## 2 Basic Theory
### Skeleton Simulation in Single-Light-Source Scenario
#### 2.2.2 Temporal-Spatial Aggregation Method  
Human Pose Classification  
In order to analyses the human pose \(P_{t_{i}}\) at each time coordinate \(t_{i}\), the denoised distance curve \(\overline{D_{t_{i}}}\) between the human pose contour and human pose gravity center is extracted based on the same method illustrated in Equation (19). Similarly, the stage Equation (26) covers the normalized distance curve extraction procedure illustrated from Equation (16) to Equation (18). The function _Pre_ presents the extraction procedure for the normalized distance curve \(\overline{D_{t_{i}}}\) based on the contour curve \(P_{t_{i}}\). \[\overline{D_{t_{i}}}=Pre(P_{t_{i}}) \tag{26}\]  
Based on the distance curve \(\overline{D_{t_{i}}}\), major peak point set \(\{JP_{t_{i}}^{k}|k=1,2,3\}\) including head and two feet are extracted from the captured human contour based on the same procedure presented in Equation (20). Similar to the stage Equation (20), stage Equation (27) covers the major joint position localization procedure illustrated in the Section 2.1.2. The function _Loc_ presents the human joint position extraction procedure for major joint position set \(\{JP_{t_{i}}^{k}\}\) based on the human contour \(Sh_{t_{i}}\) and the corresponding distance curve \(\overline{D_{t_{i}}}\). \[\{JP_{t_{i}}^{k}\}=Loc(Sh_{t_{i}},\overline{D_{t_{i}}}) \tag{27}\]  
The positions of three peak points of the human pose contour are combined into a star feature to describe the human pose in each frame [10; 18]. Then unsupervised classification is adopted to assort each frame with corresponding pose category label based on the star feature [19]. \[C_{t_{i}}=Lab(\{JP_{t_{i}}^{k}\})=j|\operatorname*{arg\,min}_{j}(\sum_{k=1}^{3 }\sum_{JP_{j}^{k}\in P_{j}}\left\|JP_{t_{i}}^{k}-JP_{j}^{k}\right\|^{2}) \tag{28}\]  
During the temporal-spatial shadow aggregation procedure shown in Figure 4c, temporal discrete light sources are aggregated in a single frame. Normally, for multiple human poses, the human pose \(P_{t_{i}}\) with median time coordinate \(t_{i}\) is chosen as the central pose \(P_{t_{c}}\). For each human pose \(P_{t_{i}}\in\{P_{j}\}\), the translation transformation parameter \(T_{t_{i}\to j_{c}}\) is defined by the vector between corresponding joint points in \(P_{t_{i}}\) and \(P_{j_{c}}\), satisfying the spatial transformation from \(P_{t_{i}}\) to \(P_{j_{c}}\). Noticeably, the joint positions \(JP_{t_{i}}^{k}\) and \(JP_{j_{c}}^{k}\) are captured in the image coordinate plane. Before calculating the translation transformation \(T_{t_{i}\to j}\) in real-world coordinates, it is necessary to transform the joint coordinates into the real- world coordinates \(SP_{t_{i}}^{k}\) and \(Sp_{j_{c}}^{k}\) based on the stage projection transformation \(F((x,y),A_{mat})\) presented in Equation (14). \[Sp_{t_{i}}^{k}=F(JP_{t_{i}}^{k},A_{mat}) \tag{29a}\] \[Sp_{j_{c}}^{k}=F(JP_{j_{c}}^{k},A_{mat}) \tag{29b}\]\[\overrightarrow{T_{(t_{i},j_{c})}}=\frac{1}{2}\sum\limits_{k=2}^{3} \overrightarrow{Sp_{t_{i}}^{k}Sp_{j_{c}}^{k}}=\Delta u_{(t_{i},j_{c})}\alpha+ \Delta v_{(t_{i},j_{c})}\beta \tag{29c}\] \[A_{t_{i}\to j_{c}}=\left[ \begin{array}{ccc}1&0&0\\ 0&1&0\\ \Delta u_{(t_{i},j_{c})}&\Delta v_{(t_{i},j_{c})}&1\end{array} \right] \tag{29d}\]  
As shown in Equation (29a), \(Sp_{t_{i}}^{k}\) is the extracted real-world human joint coordinates at the original captured position. In Equation (29b), \(Sp_{j_{c}}^{k}\) is the human joint coordinates at the destination position. Then the translation vector \(\overrightarrow{T_{t_{i}\to j_{c}}}\) is calculated based on the averaged horizontal translation vectors from the original position to the destination position. As shown in Equation (29c), \(\alpha\) and \(\beta\) are two vertical unit vectors of the real-world coordinate system on the ground surface. The translation vector \(\overrightarrow{T_{t_{i}\to j_{c}}}\) is presented as a combination of translation components \(\Delta u_{(t_{i},j_{c})}\) and \(\Delta v_{(t_{i},j_{c})}\) in two vertical directions.