## 3 The Proposed Framework
### Anomaly Detection
#### 3.2.2 Classifier
Abnormal events in this dataset vary in type, size and occurrence. It contains many occlusions and the image resolution is 240 \(\times\) 360, which is low and can complicate the detection process. While using this dataset, we evaluate two scenarios: \"SC1\" when we consider a balanced distribution for every folder of the Ped2 dataset, and another scenario \"SC2\" when we develop a distribution for the whole dataset. The objective of this experiment is to prove the robustness of the proposed method when increasing the number of images during the training phase. The first results show the effectiveness of the proposed method. The qualitative results are presented in Figure 7 when all abnormalities are detected. One can see in Table 2 how the introduction of vectors of interest reduces the number of feature vector representing normal events. Consequently, while using the first scenario of the proposed method, we apply a classifier (one classifier per folder) with less than one percent of features vectors selected as vector of interests. In the second scenario, when we consider a unique classifier for all folders containing 1920 training images, we get only 1569 vectors of interest. This number is relatively stable and low even if the training images number increases. This shows how the proposed methodology is robust when facing high number of frames. Consequently, it can be applied for real-world applications of video surveillance. To assess the performance of the proposed method and provide quantitative results, we used the Equal Error Rate of Frame Level (EERFL), the Equal Error Rate of Pixel Level (EERPL) and the Receiving Operating Characteristic (ROC). A comparison with state of the art methods is provided in Table 3. Our method gets respectively an EERFL and EERPL of 6.25% and 9.82% for the first scenario \"SC1\", and for the second scenario \"SC2\" 7.45% and 9.63% respectively, which outperforms all other state of the art methods. Figure 8 shows the receiver operating characteristic (ROC) for the UCSD Ped2 dataset, plotted as a function of the detection threshold for both scenarios. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Folder** & **NB-Frames** & **NB-FV** & **NB-VI** \\ \hline F1 & 120 & 100920 & 934 \\ F2 & 150 & 126150 & 923 \\ F3 & 150 & 126150 & 909 \\ F4 & 180 & 151380 & 1215 \\ F5 & 180 & 151380 & 1127 \\ F6 & 150 & 126150 & 1187 \\ F7 & 150 & 126150 & 1107 \\ F8 & 120 & 100920 & 981 \\ F9 & 180 & 151380 & 1134 \\ F10 & 180 & 151380 & 1177 \\ F11 & 180 & 151380 & 1109 \\ F12 & 180 & 151380 & 1108 \\ SC2 & 1920 & 1614720 & 1569 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Effect of the selection of vectors of interest on element reduction. For each folder of the dataset, one can see the number of frames (NB-Frames), number of feature vectors (NB-FV) and number of vector of interest obtained by our method (NB-VI). Figure 6: Detection of abnormal events. (**a**) Falling person; (**b**) Detection of multi-falling people; (**c**) Falling person in presence of walking one; (**d**) Detection of an object assumed as abnormal; (**e**) Falling person in presence of crouched person; (**f**) Falling person. Figure 7: Detection of abnormal events in Ped2 Dataset. (**a**) Multiple bicycles detected; (**b**) Detection of multiple targets (bicycle and car); (**c**) Detection of multiple targets (bicycle and skater); (**d**) Detection of multiple targets (bicycles and skater); (**e**) Multiple bicycles detected; (**f**) Detection of multiple targets (bicycle partially obstructed and one wheel). Also, as discussed above about including false alarms (FA). One can see in Table 4 how the EER is decreasing considerably when the operator declares false alarms. In Folder 4, the EER decreases by