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  • In most of the cases


    In most of the cases, the leftmost pixel on right views or the rightmost pixel on left views is enough to determine
    263 where mmij represents the degree of membership of the ith pixel 264 Xi to jth class Vj which is the centre of jth class and d2ðXi; VjÞ is 265 the square of the Euclidian distance between Xi and Vj. The 266 function is minimized under the following conditions:
    247 The most popular fuzzy c-means algorithm makes use of the 248 reciprocal of distances to decide the cluster centres of all 249 points, weighted by their degree of belonging to the cluster. 250 This results in a class membership to more than one cluster at 251 the same time with different degrees of association [33]. This 252 multiple association represents an important feature for 253 increasing sensitivity in medical image segmentation. Fur- 254 thermore, the fuzzy logic allows to model non-linear, impre- 255 cise, complex systems by applying human knowledge and 256 experience as a set of fuzzy rules that use linguistic variables 257 for better segmentation [15,34]. The modified fuzzy clustering 258 function for segmenting image with n pixels into c clusters 259 minimizing the within-class sum-of-square errors and is 260 defined as Eq. (1):
    Vj ¼ P in 1 mij m
    whereP ¼
    ð Þ
    the required width of the mammogram and to crop out the 279
    essential breast 555-60-2 region. Exceptionally, on a 280
    few images, the farthest pixel from breast wall lies on the 281
    border instead of the nipple of the breast. The part of the 282
    breast parenchyma with a margin of 30 pixels wide beyond 283
    this parenchyma is included in the cropped image. The 284
    resulting image of cropped parenchyma region is depicted 285
    height remains intact. The nipple position is required in 287
    locating the lesion position in the breast and the breast 288
    quadrant the lesion belongs to. The horizontal line passing 289
    quadrant' and section below the line is 'inner quadrant' 292
    on CC view. Similarly, the section above the line is 'upper 293
    quadrant' and section below the line is 'lower quadrant' on 294
    obstructs the segmentation of breast for identifying 296
    suspicious lesions [35]. Hence, it is extracted using the 297
    RANdom SAmpling Concensus (RANSAC) algorithm [36], 298
    (2) Accurate segmentation of the suspicious lesions with fuzzy, 301
    ill-defined and diffused boundaries especially on the low 302
    contrast CC or MLO view images is challenging task [37]. The 303
    literature survey reveals that the fuzzy-based region growing 304
    methods are effective in segmentation of such cases [38]. 305
    (3) Therefore, the hybrid segmentation method in the proposed 306
    work leverages the advantage of fuzzy-based systems for 307
    segmenting FFDM images. The segmentation algorithm con- 308
    sists of four major steps. 309
    Identifying the suspicious abnormal lesions with dynami- 310
    cally selected seed pixel 312
    Expanding the suspicious lesions using adaptive fuzzy 313
    region growing algorithm 314
    Please cite this article in press as: Sapate S, et al. Breast cancer diagnosis using abnormalities on ipsilateral views of digital mammograms. Biocybern Biomed Eng (2019),
    Fig. 2 – FP reduction using empirical rules during the initial detection stage: (a) CC view with suspicious lesion detected; (b) selected lesion after applying empirical rules for FP reduction; (c) MLO view of the same breast; (d) lesion after FP reduction.
    3187 Merging the similar small and close neighbouring regions
    3210 Delineating the border of abnormal lesions.
    323 It is assumed that the malignant tumours are the regions
    324 with dense core surrounded by the slowly extended transi-
    325 tions till their boundaries. The regions on mammogram with
    326 textural homogeneity, maximum entropy, maximum average
    327 intensity and minimum variance are selected as centroids of
    328 candidate lesions. The scheme assumes the fuzzy connected-
    329 ness of neighbouring pixels with homogeneity using intensity
    330 values constrained by mean and standard deviation. The
    331 procedure starts with dynamically chosen centroid of the
    332 suspicious lesion. The region being defined starts growing with
    333 neighbouring pixels surrounding the designated centroid.
    334 Subsequently, the pixel which has intensity near to the mean
    335 m of the region is included in the region. The traditional
    336 algorithms 555-60-2 with 8-connected or 6-connected region growing