## 3 Results
### Selection of Optimal Block Arrangement and Combination Scheme  
By taking the AR data as an example, the AR face database subset [22], comprising 50 males and 50 females, contains 2600 images in total. In the experiment, eight images without facial occlusion, such as smiling and not smiling, and brightness changes were selected as training samples for each object. Moreover, three face images covered by sunglasses and three face images covered by scarves were selected as test samples for each object. A total of 100 objects were selected. References [14; 17; 18; 20; 21; 25] were selected for this experiment, and the images, with a resolution of 165 \(\times\) 120 pixels, were downsampled to 15 \(\times\) 10 pixels, 20 \(\times\) 15 pixels, and 25 \(\times\) 20 pixels for experiments. The occluded face image contains face information and non-face information. Since the distribution of non-face information cannot be perceived in advance by algorithms, it is difficult to distinguish between face information and non-face information. Figure 2 shows a part of the occluded face images from the AR subset. In this paper, the block arrangement method was adopted. All the blocks were arranged, combined, and finally compared to the residual values of each scheme to determine the final arrangement (see Figures 3-5). During this process, the approximate position of the obstructions, such as sunglasses or scarves, was determined. Considering the amount of computation, when taking three blocks in the five-block image as an example, the number of permutation schemes was 10. Only the horizontal block combination is shown in the figure, but the vertical block is also considered. The residual calculation of the arrangement of scheme h is shown in Figure 5, and Figure 6 shows the minimum residuals of face images involving sunglasses with different permutations. Figure 2: Faces from the AR subset occluded by sunglasses and scarves: (**a**) face images occluded by sunglasses; (**b**) face images occluded by scarves [Reprinted with permission from Elsevier [20]. Copyright 2013, Neurocomputing]. Figure 4: Arrangement and combination scheme of a certain test sub-image (involving sunglasses) in the third group: (**a**) reserved block 1, 2, 3; (**b**) reserved block 1, 2, 4; (**c**) reserved block 1, 3, 4; (**d**) reserved block 2, 3, 4; (**e**) reserved block 1, 2, 5; (**f**) reserved block 1, 3, 5; (**g**) reserved block 2, 3, 5; (**h**) reserved block 1, 4, 5; (**i**) reserved block 3, 4, 5 [Reprinted with permission from Elsevier [20]. Copyright 2013, Neurocomputing]. Figure 5: Residual calculation of arrangement scheme h (sunglasses occluding the face). [reprinted with permission from Elsevier [20]. Copyright 2013, Neurocomputing]. Figure 3: Permutation scheme for the third group of training sub-images: (**a**) reserved block 1, 2, 3; (**b**) reserved block 1, 2, 4; (**c**) reserved block 1, 3, 4; (**d**) reserved block 2, 3, 4; (**e**) reserved block 1, 2, 5; (**f**) reserved block 1, 3, 5; (**g**) reserved block 2, 3, 5; (**h**) reserved block 1, 4, 5; (**i**) reserved block 2, 4, 5; (**j**) reserved block 3, 4, 5 [Reprinted with permission from Elsevier [20]. Copyright 2013, Neurocomputing]. It can be seen from Figure 4 that this group retains 60% of the image information, and the sunglasses part was removed in scheme h. The distance between the test sample and the subspace projected by all training samples of an object was considered as the basis for the selection of the scheme. It can be seen from Figure 6 that the residual value of scheme h (preserved block positions one, four, and five) was the smallest. This means that the reorganized training samples in Figure 3h were constructed as an optimal linear model to predict the category of the test image in Figure 4h. Thus, the prediction result of scheme h was selected at this time.