# Changed Detection Based on Patch Robust Principal Component Analysis
## 3 Methodology
### Algorithm and Flow Chart
(**a**) Reference image from DRIVE; (**b**) current image attached with the small noise patch; (**c**) corrected images of (**a**) by IRHF; (**d**) corrected images of (**b**) by IRHF; (**e**) illumination model of (**a**); (**f**) illumination model of (**b**). (**g,h**) are from Xinhua Hospital in Shanghai. (**g**) Reference image, (**h**) current image, (**i**) corrected images of (**g**) by IRHF, (**j**) corrected images of (**h**) by IRHF, (**k**) illumination model of (**g**), (**l**) illumination model of (**h**). \[Recall=\frac{TP}{TP+FN} \tag{15}\]

where \(TP\), \(FP\), \(TN\), and \(FN\) indicate true positive, false positive, true negative, and false negative, respectively. ### Results with P-RPCA Method

For P-RPCA, strictly dividing the image may not be applicable for change regions of different sizes. Hence, a sliding window with overlap is a more flexible technique than the strict division for the change detection. The P-RPCA with a sliding window is taken to improve the performance of the proposed method. After the size and stride of the sliding window are set, the slide window sweeps across the first frame of the sequence and produces many overlap subsequences with the same size. By concatenating all the subsequences together and vectorizing them, an patch image matrix is obtained. By the sliding window, the content of many patches may be redundant, which is useful to produce a consistent low-rank background and filter the local light spots well [18]. The algorithm is practiced on two groups of data shown in Figure 4. The image pair with small lesions has a resolution of \(604\times 584\) as shown in Figure 4a,b. Figure 1 presents the registered and normalized image pairs. Figure 5 gives the detection result of the low-rank decomposition by RPCA and P-RPCA after normalization and linear interpolation. Figure 5c,d are the reconstructed low-rank background by RPCA and P-RPCA, respectively, and Figure 5e,f are their sparse change regions given by RPCA and P-RPCA, respectively. The red circle in Figure 5e marks the local flare distraction. For the image pair with small lesions, as shown in Figure 5, P-RPCA with a sliding window is used to detect the change regions. Through several attempts to choose different sizes of equal intervals for the experiments, the appropriate size of the sliding window was set to be 200 and the stride was set to be 50. It can be seen that compared with the detected change features in Figure 5e,f these are less distracted by the local light spot and the detected change features are clearer. The red mark in Figure 5e is caused by the local flare. Furthermore, in Figure 5f, this distraction is greatly reduced. The change regions obtained by P-RPCA method obtain less distractions by the local flare and are clearer and cleaner than those by RPCA. The image pair with a big lesion has a resolution of \(403\times 384\). In Figure 6, (a) and (b) are the normalized reference image and the current image, respectively, after registration, and (c) and (d) are the reconstructed background image by RPCA and P-RPCA, respectively. Figure 6e is the result obtained by the image matrix and low-rank decomposition after linear interpolation. The image pair from Figure 4g,h is corrected by IRHSF and normalized to each other, and then it is expanded to a sequence. For the reference image, the number of interpolated frames is 20 in order to obtain a stable background, and for the current image, the number of interpolated frames is 3. The image sequence after interpolation includes 23 frames and each image frame has a size of \(403\times 384\). The concatenated image matrix \(D\) has a size of \(154752\times 23\). It can be seen that the features of the isolated large lesions are

Figure 5: The result of the image with small 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 regions by RPCA; and (**f**) sparse change regions by P-RPCA.