# Robust Background Subtraction via the Local Similarity Statistical Descriptor
## 3 Background Modeling
### Foreground Detection
For the box left on the floor, which should considered as foreground and never be absorbed into the background model, we observed that in LOBSTER, ViBe and GMM, the box eroded as time went on, creating false negatives, while our method maintained a lower absorption rate. In the copyMachine sequence, we can see a similar phenomenon to the sofa sequence. The segmentation results of other methods are not as good as ours. Lastly, in the library sequence from thermal, most of the methods obtain a perfect segmentation result except GMM. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **Recall** & **Specificity** & **FPR** & **FNR** & **PWC** & **Precision** & **F-Measure** \\ \hline GMM [4] & 0.6964 & 0.9845 & 0.0155 & 0.3036 & 3.1504 & 0.7079 & 0.6596 \\ KDE [7] & 0.7442 & 0.9757 & 0.0243 & 0.2558 & 3.4602 & 0.6843 & 0.6719 \\ ViBe [20] & 0.6681 & 0.9869 & 0.0130 & 0.3318 & 2.7265 & **0.8426** & 0.7074 \\ SOBS [12] & 0.8017 & 0.9831 & 0.0169 & 0.1983 & 2.4081 & 0.7315 & 0.7283 \\ PSP-MRF [14] & 0.8037 & 0.9830 & 0.0170 & 0.1963 & 2.3937 & 0.7512 & 0.7372 \\ LOBSTER [26] & 0.7658 & **0.9904** & 0.0125 & 0.2341 & 2.3409 & 0.8016 & 0.7481 \\ PBAS [33] & 0.7840 & 0.9898 & **0.0102** & 0.2160 & **1.7693** & 0.8160 & 0.7532 \\
**LSSD** & **0.8609** & 0.9800 & 0.0199 & **0.1390** & 2.4817 & 0.7771 & **0.7924** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the results on the CDnet2012 dataset by different methods. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Method** & **Baseline** & **CameraJ** & **Dynamic** & **Intermittent** & **Shadow** & **Thermal** & & **Overall** \\  & **FM** & **FM** & **FM** & **FM** & **FM** & **FM** & **Re** & **Pr** & **FM** \\ \hline LOBSTER & 0.9320 & 0.7462 & 0.5664 & 0.5940 & 0.8696 & 0.7803 & 0.7658 & **0.8016** & 0.7481 \\ LSSD & **0.9361** & **0.7803** & **0.7442** & **0.6094** & **0.8714** & **0.8134** & **0.8609** & 0.7771 & **0.7924** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Per-category average F-Measure comparisons between LOBSTER and LSSD with respect to the CDnet2012 dataset. ### Processing Speed and Memory Usage

Background subtraction is often the first step in many vision applications. Processing speed and memory usage are critical items of information for researchers to consider before choosing which method to use. Thus, we give a detailed analysis of the time and space complexity of our method in this section. The computational speed of our method is investigated with different size sequences coming from the CDnet2012 dataset [28]. Our method has been implemented in C++ and uses the OpenCV [34] image processing library. All the experiments are carried out on a 4.2-Ghz Intel Core-i7 7700 K with 32 GB RAM and a Windows 10 operating system. The results are reported in Table 6. Although the combination of color features and texture features will increase the computational complexity, we can see that our algorithm also achieves the real-time performance. Since our method operates at the pixel level, it has the potential for hardware implementation or high-speed parallel implementation. Figure 11: Qualitative performance comparison for various sequences (highway, traffic, fall, sofa, copyMachine and library, from top to bottom), reproduced with permission from [28], Copyright Mitsubishi Electric Research Laboratories, Inc., 2012. The first column is the input image, the second column is the corresponding ground-truth, gray pixels in the ground-truth indicate pixels which are not of interest, the third column shows the segmentation results of our method, the fourth column represents the segmentation results of the LOBSTER [26], the fifth column is the segmentation results of the ViBe [20], and the last column shows the output of the GMM [4] segmentation. As for the memory usage of our method, considering the size of the input image is \(W\times H\), the background model sample of each pixel is \(N\), and we find that the space complexity of our method is \(\mathcal{O}(NWH)\).