# Improving DFT-Based Image Watermarking Using Particle Swarm Optimization Algorithm
## 5 Experimental Results and Discussion
### Analysis and Discussion  
From the experimental results shown in Sections 5.1 and 5.2 which are performed in terms of imperceptibility and robustness, respectively, we view several benefits in the use of PSO algorithm to optimize the 2D DFT-based watermarking that employs spread spectrum modulation DS-CDMA. The first one is related to the use of the VIF metric in the fitness function of PSO, because as is known in the literature, the VIF value reflects perceptual distortions more precisely than PSNR. The major benefit in terms of visual quality is obtained in flat regions of digital images, where usually the conventional DFT-based watermarking causes a noise effect by considering a fixed value of watermark strength and the middle frequency bands in the magnitude of DFT to all images in a dataset. In this research a priori we known the fix \begin{table}
\begin{tabular}{c c c} \hline \hline
**Distortion** & \
\begin{tabular}{c} **Average** \\ **BCR PSO-DFT** \\ \end{tabular} &
\begin{tabular}{c} **Average** \\ **BCR Conventional DFT** \\ \end{tabular} \\ \hline Rotation by 45\({}^{\circ}\) with auto-crop & 0.98 & 0.96 \\ Rotation by 135\({}^{\circ}\) with auto-crop & 0.97 & 0.92 \\ Resizing, scaling factor = 0.6 & 0.96 & _0.77_ \\ Resizing, scaling factor = 2 & 0.99 & 0.99 \\ Central cropping 120 \(\times\) 120 & 0.98 & 0.97 \\ Translation \(x=100\), \(y=100\) & 0.96 & 0.96 \\ Affine [0.9,0.2,0.0,1.1,2,0.0,0,1] & 0.99 & 0.98 \\ Shearing (0, 20\%) & 0.99 & 0.99 \\ Aspect Ratio (1.0, 1.2) & 0.99 & 0.97 \\ Aspect Ratio (0.8, 1.0) & 0.99 & 0.98 \\ JPEG70 + Rotation by 55\({}^{\circ}\) with auto-crop & 0.90 & 0.87 \\ JPEG70 + Rotation by 115\({}^{\circ}\) with auto-crop & 0.89 & 0.85 \\ JPEG70 + Resizing, scaling factor = 0.6 & 0.92 & 0.76 \\ JPEG70 + Resizing, scaling factor = 2 & 0.95 & 0.93 \\ JPEG70 + cropping 35\% with re-scaling & 0.81 & 0.76 \\ JPEG70 + Translation \(x=100\), \(y=100\) & 0.87 & 0.85 \\ JPEG70 + Affine [0.9,0.2,0.0,1.1,2.0,0,0,1,1] & 0.97 & 0.96 \\ JPEG70 + Shearing (20\%, 0) & 0.96 & 0.96 \\ JPEG70 + Aspect Ratio (1.0, 1.2) & 0.97 & 0.95 \\ JPEG70 + Aspect Ratio (0.8, 1.0) & 0.98 & 0.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Average BCR against geometric manipulations and combined attacks composed by JPEG QF = 70 + geometric distortions. values of a pair of radiuses \(r_{1}\), \(r_{2}\), and the watermark strength \(\alpha\), based on our conventional DFT-based proposal reported in [6], all obtained in an experimental form. The second one is related to the five attacks used in the fitness function of PSO: centered cropping of 100 \(\times\) 100 for images with spatial resolution of 640 \(\times\) 480, a box filter with kernel of 5 \(\times\) 5, downsizing using scaling factor of 0.6, JPEG compression with quality factor = 30, and Gaussian noise with \(\mu\) = 0 and \(\sigma^{2}\) = 0.01. From experimental results in Section 5.2 we show the benefits of the use of the PSO algorithm in terms of robustness against JPEG lossy compression with a quality factor (QF) less than 30, Gaussian noise contamination, several filtering operations including mean, median and motion filters, cropping and downsizing as well as combined distortions, keeping the good robustness obtained by the conventional 2D DFT watermarking in the rest of the attacks, and confirming that the five attacks included in the fitness function of PSO are sufficient to improve the performance of the conventional 2D DFT watermarking, which in its original form is weak against these five attacks. The third one is related to the watermark security. In invisible watermarking, imperceptibility and robustness are not the only constraints to deal with but the security is important too. Considering the pair of radiuses \(r_{1}\), \(r_{2}\), as a secret key of a given 2D DFT-based image watermarking, the use of the same secret key for marking a lot of images may be is not the best choice, because is possible for an adversary to estimate the secret key if he owns more than one watermarked content [34].