# Changed Detection Based on Patch Robust Principal Component Analysis
## 3 Methodology
### Algorithm and Flow Chart
The red circle marks the distraction of flare in the current image for the RPCA method. obvious, but the light spot in the reference image significantly distracts the change region as the red circle marks. For the image pair with large lesions, padding the boundary of the image to let the size be \(600\times 400\) and linearly interpolating the image pair to be of 23 frames. Then, the size of patch is set to be 200 and divide the image into six patches. The image sequence is turned into 138 frames, and the concatenated image matrix \(D^{\prime}\) is of size 40,000 \(\times\) 138. Figure 6 presents the results of a low-rank decomposition on \(D^{\prime}\). Compared with the detected change features in Figure 6, the result in Figure 6 obtained by P-RPCA is clearer and cleaner, which reduces the distraction of illumination change and camera position movement. ### Discussion

The proposed method is validated from the quantitative evaluation on the ROC curve and PR curve in this section. The ground truth of the change detection is given in Figure 7. The ground truth is artificially marked. The result of the P-RPCA method in the following curves is obtained with the appropriate size by experiments. The curves from the image pair with small lesions and a big lesion are given in Figures 8 and 9 separately. The four indexes are calculated through statistical analysis of each pixel in the image. Among them, true positive means detecting the correct positive sample, and false positive means the false detection is a true negative sample, and so on. Figure 3:0 The result of the image with large lesions by RPCA method. (**a**) Normalized reference image; (**b**) normalized current image; (**c**) reconstructed low-rank background by RPCA; (**d**) reconstructed low-rank background by P-RPCA; (**e**) sparse change region by RPCA; and (**f**) sparse change region by P-RPCA. The red circle marks the distraction of the light spot in the reference image for the RPCA method. Figure 3:1 Ground truth of the image pair with small lesions and big lesions. (**a**) Big lesions; and (**b**) small lesions. For the image pair with small lesions, four change detection techniques are used to prove the performance of the proposed methods, as illustrated in Figure 3:2 RPCA, IRG-McS [33], NPSG [34], and P-RPCA. The RPCA method performs poorly in the face of local flare and the result is significantly distracted, whilst the AUC and mAP are 0.9213 and 0.0077, respectively, which is far lower than 0.9989 and 0.9614 for P-RPCA. In Figure 8, both the ROC and PR of P-RPCA are over the curves of the other three methods, which means that P-RPCA is significantly better than the other methods. For the image pair with the large lesion, five change detection techniques from the remote sensing are introduced here: IRHSF difference [11]; mean difference [16]; logarithmic quotient [16]; wavelet fusion [16]; IRG-McS [33]; and NPSG [34]. As shown in Figure 9, the AUC and mAP are 0.9832 and 0.8641, respectively, for RPCA, while 0.9893 and 0.9401 for P-RPCA. As can be seen from the curve in Figure 9, the performance of the P-RPCA method exceeds RPCA method on almost all thresholds, and far exceeds other algorithms. Figure 10 presents the detection results of the different method under the image pair with small lesions shown in Figure 3:3 For RPCA, the local flare significantly distracts the

Figure 3:4 ROC and PR curve results of the image pair with small lesions. (**a**) PR curve; and (**b**) ROC curve. Figure 3:5 ROC and PR curve results of the image pair with a large lesion. (**a**) PR curve; and (**b**) ROC curve. change regions and so does IRG-McS as shown in Figure 10b,d. IRG-McS presents the obvious change regions as the red rectangle marks but is very sensitive to the other facts such as the intensity of the optic disc. P-RPCA is obviously better than the other three methods as Figure 10 illustrates.