# Hybrid Encoding Scheme for AMBTC Compressed Images Using Ternary Representation Technique
## 4 Experimental Results
### Comparisons with [PERSON] et al.'s Work
For example, as shown in Table 7 when \(\tau_{1}=14\) and \(d_{\min}=28\), the PSNR of the Baboon image of the proposed method is \(28.84\) dB at \(1.88\) bpp. The PSNR is \(28.84-28.14=0.70\) dB higher and the bitrate is \(2.23-1.88=0.35\) bpp lower than those of [PERSON] et al. 's method. Figure 8a-f shows the visual quality comparisons of the AMBTC, [PERSON] et al. 's, and the proposed methods. As seen from Figure 8a when the block size is \(4\times 4\) and the AMBTC method is applied, apparent distortions can be seen in the image edges, and noticeable boundary artifacts are observed (see Figure 8a). Note that the PSNR of the AMBTC is \(33.27\) dB with \(2.0\) bpp. [PERSON] et al. improve the AMBTC method by adding more details to complex blocks. As a result, the PSNR (\(36.31\) dB) is significantly higher and blocks at the edges look more natural than those of AMBTC (Figure 8c, \(d_{\min}=6\)). However, their method requires \(2.35-2=0.35\) bpp more to achieve this effect. In contrast, the visual quality of the proposed method (Figure 8e, \(\tau_{1}=8\)) is comparable with that of [PERSON] et al. 's method, but the bitrate is \(2.35-2.05=0.30\) bpp lower with a slightly higher PSNR. When the block size is \(8\times 8\), the distortion of AMBTC is more apparent (Figure 8b) than that of \(4\times 4\), but the bitrate reduces from \(2.0\) to \(1.25\) bpp. The visual quality of [PERSON] et al. 's method (Figure 8d, \(d_{\min}=28\)) is significantly better than that of AMBTC, and has no noticeable block boundary artifacts. However, their method requires \(1.64-1.25=0.39\) bpp more to improve the image quality. In addition, some edges in [PERSON]'s face, eyes, and shoulder exhibit apparent distortions because the pixel splitting operation may not be triggered due to the setting of \(d_{\min}\). In contrast, the edges of the proposed method exhibit \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Images**} & \multirow{2}{*}{**Metrics**} & **Proposed** & [16] & **Proposed** & **[16]** & **Proposed** & **[16]** \\  & & \(\tau_{1}=14\) & \(d_{\min}=28\) & \(\tau_{1}=22\) & \(d_{\min}=32\) & \(\tau_{1}=30\) & \(d_{\min}=36\) \\ \hline \multirow{2}{*}{Lena} & PSNR & 33.32 & 31.88 & 32.66 & 30.85 & 32.00 & 30.27 \\ \cline{2-8}  & Bitrate & 1.09 & 1.64 & 0.90 & 1.45 & 0.79 & 1.27 \\ \hline \multirow{2}{*}{Jet} & PSNR & 32.99 & 30.37 & 32.44 & 29.66 & 31.87 & 29.23 \\ \cline{2-8}  & Bitrate & 1.09 & 1.36 & 0.94 & 1.24 & 0.84 & 1.13 \\ \hline \multirow{2}{*}{Baboon} & PSNR & 28.84 & 28.14 & 28.43 & 26.44 & 27.84 & 25.50 \\ \cline{2-8}  & Bitrate & 1.88 & 2.23 & 1.65 & 1.88 & 1.47 & 1.50 \\ \hline \multirow{2}{*}{Tiffany} & PSNR & 35.36 & 34.44 & 33.97 & 33.48 & 32.95 & 32.89 \\ \cline{2-8}  & Bitrate & 1.04 & 1.51 & 0.77 & 1.33 & 0.64 & 1.16 \\ \hline \multirow{2}{*}{Boat} & PSNR & 31.62 & 30.12 & 30.68 & 29.11 & 29.95 & 28.54 \\ \cline{2-8}  & Bitrate & 1.46 & 1.99 & 1.11 & 1.75 & 0.93 & 1.50 \\ \hline \multirow{2}{*}{Stream} & PSNR & 29.94 & 28.62 & 29.39 & 27.30 & 28.31 & 26.54 \\ \cline{2-8}  & Bitrate & 1.99 & 2.20 & 1.71 & 1.90 & 1.41 & 1.58 \\ \hline \multirow{2}{*}{Peppers} & PSNR & 33.01 & 31.35 & 32.27 & 30.52 & 31.68 & 30.03 \\ \cline{2-8}  & Bitrate & 1.14 & 1.86 & 0.91 & 1.62 & 0.81 & 1.40 \\ \hline \multirow{2}{*}{House} & PSNR & 31.71 & 30.20 & 31.22 & 28.79 & 30.45 & 28.09 \\ \cline{2-8}  & Bitrate & 1.45 & 1.70 & 1.24 & 1.47 & 1.06 & 1.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparisons of PSNR and bitrate with \(8\times 8\) block size. no apparent distortion (see Figure 8f, \(\tau_{1}=14\)). Moreover, the bitrate required in the proposed method is even lower than that of AMBTC by \(1.25-1.09=0.16\) bpp.