## 4 Experiments
### Experiments' Results
#### 4.4.1 Qualitative Evaluation  
For qualitative evaluation, the repeated pattern grids generated by the proposed method and other SOTA methods are presented in Figures 8 and 9, respectively, for scanned images of actual fabrics and computer-generated design images. Fabric images are typical fronto-parallel images with repeated patterns; most of them have rich texture information (see Figure 8). With the proposed method, repeated patterns were perfectly detected on these images, especially fabric images with dense patterns (columns 2 and 3 in Figure 8). The proposed method also performed well on fabric images with multiple design elements (columns 5 and 6 in Figure 8). Moreover, the image in column 7 was with many small  
Figure 7: Example of pre-processing for image regularization [2].  
wrinkles and shadows, and an accurate detection result was obtained by the proposed method without pre-processing. It demonstrated the robustness of the proposed method.  
[PERSON] et al. [12] (row (d) in Figure 8) leveraged almost all the CNN filters' information, and acceptable results were achieved on most of the images. Although their detection results are not exactly the minimal repeated patterns (see columns 2, 3, 4, and 7 in Figure 8), they are indeed repetitive patterns that can be tiled to recover the input images. Furthermore, their detection results are more accurate than those of [2] (row (c) in Figure 8) and the approach leveraging SIFT [7] (row (e) in Figure 8). The main difference between [PERSON]'s and [PERSON]'s work is that [PERSON] introduced filter selection while [PERSON] had used all the filter results. As a result, about one-third less filters were used in [PERSON] et al.'s [2] model than that in [PERSON] et al.'s [12], and comparatively less accurate detection results were generated. SIFT is a local image feature descriptor that does not consider global or hierarchical image information, and the results are less satisfactory in most of the example images. On the other hand, [PERSON] and [PERSON] [17] and [PERSON] et al. [15] had the worse results. In particular, [PERSON] and [PERSON] [17] only leveraged template matching, they set a relatively fixed size for template patches and chose the highest similarity value as the threshold on the \(x\) and \(y\) directions, respectively, and thus their method was less robust and easily confused by image texture. The results also demonstrate the superiority of deep feature-based methods in repeated pattern detection.  
Computer-generated design images are almost noise-free images. Although some have complex design content, most methods performed better in this category than actual fabric  
Figure 8: Qualitative comparison for processing _actual fabric scan_ images (along different columns) from results of (**a**) [PERSON] and [PERSON] [17], (**b**) [PERSON] et al. [15], (**c**) [PERSON] et al. [2], (**d**) [PERSON] et al. [12], (**e**) SIFT [7], (**f**) the ground truth, and (**g**) the proposed method, respectively.  
scan images (see Figure 9). Comparatively, the performance of [PERSON]'s, [PERSON]'s, and SIFT-based methods degraded for images with a large number of small and similar design elements, namely motif patterns (see columns 2 to 4 in Figure 9), but were reasonably good for check designs (columns 5-7). The detection results of [15; 17] in Figure 9 again were unsatisfactory as they could only detect relatively simple patterns and the output repeat sizes were not the smallest. For the computer-generated design images, the proposed method again outperformed all other methods.