The images are passed through 12 different Gabor filters. The features are obtained by convolving patches representing tumor or tumor-free areas with several Gabor filters and are employed for recognition purpose. The large dimension images are then down sampled to the size of 30 X 30 pixels. Also, these give large number of dimensions so applied to PCA to reduce the dimensionality. The results of different frequency ranges of Gabor filter coupled with PCA and different orientations are tabulated in table 1. The Gabor filter with low frequency and all orientations gives the highest recognition rate of 84.375% among all.

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