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1 Enhancement of Mammographic Images using Morphology and Wavelet Transform Harish Kumar.N 1 Amutha. S 2 Dr. Ramesh Babu.D. R 3 1 Lecturer, Dept. of CSE, Dayananda Sagar College of Engineering, Bangalore, India 2 Assistant Professor, Dept of CSE, Dayananda Sagar College of Engineering, Bangalore, India 3 Professor, Dept. of CSE, Dayananda Sagar College of Engineering, Bangalore, India 1 nhk015@gmail.com 2 amuthanandhu@gmail.com 3 bobrammysore@gmail.com Abstract Mammography is the effective technology for early detection of breast cancer and breast tumour analysis. In mammography, low dose x-ray is used for imaging. Due to the low dose X-ray the images obtained from mammography are poor in contrast and are contaminated by noise. Hence it is difficult for the radiologist to screen the mammograms for any abnormalities like microcalcifications and masses. This ensures the need for image enhancement to aid radiologist for interpretation. This paper introduces a new enhancement method for digital mammographic images based on modified mathematical morphology and biorthogonal wavelet transform. In the proposed method we adopted a level dependent threshold for thresholding the detail coefficients of wavelet transform. To evaluate the performance of the proposed method, Contrast Improvement Index (CII) and Edge Preservation Index (EPI) are used. Experimental results and performance analysis indicate that the proposed method consistently outperforms existing techniques. 1. Introduction Breast cancer is the most common cancer among women in the United States [1]. It is the leading cause for death of women between the ages 35 and 54. Early detection is the most successful method of dealing with breast cancer. Currently the best method available for early detection of breast cancer is mammography. Other techniques, such as computed tomography (CT), magnetic resonance imaging (MRI), ultrasound and transillumination have been investigated, but mammography remains the proven technique. A mammogram is a picture of breast taken with a safe, low dose X-ray machine. Generally, mammograms are poor in contrast and features that indicate the breast cancer are very minute. Digitally enhancing the mammograms will provide us confident interpretation of critical cases, as well as allowing quicker diagnosis. It is very difficult to interpret the x-ray mammograms because of small differences in image density of various breast tissues in particular for dense breasts [2]. When the radiologists screen the mammograms with low dose X-ray the images obtained are poor in contrast. In low-contrast mammograms, it is difficult to interpret between the normal tissue and malignant tissue. In general while screening the mammograms, due to imperfect machines, the obtained mammograms are contaminated by noise. Image enhancement techniques have been widely used in the field of radiology where the subjective quality of images is important for human interpretation and diagnosis. Numerous algorithms are available in literature for enhancement of medical images such as histogram equalization, unsharp masking, median filter, Gaussian filters, and morphological filters [3, 4]. Conventional image enhancement techniques do not perform well on mammographic images. Recently multiscale techniques have evolved and sparked the interest of researchers for contrast enhancement of mammographic images. Nowadays wavelet domain has gained more popularity in image denoising rather than conventional spatial domain techniques such as average, median, min-max filters. In wavelet domain each noisy coefficient is modified according to certain threshold calculated. The threshold is applied to each noisy coefficient to obtain better performance. However, soft thresholding is most widely used in the literature [5]. The organization of the rest of the paper is as follows: Section 2 presents review of recent literature. Section 3, describes the proposed Enhancement method. Section 4 highlights the results of extensive experimentation conducted on some mammographic images. Finally conclusion is discussed. 192

