# Automated Design of Salient Object Detection Algorithms with Brain Programming
## 4 Experiments and Results
### Experiments with [PERSON]'s Fitness Function on GBVSBP  
Table 3 details the experimental results after applying the k-fold cross-validation method on the FT database. As we can observe, BP optimizes the model scoring the highest value of 78.18% for the best program during training at the first run and the third fold, while achieving 77.67% during testing in the fourth run but at the fourth fold. \(\sigma\) remains low during the experimental runs. BP scores its highest value \(\sigma=2.54\) in the fourth testing run while achieving \(\sigma=0.45\) and \(\sigma=1.51\) during the sixth run for training and testing, respectively. The methodology average scores its highest fitness of 76.72% for training and 75.17% for testing. Table 4 presents the best solution. The selected program corresponds to the training stage for this kind of table. Table 5 details the experimental results after applying the k-fold cross-validation method on the IMGSAL database. The fitness function results on this dataset show high variability since, in training, the results range from 72.49% in the fourth run to 57.37% in the second run. The high dispersion is due to the complexity of the problem generated by poor manual segmentation. The experiment shows an average oscillating between 62.60% and 68.52% for training with \(\sigma=3.72\) and \(\sigma=1.52\), respectively. On the other hand, during testing, the algorithm's highest score on average is 67.04% with \(\sigma=2.48\). Table 6 reports the best solution. The experimental results of the GBVSBP model with the PASCAL-S database show excellent stability, as seen in Table 7 with a low standard deviation, especially in training with the first run, scoring 1.58. During training, fitness reaches its highest in the fifth fold of run 6, scoring 66.39%, while on average, the fifth run scores first place with 63.45%. Regarding the testing stage, the algorithm scores the best individual at the third fold with 67.66%, and on average, the best run is the fifth with 63.63%. Table 8 presents the best set of trees. \begin{table}
\begin{tabular}{c c} \hline \hline \(EVO_{d}\) and \(EF1\) Operators & Fitness \\ \hline \(EVO_{O}=I_{k}\) & Training = 0.7818 \\ \(EVO_{C}=I_{b}+1.00\) & Testing = 0.7658 \\ \(EVO_{S}=top-hat(I_{m}\times 0.31)\) & \\ \(EF1=(CM_{C})^{2^{2}}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Program structure of the operators corresponding to the best solution for the FT database. We select this solution from the 30 executions of Table 3. The final solution is simple, basically using color-chosen bands. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Fold**} & \multirow{2}{*}{**Run 1**} & \multirow{2}{*}{**Run 2**} & \multicolumn{3}{c}{**FT**} & \multirow{2}{*}{**Fold**} & \multirow{2}{*}{**Run 3**} & \multirow{2}{*}{**Run 4**} & \multirow{2}{*}{**Run 5**} & \multirow{2}{*}{**Run 6**} \\ \cline{5-10}  & & & & & & & & & & & & \\ \hline \multirow{4}{*}{1} & Trng & Test & Trng & Test & Trng & Test & Trng & Test & Trng & Test & Trng & Test \\  & 75.34 & 76.10 & 75.07 & 73.97 & 77.57 & 76.75 & 76.98 & 75.29 & 77.34 & 75.74 & 77.08 & 75.36 \\  & 74.88 & 71.60 & 72.92 & 69.81 & 75.10 & 72.97 & 74.65 & 71.27 & 73.62 & 71.87 & 76.41 & 72.25 \\  & 78.18 & 76.58 & 76.69 & 71.77 & 77.03 & 72.97 & 76.75 & 72.18 & 76.68 & 72.39 & 77.01 & 72.21 \\  & 75.30 & 77.05 & 74.78 & 74.25 & 74.90 & 71.47 & 75.86 & **77.67** & 74.60 & 76.13 & 77.03 & 74.98 \\  & 5 & 75.15 & 74.54 & 73.14 & 73.45 & 74.74 & 74.97 & 74.62 & 74.17 & 75.18 & 75.06 & 76.09 & 74.37 \\  & 75.77 & **75.17** & 74.52 & 72.32 & 75.87 & 73.83 & 75.77 & 74.12 & 75.48 & 74.24 & **76.72** & 73.83 \\  & \(\sigma\) & 1.36 & 2.21 & 1.54 & 1.97 & 1.33 & 2.05 & 1.12 & 2.54 & 1.52 & 1.97 & **0.45** & **1.51** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance of the best individuals of the GBVSBP model for all FT database runs. Each pair of training and testing corresponds to one experiment of the k-fold.