## 6 Recognition Results of the Same Gestures and Different Gestures
Therefore, a borderline of the matching points could be set to distinguish similar gestures and different gestures using our proposed method. \begin{table}
\begin{tabular}{|l|c c c c c c c c|} \hline  & **Initial** & **Run**B & **Mits**A & **Mits**B & **Find**A & **Hits**B & **Rot**A & **Rot**B \\ \hline Push A & 245 & 189 & 18 & 16 & 27 & 24 & 26 & 32 \\ \hline Push B & 179 & 262 & 12 & 11 & 26 & 23 & 48 & 36 \\ \hline Wrist A & 19 & 17 & 267 & 156 & 37 & 28 & 25 & 26 \\ \hline Wrist B & 17 & 12 & 140 & 249 & 19 & 23 & 19 & 31 \\ \hline Pinch A & 26 & 23 & 26 & 20 & 210 & 165 & 33 & 43 \\ \hline Pinch B & 24 & 20 & 11 & 19 & 149 & 232 & 34 & 35 \\ \hline Rot. A & 30 & 28 & 31 & 28 & 37 & 45 & 320 & 192 \\ \hline Rot. B & 44 & 32 & 21 & 30 & 38 & 33 & 188 & 288 \\ \hline \end{tabular}
\end{table} 
Table 1: Results of matching points for the same and different hand gestures. Figure 9: **(a) (Left)** The results of the push motion ‘A’ testing itself with 245 matching points (marked with yellow circles), and (Right) the push motion ‘B’ testing itself with 251 matching points. (b) The push motion ‘A’ to test the push motion ‘B’ with 189 matched feature points. To correlate the hand gestures and matching results quantitatively, we categorized the matching results into three groups. The first group consisted of identical hand gestures with the number of matching points between 320 and 210. The second group had the same hand gestures, but they were performed at different times. The number of matching points was between 140 and 189. The third group consisted of different hand gestures, and the number of matching points was between 48 and 11. If we define the maximum number of matching points in the aforementioned cases, which is 320, as a denominator to find the matching ratio of hand gesture recognition, then the identical hand gestures are indicated by a matching ratio beyond 0.66 (i.e., greater than 210 divided by 320). The same gestures are indicated by matching ratios above 0.44. The different hand gestures could be determined by a matching ratio of less than 0.15. The results indicate that there is a large ratio interval of 0.29 to prevent the misjudgment of hand gestures. Furthermore, if we directly find the probability density functions according to the experimental matching points shown in Table 1 for the same hand gestures and the different hand gestures, the probability of accuracy rate could be found. The mean value (\(\mu\)) and standard deviation (\(\sigma\)) are 214.44 and 53.43 for the identical gestures, 26.73 and 9.02 for the different gestures. Using the probability of normal distribution, the accuracy rate could be estimated as below:  
Let \(X_{1}\) be the matching points for the cases of failure of hand gesture recognition possessing the normal distribution \(N(\mu_{1},\sigma_{1}^{2})\) with probability density function (pdf) \(F_{1}(x)\) and cumulative density function (cdf) \(F_{1}(x)\) and \(X_{2}\) be the matching points for the cases of correct hand gesture recognition possessing the normal distribution \(N(\mu_{2},\sigma_{2}^{2})\) with pdf  
Figure 10: The results of feature points matching: (**a**) using the rotation motion ‘A’ to test push motion ‘A’. (**b**) The motion of wrist from flexion to extension ‘A’ to test pinch out motion ‘A’. (**c**) The motion of wrist from flexion to extension to test the rotation motion ‘A’. (**d**) The pinch out motion ‘A’ to test the motion of ‘wrist from flexion to extension. (**e**) The push motion ‘A’ to test the rotation motion ‘A’. \(F_{2}(x)\) and cdf \(F_{2}(x)\), \(\mu_{1}<\mu_{2}\). The area of intersection zone, which indicates the probability of faulty hand gesture recognition, could be found by  
\[ \begin{split} P(X_{1}>c)+P(X_{2}<c)\\ =1-F_{1}(c)+F_{2}(c)\\ =1-\frac{1}{2}\text{erf}(\frac{c-\mu_{1}}{\sqrt{2}\mu_{1}})+\frac {1}{2}\text{erf}(\frac{c-\mu_{2}}{\sqrt{2}\mu_{2}})\end{split} , \tag{10}\]  
where erf(.)