# Background Subtraction for Dynamic Scenes Using Gabor Filter Bank and Statistical Moments
## 3 Materials and Methods
### Segmentation Criteria
Table 7 presents the results obtained in a scenario characterized by acquisition errors and the presence of shadows on moving objects. With a sensitivity of 0.829, our method can detect foreground moving objects, even in conditions where sampling is not adequate. A specificity of 0.991 shows its efficiency in differentiating between objects of interest and the background, thus minimizing misdetections caused both by shadows and acquisition errors. Figure 13 shows the percentage of wrong classifications \((PWC)\), which shows the deviation error in the scene. This error is caused by the number of false positives \((FPR)\) and false negatives \((FNR)\) described. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Method** & **Sensibility** & **Specificity** & **FPR** & **FNR** & **PWC** & **Precision** & **F1 Measure** \\ \hline DEU & 0.380 & 0.956 & 0.043 & 0.619 & 10.821 & 0.525 & 0.440 \\ DMD & 0.393 & 0.922 & 0.078 & 0.607 & 8.648 & 0.080 & 0.133 \\ DSTEI & 0.598 & 0.935 & 0.065 & 0.402 & 7.637 & 0.238 & 0.341 \\ EigenBS & 0.900 & 0.922 & 0.078 & 0.100 & 7.844 & 0.060 & 0.113 \\ GMM & 0.940 & 0.969 & 0.031 & 0.060 & 3.308 & 0.642 & 0.763 \\ MRFMD & 0.986 & 0.943 & 0.057 & 0.014 & 5.585 & 0.331 & 0.495 \\ SDBE & 0.919 & 0.920 & 0.080 & 0.081 & 8.000 & 0.038 & 0.073 \\ SOBS & 0.710 & 0.931 & 0.069 & 0.290 & 7.391 & 0.183 & 0.291 \\ SWCD & 0.999 & 0.974 & 0.026 & 0.001 & 2.478 & 0.701 & 0.824 \\ ViBe & 0.927 & 0.993 & 0.007 & 0.073 & 1.268 & 0.920 & 0.923 \\
**GMBSM** & **0.827** & **0.988** & **0.012** & **0.172** & **0.578** & **0.863** & **0.901** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results obtained when evaluating the methods in \(S_{5}\). \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Method** & **Sensibility** & **Specificity** & **FPR** & **FNR** & **PWC** & **Precision** & **F1 Measure** \\ \hline DEU & 0.285 & 0.981 & 0.019 & 0.715 & 2.667 & 0.140 & 0.187 \\ DMD & 0.859 & 0.991 & 0.009 & 0.141 & 1.127 & 0.585 & 0.696 \\ DSTEI & 0.620 & 0.980 & 0.020 & 0.380 & 2.103 & 0.119 & 0.199 \\ EigenBS & 0.364 & 0.991 & 0.009 & 0.636 & 3.190 & 0.596 & 0.452 \\ GMM & 0.793 & 0.993 & 0.007 & 0.207 & 1.086 & 0.686 & 0.736 \\ MRFMD & 0.912 & 0.991 & 0.009 & 0.088 & 1.027 & 0.591 & 0.717 \\ SDBE & 0.688 & 0.979 & 0.021 & 0.312 & 2.130 & 0.062 & 0.113 \\ SOBS & 0.817 & 0.992 & 0.008 & 0.183 & 1.129 & 0.628 & 0.710 \\ SWCD & 0.914 & 0.991 & 0.009 & 0.086 & 0.999 & 0.604 & 0.727 \\ ViBe & 0.878 & 0.998 & 0.002 & 0.122 & 0.508 & 0.893 & 0.886 \\
**GMBSM** & **0.856** & **0.99** & **0.008** & **0.144** & **0.993** & **0.660** & **0.746** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results obtained when evaluating the methods in \(S_{4}\). Figure 13a shows that the proposed method has an error percentage similar to most methods (about 1%) due to the change in the object's perspective. This problem is the main weakness of the Gabor filter because it requires functions \(G_{\lambda,\theta,\phi}\) of different sizes and frequencies. This increases the complexity of parameter selection and the processing time. This same problem is shown in Figure 13b. However, in Figure 13c,d, we can see that the percentage of error is lower; this is because the objects in \(S_{5}\) and \(S_{6}\) scenes do not have perspective with respect to the camera. For this reason, the size of the \(G_{\lambda,\theta,\phi}\) function is fixed so that the texture can be better modeled. The problem in these scenarios is that they have lower resolution, which means that \(\sigma_{x}\) and \(\sigma_{y}\) have to be reduced, as well as, therefore, the lambda value. This effect increases the amount of noise detected and therefore impacts the amount of true positives detected. Figure 14 shows the precision of the methods, which helps us to visualize which method provides us with more information about moving objects and minimizes irrelevant information caused by noise, the presence of shadows, or changes in lighting. Although our