# A Graph-Based Approach to Recognizing Complex Human Object Interactions in Sequential Data
## 4 Experimental Results
### Experiment III: Body Part Detection Rate  
The accurate detection of human body parts leads to better classification results. Hence, the class-wise accuracies of the 12 body parts detected using the proposed key-point  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Layer Type** & **Equation** & **Complexity** & **Dataset** & **Feature Map** & **Time (s)** \\ \hline \multirow{4}{*}{Convolutional} & \multirow{4}{*}{\(z^{l}=\sum\limits_{k=1}^{K}\mu_{k}^{n-1}*w_{ij}^{n}\) (18)} & & Olympic & \multirow{4}{*}{\(1\times 3\),316,800} & \multirow{2}{*}{29,851,200} \\  & & & Sports & & & \\  & & MSR & & & & \\  & & Daily Activity & & & & \\  & & & D3D HOI & \(1\times 1\),768,960 & & 15,920,640 \\ \hline \multirow{4}{*}{Max Pooling} & \multirow{4}{*}{\(h_{xy}^{l}=max_{i=0...sj-0...sj}\mu_{(x+1)(y+l)}^{l-1}\) (19)} & & Olympic & \multirow{4}{*}{\(1\times 3\),316,800} & \multirow{4}{*}{7,462,800} \\  & & Sports & & & & \\ \cline{1-1} \cline{5-5}  
detection algorithm are also discussed. First, the Euclidean distance \(D\) between the ground truth value and the detected value of each key body part is computed using Equation (21):  
\[D_{i}=\sqrt{\left(DV_{ix}-GT_{ix}\right)^{2}+\left(DV_{iy}-GT_{iy}\right)^{2}} \tag{21}\]  
where \(DV\) is the detected value and \(GT\) is the ground truth value of a body part \(i\). Based on its distance from the ground truth value, the accuracy of the detected body part is computed using Equation (22):  
\[Acc_{i}=\frac{100}{K}\left[\sum_{n=1}^{K}\left\{ \begin{array}{ll}1\text{ \emph{if} }D_{i}\leq Th\\ 0\text{ \emph{if} }D_{i}>Th\end{array} \right.\right] \tag{22}\]  
where \(Th\) is the threshold value, which is set to 15, and \(n\) represents the total sample frames of each interaction class. Tables 3-5 show the average body part detection accuracies achieved by the proposed system over the Olympic Sports, MSR daily Activity 3D, and D3D HOI datasets, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline
**Part** & **DR** & **ET** & **RB** & **WP** & **UL** & **PG** & **CC** & **UV** & **PR** & **LS** & **AVG** \\ \hline HD & 92.23 & 90.34 & 90.03 & 90.12 & 92.24 & 93.4 & 94.32 & 90.45 & 94.35 & 90.12 & 91.76 \\ RE & 95.67 & 93.03 & 92.12 & 90.11 & 93.56 & 96.05 & 92.35 & 94.32 & 93.27 & 96.05 & 93.65 \\ LE & 93.35 & 95.67 & 91.78 & 94.38 & 96.05 & 94.38 & 93.62 & 92.23 & 93.56 & 94.32 & 93.93 \\ RH & 91.45 & 90.51 & 91.63 & 95.67 & 92.23 & 94.38 & 90.56 & 93.27 & 95.67 & 93.27 & 92.86 \\ LH & 97.59 & 90.12 & 95.67 & 91.45 & 92.35 & 97.59 & 92.03 & 93.56 & 96.05 & 92.23 & 93.86 \\ NK & 94.38 & 96.05 & 94.38 & 95.67 & 93.35 & 93.35 & 91.14 & 92.23 & 97.59 & 95.67 & 94.38 \\ TRS & 93.62 & 92.72 & 95.67 & 87.24 & 94.32 & 95.67 & 93.35 & 95.67 & 92.23 & 94.32 & 93.48 \\ BTR & 92.23 & 95.67 & 97.59 & 93.56 & 94.38 & 94.38 & 94.38 & 90.42 & 92.23 & 93.56 & 96.05 & 94.01 \\ RK & 93.35 & 91.39 & 94.38 & 92.23 & 97.59 & 92.23 & 93.24 & 93.56 & 94.38 & 92.23 & 93.46 \\ LK & 93.56 & 97.59 & 93.56 & 95.67 & 94.32 & 93.56 & 90.76 & 94.32 & 92.23 & 94.38 & 94.00 \\ RF & 93.27 & 91.45 & 92.23 & 91.45 & 94.38 & 92.23 & 91.09 & 94.38 & 97.59 & 94.32 & 93.24 \\ LF & 95.67 & 92.35 & 95.67 & 94.38 & 93.27 & 93.27 & 93.56 & 92.35 & 94.38 & 93.27 & 93.82 \\ \hline \end{tabular}
\end{table} 
Table 4: Body part detection rate achieved over MSR Daily Activity 3D dataset.