## 4 Experimental Results
### Selection of the Best Segmentation Algorithm  
To select the best segmentation algorithm, three meta-heuristic algorithms and the Otsu method were used to analyze mammographies from the Breast Cancer Digital Repository [46], which come from a Portuguese breast cancer database of real patients, which comprises 362 segmentations. The Faculty of Medicine of the University of Porto, Portugal provided this database made by expert radiologists, and they proved by biopsies the classifications provided (benign or malign). Otsu parameters were used as a default and implemented in Matlab(tm). The parameters for the NBA were: three bats, three regions, 10 iterations, and other parameters as proposed by [PERSON] et al. [40] were used. These parameters showed a lower error for segmentation according to the study of [PERSON] et al. in 2016 [42]. For the genetic algorithm, 50 individuals were used, with three regions, 10 iterations, a mutation rate of 0.05 and a crossover rate of 0.7. Finally, for simulated annealing an initial temperature of 100,000 and a cooling rate of 0.05 were used. Errors for each image were calculated and we present the mean of the results in Table 2. The following images show two of the experiments carried out using images from mammographies. The first row shows the original mammography image, the region of interest and the region of interest overlapped in the original image. The second row shows the results applying the Otsu method, and the binarized segmentation obtained by the novel bat algorithm and the genetic algorithm. The final row shows the segmented image produced by the simulated annealing algorithm applied to segmentation. Figure 5 shows a similar image (in shape) produced by Otsu and GA, while the NBA method segmented a different region. The NBA segmented a smaller region, which seems to be more accurate in relation to the original segmented image. The four algorithms got similar regions since the mammography has a very defined region of interest, however this is not the case in all images. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **\(\boldsymbol{F}\) mean** & **\(\boldsymbol{F^{\prime}}\) mean** \\ \hline Otsu method & 15.324 \(\times\) 10\({}^{6}\) & 12.880 \(\times\) 10\({}^{-3}\) \\ Simulated Annealing & 14.889 \(\times\) 10\({}^{6}\) & 12.519 \(\times\) 10\({}^{-3}\) \\ Novel Bat Algorithm & 10.758 \(\times\) 10\({}^{6}\) & 9.030 \(\times\) 10\({}^{-3}\) \\ Genetic Algorithm & 9.888 \(\times\) 10\({}^{6}\) & 8.313 \(\times\) 10\({}^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean of the errors calculated for the segmentation of the 362 mammographies. The behavior observed in the meta-heuristics results from the simplicity of the algorithms; given that GA is a more complex algorithm than the simulated annealing and the NBA. Figures 5 and 6 reveals that the images segmented by GA have a smaller area compared to the images segmented by the Otsu method or NBA. This is relevant because the region obtained by GA is more similar to the original region obtained by the expert radiologist. It is necessary to take into consideration that the image acquired by some algorithms includes noisy pixels that do not correspond to the desired image, which is why in the results it is shown that GA got a better segmentation when contemplating all the corresponding pixels. In both cases, the algorithm which produced the most similar region to the original segmented image by the expert was genetic algorithms. Table 2 and Figure 7 show the mean of the errors for all the 362 mammography images of the dataset. Figure 5: (**a**) Original image, (**b**) Region of interest (ROI) segmented by an expert radiologist, (**c**) Overlap of the ROI over the original image, (**d**) Image segmented by the Otsu method, (**e**) Image segmented by the novel bat algorithm (NBA), (**f**) Image segmented by the genetic algorithm (GA), (**g**) Image segmented by simulated annealing (SA).