## 2 The Proposed Method
F-measure is the comprehensive evaluation index which represents the weighted harmonic mean and ranges between 0 and 1. Obviously, the higher are recall, precision and F-measure, the better is the performance, while the lower are FPR, FNR, and PWC, the better is the performance. We applied the proposed framework to the following traditional background modeling methods: GMM, SuBSENSE, PBAS, KDE, LOBSTER, and ViBe. Details for the implementation of these traditional methods are available in the BGSlibrary [38], and, consequently, these implementations were used in this study. Figure 4 presents the refinements of the traditional background subtraction methods using the proposed method for foreground detection in dynamic scenes. It is noteworthy that the convolution feature methods (\(BGS_{\text{con}}\)) further suppressed the disturbance of dynamic background such as branch swaying, water ripple, and so on as compared with the corresponding background subtraction methods (\(BGS\)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Videos** & **Size** & **Number of Frames** & **Dynamic Scenes** \\ \hline Boats & \(320\times 240\) & 7999 & water rippling \\ Canoe & \(320\times 240\) & 1189 & water rippling \\ Fountain01 & \(432\times 288\) & 1184 & fountains \\ Fountain02 & \(432\times 288\) & 1499 & fountains \\ Overpass & \(320\times 240\) & 3000 & waving trees \\ Fall & \(720\times 480\) & 4000 & waving trees \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Dynamic background videos. Comparisons of the performance between these background subtraction methods (\(BGS\)) and the corresponding convolution feature methods (\(BGS_{\text{con}}\)) are shown in Table 4 and illustrates that the convolution feature framework improves the performance of background subtraction methods to some extent. To show the refinements of the traditional background subtraction methods by the proposed framework intuitively, the average values and standard deviations for F-measure, which are general international standards for binary classification, are presented in Figure 5. In the figure, the blue bars are the F-measure values of traditional background modeling methods while the red bars are the corresponding F-measure values of the convolution feature methods. The KDE method had the highest performance improvement, with an increase of more than 160%. GMM's performance was improved by 42%, ViBe by 21%, LOBSTER by 12%, PBAS by 9%, and SuBSENSE by 0.1%. SuBSENSE, which is a state-of-the-art BCS method, had very high performance and surpassed most of the other unsupervised BGS methods. When the proposed method was applied, the performances of other background subtraction methods, with the exception of SuBSENSE, improved significantly. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Category** & **Methods** & **Recall** & **FPR** & **FNR** & **PBC** & **Precision** & **F-Measure** \\ \hline \multirow{8}{*}{dynamic background} & GMM & 0.7568 & 0.0440 & 0.2432 & 4.7859 & 0.2109 & 0.3062 \\  & GMM\({}_{\text{con}}\) & 0.7683 & 0.0232 & 0.2317 & 2.7252 & 0.3484 & 0.4338 \\  & SuBSENSE & 0.7713 & 0.0006 & 0.2287 & 0.4084 & 0.8915 & 0.8132 \\  & SuBSENSE\({}_{\text{con}}\) & 0.8228 & 0.0017 & 0.1772 & 0.3645 & 0.8228 & 0.8138 \\  & PBAS & 0.5634 & 0.0005 & 0.4366 & 0.7252 & 0.8787 & 0.6154 \\ \multirow{2}{*}{dynamic background} & PBAS\({}_{\text{con}}\) & 0.6095 & 0.0005 & 0.3905 & 0.5800 & 0.8848 & 0.6712 \\  & KDE & 0.8562 & 0.0788 & 0.1438 & 7.8212 & 0.1062 & 0.1855 \\  & KDE\({}_{\text{con}}\) & 0.4765 & 0.0041 & 0.5235 & 0.9584 & 0.5691 & 0.4884 \\  & LOBSTER & 0.7646 & 0.0189 & 0.2354 & 2.0795 & 0.5948 & 0.5682 \\  & LOBSTER\({}_{\text{con}}\) & 0.6572 & 0.0047 & 0.3428 & 0.7922 & 0.7411 & 0.6367 \\  & ViBe & 0.5852 & 0.0100 & 0.4148 & 1.3884 & 0.4521 & 0.4733 \\  & ViBe\({}_{\text{con}}\) & 0.6020 & 0.0047 & 0.3980 & 0.8203 & 0.6237 & 0.5739 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparisons between \(BGS\) and \(BGS_{\text{con}}\) by the proposed method.