2 Harish Kumar N et al,int.j.computer Techology & Applications,Vol 3 (1), Review of Literature Some work has been done in the past for the enhancement of mammograms. Dhawan et al. [6] proposed an optimal adaptive neighborhood processing algorithm with a set of contrast enhancement functions to enhance the mammographic features. The method was the improvement of the earlier work developed by Gordon and Ranagayyan [6].The method can enhance the desired, but unseen or barely seen features of an image with little enhancement of the noise and other background variations. Tomklav StojiC et.al. [7] Proposed a new algorithm for both local contrast enhancement and background texture suppression in digital Mammographic images. The algorithm was based on mathematical morphology applied to grayscale image processing. The algorithm was not efficient in enhancing the micro calcifications in digital mammograms. Yajie Sun et.al. [8] developed an adaptive-neighborhood contrast enhancement algorithm (ANCE) for skin-line extraction. ANCE is used to enhance the parenchyma of the breast and suppress the background noise. Suppression of the background noise can improve skin-line extraction and skin line extraction is an important step in CAD. The method can enhance only the skin-line rather than the whole image. Heinlein et al. [9] proposed an algorithm for enhancing microcalcifications in mammograms based on filter banks derived from continuous wavelet transformation, which were called integrated wavelets. The major disadvantage of the method was that it required an empirical selection of appropriate thresholds for image denoising, as well as the specification of an appropriate size range for the structures to be enhanced [10]. Sakellaropoulos et al. [10] developed a method to enhance contrast with redundant dyadic wavelet transform. The method can enhance the contrast of the mammograms and depress the image noise. Jiang et al. [11] developed a method to enhance possible microcalcifications combining fuzzy logic and structure tensor. In the method, a structure tensor operator was first produced and was then applied to each pixel of the mammographic image, which resulted in an eigenimage. The eigenimage was used to combine with the fuzzy image which was obtained by a fuzzy transform from the original image to enhance the contrast. This method can suppress non-mcs regions while enhancing the MC s regions. The method is complex in nature due to fuzziness and combination of two different domains need expertise. Scharcanski et al. [12] developed a wavelet transform based adaptive method for contrast enhancement and noise reduction in mammographic images. In this method, the images were first pre-processed to improve the local contrast and subtle details, then the pre-processed images were transformed into wavelet domain for noise reduction and edge enhancement. Although the method gave good enhancement results the complexity of the algorithm is more due to the wavelet domain.. Hence a method with better results for improvement in contrast as well as denoising of mammogram images is necessary. 3. Proposed Method The basic enhancement needed in mammography is the increase in contrast and denoising, especially for dense breasts. The enhancement model takes mammographic image I(x, y) as input. The image I(x, y) is separated into low frequency and high frequency components by using Gaussian low pass filter to get a higher degree of control over dynamic range. For the low pass filtered image L(x,y), modified mathematical morphology is applied. The high pass filtered image H(x,y) contains the edge information and the noise. Edge Enhancement algorithm is applied to the high pass filtered image to enhance the edge information and to attenuate the noise. Then morphologically processed image M(x,y) and Edge Enhanced image EE(x,y) are added to get the contrast enhanced Image C(x,y). To remove the noise wavelet transform is applied. Wavelet transform consists of three operations: wavelet decomposition, thresholding detail coefficients and wavelet reconstruction. Approximation and detail coefficients are obtained by decomposition. For the detail coefficients level dependent threshold is applied. Finally the decomposed image is reconstructed by the approximation and the modified detail coefficients E(x,y).In the following subsections the methods used for enhancement of mammographic images are discussed in detail. 3.1 Modified Mathematical Morphology Mathematical morphology originated in set theory and finds its place in any disciplines when it is necessary to establish the relationship between the geometry of physical system and some of its property. As such, morphology offers a unified and powerful approach to different image processing problems [15], [16]. Two simple morphological operations: Erosion and Dilation are fundamental to morphological processing. By combining them one can derive different image processing algorithms. The dilation of a gray-scale digital image I(x,y) by a structural element S(i,j) is defined as: I S m, n = max I m i, n j + s i, j (1) The gray-scale erosion is given by Eqn. (3.2): 193

