Capability to detect masses

This aspect of the evaluation mimics the radiologist in detecting abnormalities (in this case abnormal masses). The FROC curves of the eight algorithms based on the $120$ mammograms are shown in Figure . In general, all the implemented approaches have a tendency to over-segment and hence produce a large number of false positives at high sensitivity rates.

Algorithms $d2$ , $b2$ and $d1$ show the best trade-off between sensitivity and false positives per image. This improved performance might be due to one aspect that these three approaches have in common, which is the incorporation of directional distribution information. This aspect is expected to reduce the number of false positives which are likely to have a more random distribution than true positive regions. This indicates that spatial information is essential to reduce false positive regions to more acceptable levels.

Computational Cost

We briefly evaluate and compare the computational cost of the algorithms. Although the cost is not a relevant feature, it could be taken into account if the aim of the system is to develop an interactive tool, where the segmentation stage should be relatively fast. Table  shows the comparison of the execution times for the $8$ implemented algorithms. As the MIAS database contains mammograms of different sizes, we compute the mean time of segmentation (and its standard deviation) of the algorithms at each size. It should be noted that the large standard deviation in the segmentation time is caused by variation in breast area.

Algorithms $a1$ and $b1$ are extremely fast in comparison with the rest. This is due to the fact that both algorithms are based on the use of filters which affect the whole image, whilst the other algorithms are pixel-based. On the other hand, the necessity of applying different size and shapes of the template in the pattern matching ($d1$ ) algorithm makes it extremely slow compared to the rest. In addition, the necessity of algorithm $d2$ to search a neighbourhood makes it also relatively slow.

Table 2.4: Segmentation time in seconds of the algorithms for the four mammogram sizes (small, medium, large, extra) present in MIAS database. Note that each mammogram is downsampled by a factor of $4 \times 4$ .

MIAS Image Sizes
		Small	Medium	Large	Extra
-||--	a1	$11\pm 1$	$14\pm 3$	$18\pm 5$	$34\pm 6$
	-||--	a2	$31\pm 1$	$40\pm 3$	$51\pm 4$
	-||--	b1	$2\pm 1$	$3\pm 1$	$4\pm 1$
	-||--	b2	$17\pm 1$	$22\pm 2$	$28\pm 4$
	-||--	c1	$20\pm 5$	$34\pm 9$	$56\pm 12$
	-||--	c2	$68\pm 27$	$95\pm 29$	$146\pm 40$
	-||--	d1	$1766\pm 143$	$2211\pm 155$	$2767\pm 183$
	-||--	d2	$1096\pm 123$	$1756\pm 160$	$2504\pm 199$
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