DDSM Database

The algorithm was also evaluated using a database of $1,792$ RoIs extracted from the DDSM mammographic database [67]. From this set, $256$ depicted a true mass, while the rest, $1,536$ , were normal, but suspicious tissue. According to the size of the lesion, we used six different groups of RoIs. Each group of RoIs corresponded to the following mass sizes intervals: $<0.10 cm^2, (0.10-0.60) cm^2, (0.60-1.20) cm^2, (1.20-1.90) cm^2, (1.90-2.70) cm^2,> 2.70 cm^2$ , and the number of masses en each interval was respectively, $28$ , $32$ , $37$ , $57$ , $69$ , and $33$ masses.

Figure  shows the mean $A_z$ value obtained using the leave-one-out strategy and varying the ratio between both kind of RoIs. Note that, again, the performance of both PCA and 2DPCA approaches decreases as the ratio of RoIs depicting masses decrease. For the PCA approach we obtained $A_z = 0.73$ for the ratio $1/1$ and $A_z = 0.60$ for the ratio $1/6$ , while using the 2DPCA approach we obtained $A_z = 0.92$ and $A_z = 0.81$ respectively. Thus, the 2DPCA approach obtained better performances than the PCA.

Figure: Performance of the system for the DDSM database.

The $A_z$ values for the ratio $1/3$ are detailed in the first row of Table . The overall performance of the system at this ratio is $0.65$ for PCA and $0.86$ for the 2DPCA. As in MIAS results, both approaches are more suitable for false positive reduction of larger masses than smaller ones. As already explained, this is due to the fact that larger masses have a larger variation in grey-level contrast with respect to their surrounding tissue than smaller masses, which are usually more subtle, even for an expert.

Comparing the results between both MIAS and DDSM databases, it is obvious that the ones obtained using MIAS were better than the obtained using the DDSM database. This is mainly due to two different reasons: firstly, the fact that we can extract a more larger subset of RoIs using the DDSM than using the MIAS database, and secondly, the masses in MIAS database were larger than in the DDSM, and as we have explained, this is an important increasing factor of the performance of both algorithms.

Table 5.3: $A_z$ results for the classification of masses using RoIs extracted from the DDSM database, detailed per size (in $cm^2$ ).

		Lesion Size (in $cm^2$ )
		$<$ 0.10	0.10-0.60	0.60-1.20	1.20-1.90	1.90-2.70	$>$ 2.70
-||---	PCA	$0.53$	$0.70$	$0.70$	$0.68$	$0.72$	$0.83$
	-||---	2DPCA	$0.81$	$0.83$	$0.87$	$0.84$	$0.89$
-||---

Finally, Figure  shows the mean kappa statistic obtained using the leave-one-out strategy at a determined threshold ($0.5$ ). The same behaviour found for the $A_z$ values is repeated. Thus, the performance of both approaches are reduced when increasing the number of normal tissue. Comparing with the results obtained using the MIAS database, accuracy is also reduced. For the 2DPCA approach, only when there is one or two RoIs with normal tissue for each RoI with masses the agreement is almost perfect, while for ratio one-to-three the agreement is substantial and for the rest of cases it is in the high part of the moderate agreement.

Figure 5.4: Mean Kappa values obtained by the system using the DDSM database.

Using this large dataset, we can compare the proposed PCA and 2DPCA-based algorithms with the ones surveyed at the beginning of this chapter. With the same ratio $1/3$ Sahiner et al. [157] and Qian et al. [144] obtained $A_z$ values of $0.90$ and $0.83$ respectively. While the performance of the PCA-based approach is inferior to the other algorithms, the 2DPCA-based approach clearly outperforms the results of Qian et al. In contrast, the mean value obtained using this approach is inferior to the one obtained by Sahiner et al.

Comparing with the other approaches where the authors use the ratio $1/1$ , the PCA approach still has inferior values. However, the 2DPCA approach outperforms the existing approaches.

Figure 5.5: The first nine eigenimages found using the third group of RoIs, obtained using PCA analysis.

(1)	(2)	(3)
(4)	(5)	(6)
(7)	(8)	(9)

As an illustration of the information provided by PCA analysis^5.4. Figure  shows the nine images constructed by using the nine first eigenvectors of the third group of RoIs. Note that each image contributes with different information to the system. For instance, the first image (the first eigenvalue) represents the main variation in the grey-level transition going from top-left to down-right. The second one represents the variation of the grey-level values from the outside and the inside of the image. Note also that this second eigenvector is related to the non-presence of masses, as well as eigenvectors $6$ and $7$ are related to their presence.