## 2 Extreme Learning Machine (ELM)-Based Moving Cast Shadow Detection
### Moving Cast-Shadow Detection Algorithm
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Scene**} & \multirow{2}{*}{**Metric**} & **[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** & **[PERSON]** \\  & & **et al.** & **et al.** & **et al.** & **et al.** & **et al.** & **et al.** & **et al.** & **et al.** & **et al.** & **et al.** \\ \hline \multirow{3}{*}{PeopleInShade} & \(\eta\) & 9.83 & 57.34 & 8.96 & 51.88 & 32.99 & 35.56 & — & 75.90 & 99.65 \\ \cline{2-11}  & \(\xi\) & 97.10 & 52.50 & 97.31 & 79.64 & 97.37 & 90.32 & — & 94.40 & 97.88 \\ \cline{2-11}  & _Avg_ & 53.47 & 54.92 & 53.14 & 65.76 & 65.18 & 62.94 & — & 85.15 & 98.76 \\ \hline \multirow{3}{*}{BusStation} & \(\eta\) & 50.72 & 20.52 & 60.15 & 51.62 & 36.00 & 63.49 & 93.80 & 65.18 & 88.06 \\ \cline{2-11}  & \(\xi\) & 83.05 & 64.45 & 94.30 & 84.95 & 94.33 & 89.72 & 88.90 & 95.00 & 95.17 \\ \cline{2-11}  & _Avg_ & 66.89 & 42.49 & 77.22 & 68.28 & 65.17 & 76.60 & 91.35 & 80.09 & 91.62 \\ \hline \multirow{3}{*}{Cubic} & \(\eta\) & 92.37 & 59.27 & 67.11 & 26.95 & 89.40 & 69.64 & — & 89.81 & 99.96 \\ \cline{2-11}  & \(\xi\) & 91.56 & 68.66 & 91.10 & 89.64 & 94.66 & 84.39 & — & 87.19 & 97.36 \\ \cline{2-11}  & _Avg_ & 91.96 & 63.96 & 79.10 & 58.30 & 92.03 & 77.01 & — & 88.50 & 98.66 \\ \hline \multirow{3}{*}{Bungalows} & \(\eta\) & 3.81 & 59.91 & 15.79 & 8.13 & 70.23 & 3.57 & 90.90 & 85.02 & 89.50 \\ \cline{2-11}  & \(\xi\) & 74.75 & 55.43 & 89.79 & 78.26 & 64.16 & 94.57 & 92.10 & 78.08 & 84.46 \\ \cline{2-11}  & _Avg_ & 39.28 & 57.67 & 52.79 & 43.20 & 67.20 & 49.07 & 91.50 & 81.55 & 86.98 \\ \hline \multirow{3}{*}{Seam} & \(\eta\) & 19.22 & 57.39 & 56.04 & 69.06 & 22.66 & 73.44 & 99.60 & 79.10 & 97.78 \\ \cline{2-11}  & \(\xi\) & 59.92 & 64.61 & 87.11 & 67.75 & 79.08 & 77.65 & 72.80 & 85.70 & 99.35 \\ \cline{2-11}  & _Avg_ & 39.57 & 61.00 & 71.57 & 68.40 & 50.87 & 75.54 & 86.20 & 82.40 & 98.57 \\ \hline \multirow{3}{*}{Senon} & \(\eta\) & — & — & — & — & — & — & 95.60 & 52.69 & 99.19 \\ \cline{2-11}  & \(\xi\) & — & — & — & — & — & — & 85.30 & 68.54 & 98.69 \\ \cline{2-11}  & _Avg_ & — & — & — & — & — & — & 90.45 & 60.62 & 98.94 \\ \hline \multirow{3}{*}{Sepm} & \(\eta\) & — & — & — & — & — & — & 95.80 & 44.95 & 94.96 \\ \cline{2-11}  & \(\xi\) & — & — & — & — & — & — & 78.90 & 83.73 & 98.09 \\ \cline{2-11}  & _Avg_ & — & — & — & — & — & — & 87.35 & 64.34 & 96.52 \\ \hline \multirow{3}{*}{Average} & \(\eta\) & 54.21 & 41.78 & 53.23 & 62.32 & 60.11 & 68.45 & 95.14 & 70.38 & 95.59 \\ \cline{2-11}  & _Avg_ & 68.30 & 85.11 & 81.81 & 72.06 & 92.35 & 89.00 & 83.60 & 84.66 & 95.86 \\ \cline{2-11}  & _Avg_ & 61.25 & 63.45 & 67.52 & 67.19 & 76.23 & 78.73 & 89.37 & 77.52 & 95.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Shadow detection results of the proposed method and compared methods on the large dataset. Figure 4: Visual comparisons of shadow-detection results on the large dataset. (**a**) input frame; (**b**) groundtruths; (**c**) results obtained by [22]; (**d**) results obtained by our method. discrimination rate \(\xi\) and the average among of them, the proposed method is superior to the method suggested by [PERSON] et al. [37] on the most scenes except on Campus, and it performs better than the method designed by [PERSON] et al. [38] on all test scenes. The reasons are summarized as follows. (1) our method is implemented with the learning features obtained by ELM based on the discriminative hand-crafted features, while shallow features derived from original frames are learnt by convolutional neural network methods. (2) The deep-learning methods have a large number of parameters to estimate. When the sample size is small, the deep-learning methods cannot be able to optimize parameters well, which will lead to the under-learning phenomenon. While our method based on ELM requires fewer optimization parameters, it can achieve better performance with fewer labelled samples.