# Sensor-Based Hand Gesture Detection and Recognition by Key Intervals
## 4 Experimental Results
The detection performance was evaluated by the receiver operating characteristic (ROC) curve [34], which is a curve formed by pairs of true positive rate (TPR) and false positive rate (FPR) for various threshold values \(T\) for gesture detection. The TPR is defined as the number of correctly detected foreground gestures divided by the total number of foreground gestures in the testing set. The FPR is defined as the number of falsely detected background gestures divided by the total number of background gestures in the testing set. The neural network for the experiment was trained by a set with \(M_{\textsc{tr}}=750\) gestures. The ITR ratio \(r\) in Equation (5) was set to 0.3. That is, the key interval length \(l\) was only 30% of the gesture radius \(R\). Figure 8 shows the corresponding ROC curve, where the corresponding area under the ROC (AUROC) is 0.954. Therefore, with a low FPR, a high TPR can be achieved by the proposed algorithm. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Layer** \\ **Name** \\ \end{tabular} } & \multirow{2}{*}{**GN**6} & \multirow{2}{*}{**C1**} & \multicolumn{3}{c}{**Backbone**} & \multicolumn{3}{c}{**Branch 1**} & \multicolumn{3}{c}{**Branch 2**} & \multicolumn{3}{c}{**Branch 3**} \\  & & & **C2** & & **C3** & & **C4** & & **F1** & **C5** & **C6** & **F2** & **C7** & **C8** & **F3** \\ \hline
\begin{tabular}{c} Weight \\ size \\ \end{tabular} & 12 & 2560 & 33,024 & 33,024 & 33,024 & 16,134 & 33,024 & 33,024 & 16,134 & 33,024 & 33,024 & 16,134 \\ \hline \hline \multicolumn{1}{c}{Subtotal} & & 101,644 & & 16,134 & & 82,182 & & & 82,182 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The size of the proposed neural network model. The total number of weights in the model is 282,142. Figure 7: The background gesture classes considered in the testing set. To further evaluate the detection performance of the proposed algorithm, we compared the AUROC of the proposed algorithm with that of the CornerNet [26] for various sizes \(M_{\text{TR}}\) of training sets. For the proposed algorithm, we set the ITR ratio \(r=0.3\). The CornerNet is based on keypoints for object detection. The corresponding results are revealed in Table 2. All the training set contained the same number of classes \(K=5\). We can see from Table 2 that the proposed algorithm has a high AUROC even when the size of the training set is small. Furthermore, the AUROC becomes higher as the size of the training set increases. Based on the same training set, the proposed algorithm outperforms the CornerNet in AUROC for detection. These results justify the employment of key intervals for the detection of hand gestures. The impact of the ITR ratio \(r\) on the performance of the proposed algorithm is revealed in Table 3 for various training set sizes \(M_{\text{TR}}\). As \(r\) increases, it can be observed from Table 3 that the performance of the proposed algorithm can be improved. In fact, when ITR ratio \(r\) is above 0.2, the proposed algorithm is able to achieve an AUROC above 0.91 for all the training set sizes considered in the experiments. On the contrary, when \(r=0.1\), the AUROC may be below 0.9 when \(M_{\text{TR}}=180\). Therefore, larger values of ITR ratio \(r\) are beneficial for improving the accuracy and robustness of the proposed algorithm. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Training Set** & **180** & **320** & **450** & **590** & **750** \\
**Size \(M_{\text{TR}}\)** & & & & & \\ \hline Proposed & 0.920 & 0.938 & 0.940 & 0.941 & 0.954 \\ CornerNet [26] & 0.845 & 0.862 & 0.875 & 0.878 & 0.882 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The AUROC performance of the proposed algorithm and CornerNet [26] for gesture detection for various sizes of training sets. The ITR ratio for the proposed algorithm was \(r=0.3\). Figure 8: The ROC curve of the proposed algorithm for the testing set. The neural network was trained by a set with size \(M_{\text{TR}}=750\) and ITR ratio \(r=0.3\). The corresponding AUROC is 0.954.