## 2 Extreme Learning Machine (ELM)-Based Moving Cast Shadow Detection
### Moving Cast-Shadow Detection Algorithm
### Parameter Sensitivity Analysis

In this section, to analyze the influence of different hidden layers \(L\) on the proposed method, Figure 5 illustrates the variation curves of classification rates on the two datasets. Obviously, the classification rate is not sensitive to the value of the parameter \(L\). Specifically, with an increase of the value of \(L\), the performance of the proposed method is being improved. After achieving the peak of classification rate, the performance of the proposed method is decreasing with an increase of the value of \(L\). Therefore, we can see that neither too small nor too large \(L\) is appropriate for our method from Figure 5. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Scene** & **Metric** & **Campus** & **Highway** & **Hallway** & **Laboratory** & **Intelligent Room** & **CAVIAR** \\ \hline \multirow{3}{*}{[PERSON] et al. [37]} & \(\eta\) & 86.32 & 81.85 & 81.22 & 83.34 & 91.45 & — \\ \cline{2-7}  & \(\xi\) & 96.97 & 90.42 & 83.27 & 76.54 & 85.31 & — \\ \cline{2-7}  & \(Avg\) & 91.65 & 86.14 & 82.25 & 79.94 & 88.38 & — \\ \hline \multirow{3}{*}{[PERSON] et al. [38]} & \(\eta\) & 74.30 & — & 89.60 & 86.20 & 80.90 & 84.00 \\ \cline{2-7}  & \(\xi\) & 84.90 & — & 92.20 & 84.30 & 93.70 & 93.70 \\ \cline{2-7}  & \(Avg\) & 79.60 & — & 90.90 & 85.25 & 87.30 & 88.85 \\ \hline \multirow{3}{*}{Proposed} & \(\eta\) & 79.35 & 86.24 & 94.02 & 92.72 & 96.65 & 97.28 \\ \cline{2-7}  & \(\xi\) & 96.22 & 94.66 & 98.01 & 92.73 & 95.26 & 98.34 \\ \cline{1-1} \cline{2-7}  & \(Avg\) & 87.79 & 90.45 & 96.02 & 92.72 & 95.95 & 97.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Shadow detection comparison results with some representative deep-learning methods. Figure 5: \(Cont.\)

To analyze the performance of the proposed MCSD-ELM with varying the number of training samples, Figure 6 displays classification rates of our method with different numbers of training samples on two datasets. It can be seen that with the increase of training samples, the classification rates of the proposed method are increasing. Moreover, when the number of training samples increases to a certain extent, the accuracy tends to be stable. It is well known that the time cost will be higher with increasing the number of training samples. Therefore, neither too small nor too large the number of training samples is appropriate for our method. Figure 5: Classification rates of our method with a different number of hidden-layers on two datasets. (**a**) variation tendency on the popular dataset; (**b**) variation tendency on the large dataset. Figure 6: _Cont._

## 4 Conclusions

In this study, we have proposed a novel moving cast-shadow detection method using the supervised ELM. In contrast to the conventional methods, the proposed method not only incorporates pixel-level features but also explores region-level features according to the correlations among neighboring pixels to form input data for constructing the MCSD-ELM model. On the one hand, the proposed model only needs to turn one parameter which has little effect on the accuracy and can automatically determine one pixel whether it is a shadow or not. On the other hand, the post-processing operation can further improve the classification performance and guarantee the integrity of moving cast shadows and moving objects. We have evaluated the performance of the proposed method on two publicly available datasets. Compared with some representative state-of-the-art methods, the extensive experimental results indicate the effectiveness and robustness to noises of our method. Considering that the process of labelling data could be time-consuming and infeasible, we will research the semi-supervised methods for moving cast-shadow detection using labelled and unlabeled data in the future work. Moreover, we have also discovered that some researchers have proposed active annotation methods [42] for the single image or video sequences. Therefore, we also will study moving shadow detection based on deep learning on video sequences.