# New Evolutionary-Based Techniques for Image Registration
## 6 Experimental Results
We conducted the tests using the following parameters setting:  
* ES \(\mu=50,\ \lambda=300,\ \text{NMax}=200,\ \tau=0.2\),\(\sigma_{\text{ini}}\) \(=\) \([1,\ 1,\ 0.01,\ 0.01\ 0.01]\) and \(\varepsilon_{\sigma}\)\(=[0.0075,\ 0.0075,0.004,\ 0.004,0.004]\);
* APSO--\(\beta_{0}\)\(=2,\ \gamma=2,\ \alpha_{\text{damp}}\)\(=0.99\), and the population size is 22. The results of applying ES-APSO1 and ES-APSO2 techniques to register the images belonging to \(\mathcal{SJ}\) are displayed in Tables 1-4. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Input** & **APSO1** & **APSO2** & **Firefly1** & **Firefly2** & **ES-APSO1** & **ES-APSO2** \\ \hline \(\mathcal{PJ}_{1}\) & 9.45 & 11.46 & 32 & 24.42 & 6.92 & 7.67 \\ \(\mathcal{PJ}_{2}\) & 8.73 & 10.04 & 29.89 & 21.7 & 6.81 & 7.73 \\ \(\mathcal{PJ}_{3}\) & 13.37 & 15.43 & 45.12 & 32.61 & 9.35 & 10.33 \\ \(\mathcal{PJ}_{4}\) & 10.92 & 12.98 & 37.99 & 26.33 & 8.2 & 9.1 \\ \(\mathcal{PJ}_{5}\) & 12.07 & 14.21 & 41.97 & 29.38 & 8.95 & 9.99 \\ \(\mathcal{PJ}_{6}\) & 10.44 & 10.87 & 29.55 & 21.36 & 6.9 & 7.66 \\ \(\mathcal{PJ}_{7}\) & 10.71 & 11.61 & 36.88 & 26.45 & 8.43 & 9.46 \\ \(\mathcal{PJ}_{8}\) & 10.34 & 11.47 & 31.49 & 23.17 & 7.33 & 8.45 \\ \(\mathcal{PJ}_{9}\) & 10.73 & 6.09 & 37.62 & 26.13 & 8.72 & 9.77 \\ \(\mathcal{PJ}_{10}\) & 12.34 & 13.63 & 39.53 & 29.86 & 8.99 & 10.32 \\ \(\mathcal{PJ}_{11}\) & 9.5 & 5.75 & 32.6 & 24.13 & 7.12 & 8 \\ \(\mathcal{PJ}_{12}\) & 15.74 & 16.77 & 61.61 & 45.48 & 12.96 & 16.05 \\ \(\mathcal{PJ}_{13}\) & 10.61 & 6.02 & 35.67 & 26.18 & 8.15 & 9.18 \\ \(\mathcal{PJ}_{14}\) & 18.41 & 18.61 & 43.65 & 32.9 & 10.86 & 11.84 \\ \(\mathcal{PJ}_{75}\) & 19.68 & 19.76 & 46.96 & 35.85 & 12.94 & 14.03 \\ \(\mathcal{PJ}_{16}\) & 18.28 & 19.58 & 40.98 & 30.79 & 10.52 & 11.31 \\ \(\mathcal{PJ}_{17}\) & 11.86 & 13.74 & 40.99 & 30.02 & 9.25 & 10.11 \\ \(\mathcal{PJ}_{18}\) & 14.24 & 15.4 & 44.77 & 33.93 & 13 & 12.86 \\ \(\mathcal{PJ}_{19}\) & 11.71 & 12.81 & 37.57 & 28.81 & 9.79 & 10.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The mean run times (s). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Input** & **APSO1** & **APSO2** & **Firefly1** & **Firefly2** & **ES-APSO1** & **ES-APSO2** \\ \hline \(\mathcal{PJ}_{9}\) & 0.868 & 0.865 & 0.871 & 0.869 & 0.871 & 0.872 \\ \(\mathcal{PJ}_{10}\) & 0.798 & 0.85 & 0.871 & 0.872 & 0.871 & 0.867 \\ \(\mathcal{PJ}_{11}\) & 0.838 & 0.839 & 0.873 & 0.873 & 0.871 & 0.868 \\ \(\mathcal{PJ}_{Taking into account both accuracy and efficiency points of view, the proposed hybrid methods prove excellent results. Note that the APSO and Firefly parameters \(\beta_{0}\) and \(\gamma\) are usually set in \((0,10)\)[25; 31]. In order to tune the parameters values to the considered registration problem, we have implemented a standard self-adaptive method. The initial values of \(\beta_{0}\) and \(\gamma\) are set to 2. As the APSO/Firefly self-adaptive procedure evolves, the values of \(\beta_{0}\) and \(\gamma\) vary between 1.8 and 2.1. We conclude that we can set \(\beta_{0}\) and \(\gamma\) to 2, the result being consistent to the parameters used in reference [32] for the PSO algorithm. The parameter \(\alpha\) was set either using (31) or (36). In case of the Firefly algorithm, the recommended population size is usually between 15 and 100 [25]. Since the APSO algorithm is a reduced variant of the Firefly algorithm, we used \(\mu=50\) individuals for APSO and \(\mu=30\) for Firefly. In case of the hybrid approaches, the initial population generation is replaced by an ES method that computes \(\mu=50\) sized populations with best individual having the fitness value above a certain threshold. The APSO algorithms are implemented next taking into account only the best \(\mu=22\) individuals. Also, a series of tests to evaluate the quality of the proposed classes of algorithms against the quality of the well-known One Plus One Evolutionary Optimizer (EO) have been performed [33].