The Importance of the Segmentation Step

We include in this section a comparison between our strategy for breast density classification and the others found in the literature. In fact, the main difference among these approaches is the density segmentation, which can be divided in three general approaches: no density segmentation, segmentation according to the distance to the skin-line, and segmentation according to the internal tissue.

To quantitatively compute the improvement provided by our strategy, the same features and classifier as proposed are used. Below, the strategies are explained in more detail.

• No Segmentation. The first approach is the extraction of features of the global breast, without any kind of segmentation.

• Segmentation According to the Distance to the Skin-Line. This approach was first suggested by Karssemeijer [83]. The main idea is the assumption that a strong correlation exists between tissue thickness and distance to the skin line. To compute the distance to the skin line of the breast a distance transform is used. First, a binary object is formed by merging the breast tissue and the pectoral (or the equivalent segmented region). This object is eroded repeatedly using a circular structuring element. The number of erosions done for a particular pixel in order to remove itself is taken as the distance to the skin-line. Figure (c) shows the result of applying this algorithm in four different mammograms.

• Segmentation According to the Breast Density. Three different approaches have been implemented using such strategy. The first one is our evaluated proposal, which is based on the Fuzzy C-Means clustering (Figure (d)). The second approach is based on the work of Raba et al. [149], in which the breast was divided using a fractal scheme. Figure (e) shows some results using this algorithm. Finally, we construct a novel approach based on a statistical analysis of the breast. Thus, patches of $25 \times 25$ pixels from a single mammogram are extracted and used as the ground-truth in order to segment the rest of mammograms. Some of the windows represent dense breast tissue while others represent non-dense tissue. Hence, using the fisherfaces approach [7], these windows are used to construct a model from each part of the mammogram, and subsequently, each subwindow of the mammogram is classified as one of those regions. Thus, we finally obtain a segmentation of the breast in two regions, which represents fatty and dense tissue, as is shown in Figure (f).

To quantitatively measure the improvement of our proposal we used in this experiment the MIAS database [169] with the annotations obtained from the consensus opinion (the set $322$ mammograms divided as $87$ BIRADS I, $103$ BIRADS II, $95$ BIRADS III, and $37$ BIRADS IV). The same leave-one-woman-out procedure explained is used to evaluate each strategy.

The confusion matrix for the first strategy (no segmentation) is shown in Table (a). The overall performance of this approach is $67\%$ , and detailed for each class, we obtained $77\%$ , $74\%$ , $55\%$ , and $57\%$ , from BIRADS I to BIRADS IV respectively. Note that mammograms with low density are better classified than mammograms with high density.

Table (b) shows the results obtained by the second approach, which is the segmentation of the breast in regions according the distance to the skin-line. Note that the performance is highly increased compared with the no-segmentation approach, resulting in $75\%$ correct classification. The highests improvement are found in mammograms belonging to BIRADS I and BIRADS III, obtaining respectively $89\%$ and $69\%$ correct classification.

Table 3.7: Confusion matrix for the classification of the mammograms of MIAS database (a) without segmentation of the breast and (b) segmenting according the distance to the skin-line.

                No Seg. ( $67\%,\kappa = 0.54$ )

  Skin-line ( $75\%,\kappa = 0.65$ )

		B-I	B-II	B-III	B-IV
	B-I	$67$	$19$	$1$	0
		B-II	$11$	$76$	$16$
		B-III	$7$	$22$	$52$
		B-IV	0	$1$	$15$

B-I	B-II	B-III	B-IV
$77$	$9$	$1$	0
$11$	$77$	$14$	$1$
0	$25$	$66$	$4$
$1$	$5$	$9$	$22$

(a)

(b)

Finally, Table  shows the results obtained by using a segmentation of the breast according to the internal breast tissue. Here (a) shows the results obtained by the Fuzzy C-Means approach, (b) based on the Fractal approach, and (c) using the Statistical approach. Note that the overall performance for each algorithm is similar: $86\%$ , $84\%$ , and $85\%$ , respectively, and all of them are clearly better than the results obtained by the other two approaches.

The results obtained by the Fuzzy C-Means and the Statistical approach are quite similar for all classes except BIRADS III. For BIRADS I both approaches obtained $91\%$ correct classification, for BIRADS II the Statistical approach obtained $84\%$ while the Fuzzy C-Means $83\%$ , and for BIRADS IV both approaches obtained $73\%$ . In contrast, for BIRADS III the performance of the Fuzzy C-Means is better, increasing the percentage of correct classification from $85\%$ to $89\%$ . On the other hand, the performance of the Fractal approach is slightly different. It obtains $95\%$ correct classification for mammograms belonging to BIRADS I, while for the rest of classes this is reduced to $82\%$ , $83\%$ , and $62\%$ from BIRADS II to BIRADS IV, respectively.

Table 3.8: Confusion matrices for MIAS mammogram classification by using the internal breast density as a segmentation strategy: (a) Fuzzy C-Means, (b) Fractal, and (c) Statistical approaches.

               FCM ( $86\%,\kappa = 0.81$ )

Fractal ( $84\%,\kappa = 0.77$ )

Statistical ( $85\%,\kappa = 0.79$ )

		B-I	B-II	B-III	B-IV
	B-I	$79$	$1$	$3$	$4$
		B-II	$3$	$86$	$6$
		B-III	0	$2$	$85$
		B-IV	0	$6$	$4$

B-I	B-II	B-III	B-IV
$83$	$2$	$2$	0
$8$	$84$	$9$	$2$
0	$5$	$79$	$11$
$2$	$8$	$4$	$23$

B-I	B-II	B-III	B-IV
$79$	$3$	$4$	$1$
$1$	$87$	$10$	$5$
0	$8$	$81$	$6$
$1$	$4$	$5$	$27$

(a)

(b)

(c)

Figure  shows the segmentation of the breast according to the compared strategies. Except for BIRADS I, the three last columns (which corresponds to the segmentation algorithms that use breast tissue information) show similar results, and thus the classification results for these strategies are also similar. Note that for

Figure 3.3: The reviewed strategies for dividing into regions a mammogram. The density of the mammograms shown in column (a) increases from the top row (BIRADS I) to the bottom row (BIRADS IV). Segmentation using (b) a single breast area, (c) the distance between the pixels and the skin-line, (d) a Fuzzy C-Means clustering of pixels with similar appearance, (e) the fractalization of the image, and (f) the statistical approach.

(a)	(b)	(c)	(d)	(e)	(f)

BIRADS I the Fuzzy C-Means obtains a singular result, grouping in a cluster most of the pixels of the breast except those located near the skin-line, which form the second cluster. This is due to the fact that, for this set of mammograms, the breast is almost homogeneous and the algorithm only can distinguish between those pixels with different compressed tissue (the region is darker in those regions with less compressed tissue). As discussed in Section , the breast texture information is in the breast tissue cluster, while the small ribbon-like cluster does not provide significant information to the system.

Analyzing in more detail the segmentations of the mammograms belonging to the rest of BIRADS categories, one can conclude that the fractal approach provides a pixelated segmentation, while the statistical approach obtains larger and clearly separated regions. On the other hand, the Fuzzy C-Means performance is an intermediate solution and, thus, classification results are slightly improved compared to the other two.

The obtained results show that the segmentation step increase the performance of the classification, improving the results by, at least, $8\%$ . Moreover, we have noticed that using the segmentation according to the breast tissue clearly outperforms the segmentation according to the distance to the skin-line. We have also noted that the strategy used to segment the internal breast tissue does not provide a major variation in the results, with the Fuzzy C-Means based results slightly better than the other ones.