Wavelet and Curvelet Analysis for the Classification of Microcalcifiaction Using Mammogram Images

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1 517 Wavelet and Curvelet Analysis for the Classification of Microcalcifiaction Using Mammogram Images B.Kiran Bala Research Scholar, St.Peter s University,Chennai Abstract Breast cancer is the second of the deadliest cancers causing women mortality around the world. The early prediction of breast cancer is the key to reduce women mortality. The major sign of breast cancer is the occurrence of microcalcification clusters in the breast. To efficiently diagnose the breast cancer, an efficient classification system for microcalcification in digital mammogram image is proposed in this study. The classification of microcalcification system is presented based on discrete curvelet transform (DCT) and discrete wavelet transforms (DWT). The energy features are extracted from the mammogram images by using aforementioned transformations at various level of decomposition and k nearest neighbor (KNN) classifier is used for classification task. Experimental results show that the DCT based classification system provides satisfactory result over DWT. Key words: Digital Mammogram, Microcalcification, Discrete Wavelet, Discrete Curvelet, K Nearest Neighbor I. INTRODUCTION The classification of clustered microcalcifications (MCs) in digital mammograms based on various classifiers is presented in [1]. Support Vector Machine (SVM), Relevance Vector Machine (RVM), and committee machines are used as classifier. The image features are extracted from the MCs based on supervised learning quantitative analysis for the preparation of training and testing samples for the classifier models. The detection of microcalcification in digital mammogram based on SVM is described in []. SVM is trained through supervised learning to classify each location in the image whether MCs present or not. The formulation of SVM learning is based on the principle of structural risk minimization. The decision function of the trained SVM classifier is determined in terms of support vectors that are identified from the examples during training and it has lower generalization error. An approach for microcalcification detection by using RVM in digital mammograms is explained in [3]. From the digital mammogram images, MCs regions are detected at each pixel location and their corresponding features are extracted. Two step classifier approaches is used. MCs are detected by SVM classifier and the non MC region is classified by RVM classifier. Dr.S.Audithan Principal, PRIST University, Tanjore, Tamilnadu. Breast cancer diagnosis in mammogram images according with microcalcification is presented in [4]. At first, mammogram image is preprocessed by wavelet-based spatially adaptive method. Texture and wavelet features such as Graylevel first-order statistics features, Gray-level co occurrence matrices features are extracted from the preprocessed images. The extracted features are normalized to zero mean and unit standard deviation and subsequently used for classification. probabilistic neural network is used as classifier. Best automatic classification of microcalcifications and microcalcification clusters is described in [5]. The features are extracted from mammogram images using various algorithms such as the scalar feature selection, fisher's discriminant ratio and the area under receiver operating curve is used as secondary distance measurements. The various feed forward neural network is employed for classification of microcalcifications and microcalcification clusters. Feature based detection and classification of microcalcifications based on immune algorithm (IA) and SVM in digital mammograms is explained in [6]. IA based feature selector is used to select the optimal microcalcifications feature set, which is used for SVM training. Finally, SVM classifier is used to classify the microcalcifications in mammogram images. A new approach for the detection of microcalcification clusters, based on neural networks is explained in [7]. The algorithm is composed of three modules: the image preprocessing, the feature extraction component and the back propagation neural network module. The first module comprises the use of several algorithms such as h-dome transformation, masking, binarization of grayscale images and connected components labeling. In feature extraction features from the input mammogram images are extracted and the dimension of the extracted features is reduced by dimensionality reduction approach. Then the reduced features are used as input to the back propagation neural network A novel computer aided diagnosis method for the detection and classification of microcalcifications based on DWT and Adaptive Neuro Fuzzy Inference System (ANFIS) is discussed in [8]. DWT is used to extract the high frequency signal of the images, and thresholding with hysteresis is applied to locate the suspicious MCs. Then, filling dilation was applied to segment those desired regions. During the detection, ANFIS is used to adjust the parameters, making the algorithm more

