## 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} \hline \hline
**Scene** & **Highway** & **Hallway** & **Laboratory** & **CAVIAR** & **Campus** & **Intelligent Room** \\ \hline Video frame & & & & & & \\ \hline Groundtruth & & & & & & \\ \hline Scene Type & Outdoor & Indoor & Indoor & Indoor & Outdoor & Indoor \\ \hline Labeled frames & 10 & 13 & 14 & 164 & 53 & 100 \\ \hline Total frames & 440 & 1800 & 887 & 2725 & 1181 & 300 \\ \hline Frame size & \(320\times 240\) & \(320\times 240\) & \(320\times 240\) & \(384\times 288\) & \(352\times 288\) & \(320\times 240\) \\ \hline Shadow strength & Strong & Weak & Weak & Weak & Weak & Weak \\ \hline Object type & Vehicle & People & People & People & Vehicle/People & People \\ \hline Shadow size & Large & Large/Medium & Medium & Variable & Large/Medium & Medium \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The detailed information of a popular dataset. (1) **Cubic**: It is a typical indoor scene with strong light in the front of the view and has strong camouflages between the walking staffs and the background. (2) **Bungalows**: It is an outdoor scene of the traffic with various vehicles, in which the shadow is relatively large and strong. (3) **BusStation**: It is an outdoor scene, in which the shadow is static, medium and strong casting by buildings in front of the bus station and peoples coming out from the station or passing in front of the station. (4) **PeopleInShade**: It is a challenging outdoor scene, in which people walk under a large shaded area. It has foreground-background camouflages and non-textured-dark regions except strong shadows. (5) **Seam, Senoon, Sepm**: They are outdoor scenes acquired from the same camera with different time. They have strong shadows with various sizes. ### Evaluation Metrics

To quantitively evaluate the performance of shadow detection methods, two metrics [5], shadow detection rate (\(\eta\)) and shadow discrimination rate (\(\xi\)) are defined as follows:

\[\eta=\frac{\mathit{TP}_{S}}{\mathit{TP}_{S}+\mathit{FN}_{S}}\times 100\%,\ \xi=\frac{ \mathit{TP}_{O}}{\mathit{TP}_{O}+\mathit{FN}_{O}}\times 100\% \tag{20}\]

where \(\mathit{TP}_{S}\) and \(\mathit{TP}_{O}\) are the numbers of moving shadow pixels and moving object pixels correctly detected, respectively. \(\mathit{FN}_{S}\) is the number of moving shadow pixels classified as moving object pixels incorrectly. Likewise, \(\mathit{FN}_{O}\) is the number of moving object pixels classified as moving shadow pixels incorrectly. To consider the performance of shadow detection and shadow discrimination simultaneously, the third measure is given by:

\[Avg=\frac{\eta+\xi}{2} \tag{21}\]

where \(Avg\) is the mean value of the shadow detection rate \(\eta\) and shadow discrimination rate \(\xi\). ### Comparisons on a Popular Dataset

The quantitative results obtained by the proposed method and nine comparative methods are summarized as Table 3 and the best result \(Avg\) of each scene is marked with bold. Some quantitative \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Scene** & **Cubicle** & **BusStation** & **Bungalows** & **Seam** & **Senoon** & **Sepm** & **PeopleInShade** \\ \hline Video & & & & & & & \\ frame & & & & & & & \\ \hline Groundtruth & & & & & & & \\ \hline Scene Type & Indoor & Outdoor & Outdoor & Outdoor & Outdoor & Outdoor \\ \hline Labeled & & & & & & & \\ frames & & & & & & & \\ \hline Total & & & & & & & \\ frames & & & & & & & \\ \hline Frame size & & & & & & & \\ \hline Shadow & & & & & & & \\ strength & & & & & & \\ \hline Object & & & & & & & \\ type & & & & & & \\ \hline Shadow & & & & & & & \\ size & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The detail information of a large dataset. results of comparative methods refer to original literature [9; 22] and some are provided by the authors of the literature [26; 31]. It can be observed that the proposed method has the highest shadow detection rate \(\eta\) on CAVIAR, Hallway, Laboratory and Intelligent Room and has the best shadow discrimination rate \(\xi\) on Campus.