# A Robust Image Watermarking Scheme Based on SVD in the Spatial Domain
## 5 Experimental Results and Performance Analysis
### Algorithmic Complexity Analysis  
To test the algorithmic complexity, the computational time of the proposed spatial domain watermarking scheme is calculated. In addition, we also perform the proposed watermarking scheme in the SVD domain. Unlike the proposed scheme implemented in the spatial domain, it embeds the watermark information into the largest singular values in the SVD domain. Table 5 lists the average computational times of the proposed watermarking scheme and the other two SVD domain watermarking schemes in references [8; 14]. To make the conclusions more reliable, we conduct this comparison experiments under the same test conditions. The experiments are performed in the MATLAB R2012a environment and on a 3.10 GHz computer with 6 GB memory. It can be observed  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Attack** & **[PERSON] et al. [8]** & **[PERSON] and [PERSON] [14]** & **The Proposed** \\ \hline PSNR (dB) & 21.14 & 39.26 & 48.99 \\ No Attack & 0.9882 & 0.9803 & 1 \\ Salt and Pepper Noise (0.001) & 0.8918 & 0.8290 & 0.9910 \\ Salt and Pepper Noise (0.005) & 0.6257 & 0.5150 & 0.9595 \\ Gaussian Noise (0, 0.0001) & 0.9524 & 0.9300 & 0.9663 \\ Gaussian Noise (0, 0.0005) & 0.8347 & 0.7731 & 0.6936 \\ Speckle Noise (0.0001) & 0.9783 & 0.9657 & 0.9939 \\ Speckle Noise (0.0005) & 0.9430 & 0.9118 & 0.8316 \\ Median Filter (3 \(\times\) 3) & 0.1548 & 0.5221 & 0.7897 \\ Average Filter (3 \(\times\) 3) & 0.1756 & 0.4552 & 0.7469 \\ Image Sharpening & 0.8547 & 0.7921 & 0.9138 \\ JPEG (\(Q\) = 90) & 0.9425 & 0.9733 & 1 \\ JPEG (\(Q\) = 80) & 0.8853 & 0.9566 & 0.9952 \\ JPEG (\(Q\) = 70) & 0.8340 & 0.9168 & 0.9621 \\ Rescaling (2, 0.5) & 0.7447 & 0.9582 & 0.9552 \\ Rescaling (0.5, 2) & 0.2080 & 0.8135 & 0.8497 \\ Cropping (top 25\%) & 0.2802 & 0.4705 & 0.6848 \\ Cropping (middle 25\%) & 0.3387 & 0.2955 & 0.6393 \\ Cropping (right 25\%) & 0.3987 & 0.0192 & 0.8414 \\ \hline \hline \end{tabular}
\end{table}
Table 4: NCC values of the extracted watermarks in image Barbara under different attacks.  
Figure 8: Robustness comparisons for host image Barbara: (**a**) No attack; (**b**) Salt and pepper noise (0.001); (**c**) Salt and pepper noise (0.005); (**d**) Gaussian noise (0, 0.0001); (**e**) Gaussian noise (0, 0.0005); (**f**) Speckle noise (0.0001); (**g**) Speckle noise (0.0005); (**h**) Median filter (3 \(\times\) 3); (**i**) Average filter (3 \(\times\) 3); (**j**) Image sharpening; (**k**) JPEG (\(Q\) = 90); (**l**) JPEG (\(Q\) = 80); (**m**) JPEG (\(Q\) = 70); (**n**) Rescaling (2, 0.5); (**o**) Rescaling (0.5, 2); (**p**) Cropping (top 25%); (**q**) Cropping (middle 25%); (**r**) Cropping (right 25%).  
from Table 5 that the proposed spatial domain watermarking scheme has much lower execution times than the proposed scheme implemented in the SVD domain. Compared with the other two watermarking schemes in references [8; 14], the computational complexity of the proposed spatial domain watermarking scheme is also reduced. The reason is that the proposed method avoids the forward and inverse SVD transforms used in the SVD domain watermarking schemes.