# New Evolutionary-Based Techniques for Image Registration
## 6 Experimental Results  
In order to derive conclusions regarding the accuracy and the computational complexity of the proposed methods, we have conducted a long series of experiments on various images representing signatures. The quality of each algorithm from the accuracy of resulted alignment point of view has been measured in terms of success rate, computed as follows. For each input pair of images, we denote by Tests the number of tests and let Success be the number of successful tests. We call an algorithm test a success if the fitness of the resulted best individual exceeds 0.85. Note that, for each image, each technique has been tested 500 times to obtain meaningful results. The success rate of a certain algorithm, SR, is given by  
\[\text{SR}=\frac{\text{Success}}{\text{Tests}}\cdot 100\% \tag{45}\]  
Moreover, one of the most commonly used quantitative similarity measures, SNR, has been computed to derive conclusions on the registration quality. The SNR value computed for a certain sensed image S versus a reference image T of the same size \((\text{M},\text{N})\) is defined by  
\[\text{SNR}(\text{T},\text{S})=10^{*}\log_{10}\left[\frac{\sum_{\text{x}=1}^{ \text{M}}\sum_{\text{y}=1}^{\text{N}}(\text{S}(\text{x},\text{y}))^{2}}{\sum_{ \text{x}=1}^{\text{M}}\sum_{\text{y}=1}^{\text{N}}(\text{T}(\text{x},\text{y}) -\text{S}(\text{x},\text{y}))^{2}}\right] \tag{46}\]  
The computational complexity/efficiency of each algorithm is evaluated in terms of execution time. Our tests have been conducted on a computer with the following configuration: Processor--Intel Core I7-7700 3.60 GHZ, Memory--8 GB DDR4 2400 MHZ, Storage--1 TB HDD 7200 RPM, SATA3. In the following we present the experimentally established results in case of using each class of metaheuristics. The success rate and the mean values of mutual information ratio (MIR), SNR and run time respectively are reported below. The mean value corresponding to each above-mentioned performance measure has been computed by averaging the values of the corresponding measure resulted for each run. Note that each algorithm has been run 500 times for each input pair of images \(\mathcal{PJ}\). The reported results correspond to a set of 19 pair of images representing signatures, \(\mathcal{SPJ}\), perturbed by the same degradation model (8). The techniques belonging to the first class, APSO1 and APSO2, implement APSO algorithms using the updating rules (41) and (42) respectively. In our tests the parameters were set as follows: \(\beta_{0}\)\(=2,\ \gamma=2,\ \alpha_{\text{damp}}\)\(=0.99\) and the population size is 50. The results of applying APSO1 and APSO2 techniques to register the images belonging to \(\mathcal{SJ}\) are displayed in Tables 1-4. The tests pointed out that APSO2 persistently obtains better results from the accuracy point of view, but the computational effort is slightly increased as compared to APSO1. Note that there are situations in which the accuracy of APSO2 is significantly better than the accuracy of APSO1. Nevertheless, the accuracy of APSO-based recognition procedure is still low for some input pairs of images. The second class of algorithms includes Firefly1 and Firefly2, variants of Firefly algorithms considering the updating rules (31) and (36) respectively. In our tests the parameters were set as follows: \(\beta_{0}\)\(=2,\ \gamma=2,\ \alpha_{\text{damp}}\)\(=0.98\) and the population size is 30. Obviously, the firefly approaches involve a significantly larger computational effort as compared to APSO algorithms. From the accuracy point of view, SR = 100% for all pair of images in \(\mathcal{SJ}\), while MIR values are around 0.87 and the SNR index frequently exceeds 24. The results are displayed in Tables 1-4. Note that the computational effort is significantly reduced in case Firefly technique is implemented based on the updating rule (36). The hybrid techniques belonging to the third class of proposed methods, ES-APSO1 and ES-APSO2, implement the algorithm described in Section 5.2 based on the updating rules (41) and (42) respectively.