# Changed Detection Based on Patch Robust Principal Component Analysis
## 3 Methodology
### Algorithm and Flow Chart
Figure 11 presents the detection results of a different method for the image pair with the large lesion shown in Figure 3:6 Compared with Figure 11e-g, Figure 11a,b are more robust to the local illumination variations and less affected by the vascular tissue. In Figure 11d, the result is evidently significantly distracted by the boundary. The result in Figure 11a is clearer and cleaner than in Figure 11b and less distracted by the light spot in the reference image. Figure 12 shows the influence of IRHSF on AUC and mAP values. The dataset used in the experiment is the image pair with small lesions. When intensity correction methods are not used, the AUC and mAP are 0.9981 and 0.957, respectively. After using intensity correction methods, such as IRHSF, the AUC and mAP are 0.9989 and 0.9614, respectively. This shows that after using the intensity correction method to correct global illumination variations for the image pair, change regions detected by P-RPCA method are more accurate. Figure 3:7 Detected change region for the image pair with the big lesion in Figure 3:8 (**a**) P-RPCA; (**b**) RPCA; (**c**) NPSG; (**d**) IRG-McS; (**e**) logarithmic quotient; (**f**) mean difference; (**g**) wavelet fusion; and (**h**) IRHSF difference. Figure 3:9 Detected change region for the image pair with small lesions in \[TPR =\frac{TP}{TP+FN} \tag{12}\]0 (**a**) P-RPCA; (**b**) RPCA; (**c**) NPSG; and (**d**) IRG-McS. The red rectangle marks the small change regions. Figure 13 shows the influence of patch size on AUC and mAP values in the P-RPCA method. The dataset used in the experiment is the image pair with small lesions. The blue line, the orange line, the green line, and the red line indicate that the size of the patch is taken as 50, 100, 200, and 300, respectively. When the size of the patch is taken as 200, the AUC and mAP obtain the maximum value, which is 0.9989 and 0.9614, respectively. Figure 14a-d show the change detection results of the image pair when the patch size in the P-RPCA method is 50, 100, 200, and 300, respectively, and the detection results are shown in red circles. Hence, for the image pair with small lesions, the size of the patch selected by the P-RPCA method is 200. As the size of the sliding window will affect the result of change detection, we repeat the experiment by changing the size to obtain the best value for different image pairs. If the sliding window is too small, it is difficult for the method to detect the change regions. If the sliding window is too big, the method will only weakly reduce the distraction due to local illumination variations. \[TPR =\frac{TP}{TP+FN} \tag{12}\]1 Influence of IRHSF on AUC and mAP values. (**a**) PR curve, (**b**) ROC curve. \[TPR =\frac{TP}{TP+FN} \tag{12}\]2 Influence of patch size on AUC and mAP values in the P-RPCA method. (**a**) PR curve, (**b**) ROC curve. Generally, when there are fewer frames in the sequence, the background of the sequence is more susceptible to illumination variations since the single background frame is complicated to correct to the variable illumination variations of the current frames. Linear interpolation reduces the global illumination variation between the successive frames and makes the intensity slowly change in the sequence. The global illumination variation becomes smooth so that it can be filtered as the reconstruction error when the sequence is decomposed into a low-rank component and the sparse component, which is the advantage of RPCA. P-RPCA further reduces the distraction of illumination variation by dividing the sequence into several subsequences and decomposes the concatenated subsequences which is more robust than RPCA. ## 5 Conclusions

For the change detection of the retinal fundus image pair, the method based on P-RPCA is proposed in this paper which is the improved version to matrix RPCA. Decomposing the image matrix by patches can deal with both the global and local illumination and is more robust for the distraction of the illumination variations than RPCA and obtains clearer change regions.