Computational Intelligence - February 2013 - 31

the interface between the external air and
We compare the mean performance over the ten runs
the tissue. Fig. 18(a)-(c) show some examples of the problems described. On the synfor each image. Each pair is composed of the result
thetic images, LS obtained slightly better
of our SS proposal and the best result among those
results. It was able to segment the holes in
achieved by the other three algorithms.
the images and to successfully filter the two
kinds of punctual noise. However, the algorithm tends to segment the small dots and other structural
D. Statistical Analysis of the Results
noise, even getting stuck into them, like in the case of image s8.
In the previous section, we provided a detailed analysis of the
The segmentations obtained by MS are expressions of differnumerical results obtained, giving an insight of the performance
ent local minima [see Fig. 18(d)-(f) for illustrative examples]. In
of the four compared methods. To prove the significant superiorthese cases, the algorithm found meshes with a lower energy
ity of the segmentation capabilities of our proposal, in this secthan LS. However, in doing so, it lost some high energy objects,
tion we provide a statistical analysis of the obtained results. With
not being able to cut the connections between these objects and
this aim, we performed a two-tailed Wilcoxon signed-rank test
the background. Indeed, it often was unable to segment the
[24] for each of the four segmentation metrics as follows.
smallest object in images k2, k3 and k4. Moreover, the segmentaLet N = 20 be the sample size, that is, the number of images
tion of the lungs are often incomplete, lacking some important
in the dataset and hence the number of pairs in the test.We comparts. Connections with external borders are also present, as in
pare the mean performance over the ten runs for each image.
the case of LS, but to a lesser extent. The values of the dRT and
Each pair is composed of the result of our SS proposal and the
best result among those achieved by the other three algorithms.
the dTR distances for the LS and MS algorithms confirm the
This is the hardest case since, for every image, we always compare
analysis of the segmentation defects. Unsurprisingly, on the synSS against an aggregate algorithm whose performance is the best
thetic images, MS was able to filter the structural noise better
one obtained by the set C = {LS, MS, DE}. Since we are now
than LS, but it showed the same tendency to undersegment the
comparing only two algorithms (C and SS), we are allowed to use
objects. It successfully filtered the two kinds of punctual noise.
the Wilcoxon test, as outlined in [25]. The null and alternative
The results obtained by DE are poor. The meshes got stuck
hypothesis are defined, respectively, as:
in both kinds of local optima exposed so far. In addition, they
failed in locating the objects, eventually taking degenerated
shapes. The only successful result was s1, which is only affected
by tiny-objects noise, showing how the global search is able to
filter these kinds of structures. Conversely, the algorithm proved
to be heavily affected by the punctual noise on the synthetic
images. Although DE achieved good performance in [8], the
images considered there were significantly simpler than the
ones in our dataset. The lack of an energy term rewarding the
segmentation of multiple objects, the loss of the topology
(a)
(b)
(c)
information of every net but the best individual at every new
generation, the inability of the BILS to adjust the mesh to
objects with complex shapes, and the absence of crossover
operators considering the characteristics of the problem
strongly limit the performance of that proposal.
Finally, the results obtained by SS are clearly the best ones.
(d)
(e)
(f)
For all the images, it performed better than the other three
methods in almost every statistic. Indeed, it respectively ranked
Figure 18 Examples of LS and MS inaccuracies (in red). (a) LS on k2,
first 20 and 19 out of 20 times, according to the mean of the S
(b) LS on l1, (c) LS on s3, (d) MS on k2, (e) MS on l1, and (f) MS on s3.
and dH index values, as shown in Table 2. The low values of the
dRT and the dTR distances, smaller than the three competitors, are
in line with the quality of the segmentations. SS gets the best
Table 3 The results obtained by the Wilcoxon test.
result in 19 cases for dRT and in 15 cases for dTR. Focusing on the
medical images, the resulting nets on images k2, k3 and k4 propMeTric
p-value
Median (c)
Median (SS)
erly segment the small objects and there are few connections to
-6
S
1.907 · 10
0.958
0.977
the background on all the images of this category.The segmenta-6
3.815 · 10
4.266
1.164
Md
tions are almost complete but, in some cases, SS was not able to
segment some small structures, as in Fig. 17(g), (h), and (i). As for
-2
2.958 · 10
1.700
1.465
Md
the synthetic images, the segmentations are complete while there
-6
dH
5.722 · 10
47.036
17.328
is almost no presence of structural noise.
RT

February 2013 | Ieee ComputatIonal IntellIgenCe magazIne

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