## 3 Proposed Method
\[Sh_{t_{i}}=F(Shc_{t_{i}},A) \tag{37}\]  
Temporal-Spatial Aggregation  
Preprocessed shadow contours \(Sh_{t_{i}}\) are aggregated according to category \(P_{i}\) of corresponding human pose \(P_{t_{i}}\). Nevertheless, the real-world coordinates of \(P_{t_{i}}\in P_{j}\) are spatially dispersed due to the human movement as shown in Figure 4a. Thus it is necessary to aggregate shadow contours \(Sh_{t_{i}}\) of the same central human pose \(P_{t_{i}}\) to deploy precise joint position estimation. For each pose category, one central human pose \(P_{t_{k}}\) is set up as the aggregating destination for other human shadow \(Sh_{t_{i}}\) related with \(P_{t_{i}}\in P_{j}\). The translation of each human shadow \(Sh_{t_{i}}\) is based on the translation transformation calibration matrix \(A_{t_{i}\to j_{c}}\). The translation transformation matrix is calculated based on the Equation (30). Since the major peak joint position sets \(\{JP_{t_{i}}^{k}\}\) and \(\{JP_{j_{c}}^{k}\}\) are obtained in the pose classification step, the translation transformation calibration matrix \(A_{t_{i}\to j_{c}}\) can be extracted as shown in Equation (38). \[A_{t_{i}\to j_{c}}=Par(\{JP_{t_{i}}^{k}\},\{JP_{j_{c}}^{k}\}) \tag{38}\]  
Along with the 2D translation of each \(Sh_{t_{i}}\), the corresponding 3D light source position \(S_{i}\) is moved with the identical translation as shown in Equation (39b). The aggregated human shadow \(Sh_{t_{i}}^{\prime}\) and light source \(S_{t_{i}}^{\prime}\) offer the ideal multiple light source situation for 3D joint position estimation. As shown in Figure 4b, when \(P_{t_{2}}\) is setup as the aggregating destination, other \(Sh_{t_{i}}\) are aggregated to the aggregating destination through the 2D translation as shown in Equation (39a). \[Sh_{t_{i}}^{\prime}=F(Sh_{t_{i}},A_{t_{i}\to j_{c}}) \tag{39a}\] \[S^{\prime}t_{i}=f(S,A_{t_{i}\to j_{c}}) \tag{39b}\]  
Joint Position Estimation and Skeleton Synthesis  
For each aggregated human shadow contour \(Sh_{t_{i}}^{\prime}\), joint area estimation is launched based on the algorithm introduced in the basic theory section. First of all, the gravity center \(G_{t_{i}}^{\prime}\) of curve \(Sh_{t_{i}}^{\prime}\) is calculated. Then, the denoised distance curve \(\overline{D_{t_{i}}^{\prime}}\) between each point \((x_{t_{i}}^{\prime},y_{t_{i}}^{\prime})\in Sh_{t_{i}}^{\prime}\) and \(G_{t_{i}}^{\prime}\) is available based on the preprocess procedure illustrated in Section 2.1.2. \[\overline{D_{t_{i}}^{\prime}}=Pre(Sh_{t_{i}}^{\prime}) \tag{40}\]  
The 2D positions of major joint areas including head \(Sp_{i}^{\prime 1}\), neck \(Sp_{i}^{\prime 2}\), hip center \(Sp_{i}^{\prime 3}\), left keen \(Sp_{i}^{\prime 4}\), right keen \(Sp_{i}^{\prime 5}\), left foot \(Sp_{i}^{\prime 6}\) and right foot \(Sp_{i}^{\prime 7}\) can be obtained through locating the peak and nadir points in \(\overline{D_{t_{i}}^{\prime}}\). Figure 5:0  
In each simulated scenario, silhouette information extraction is applied to each joint area \(Sh_{i_{-}k}^{\prime}\). In order to estimate the 3D joint position based on \(Sp_{t_{i}}^{\prime}\), the ray set \(L_{t_{i}}^{\prime k}\) connecting light source \(S_{t_{i}}^{\prime}\) and joint shadow area \(Sp_{t_{i}}^{\prime}\) is simulated. Figure 5:1  
Since more than two simulated light sources \(S_{t_{i}}^{\prime}\) exist in the scenario, silhouette information of single joint area is extracted separately for each light sources. Based on all ray sets \(L_{t_{i-}k}^{\prime}\) targeting at the same joint, 3D joint position \(M_{p_{j}}^{k}\) can be calculated based on Equation (43). Figure 5:2  
Repeating steps above for each major joints, 3D joint position set \(\{Mp_{j}^{k}\}\) containing all joint positions can be figured out. Then joint positions can be synthesized based on the combination Equation (44). Figure 5:3  
In order to simplify the presentation in Algorithm 4, the illustrated joint position estimation and skeleton synthesis procedure is simplified into Equation (45).