2 adaptive. Finally, the suspicious MCs are classified with multilayer perception. Ant colony optimization based classification and feature selection of microcalcifications in digital mammograms is described in [9]. The spatial gray level dependence method is used for feature extraction. The selected features are fed to a three-layer back propagation network hybrid with ant colony optimization for classification. In this study, an approach based on DWT and DCT is proposed for microcalcification classification. The mathematical background of DWT and DCT is described in section. The efficient approach and the results of the experimentation are discussed in section 3 and 4 respectively. Section 5 discusses the conclusion. II. METHODOLOGY The classification of microcalcification abnormalities present in the digital mammogram images is analyzed by using DWT and DCT. The mathematical background of these techniques is discussed in this section. A. Discrete Wavelet The Wavelets are families of basis functions generated by dilations and translations of a basic filter function. The wavelet functions construct an orthogonal basis and the discrete wavelet transform is thus a decomposition of the original signal in terms of these basis functions [10]: f ( x) Cnm U m, n ( x). (1) m 0 n 0 where U m, n ( x) m / U ( m x n ) are dilations and translations of the basic filter function U (x ). Unlike Fourier bases which are composed of sines and cosine that have infinite length. Wavelet basis functions are of finite duration. The discrete wavelet transform coefficients Cnm are the estimation of signal components cantered at ( m n. m ) in the time frequency plane and can be calculated by the inner products of U m, n ( x) and f (x). It is obvious that the wavelet transform is an octave frequency band decomposition of the original signal. The narrow band signals then can be further down-sampled and provide a multi-resolution representation of the original signal. The discrete wavelet coefficients Cnm can be efficiently computed with a pyramid transform scheme using a pair of filters (a low-pass filter and a high-pass filter) [11]. For images which have two dimensions, the filtering and down sampling steps will be repeated in rows and columns respectively. At each level the image can be transformed into four sub-images: LL (both horizontal and vertical directions have low frequencies). LH (the vertical direction has low frequencies and the horizontal has high frequencies). HL (the 518 vertical direction has high frequencies and the horizontal has low frequencies) and HH (both horizontal and vertical directions have high frequencies). The algorithm for DWT for an image is as follows: Let us consider G and H is the low pass and high pass filter respectively. 1. Convolve each row in the input image with the low pass filter followed by the high pass filter to obtain row wise decomposed image.. Down sample the row wise decomposed image by. 3. Convolve the column of the row wise decomposed image with the low pass filter followed by the high pass filter to obtain column wise decomposed image 4. Down sample the column wise decomposed image by that produces one approximation sub-band and three high frequency sub-band. This is called 1-level decomposition 5. Apply steps 1-4, for higher level decomposition to the approximation sub-band which is obtained from the previous level of decomposition. B. Discrete Curvelet The Donoho [1] introduced a new multi-scale transform named curvelet transform which was designed to represent edges and other singularities along curves much more efficiently than traditional transforms, i.e., using fewer coefficients for a given accuracy of reconstruction [1-13]. Curvelet transform based on wrapping of Fourier samples takes a -D image as input in the form of a Cartesian array f [m, n] such that 0 m M,0 n N and generates a number of curvelet coefficients indexed by a scale j, an orientation l and two spatial location parameters (k 1, k ) as output. Discrete curvelet coefficients can be defined by [14]. c D j, l, k1, k f [ m, n] D j, l, k1, k [m, n ]. 0 m M 0 n N where each D j, l, k1, k [ m, n] is a digital curvelet waveform. With increase in the resolution level the curvelet becomes finer and smaller in the spatial domain and shows more sensitivity to curved edges which enables it to effectively capture the curves in an image. As a consequence, curved singularities can be well approximated with few coefficients. Components of an image play a vital role in finding distinction between images. Curvelets at fine scales effectively represent edges by using texture features computed from the curvelet coefficients. If we combine the frequency responses of curvelets at different scales and orientations, we get a rectangular frequency tiling that covers the whole image in the spectral domain. Thus, the curvelet spectra completely cover the frequency plane and there is no loss of spectral information like the Gabor filters. To achieve higher level of efficiency, curvelet transform is usually implemented in the frequency domain. That is, both