3 I S m, n = min I m + i, n + j S i, j (2) are assumed to be the edge pixels (3.2) and the pixels above the arbitrary pixel value are noisy pixels. The arbitrary The opening of image I(x,y) by structuring element S is defined as erosion followed by dilation and is expressed as Eqn. (3.3). The closing of image I(x,y) is defined as dilation followed by erosion and is given by pixel in this context is selected by taking min and max pixel value in the high-pass filtered image and taking the average of both. The Edge Enhancement Algorithm is given below: Eqn. 3 and Eqn. 4: Step1: Select an arbitrary pixel a(x, y) from the highpass I S = I S S (3) filtered image and gains G1 and (3.3) G2. Step 2: If the pixel in the image is less than a(x, y), go I S = I S S (4) to step 3. Else go to step 4. Step 3: Multiply the pixel in image with gain G1. Step 4: Multiply the pixel in image with gain G2, where G2<G1. Step 5: Add the resulting images. Gray-scale opening can remove light details smaller than the structuring element. Similarly gray-scale closing removes dark details smaller than structuring element. The top-hat by opening is defined as the difference between the original image and its gray scale opening using structuring element S and it is defined as Eqn. 5: TO = I I S (5) Similarly dual bottom-hat by closing is the difference between the gray-scale closing image and original image is represented by Eqn. 6: Top-hat by opening yields an image that contains all residual features removed by opening. Adding these features back to original image has the effect of attenuating the high intensity structures. The dual residual obtained by using bottom-hat by closing is then subtracted from resulting image to attenuate low intensity structures: C x, y = I x, y + TO BC (7) The mathematical morphological approach is shown in Figure Edge Enhancement Algorithm High-pass filtered image H(x,y) is mainly composed of edge information and noise. The high-pass filtered image is obtained by subtracting the low-pass filtered image L(x,y) of the given input image from the original input image I(x,y). Usually the edge information pixels have small values where as the noisy pixels have high values. The edge information has to be enhanced mean while the noisy pixels are to be attenuated. To accomplish this we adopt two gain parameters namely g1 and g2. The first gain parameter is used to enhance the edge information while the other gain parameter is used to attenuate the noise. These gain parameters are applied based on selecting an arbitrary pixel value such that, the pixel values below the arbitrary pixel selected 3.3 Wavelet Denoising Wavelets are mathematical functions that cut up data into different frequency components and then study each component with a resolution matched to its scale. They have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. The wavelet denoising is accomplished in the following three steps BC = I S I (6) namely Wavelet Decomposition, (3.6) Threshold Detail Coefficients, Wavelet Reconstruction. In this proposed method bi-orthogonal wavelet is used for decomposition. The input image I(x,y) is decomposed at two levels. After decomposition the given image is realized by one approximation coefficient and 6 detail coefficients. Bi-orthogonal wavelet representation has many advantages compared to orthogonal. The subband images are invariant under translation and do not have aliasing. Smooth symmetrical or anti symmetrical wavelet functions are used for alleviation of boundary effects via mirror extension of the signal. The detail coefficients obtained after decomposition are horizontal, vertical, and diagonal coefficients. These detail coefficients are mainly composed of noisy details so they have to be denoised using appropriate threshold value. In the proposed method soft-thresholding is employed. The level dependent threshold is calculated at each level. The threshold is given by equation as shown below. T = j/2 max(d j ) (8) Where, j is level at which threshold T is computed. In this step we perform wavelet reconstruction using the last approximation coefficients and the modified detail coefficients after thresholding from level N to 1. The resulting image E(x,y) will be a contrast enhanced denoised image which is clearer than the original image 194

4 Input mammographic image and it will aid the radiologist I(x,y) to mark any abnormalities like lesions, microcalcifications, and masses. Low pass filtered Image Apply Gaussian Low Pass Filter G(x,y) Low frequency components L(x,y) Tophat by opening Erosion Dilation Bottom hat by closing Dilation Erosion Modified Mathematical Morphology M(x,y) High frequency components EE(x,y) H(x,y) Edge Enhancement Algorithm Morphologically Contrast Enhanced Image Figure 2. Modified Mathematical Morphology High frequency component image f(x, y) Contrast Enhanced Image C(x,y) Wavelet Denoising Select an Arbitrary pixel a(x, y) a(x,y)=(min f(x,y)+max f(x,y))/2 If a(x, y) < f(x, y) W(x,y) Enhanced Image E(x,y) These are edge pixels and multiply by gain G1 These are noisy pixels and multiply by gain G2 (G2<G1) Edge Enhanced image Figure 1. Enhancement Model Figure 3. Edge Enhancement Algorithm Figure3. Shows the flow chart of Edge Enhancement algorithm. Finally the resulting image will be an edge 195

