# Feature-Based Image Watermarking Algorithm Using SVD and APBT for Copyright Protection
## 4 Experimental Results and Comparative Analyses
### Performance Comparisons  
In this section, owing to APDCBT and APDCBT having similar performance when applied in the proposed algorithm, one of the typical transforms, the APDCBT matrix in APBT theory, is taken to test the performance of the proposed algorithm concretely. To demonstrate applicability of the proposedalgorithm, different images with different entropies are tested in this section, which are shown in Figure 6.  
To give more detailed subjective experimental results, an original image and a watermarked image, as well as a watermarked image and an APDCBT-based extracted watermark are compared in Figure 7. Considering the symmetry and asymmetry of the watermark, logo watermark 1 and letter watermark 2, defined as \(w_{1}\) and \(w_{2}\), are applied in this experiment. As Figure 7 shows, the embedded watermark cannot be distinguished by the naked eye, which illustrates that the proposed algorithm achieves good imperceptibility. Figure 6: Tested images: (**a**) Airplane; (**b**) Baboon; (**c**) Barbara; (**d**) Bank; (**e**) Elaine; (**f**) Barche; (**g**) Milkdrop; (**h**) Panzer; (**i**) Announcement; (**j**) Vogue; (**k**) Cablecar; (**l**) Canyon; (**m**) Clown; (**n**) Cornfield; (**o**) Frog; (**p**) Fruits. Table 1 gives PSNR, NC, and BER values of experimental results. Owing to different entropies of images, the number of selected feature points is different according to Section 3.1. Images with a large number of refined feature points (more than 256), which contains images Airplane, Crown, Cornfield, are tested with a 64 \(\times\) 64 watermark image. Images with a small number of refined feature points (less than 256), containing images Baboon, Barbara, Bank, Elaine, Barche, Milkdrop, Announcer, Vogue, Cablecar, Canyon, Frog, Fruits, are tested with a 32 \(\times\) 32 watermark. As can be seen, performance of using symmetrical watermarks and asymmetrical watermarks both have good performance in PSNR. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Images**} & \multicolumn{2}{c}{**PSNR**} & \multicolumn{1}{c}{**NC**} & \multicolumn{1}{c}{**BER**} \\ \hline \multirow{2}{*}{Airplane} & \(w_{1}\) & 90.56 & 0.9994 & 0.0008 \\  & \(w_{2}\) & 93.28 & 0.9961 & 0.0137 \\ \hline \multirow{2}{*}{Baboon} & \(w_{1}\) & 79.31 & 0.9683 & 0.0156 \\  & \(w_{2}\) & 89.76 & 0.9043 & 0.0068 \\ \hline \multirow{2}{*}{Barbara} & \(w_{1}\) & 91.18 & 0.9648 & 0.0176 \\  & \(w_{2}\) & 90.27 & 0.8681 & 0.0447 \\ \hline \multirow{2}{*}{Bank} & \(w_{1}\) & 82.92 & 0.9577 & 0.0195 \\  & \(w_{2}\) & 91.18 & 0.9137 & 0.0317 \\ \hline \multirow{2}{*}{Elaine} & \(w_{1}\) & 74.59 & 0.9401 & 0.0225 \\  & \(w_{2}\) & 77.68 & 0.7354 & 0.0680 \\ \hline \multirow{2}{*}{Barche} & \(w_{1}\) & 79.55 & 0.9542 & 0.0195 \\  & \(w_{2}\) & 92.32 & 0.8772 & 0.0391 \\ \hline \multirow{2}{*}{Milkdrop} & \(w_{1}\) & 78.12 & 0.9225 & 0.0273 \\  & \(w_{2}\) & 81.05 & 0.7129 & 0.0653 \\ \hline \multirow{2}{*}{Panzer} & \(w_{1}\) & 78.85 & 0.9683 & 0.0146 \\  & \(w_{2}\) & 85.78 & 0.8803 & 0.0389 \\ \hline \multirow{2}{*}{Announcer} & \(w_{1}\) & 76.48 & 0.8121 & 0.0957 \\  & \(w_{2}\) & 85.50 & 0.8973 & 0.0376 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental results on different images with different entropies. Figure 7: Experimental results on APDCBT-based algorithms: (**a**) original image and \(w_{1}\); (**b**) watermarked image and extracted \(w_{1}\) based on APDCBT; (**c**) original image and \(w_{2}\); (**d**) watermarked image and extracted \(w_{2}\) based on APDCBT. To give more detailed results, the Airplane image and Shandong University logo are taken as examples for further demonstration. Table 2 indicates the PSNR and NC comparison among methods proposed by [PERSON] et al. [30], [PERSON] et al. [31], [PERSON] and [PERSON]'s scheme [32], and the proposed algorithm. In [30], principal components of the watermark are embedded into the host image. In [31], the watermark is scrambled by shuffled SVD (SSVD), and principal components are extracted for watermark embedding.