# Robust Image Watermarking in Spatial Domain Utilizing Features Equivalent to SVD Transform
## 4 Experimental Results Discussion
### Comparison with Similar Schemes  
This section compares the proposed watermarking scheme with other related watermarking schemes, as presented by [PERSON] et al. [48], [PERSON] et al. [49], [PERSON] et al. [50], [PERSON] et al. [47], and [PERSON] et al. [26]. The schemes selected for the comparison in this study are denoted by scheme1, scheme2, scheme3, scheme4, and scheme5 respectively in Figures 10-13. The reason behind the selection of the schemes is that all these schemes have, in some way or another, utilized an idea that is similar to the proposed scheme. The imperceptibility of the schemes was compared by calculating the average of the imperceptibility measurements of all watermarks for each host image, and the findings are shown in Figures 10 and 11 with the help of bar charts. From these Figures, it can be observed that the _PSNR_ and _SSIM_ values achieved by the proposed watermarking approach are relatively better than those achieved by the other approaches in most cases. The scheme proposed by [PERSON] et al. [49] is second best in terms of imperceptibility. The proposed scheme's average PSNR and SSIM are also greater than those of competing schemes.  
Figure 8: Average BER values corresponding to each image, taking all the attacks.  
Figure 7: Average NCC values corresponding to each image, taking all the attacks.  
Figure 9: _Cont._  
Figure 11: Average _SSIM_ over all the watermarks and all the attacks corresponding to each image.  
Figure 10: Average _PSNR_ over all the watermarks and all the attacks corresponding to each image.  
Figure 9: Extracted watermarks from watermarked images corresponding to various distortion attacks.  
To evaluate the robustness of the schemes, the average NCC values for all test images and all watermarks corresponding to each attack were calculated and are reported in Figure 12. The results of using a similar approach to determine the _BER_ are shown in Figure 13. A close examination of these Figures reveals that, for attack _indices_ 2, 11, and 12, which are rotation, row flipping, and column flipping, respectively, the performance of the other schemes is noticeably worse than the proposed scheme. The proposed watermarking scheme's ability to retrieve the watermarks exactly as they were inserted is demonstrated by the _NCC_ values of 1 and _BER_ values of 0 in the cases of 90-degree rotation and row and column flipping (_index_2, _index_11, and _index_12). Similarly, in the other instances, the proposed scheme performed reasonably well compared to the alternative schemes. In a few instances, such as _indices_ 1, 3, and 7, it did not perform as expected, requiring further investigation into the causes of its failure to meet expectations.  
Schemes were also compared based on their computational time in terms of embedding and extraction times, and they are provided in Table 6. The basic purpose of copyright protection watermarking schemes is to demonstrate ownership regardless of time. Therefore, this is not a vital element in these situations; however, it cannot be ignored in broadcast monitoring when embedding and extraction are conducted live. In Table 6, it is evident that the computational complexity of the proposed scheme is greater than the other schemes but comparable to the scheme provided by [PERSON] et al. [49] and is less than the scheme proposed by [PERSON] et al. [26]. This is due to the time required to redistribute the pixels in the image to their new locations in order to obtain singular values that are invariant.  
Figure 12: Average NCC over all watermarks and all images corresponding to each attack.  
Figure 13: Average _BER_ over all watermarks and all images corresponding to each attack.  
The proposed scheme achieved better imperceptibility and robustness at the cost of high complexity. Hence, reducing the complexity of this approach may be a future study topic.