## 6 Optimal Features for Earthquake-Induced Structural Displacement Monitoring  
As the proposed UAV vision-based earthquake-induced structural displacement monitoring method is evaluated using the shake table test results of a full-scale 6-story mass timber building, a statistical analysis of the error characteristics across various patterns is conducted to aid in identifying the optimal features for structural displacement tracking under earthquakes. As a metric, the statistical analysis uses the root-mean-square error (RMSE) of the displacement tracking result from each individual target. Figure 15 presents the statistics of RMSEs for tracking the displacements of the 6-story mass timber building specimen, focusing on the comparison between the different reference target patterns. The RMSEs of displacement tracking from three 67% \(\mathrm{MCE_{R}}\) tests (i.e., MID 7, 12, and 13) and four 100% \(\mathrm{MCE_{R}}\) tests (i.e., MID 8, 15, 16, and 17) are included in this result. For a particular test, every target provides two measurements (one in the X-direction and the other one in the Y-direction), and each measurement leads to a data point in the RMSE statistics. Therefore, the total number of data points \(n\) for each pattern in the RMSE statistics can be calculated as follows:  
\[n=2\cdot n_{\mathrm{target}}\cdot n_{\mathrm{test}} \tag{13}\]  
where \(n_{\mathrm{target}}\) is the number of targets with a specific pattern, and \(n_{\mathrm{test}}\) is the number of tests with a specific earthquake motion input intensity level. Several insights are observed from the RMSE statistics:  
* **Overall Tracking Accuracy Evaluation**: RMSEs in these analyses are consistently less than 8 mm for the 67% \(\mathrm{MCE_{R}}\) tests and less than 10 mm in general for the 100% \(\mathrm{MCE_{R}}\) tests (only 6 data points have errors that exceed 10 mm among the 224 data points in total for the \(\mathrm{MCE_{R}}\) tests). Thus, the proposed structural displacement monitoring method can achieve an overall tracking accuracy at the millimeter level. * **Feature Size**: For a certain pattern shape (2-tile black-and-white checkerboard), significantly larger RMSEs are observed for smaller pattern sizes (Type 3\({}_{\mathrm{M}}\) and Type 3\({}_{\mathrm{S}}\)) compared to a larger pattern size (Type 3). Smaller reference targets have less pixel dimensions in the video frame. For example, the side length of the black square in the Type 3\({}_{\mathrm{S}}\) pattern is 5 cm, which corresponds to only four to five pixels in the video frame. The intensity contrast between the target region and the background is significantly reduced, leading to reduced performance on the refined ROI generation with Otsu's thresholding and edge detection. Additionally, as previously mentioned in Section 3.1, the small pixel dimensions of reference targets reduce the values in the spatial gradient matrix of the corner point in Harris-Stephens feature detection. Therefore, it is observed that targets with smaller dimensions have larger RMSEs for displacement tracking by comparing 2-tile black-and-white checkerboard targets with different sizes. Aiming to investigate the minimum required feature (pattern) size for reasonable displacement tracking under different intensities of earthquakes, a statistical analysis on the normalized RMSEs for displacement tracking with respect to normalized tile dimensions of targets is conducted for all the black-and-white checkerboard targets (specifically, Type 1, 2, 3, 3\({}_{\mathrm{M}}\), and 3\({}_{\mathrm{S}}\)) in all nine tests. For each individual target during a specific test, both the tracking RMSE (in X/Y-direction) and the tile dimension \(D\) (the side length of each black square) are normalized by the peak displacement \(\Delta_{\mathrm{GT,max}}\) (in the X/Y-direction) in each ground truth measurement. Figure 16 presents a compilation of the statistical analysis results.