# Vision-Based Hand Rotation Recognition Technique with Ground-Truth Dataset
## 5 Results  
In this study, the aforementioned ground-truth dataset was used to verify behavioral data measurement technology through hand rotation recognition. We verified our method for measurement by using the predicted values through the relevant hand motion recognition technology and the label values stored in the log of robot arm's actual driving value, as shown in Figure 8. As shown in Table 2 and Figure 9, the average accuracy for the number of rotations is 99.21% (4.64), the average accuracy for the angle of rotation is 91.90% (6.98), and the average accuracy for the time of rotation is 68.67% (16.59). Figure 9 is a visualization of Table 2 and shows the accuracy and standard deviation for each measurement element in the entire dataset used in the experiment (N = 540). In detail, as can be easily seen, the number of rotations showed very high accuracy of 99.21%, \begin{table}
\begin{tabular}{l c c c c} \hline
**Measurement Factor** & **N** & **Average (std)** & **Minimum** & **Maximum** \\ \hline Number of rotations & 540 & 99.21 (4.64)\% & 40.00\% & 100.00\% \\ \hline Angle of rotations & 540 & 91.90 (6.98)\% & 46.29\% & 99.97\% \\ \hline Time of rotations & 540 & 68.67 (16.59)\% & 0.00\% & 99.77\% \\ \hline \end{tabular}
\end{table} 
Table 2: Accuracy results between ground-truth dataset and predicted values as measured by robot arm elements. Figure 8: Architecture of our robot arm. The black arrow represents the task flow, and the red color represents the flow receiving status information. Figure 9: Boxplot of experimental results by measurement element. The blue box indicates the interquartile range from 25 percentile to 75 percentile. The orange line is the median value. while the angle of rotations also showed high accuracy of 91%. However, the time of rotations shows relatively low accuracy at 68.67%, which is considered to be the compliance accuracy considering that the FPS of the input device used in the system proposed in this study was 30 and the unit of measurement of the time of rotations was ms.  
Additionally, when we classified the experimental results by task, they appear as shown in Table 3. The MAPEs for the inference value (N = 18) of the right hand and the left hand are repeated three times for each distance of 97 cm, 77 cm, and 57 cm. To explain the accuracy evaluation metric mentioned in Experiment Section 4 again easily, when the predicted value is 11 but the ground-truth value is 10, accuracy is 90%; likewise, when the predicted value is 110\({}^{\circ}\), accuracy is equally 90% when the ground-truth value is 100\({}^{\circ}\). At this time, the sample (N) values are all ones. As such, this calculation method has the advantage of conveniently comparing performance between measurement indicators by expressing measurement indicators with different units as percentages, but it is not easy to understand how many errors occurred in the number of rotations or how many degrees of error the angle of rotations had. For this reason, MAE, which can represent actual errors, is additionally indicated in Table 3. MAE was calculated using Equation (9), where \(A_{t}\) means ground-truth value and \(F_{t}\) is the value predicted by this system when calculating accuracy. \[MAE=\frac{\sum\lvert A_{t}-F_{t}\rvert}{A_{t}} \tag{9}\]  
The meaning of the MAE evaluation metric can be explained by an example situation for which the sample (N) is one: When the ground truth of the number of rotations is 10, if the predicted value is 11, the MAE is expressed as 0.1, indicating that the value of the error is 0.1. When the ground truth of another measurement index, the angle of rotation, is 100 degrees, if the predicted value is 110 degrees, MAE is expressed as 10, and the known error angle means 10 degrees. Likewise, the MAE of the time of rotation is also expressed with the measured unit (ms), indicating the actual absolute error value in the same unit as the measurement index.