## 6 Results of the Simulations
### Comparison of the Results Among the Pattern-Matching Methods
#### 6.6.2 Comparison of the Best Results Obtained That Minimize the Error Distance  
From the results for all of the pattern-matching methods, we select the best ones that minimize the error distance for the three side lengths of the sub-tiles considered. The best results found for each sub-tile size and pattern-matching method are summarized in Table 16. The table lists the number of NN parameters for each combination of \(S_{S}\) and \(N_{SS}\) and pattern-matching method. Next, we compare how the different pattern-matching methods perform one against the other for these cases. This comparison is presented in Figure 22. The results present the same pattern for the three side lengths of the sub-tiles \(S_{S}\) considered. The method 4-MultFingIn-ClassOut performs better than the other methods. This is followed, in decreasing order of error, by the method 3-MultFingIn-PosOut, the method 2-SingFingIn-AggPosOut, and finally by the method 1-SingFingIn-PosOut. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{\(S_{S}\)} & \multicolumn{8}{c}{**Pattern-Matching Method**} \\ \cline{2-10}  & \multicolumn{3}{c}{**2-SingFingIn-AggPosOut**} & \multicolumn{3}{c}{**3-MultFingIn-PosOut**} & \multicolumn{3}{c}{**4-MultFingIn-ClassOut**} \\ \cline{2-10}  & \multicolumn{3}{c}{**Best**} & \multicolumn{3}{c}{**Number of**} & \(S_{T}\) & **Best** & **Number of** & \(S_{T}\) & **Best** & **Number of** & \(S_{T}\) \\  & \(N_{SS}\) & \multicolumn{3}{c}{**NN Param.**} & **[mm]** & \(N_{SS}\) & **NN Param.** & **[mm]** & \(N_{SS}\) & **NN Param.** & **[mm]** \\ \hline
30 & 14 & 2358 & (196 instances) & 420 & 10 & 11,998,354 & 300 & 13 & 378,378,636 & 390 \\
50 & 15 & 2358 & (225 instances) & 750 & 8 & 11,608,834 & 400 & 10 & 189,356,292 & 500 \\
70 & 15 & 2358 & (225 instances) & 1050 & 6 & 11,334,546 & 420 & 9 & 142,973,068 & 630 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Best results for each side length of the sub-tiles \(S_{S}\) and pattern-matching method. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{\(S_{S}\)} & \multicolumn{8}{c}{**Pattern-Matching Method**} \\ \cline{2-10}  & \multicolumn{3}{c}{**2-SingFingIn-AggPosOut**} & \multicolumn{3}{c}{**3-MultFingIn-PosOut**} & \multicolumn{3}{c}{**4-MultFingIn-ClassOut**} \\ \cline{2-10}  & \multicolumn{3}{c}{**Small.**} & \multicolumn{3}{c}{**Number of**} & \(S_{T}\) & **Small.** & **Number of** & \(S_{T}\) & **Small.** & **Number of** & \(S_{T}\) \\  & \(N_{SS}\) & \multicolumn{3}{c}{**NN Param.**} & **[mm]** & \(N_{SS}\) & **NN Param.** & **[mm]** & \(N_{SS}\) & **NN Param.** & **[mm]** \\ \hline
30 & 6 & 2358 & (36 instances) & 180 & 6 & 11,334,546 & 180 & 6 & 58,589,080 & 180 \\
50 & 5 & 2358 & (25 instances) & 250 & 5 & 11,233,654 & 250 & 5 & 44,153,872 & 250 \\
70 & 5 & 2358 & (25 instances) & 350 & 5 & 11,233,654 & 350 & 5 & 43,084,294 & 350 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Results for the smallest 2D sensor array for each side length of the sub-tiles \(S_{S}\) and pattern-matching method. Figure 21: Comparison of the results obtained using the smallest 2D sensor array considered among different pattern-matching methods for the three side lengths of the sub-tiles, \(S_{S}\), considered. Figure 22: Comparison of the best results obtained that minimize the error distance among different pattern-matching methods for the three side lengths of the sub-tiles, \(S_{S}\), considered. Similar to the case for the smallest 2D sensor array, the first and most important observation is that all of the methods that include spatial side information perform much better than the method that does not use side information, 1-SingFingIn-PosOut. The second observation is that by relying on a more expensive NN model, in terms of the number of NN parameters, a better performance result can be obtained for the same input data.