## 4 Experimental Tests  
### Verification of Displacement Estimation Using Model Structures  
To verify the performance of the application of a genetic algorithm, experimental tests with artificial structures and a motion stage were performed. The structures were produced by simulating the shapes of actual port structures, and the relative displacement between the target structure placed on the motion stage and the fixed structure were estimated (see Figure 6). Figure 7 shows the graphic user interface based on visual c++, which employs image binarization using adaptive threshold, edge detection in subpixel level, and the camera extrinsic parameter estimation, which is developed to find the relative displacement \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Checker-Boards**} & \multicolumn{2}{c}{**Facal Length**} & \multicolumn{2}{c}{**Principal Points**} & \multicolumn{2}{c}{**Radial Distortion**} & \multicolumn{2}{c}{**Tangential Distortion**} \\ \cline{2-9}  & \(\mathbf{F_{x}}\) & \(\mathbf{F_{y}}\) & \(\mathbf{C_{x}}\) & \(\mathbf{C_{y}}\) & \(K_{1}\) & \(\mathbf{K_{2}}\) & \(K_{3}\) & \(K_{4}\) \\ \hline (a) & 2654.95 & 2667.25 & 692.02 & 421.61 & \(-\)0.3975 & 0.1285 & \(-\)0.0012 & 0.0130 \\ (a), (b) & 2634.64 & 2624.02 & 1023.62 & 380.04 & \(-\)0.4629 & 0.3087 & 0.0059 & 0.0008 \\ (a), (c) & 2578.67 & 2572.71 & 948.75 & 459.45 & \(-\)0.4461 & 0.1865 & 0.0017 & 0.0037 \\ (a), (d) & 2586.03 & 2584.54 & 1001.43 & 424.18 & \(-\)0.4436 & 0.2398 & 0.0002 & 0.0006 \\ (a), (e) & 2598.73 & 2582.47 & 990.96 & 431.47 & \(-\)0.4178 & 0.0585 & 0.0050 & 0.0029 \\ (a), (f) & 2363.73 & 2370.19 & 1044.13 & 347.82 & \(-\)0.4688 & 0.3937 & \(-\)0.0005 & \(-\)0.0020 \\ (b) & 2705.33 & 2673.96 & 1029.39 & 219.31 & \(-\)0.4917 & 0.5865 & 0.0155 & \(-\)0.0029 \\ (b), (c) & 2615.95 & 2614.07 & 997.06 & 411.56 & \(-\)0.4325 & 0.2560 & 0.0014 & 0.0037 \\ (b), (d) & 2734.70 & 2649.68 & 930.35 & 253.04 & \(-\)0.3618 & \(-\)1.0397 & 0.0278 & 0.0034 \\ (b), (e) & 2621.91 & 2601.25 & 981.15 & 414.57 & \(-\)0.4233 & 0.1851 & 0.0070 & 0.0043 \\ (b), (f) & 2645.72 & 2647.74 & 998.71 & 327.04 & \(-\)0.4519 & 0.3165 & 0.0025 & 0.0003 \\ (c) & 2665.99 & 2665.67 & 887.69 & 365.05 & \(-\)0.5030 & 0.9319 & 0.0060 & 0.0119 \\ (c), (d) & 2590.24 & 2598.32 & 921.28 & 451.59 & \(-\)0.4460 & 0.2329 & \(-\)0.0035 & 0.0065 \\ (c), (e) & 2611.21 & 2601.35 & 984.80 & 439.40 & \(-\)0.4289 & 0.1636 & 0.0026 & 0.0034 \\ (c), (f) & 2584.71 & 2574.96 & 1007.15 & 351.71 & \(-\)0.4498 & 0.0726 & 0.0016 & \(-\)0.0016 \\ (d) & 2716.70 & 2700.58 & 938.09 & 197.31 & \(-\)0.4994 & 0.4672 & 0.0163 & 0.0039 \\ (d), (e) & 2585.51 & 2583.79 & 1009.34 & 408.67 & \(-\)0.4050 & 0.1307 & 0.0002 & 0.0029 \\ (d), (f) & 2658.12 & 2629.06 & 1053.09 & 263.17 & \(-\)0.4885 & 0.2479 & 0.0145 & \(-\)0.0042 \\ (e) & 2552.71 & 2543.47 & 979.48 & 434.32 & \(-\)0.4422 & 0.5115 & \(-\)0.0010 & 0.0042 \\ (e), (f) & 2621.56 & 2604.26 & 994.28 & 321.01 & \(-\)0.4891 & 0.2585 & 0.0120 & \(-\)0.0048 \\ (f) & 2770.83 & 2755.42 & 1027.54 & 124.33 & \(-\)0.4865 & 0.5711 & 0.0137 & 0.0018 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Estimated intrinsic parameters using different sets of checkerboards. The checkerboard ’(a)’ denotes the size and configuration of the checkerboard presented in Figure 3(a). Figure 5: Box plot ((a) parameters of the focal length and principal points, (b) parameters of the distortion) and coefficient of variation of the estimated intrinsic parameters of the vision sensor. in a captured image. The estimated relative displacement between the two structures in the before and after images, the movement of the target structure according to the change of time, is calculated. By using different patterns and size of the checkerboards and experimental data sets with the \(X\)-axis translational displacement and \(Y\)-axis rotational displacement, intrinsic parameters are calculated (see Table 1). The median, minimum, and maximum values are used to generate populations of the chromosomes in GA.