MIAS Database

The performance of our approach is evaluated using a total of $120$ mammograms extracted from the MIAS mammographic database [169]. Among them, $40$ show confirmed masses (the ground-truth provided by an expert) while the rest were normal mammograms. We used four different groups for the $40$ mass RoIs according to their size. Each group corresponds to the following intervals of mass sizes: $<1.20 cm^2$ , $(1.20-1.80) cm^2$ , $(1.80-3.60) cm^2$ , $> 3.60 cm^2$ . In each interval there were, respectively, $10$ , $8$ , $10$ and $9$ masses. Three masses were excluded from the modeling: one for being much larger than the rest, and the other two for being located at the border of the mammogram. In order to evaluate our proposal a direct comparison with algorithms d1 and d2, described in Sections  and  respectively, is given.

As is shown in Figure , the proposed approach has a better performance compared to both d1 and d2 approaches. Note that algorithm d1 has a tendency to produce a large number of false positives at high sensitivity rates. For instance, at a sensitivity of $0.8$ , d1 has $9.69$ false positive per image in mean, while d2 $4.33$ , and our approach (Eig) $2.33$ .

Figure 4.8: FROC analysis of the algorithm over the set of $120$ mammograms. The proposed algorithm performs better than both others approaches.

Figure  shows the behaviour of the proposed algorithm according to the size of the lesions (note that we have reduced the scale on the x-axis for a better visualization). At lower sensitivities the algorithm is more or less independent of the size of the lesion. However, when sensitivity is around $0.7$ becomes an important factor, being the performance of the algorithm inversely proportional to the size of the mass. This is due to the fact that the proposed algorithm only detects the centre and the bounding square of the mass: if the mass is larger than the bounding square the sensitivity decreases because there are some pixels not considered as a mass. The opposite can also happen, when the bounding square is larger than the mass the sensitivity decreases because there are some pixels being considered as a mass which are not really part of a mass. Note that both problems are more likely to appear in large masses with spicules than in small masses.

Figure 4.9: FROC analysis of the algorithm detailed for each lesion size.

Once the mammograms containing masses are detected, ROC curves are obtained measuring the accuracy with which the masses have been detected. The overall performance of the developed approach over the $40$ mammograms containing masses resulted in a $A_z = 89.3 \pm 5.9$ , while using d1: $A_z = 84.1 \pm 7.9$ and using d2: $A_z = 88.1 \pm 8.4$ . Thus, the proposed approach obtains a better performance compared to the original algorithms.

Table  shows the effect of the lesion size for the different algorithms in terms of $A_z$ mean and standard deviation. Note that the proposed algorithm has a similar performance for the three smallest sizes, while for the largest one the performance decreases. This is due to the shape variability of larger masses. For example, Figure (c) shows an elliptic mass correctly detected, but with a high number of pixels not being part of a mass classified inside the bounding square. Comparing the performance with algorithms d1 and d2, our approach has a similar trend to d1, with a better performance for smaller masses than for larger masses. In contrast, algorithm d2 tends to increase its performance proportionally to the mass size.

Table 4.1: $A_z$ mean and standard deviation obtained by the different algorithms using the MIAS database, detailed for each mass size (in $cm^2$ ).

		Lesion Size (in $cm^2$ )
		$<$ 1.20	1.20-1.80	1.80-3.60	$>$ 3.60
-||--	d1	$92.1\pm 5.5$	$85.8\pm 8.2$	$82.4\pm 7.3$	$79.1\pm 7.2$
	-||--	d2	$84.9\pm 8.8$	$86.7\pm 8.1$	$89.1\pm 9.6$
	-||--	Eig	$91.3\pm 7.4$	$90.3\pm 3.3$	$89.6\pm 4.7$
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