3 the curvelet and the image are transformed and are then multiplied in the Fourier frequency domain. The product is then inverse Fourier transformed to obtain the curvelet coefficients. The process can be described as Curvelet = IFFT [FFT (Curvelet) x FFT (image)] and the product from the multiplication is a wedge. The trapezoidal wedge in the spectral domain is not suitable for use with the inverse Fourier transform which is the next step in collecting the curvelet coefficients using IFFT. The wedge data cannot be accommodated directly into a rectangle of size j j /. To overcome this problem, A wedge wrapping procedure is described [14] where a parallelogram with sides j and j / is chosen as a support to the wedge data. The wrapping is done by periodic tiling of the spectrum inside the wedge and then collecting the rectangular coefficient area in the center. The center rectangle of size j j / successfully collects all the information in that parallelogram. Thus we obtain the discrete curvelet coefficients by applying -D inverse Fourier transform to this wrapped wedge data. The algorithm is as follows: 1. Apply the D FFT and obtain Fourier samples fˆ [ n, n ], n / n, n n / DWT at two to five levels. Then their energy features are extracted from the decomposed image by averaging their transform coefficients in each sub-band individually. Similarly, curvelet energy features are extracted by applying DCT into the given ROI images. These steps are repeated for all the training mammogram images and the extracted curvelet and wavelet energy features are stored in separated databases to analyze the performance of DWT and DCT. The second module of the proposed mammogram classification system is classification. Two step classifications are implemented for efficient mammogram classification. The unknown mammogram image undergoes the same feature extraction process as similar as training image feature extraction. Training Normal/ Images Training Benign/Malignant Images DCT /DWT DCT /DWT Database (DCT / DWT ) Database (DCT /DWT ). For each scale/angle pair ( j, l ), resample (or interpolate) fˆ [ n1, n ] to obtain sampled values fˆ [ n1, n n1 tan l ] for (n1, n ) p j 3. Multiply the interpolated (or sheared) object ˆf with the parabolic window U j, effectively Localizing fˆ near the parallelogram with orientation l, and obtain f j, l [n1, n ] = fˆ[n1, n n1 tan l ]U j [n1, n ] Apply the inverse D FFT to each f j, l, hence collecting the discrete coefficients III.PROPOSED METHOD The classification of microcalcification system is developed in two modules. The first module of the proposed system is feature extraction in which the best discriminate features represented by clusters of microcalcifications and features represented by normal tissues are extracted by DWT and DCT transforms. The second module of the proposed system is a two stage classification, in which the mammogram image is classified in to whether it is normal or abnormal and then the abnormality into benign or malignant by using KNN classifier. Figure 1 shows the block diagram of the microcalcification system using DWT and DCT. Feature extraction is an important preprocessing step for variety of machine learning and pattern recognition approach. At first, the given mammogram ROI image is decomposed by DCT / DWT KNN Classifier Normal/ KNN Classifier Benign/ Malignant Test Mammogram Image Figure 1: Proposed two stage classification of microcalcification system

