MIAS Database

For the MIAS database four groups of RoIs were used according to their size. Each group corresponds to the following intervals for 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, while the rest of RoIs represent normal tissue.

Figure  shows the mean $A_z$ obtained using the leave-one-out strategy according to increasing number of RoIs representing normal tissue (from the same number of RoIs to six times this number). Obviously the performance of both systems decreases as the number of normal tissue RoIs increases. For instance, for the PCA approach, the performance is reduced from $A_z = 0.88$ to $A_z = 0.74$ , while the 2DPCA approach goes from $A_z = 1.00$ to $A_z = 0.96$ . Note that the 2DPCA clearly outperforms the normal PCA.

Table  shows the $A_z$ values for both approaches for the ratio of one RoI with mass and three normal RoIs in the database ($1/3$ ). The overall performance of the system at this relation is $0.80$ for PCA and $0.97$ for the 2DPCA. In the first row of the table, a detailed comparison of the performance for each group is shown. Clearly, both approaches are more suitable for larger masses than for small ones. This is due to the fact that larger masses have a larger variation in grey-level contrast with respect to their surrounding tissue than small masses, which are usually more subtle.

Table 5.2: Detailed $A_z$ results per size for the classification of masses for both approaches using the MIAS database. The results are detailed for each size group.

		Lesion Size (in $cm^2$ )
		$<$ 1.20	1.20-1.80	1.80-3.60	$>$ 3.60
-||--	PCA	$0.72$	$0.82$	$0.83$	$0.92$
	-||--	2DPCA	$0.92$	$0.98$	$1.00$
-||--

Observing Figure  at different ratios we can also quantitatively compare our approach with the ones found in the literature. With the same $1/3$ ratio that studied above, Sahiner et al. [157] and Qian et al. [144] obtained $A_z$ values of $0.90$ and $0.83$ respectively. Both values are superior to the obtained by the PCA approach, but clearly inferior to the obtained by the 2DPCA approach. On the other hand, with the ratio of one RoI of each class our approaches outperforms the presented by the rest of surveyed works. Note however, that the total number of RoIs is too small in order to extract significant conclusions. We leave this discussion for Subsection .

Figure  shows the obtained mean kappa statistic (defined in Equation ) when using the leave-one-out strategy at a determined threshold^5.3 for all the ratios of number of masses vs number of normal RoIs (from the ratio $1/1$ to the ratio $1/6$ ). Obviously the same behaviour found for the $A_z$ values is now repeated. Thus, the performance of both systems when the number of normal tissue RoIs increases is reduced from $\kappa = 0.68$ to $\kappa = 0.37$ for the PCA approach, and from $\kappa = 1.00$ to $\kappa = 0.82$ for the 2DPCA. Note that the differences in performance are clearer analyzing the kappa statistic than the $A_z$ value.

Figure 5.2: Performance of the system using the MIAS database using the Kappa statistic.