# Background Subtraction for Dynamic Scenes Using Gabor Filter Bank and Statistical Moments
## 3 Materials and Methods
### Segmentation Criteria
\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 & 0.318 & 0.949 & 0.051 & 0.682 & 6.173 & 0.096 & 0.148 \\ DMD & 0.742 & 0.958 & 0.042 & 0.258 & 4.618 & 0.260 & 0.385 \\ DSTEI & 0.645 & 0.949 & 0.051 & 0.355 & 5.340 & 0.088 & 0.155 \\ EigenBS & 0.619 & 0.978 & 0.022 & 0.381 & 4.211 & 0.630 & 0.625 \\ GMM & 0.985 & 0.956 & 0.044 & 0.015 & 4.317 & 0.227 & 0.369 \\ MRFMD & 0.732 & 0.947 & 0.053 & 0.268 & 5.413 & 0.042 & 0.079 \\ SDBE & 0.576 & 0.956 & 0.044 & 0.424 & 5.227 & 0.227 & 0.326 \\ SOBS & 0.997 & 0.979 & 0.021 & 0.003 & 2.016 & 0.640 & 0.779 \\ SWCD & 0.927 & 0.993 & 0.007 & 0.073 & 1.054 & 0.879 & 0.903 \\ ViBe & 0.977 & 0.978 & 0.022 & 0.023 & 2.245 & 0.611 & 0.752 \\
**GMBSM** & **0.829** & **0.991** & **0.008** & **0.171** & **0.271** & **0.736** & **0.780** \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results obtained when evaluating the methods in \(S_{6}\). Figure 13: Percentage of wrong classifications comparison. (**a**) Scene \(S_{3}\); (**b**) Scene \(S_{4}\); (**c**) Scene \(S_{5}\); (**d**) Scene \(S_{6}\). method has good precision regarding positive predictions, its performance is reduced when the images are smaller or difficult to characterize lighting changes. ## 5 Discussion

According to the results obtained in Table 2, only methods such as DEU, DSTEI, and RFMD obtained the objects' contour. The methods DMD, GMM, Sigma-Delta, and SWCD, although they partially preserve the structure of the objects, present loss of information in distant objects and are susceptible to shadows and reflections caused by lighting.From our point of view, the Eigen-Background, SOBS, ViBe, and our GMBSM method provide better results in preserving the object structure, but they cause the loss of information about distant objects. Among them, GMBSM is the best, and the results in Figures 13 and 14 show a lower error percentage and higher accuracy. Nevertheless, distant objects in scenes \(S_{3}\) and \(S_{4}\) will lose information due to the perspective of these scenes. As mentioned in Section 3.2, a larger object in the image requires a higher density Gaussian so that the noise attenuation is greater. Although the object is smaller, it requires a lower frequency response and Gaussian density, producing more noise and possible false contours. This effect is one of the weaknesses of our method because it requires different G functions to be applied to the scene. This will increase the execution time and the complexity of adjusting the parameters. The advantages of our method are that (i) the representation of an object whose texture is almost the same as its environment, (ii) it can recover quickly when the object in motion remains stationary, (iii) according to experiments, it exhibits invariance to light changes, and (iv) it allows the analysis of texture levels to obtain different texture details. However, it also has disadvantages: (i) the proper selection of the size of \((G_{\lambda,\theta,\phi})\) depends on the size of the objects in the scene, (ii) experience is required to select the appropriate filter parameters and finally, and (iii) the suggested threshold is not the best method because it depends on the variance of the data, and in the absence of objects, it will only produce noise. These issues are being considered for future work, as well as improvements to the method. ## 6 Conclusions

We introduced a background subtraction technique that leverages texture-level analysis through the integration of a Gabor filter bank and statistical moments. This approach is differentiated by its capacity to distinguish between foreground and background entities in dynamic scenes, a critical challenge where traditional methods often need to improve. Our method has demonstrated superior performance in maintaining the structural integrity of the objects while effectively addressing gradual changes in lighting, shadows, and scenarios with nearly uniform environmental textures.