# Changed Detection Based on Patch Robust Principal Component Analysis
###### Abstract  
Change detection on retinal fundus image pairs mainly seeks to compare the important differences between a pair of images obtained at two different time points such as in anatomical structures or lesions. Illumination variation usually challenges the change detection methods in many cases. Robust principal component analysis (RPCA) takes intensity normalization and linear interpolation to greatly reduce the illumination variation between the continuous frames and then decomposes the image matrix to obtain the robust background model. The matrix-RPCA can obtain clear change regions, but when there are local bright spots on the image, the background model is vulnerable to illumination, and the change detection results are inaccurate. In this paper, a patch-based RPCA (P-RPCA) is proposed to detect the change of fundus image pairs, where a pair of fundus images is normalized and linearly interpolated to expand a low-rank image sequence; then, images are divided into many patches to obtain an image-patch matrix, and finally, the change regions are obtained by the low-rank decomposition. The proposed method is validated on a set of large lesion image pairs in clinical data. The area under curve (_AUC_) and mean average precision (_mAP_) of the method proposed in this paper are 0.9832 and 0.8641, respectively. For a group of small lesion image pairs with obvious local illumination changes in clinical data, the _AUC_ and _mAP_ obtained by the P-RPCA method are 0.9893 and 0.9401, respectively. The results show that the P-RPCA method is more robust to local illumination changes than the RPCA method, and has stronger performance in change detection than the RPCA method. c 2022  
However, due to the different imaging conditions, it is difficult to remove the illumination variations on image change detection only by preprocessing, which makes it necessary for the detection algorithm to be robust to illumination. Recently, many researchers have used supervised learning methods to detect changes, and although these methods are robust to complex intensity, they requires a large amount of labelled data [12; 13; 14]. For medical image pairs, it is impossible to use supervised methods because of the great variations of change regions and a few available training samples. In the past, most unsupervised change detection algorithms focused on comparing the image pairs pixel wisely such as the method based on image difference or image quotient [11; 15; 16]. However, nonuniform illumination is very common in retinal imaging [17], and the pixel-by-pixel comparison method is frangible to the illumination variations between the images, which immensely challenges intensity normalization techniques. Many researchers have put great efforts to designing various models to deal with illumination [5]. The iterative robust homomorphic surface fitting (IRHSF) was especially conceived to model the illumination for the fundus image by calculating the curvature of the retinal surface [11], which can correct the intensity of the image well, but the change regions are still distracted obviously by the illumination variation. Change detection methods based on background modeling have been proposed in recent years [10; 18] whose core idea stems from video surveillance [19]. For longitudinal fundus images, the anatomic structures with the illumination together are modeled as the background, and only the interested change regions are kept as the foreground [10; 18]. For the fundus image pair, the normal anatomical structures evolve slowly and change little over time, which can be regarded as the background model. In order to obtain an invariant background, the illumination variations between the image pair are filtered as the unimportant change after intensity normalization and linear interpolation, so that they are removed from the background model and change regions as the reconstructed error by low-rank decomposition. In order to remove the distraction of intensity from the background model and change regions, [PERSON] et al.