5 enhanced image. The edge enhanced image and the morphologically enhanced image of the both high-pass and low-pass filtered images respectively, are added to give contrast enhanced edge preserved image. Mean while the noise content may also be enhanced due to morphological operations and edge enhancement. 4. Experimental Results The proposed method has been applied to more than 40 mammographic images from the standard Database, Mammographic Image Analysis Society (MIAS) [17]. To measure the quantitative performance analysis of the proposed method, parameters such as Contrast Improvement Index (CII) and Edge Preservation Index (EPI) are employed. 4.1 Contrast Improvement Index (CII) A quantitative measure of contrast improvement can be defined by a contrast improvement index. The contrast improvement index is defined as follows [13]: CII = C processed C original (10) Where, C Processed and C Original are the contrasts for the processed and original images, respectively. The contrast C of an image is defined by the following form: C = f b (11) f+b Where, f and b denote the mean gray-level value of the foreground and the background, respectively. The local contrast at each pixel is measured within its 5x5 pixel neighbourhood. More the value of CII, better improvement in contrast. 4.2 Edge Preservation Index (EPI) The edge preservation index [14] is defined as follows: EPI = I p i,j I p i+1,j + I p i,j I p i,j+1 I o i,j I o i+1,j + I 0 i,j I 0 i,j+1 Where I o (i,j) is an original image pixel intensity value for the pixel location (x,y), I p (i, j) is the processed image pixel intensity value for the pixel location (x,y). The greater value of EPI gives a much better indication of image quality. Table 2. EPI Values of enhanced mammograms at the second wavelet decomposition level Image ID VisuShrink Bayes shrink The proposed method achieved highest CII and EPI values as shown in Table 1and Table 2 respectively. Figure 4 shows the resulting output for some existing Mdb Mdb Mdb Mdb methods took for comparison with the proposed approach. 5. CONCLUSION SURE Shrink Mdb In this paper a new method for enhancement of mammograms for early detection and diagnosis of breast cancer has been introduced. It is based on modified mathematical morphology and Bi-orthogonal wavelet transform. The algorithm has been applied to more than 40 mammographic images from the standard Database MIAS. For performance evaluation of the proposed method, Contrast Improvement Index (CII) and Edge Preservation Index (EPI) are adopted. Experimental results show that the proposed method yields significantly better image quality when compared with other contemporary methods. (12) (4.2) Proposed Mdb Mdb Mdb Image ID VisuShrink Bayes shrink SURE Shrink Proposed Table 1. CII Values of enhanced mammograms at the second wavelet decomposition levels 196

6 6. References 1] Canadian Cancer Society, Facts on Breast Cancer, Apr [2] P.C. Johns, M.J. Yaffe, X-ray characterization of normal and neoplastic breast tissues, Physics Medical and Biology, Vol.32, no. 6, 1987, pp [3]K.Thangavel, M.Karan, R.Sivakum-ar, A. Kaja Mohideen, Automatic detection of microcalcification in mammograms: a review, ICGST-GVIP Journal, Volume (5), Issue (5), May [4]Issac N. Bankman, Handbook of medical imaging, Academic Press, [5]D. L. Donoho, Denoising by soft-thresholding, IEEE Transaction on Information Theory, vol. 41, May [6] A. P. Dhawan, G. Buellon, and R. Gordon, Enhancement of mammographic feature by optimal adaptive neighborhood image processing, IEEE Trans. Med. Imag., vol. MI-6, no. 1, 1986, pp [7]Tomklav StojiC, Irini Reljin, Branimir Reljin, Local contrast enhancement in digital mammography by using mathematical morphology, IEEE Transactions, [8]Yajie Sun, Jasjit Suri, Zhen Ye, Rangaraj M. Rangayyan, Roman Janer, Effect of adaptive neighborhood contrast enhancement on the extraction of the breast skin line in mammograms, Proceedings of the IEEE, Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China, September 1-4, [9] P. Heinlein et al., Integrated wavelets for enhancement of microcalcifications in digital mammography, IEEE Transactions on Medical Imaging, vol. 22, no. 3, 2003, pp [10] P. Sakellaropoulos etal, A wavelet-based spatially adaptive method for mammographic contrast enhancement, Phys. Med. Biol., vol. 48, no. 6, 2003, pp [11] J. Jiang et al., Integration of fuzzy logic and structure tensor towards mammogram contrast enhancement, Computer Medical Imaging and Graphics, vol. 29, no. 1, 2005, pp [12] J. Scharcanski and C. R. Jung, Denoising and enhancing digital mammographic images for visual screening, Computer Medical Imaging and Graphics, vol. 30, no. 4, 2006, pp [13] W. M. Morrow, R. B. Paranjape, R. M. Rangayyan, and J. E. L. Desautels, Region-based contrast enhancement of mammograms, IEEE Trans. Med. Imag., vol. 11, no. 3, pp , [14] M H Xie and Z M Wang, The partial Differential Equation Method for Image resolution Enhancement, Journal of Remote Sensing, Vol. 9, No. 6, 2005, pp [15] Gonzalez R. C and Woods R. B., Digital Image Processing, Pearson Education, Asia, [16] J Sara, Image analysis and mathematical morphology, Academic Press, London (UK), [17] The Mammographic Image Analysis Society: Mini Mammography Database, a c a c Mdb057 Mdb147 e Mdb148 e b d d b 197

7 a b Mdb 186 c d e Figure 4. (a) Original image (b) VisuShrink (c) Bayesshrink (d) Sureshrink (e) Proposed 198

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