Mammographic Image Enhancement using Double Sigmoid Transformation Function Vikrant Bhateja1, Swapna Devi2 1
Department of Electronics & Communication Engineering SRMCEM, Lucknow-227105; 2NITTTR, Chandigarh, 160019. vikrant_bhateja@ yahoo.co.in
[email protected]
Abstract—Micro-calcifications are the earliest sign of breast carcinomas and their accurate detection is one of the key issues of breast cancer control. In this paper, a new image enhancement technique which would aid automated detection of microcalcifications, leading to efficient computer-aided diagnosis of breast cancer is proposed. The proposed non-linear transformation function used for contrast enhancement is a scaled version of a linear combination of double sigmoid function. The effect of this transformation function has been evaluated using two assessment parameters, viz., PSNR & a universal Q-Metric. The enhancement technique has been tested on different types of mammographic images (with various categories of background tissues) which usually suffer from poor contrast. Significant contrast improvement is the speciality of this technique, leading to more accurate detection of micro-calcifications in mammographic images. Keywords—Micro-calcifications, Double Sigmoid Function, Contrast Enhancement, PSNR, Q-Metric.
I. INTRODUCTION Breast cancer is the one of the most commonly diagnosed cancers in women. It is the second leading cause of cancerrelated death in women. This cancer is a kind of malignant tumour formed from abnormal cell division and growth in breast cells. The discovery of a lump in the breast is typically the first sign of breast cancer. Mammography (X-ray imaging of the breast) is currently the most prominent method for initial detection and examination of breast cancers, revealing the potential breast carcinomas. Once a mammogram reveals a lump in the breast, cells from the tumour are removed and analyzed under microscope to determine whether or not the lump is cancerous. Masses and micro-calcifications are the most common abnormalities in mammograms. A mass is a space-occupying lesion seen in at least two mammographic projections. A micro-calcification is a deposit of calcium salt in a tissue. Both can be associated with either malignant or benign abnormalities, and can have a variety of visual appearances. Calcifications are small densities that appear as bright spots on mammograms. Micro-calcifications vary in size, shape, signal intensity and contrast, and might be located in areas of dense parenchymal tissue making their detection difficult. Also, their classification as benign or malignant requires accurate preservation of their edges and other morphological details. Mammographic density has been shown to be one of the most powerful predictors of breast cancer risk; of which microcalcifications are the most common. Hence, the detection of micro-calcifications becomes an important component of CAD [1]. Mammographic images do not suffer much deterioration due to noise but have a poor contrast because of the nature and superimposition of the soft tissues of the breast. Thus, any
improvement in the appearance and visual quality of the image may help the radiologists to a greater extent [2]-[4]. N. Hassan et al. proposed contrast enhancement using sigmoid function [5] on the original image. J.Scharcanski et al. [6] used wavelet transform for mammographic image enhancement which combines the wavelet shrinkage and scale space constraints. This method enables the user to select the requisite image enhancement and scale of analysis, but does not provide for any adjustment of parameters for the purpose of denoising. J. Salvado et al. presented a method [7] that comprises of three steps, viz, image de-noising, wavelet image analysis and image enhancement by local adaptive operators integrated in the wavelet domain. Papadopoulos et al. [8] brought out a comparison of five image enhancement algorithms for the detection of micro-calcifications in mammograms. The contrast-limited adaptive histogram equalization (CLAHE), the local range modification (LRM), 2-D redundant dyadic wavelet transforms (RDWT), Wavelet Based Linear stretching (WLST) and wavelet shrinkage (WSRK) techniques, and showed that LRM and WLST are better. N. R. Parveen et al. in their work [9] presented the comparison between the Histogram Equalization & Adaptive Histogram Equalization techniques for the enhancement of X-ray images. Comparison shows that Contrast Limited Adaptive Histogram Equalization (CLAHE) gives better result than other equalization methods. J.Q. Domínguez et al. proposed a method [10] for mammographic image feature extraction using Co-ordinate Logic Filters (CLF) and Artificial Neural Networks. The work employs image contrast enhancement by modifying gray levels, applying a nonlinear adaptive transformation function and then the edge detection by CLF. E. Athanasiadis, et al. [17] investigated the effectiveness of different wavelet-based filters over histogram equalization filters. But in these filters, the common tuning parameters (gain & threshold) were left to be manually chosen by the user. M. Hadhoud et al. proposed an algorithm [18] based on mathematical morphology and wavelet analysis. However, a significant drawback of enhancement via morphological filter is that it is unable to filter noise completely from images. After a wide survey of such algorithms it can be concluded that Histogram Modification, Wavelet Transform, Image Morphology are among the most successful methods. In this paper, a new method has been proposed to improve the contrast of mammographic images which could serve to be an important step for early detection of breast cancer. A type of non-linear mask is prepared which uses a linear combination of double sigmoid functions as the gray level transformation function. The mask is spatially moved over the region of interest (ROI) to produce an enhanced image. The performance of this method is evaluated using PSNR and a universal Qmetric. Simulation results show significant improvement in
comparison to other methods. This paper is organized as follows: In section II; the proposed method is presented. This is followed by the objective evaluation of the enhanced image quality in section III; results and discussion is presented in section IV; in the last section V, conclusions are drawn. II. PROPOSED METHOD An enhancement method for the mammographic images is proposed by suggesting an improved version of Histogram Equalization with the multi-scale adaptive gain [11]. It suppresses pixel values of very small amplitude, and enhances only those pixels larger than a certain threshold T within each level of the transform space. The following non-linear transformation function is proposed, to accomplish the above operation: (1) f ( x) a[dsigm(k ( x b) dsigm(k ( x b)] where x denote the gray level value of the pixel of the original input image at co-ordinate (i,j), a is given by: 1 a [dsigm(k (1 b) dsigm(k (1 b)] (
x x1
)2
dsigm( x) sgn( x x1 )[1 e s ] 1 sigm( x) 1 e x k and b are the rate of enhancement and the control of threshold respectively while x1 is the centre and s is the steepness factor of the transformation function. dsigm(x) is a double sigmoid function which is a logistic function similar to the sigmoid function. It is a continuous, non-linear function. Graphically, it is equivalent to two identical sigmoid functions bonded together at a point (x=x1).
through the parameters k and s. These parameter are bounded in the range as, b, s Є R (0
