# Chinese Traffic Police Gesture Recognition Based on Graph Convolutional Network in Natural Scene
## 3 Methods
### Spatial Graph Convolution  
To better explain the module, here, we describe it from skeleton data in a single frame. The skeleton graph of the ST-GCN in the same frame only represents the physical structure of the human body, which is not the optimal representation with regard to gestures used by traffic police. For example, the spatial locations of hands are crucial in traffic police gesture semantic representation, which have potential contact. Thus, in this paper, an AGS was constructed to find the potential features in human joints. The left figure in Figure 6 shows the connection method of the ST-GCN; the right figure of Figure 6 is the spatial-temporal graph extended by this paper, which connects several neighbor joints. The skeleton graph constructed in this paper is a nondirectional spatial-temporal graph in the same frame, \(G=<V,E>\), which contains skeleton sequence data of N joints and T frames. The set for nodes is shown in Equation (1):  
\[V=\{v_{ti}|t=1,\cdots,T,i=1,\cdots,N\} \tag{1}\]  
In Equation (1), \(v_{ti}\) represents the \(i\) joints in \(t\) frame, \(t\) means the serial number of frame, and \(i\) means the number of joints. There are two kinds of edges in the skeleton graph, and no manual distribution is added in the process of connecting edges, which means that the model can deal with more datasets and improves its universality. In the traditional convolution method, the output of a single channel in the spatial position \(x\) can be represented as Equation (2):  
\[f_{out}(X)=\sum_{h=1}^{K}\sum_{w=1}^{K}f_{in}(P(x,h,w))\cdot W(h,w) \tag{2}\]  
The size of convolution kernel is \(K\times K\), \(f_{in}\) is input feature graph, \(P(\cdot)\) is the sampling function, and \(W(\cdot)\) is the weight function. For the sampling function, images have the same number of neighbor pixels. Sampling function \(P(\cdot)\) means the selection of the surrounding neighbor pixels centered on the \(X\) pixel. However, in skeleton graphs, the number of neighbor nodes is different: the neighbor nodes set is defined by Equation (3):  
\[B(v_{ti})=\{v_{ti}|d(v_{ti},v_{ti})\leq D\} \tag{3}\]  
In Equation (3), \(d(v_{ti},v_{ti})\) represents the shortest path from skeleton joints \(v_{ti}\) to \(v_{ti}\); take \(D=1\). Sampling function \(P:B(v_{ti})\to V\) is shown in Equation (4):  
\[p(v_{ti},v_{tij})=v_{tj} \tag{4}\]  
The sampling function in this paper takes the self-learning method to avoid loss in long-distance cross-information from partial convolution, for example, cooperating information between hands. Figure 6: The proposed skeleton graph on spatial dimension. Compared with the sampling function, the weight function is more complicated. A rigid mesh exists around the center of the image, and neighbor pixels have a fixed spatial sequence. However, there is no potential sequence in skeleton graphs. The skeleton graph in one frame is shown as in Figure 7a, in which root joints were painted in red. The ST-GCN proposed three partitioning strategies, which were Uni-labeling (Figure 7b), Distance partitioning (Figure 7c), Spatial configuration partitioning (Figure 7d), respectively. Here, we use the spatial configuration partitioning strategies from the the ST-GCN model, as shown in Figure 7d. This strategy divides the set into three subsets: root joints themselves (green nodes in Figure 7d), joints closer to the skeleton center of gravity than root joints (blue nodes in Figure 7d), and joints further from the skeleton center of gravity than root joints (yellow joints in Figure 7d). The specific indication is shown in Equation (5). \[l_{tt}(v_{tj})\begin{cases}0&\quad\quad\quad\  
multilayer perceptron to calculate the two different channels above and summed them element-by-element. Finally, we generated the final channel attention traffic police gesture feature graph \(M_{C}\) through the activation function, as shown in Equation (8):  
\[ \begin{split} M_{C}(F)&=\sigma(MLP(AvgPool(F))+MLP( MaxPool(F)))\\ &=\sigma(W_{1}\Big{(}W_{0}\Big{(}F^{c}_{avg}\Big{)}\Big{)}+W_{1}(W _{0}(F^{c}_{max})))\end{split}