4 The sample feature space is compared with every training feature spaces by using KNN classifier, in which DCT and DWT databases are compared individually with the unknown features. The proposed system first classifies whether the given sample image is normal or abnormal based on the minimum distance metric between the sample and training feature space. The proposed classification of microcalcification system uses city block measure as distance metric. If the first step classification system classifies the sample image as abnormal, then it goes to second step classification. Based on severity of abnormality, the abnormal image is classified again into benign or malignant using the same classifier. IV. EXPERIMENTAL RESULTS In order to evaluate the proposed mammogram classification system, the system is applied on a benchmark mammogram MIAS database. It consists of 05 normal and 5 microcalcification images. Also it has mass abnormality images. However, in comparison with mass abnormality, the microcalcification is very difficult to diagnose. Hence, the proposed system considers only the microcalcification for classification. The proposed system is designed that uses DWT and DCT for the classification. Table 1 shows the classification accuracy achieved by the proposed stage at first stage in which the given unknown image is classified into normal or abnormal. Table 1: Classification accuracy obtained by the first stage Classification accuracy in percentage Level DWT Curvelet Normal Normal provides better classification accuracy than DWT based features. V. CONCLUSION A two-stage classification approach for the classification of microcalcification in digital mammogram images is proposed and comparative analysis is done by using DCT and DWT techniques. The energy features are extracted from ROI images initially by DCT and DWT decomposition. The nearest neighbor classifier classifies the given unknown image into normal/abnormal in the first stage. If the classified image is abnormal, it is further classified by the second stage classification to discriminate whether it is benign or malignant. As the curvelet transform is multi-scale in nature, it provides better classification than DWT based features. REFERENCES [1] [] [3] [4] It is observed from the Table 1, DCT based classification system achieves maximum accuracy of % at 5th level decomposition. At the same level of decomposition, DWT based system achieves only accuracy of %. Table shows the classification accuracy achieved by the proposed system at second stage. Table : Classification accuracy obtained by the second stage Level Normal Classification accuracy in percentage DWT Curvelet Normal [5] From the above table, it is inferred from that the DWT and DCT based approach achieves a maximum of 87.8% and 91.67% accuracy respectively at 5th level decomposition. It is observed from the Table 1 and curvelet based approaches 50 [6] Wei, Liyang, Yongyi Yang, Robert M. Nishikawa, and Yulei Jiang. "A study on several machinelearning methods for classification of malignant and benign clustered microcalcifications." Medical Imaging, IEEE Transactions on 4, no. 3 (005): El-Naqa, Issam, Yongyi Yang, Miles N. Wernick, Nikolas P. Galatsanos, and Robert M. Nishikawa. "A support vector machine approach for detection of microcalcifications." Medical Imaging, IEEE Transactions on 1, no. 1 (00): Wei, Liyang, Yongyi Yang, Robert M. Nishikawa, Miles N. Wernick, and Alexandra Edwards. "Relevance vector machine for automatic detection of clustered microcalcifications." Medical Imaging, IEEE Transactions on 4, no. 10 (005): Karahaliou, Anna N., Ioannis S. Boniatis, Spyros G. Skiadopoulos, Filippos N. Sakellaropoulos, Nikolaos S. Arikidis, Eleni A. Likaki, George S. Panayiotakis, and Lena I. Costaridou. "Breast cancer diagnosis: analyzing texture of tissue surrounding microcalcifications." Information Technology in Biomedicine, IEEE Transactions on 1, no. 6 (008): de Melo, Charles LS, Cícero FF Costa Filho, Marly GF Costa, and Wagner CA Pereira. "Matching input variables sets and feedforward neural network architectures in automatic classification of microcalcifications and microcalcification clusters." In Biomedical Engineering and Informatics (BMEI), 010 3rd International Conference on, vol. 1, pp IEEE, 010. Gulsrud, T. O., and S. O. Gabrielsen. "Classification of microcalcifications using a multichannel filtering approach." In Engineering in Medicine and Biology Society, 1995., IEEE 17th Annual Conference, vol., pp IEEE, 1995.

5 [7] [8] [9] [10] [11] [1] [13] [14] Cheran, S. C., R. E. N. A. T. O. Cataldo, P. Cerello, F. De Carlo, F. Fauci, G. Fomi, B. Golosio et al. "Detection and classification of microcalcifications clusters in digitized mammograms." In Nuclear Science Symposium Conference Record, 004 IEEE, vol. 7, pp IEEE, 004. Xu, Weidong, Lihua Li, and Shaofang Zou. "Detection and Classification of Microcalcifications Based on DWT and ANFIS." In Bioinformatics and Biomedical Engineering, 007. ICBBE 007. The 1st International Conference on, pp IEEE, 007. Karnan, M., K. Thangavel, R. Sivakuar, and K. Geetha. "Ant Colony Optimization for Feature selection and Classification of Microcalcifications in Digital Mammograms." In Advanced Computing and Communications, 006. ADCOM 006. International Conference on, pp IEEE, 006. S.G.Mallat, A theory for multi resolution signal Decomposition: The wavelet representation, IEEE transactions on pattern analysis and machine intelligence, Vol 11, no.7, 1989, pp Riaz, Farhan, Ali Hassan, Saad Rehman, and Usman Qamar. Texture Classification Using Rotation-and Scale-Invariant Gabor Texture. IEEE Signal processing letter Vol.0, no.6, 013, pp David L. Donoho & Mark R. Duncan, Digital Curvelet : Strategy, Implementation and Experiments, Stanford University, November, J.L. Starck, E. Candes, and D.L. Donoho, The Curvelet for Image Denoising, IEEE Transactions on Image Processing, vol.11,no.6, 00,pp E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, Fast Discrete Curvelet s, Multiscale Modeling and Simulation, vol. 5, 005, pp

Chapter 7 UNSUPERVISED LEARNING TECHNIQUES FOR MAMMOGRAM CLASSIFICATION

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