# 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):

in¼1ðmijÞmXi

Vj ¼
P
in
1
mij
m

whereP
¼

ð
Þ

dij

c

X

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), https://doi.org/10.1016/j.bbe.2019.04.008

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 with 8-connected or 6-connected region growing