## 3 Results and Discussion
### Road_Analysis of Vehicle Image Experiment Results  
In this dataset, the image mainly includes road, grass, trees, soil, cars, and other ground objects, of which three smaller objects on the road are abnormal objects, and the rest are background components. \(\Lambda\) is set to \(10^{-6}\) for the regularization parameter in the collaborative representation. The parameters in the improved trilateral filtering \(\sigma_{\text{sedw}}\), \(\sigma_{\text{svdw}}\), and \(\sigma_{\text{Lgd}}\) are set to be 5, 5, and 5. The size of the inner and outer windows, \(W_{\text{in}}\) and \(W_{\text{out}}\), are 7 and 9, and the threshold \(th\) is set to be 0.3. Results and discussion  
The experimental results on this dataset are shown in Figure 11. The true value diagram of the abnormal object is shown in Figure 11, and the detection results of the comparison algorithms and the algorithm of this paper are shown in Figure 11b-i. In Figure 11, all algorithms do not miss the abnormal detection. In the detection diagram of the RX and RPCA-RX algorithms, the detection effect of the abnormal objects in the middle is not obvious. At the same time, the RX, LRX, WSCF, RPCA-RX, and KIFD algorithms have more obvious yellow highlights on the right side of the image, indicating the obvious false alarm. The object detection effect of the LRASR algorithm is good, but there are some background residues on the left side of the image. The background suppression effect of  
Figure 8: Experiment results of the Saliens_Synthetic dataset. Graph of true abnormal object **(a)**; RX **(b)**; LRX **(c)**; CRD **(d)**; WSCF **(e)**; RPCA-RX **(f)**; LRASR **(g)**; KIFD **(h)**; ours **(i)**. the KIFD algorithm is poor, and the object detection is not obvious. In the detection results of the CRD algorithm and the algorithm of this paper, the obvious false alarm phenomenon on the right side of the image and the background residual phenomenon on the left side are better than other algorithms. The object shape in the CRD algorithm is significantly different from the real object, and the contour shape of the object detected by the algorithm of this paper is closer to the contour shape of the real object in the truth map. Figure 10: ROC curve of the Saliens_Synthetic dataset. ROC curves (**a**); Enlarged image of the top left of ROC curves (**b**). Figure 9: Three-dimensional grid detection results of the Saliens_Synthetic dataset. Graph of true abnormal object (**a**); RX (**b**); LRX (**c**); CRD (**d**); WSCF (**e**); RPCA-RX (**f**); LRASR (**g**); KIFD (**h**); Ours (**i**). Figure 12a-i shows the 3D grid corresponding to the real abnormal object and the detection results of all the algorithms. In Figure 12, it can be clearly seen that the amplitude of the abnormal object position in the middle is small in the detection results of the RX and RPCA-RX algorithms, indicating that the detection effect is not good. In the detection results of the RX, WSCF, and RPCA-RX algorithms, the residual parts of the road near the abnormal object are obvious. The LRASR algorithm can detect three abnormal objects well, but there are some background residues at the edge of the image. The overall amplitude of the KIFD algorithm detection result is large, indicating poor background suppression. The right part of the detection results of the RX, LRX, and WSCF algorithms has a large numerical peak, corresponding to the relatively significant false alarm. The amplitude of the three objects is large for the algorithm of this paper. The false alarm and background residues are relatively small. The results of all the algorithms are further analyzed and evaluated quantitatively. The corresponding ROC curves are shown in Figure 13, and the corresponding AUC values are shown in Table 3. It can be seen from the enlarged part in the upper left corner of Figure 13 that the detection probability of the algorithm of this paper and LRASR algorithm is higher