# Background Subtraction for Dynamic Scenes Using Gabor Filter Bank and Statistical Moments
## 3 Materials and Methods
### Segmentation Criteria
The results analysis can be seen in Table 2.

\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Method** & \(\mathbf{S_{3}}\) & \(\mathbf{S_{4}}\) & \(\mathbf{S_{5}}\) & \(\mathbf{S_{6}}\) \\ \hline \multirow{2}{*}{Image} & \multirow{2}{*}{} & \multirow{2}{*}{} & \multirow{2}{*}{} & \multirow{2}{*}{} \\  & & & & \\ Groundtruth & & & & \\ DEU & & & & \\ DMD & & & & \\ DSTEI & & & & & \\ Eigen-Background Subtraction GMM & & & & & \\ MRFMD & & &



According to the results, in \(S_{3}\), the proposed method helps to reduce the effects produced by shadows while preserving most of the structure, but a value of \(\lambda=1.5\) causes the filter to be susceptible to noise, and objects that are not in motion can be seen. In \(S_{4}\), the vehicle structure is preserved, but the disadvantage is that the light changes of the leaves are detected as a movement. In scenario \(S_{5}\), unlike the other methods, our proposal can obtain a large part of the object structure without noise or deformations. Finally, in \(S_{6}\), there is an acquisition error because the speed of movement of the cyclist is greater than the speed of acquisition of the images, so the cyclist is not clearly seen. Nevertheless, we obtained good results because the complete structure of the cyclist can be appreciated regardless of the shadow and noise; classic noise reduction methods can minimize noise reduction and residual. The morphological closing method can be applied to obtain a complete object structure if necessary. The parameters used in each model are shown in Table 3, which were reported by each author so that each model maintains the best performance of its algorithm. In addition to the qualitative tests performed, we conducted quantitative tests on 3600 images, corresponding to a sequence of 900 images from each scene, to estimate the rates of true positives and false positives. Although there are different ways to evaluate performance, the evaluation here is performed at the pixel level. In addition to measurement accuracy and sensitivity, the indicators described below are also used to evaluate and verify data. According to [68], these are defined as follows. Sensitivity (also known as True Positive Rate or Recall): This metric measures the proportion of actual positives that are correctly identified as such. It is calculated as:

\[Sensitivity=\frac{T_{P}}{T_{P}+F_{N}} \tag{10}\]

Specificity: It measures the proportion of actual negatives that are correctly identified. It is calculated as:

Figure 8:0

False Positive Rate (FPR): This is the proportion of actual negatives that are incorrectly identified as positives. It is calculated as:

Figure 8:1 \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Method** & **Parameters** & & & & \\ \hline DSTEI & \(size=3\times 3\times 5\) & \(Q=100\) & \(T_{h}=20\) & & \\ Eigen & \(N=28\) & \(\Sigma=3\) & & & \\ MRFMD & \(\beta_{s}=20\) & \(\beta_{p}=10\) & \(\beta_{f}=30\) & \(\alpha=20\) & & \\ \(\Sigma\Delta\) & \(\mu_{t}=3\) & & & & & \\ SOBS & \(n=3\) & \(e_{2}=0.03\) & \(\gamma_{f}=0.07\) & \(\beta_{f}=1\) & \(\tau_{5}=0.1\) & \(\tau_{H}=10\) \\ SWCD & \(N=35\) & \(T_{l}=2\) & \(T_{u}=0.07\) & \(R=0.01\) & & \\ ViBe & \(N=205\) & \(\sigma=20\) & \(\rho=16\) & & & \\ DMD & \(D_{l}=1\) & \(T_{h}=0.25\) & & & & \\ DEU & \(\rho=0.9\) & \(\alpha=0.1\) & & & & \\ GMM & \(\sigma=3.5\) & \(\rho=0.9967\) & & & & \\
**GMBSM** & \(\sigma=1.5\) & \(\phi=0\) & \(\lambda=0.35\) & \(\sigma_{x}=3.25\) & \(\sigma_{y}=1.5\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Background model parameters. False Negative Rate (FNR): This metric measures the proportion of actual positives that are incorrectly identified as negatives. It is calculated as:

\[FNR=\frac{F_{N}}{T_{P}+F_{N}} \tag{13}\]

PWC (Percentage of Wrong Classifications): It represents the percentage of all classifications that were incorrect.