# Hybrid Encoding Scheme for AMBTC Compressed Images Using Ternary Representation Technique
## 4 Experimental Results
### Comparisons with [PERSON] et al.'s Work
### Comparisons with [PERSON] et al. 's Work  
[PERSON] et al. 's method [16] also improves the AMBTC method by dynamically splitting images into multiple groups and achieves a good performance. In this section, we compare the proposed method with that of [PERSON] et al. in terms of PSNR and bitrate. To make a fair comparison, threshold \(\tau_{0}=4\) and \(\gamma=64\) are set in both methods. The proposed method uses \(\tau_{1}\) to control the number of smooth and complex blocks, whereas [PERSON] et al. 's method uses \(d_{\min}\) to control the number of pixel groups. We select \(\tau_{1}=8\), \(16\), and \(24\) in the proposed method and compare the results with those of [PERSON] et al. by setting \(d_{\min}=6\), \(7\), and \(8\) for block size \(4\times 4\). The results are shown in Table 6. Table 7 shows the same experimental results, except block size is \(8\times 8\) and \(d_{\min}=28\), \(32\), and \(36\). The settings of \(d_{\min}\) in [PERSON] et al. 's method ensure that best performance can be achieved. Table 6 shows that in [PERSON] et al. 's method, as \(d_{\min}\) increases, the image quality and bitrate decrease. The reason is that a large \(d_{\min}\) prevents more blocks from being split, leading to a decrease in bitrate and PSNR. Note that for most of the test images, the proposed method performs better than that of [PERSON] et al. We take the Lena image as an example: when \(\tau_{1}=16\) and \(d_{\min}=7\) are set, the PSNR of the proposed and [PERSON] et al. 's methods are \(36.05\) dB with \(1.68\) bpp and \(35.12\) dB with \(2.20\) bpp, respectively. The PSNR of the proposed method is \(36.05-35.12=0.93\) dB higher and the bitrate is \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]** \\  & & \(\tau_{1}=8\) & \(d_{\min}=6\) & \(\tau_{1}=16\) & \(d_{\min}=7\) & \(\tau_{1}=24\) & \(d_{\min}=8\) \\ \hline \multirow{2}{*}{Lena} & PSNR & 36.98 & 36.31 & 36.05 & 35.12 & 35.31 & 33.91 \\  & Bitrate & 2.05 & 2.35 & 1.68 & 2.20 & 1.54 & 1.95 \\ \hline \multirow{2}{*}{Jet} & PSNR & 36.53 & 34.96 & 35.97 & 33.74 & 35.36 & 32.69 \\  & Bitrate & 1.80 & 1.98 & 1.57 & 1.87 & 1.45 & 1.71 \\ \hline \multirow{2}{*}{Baboon} & PSNR & 31.28 & 31.40 & 30.89 & 29.59 & 30.32 & 28.11 \\  & Bitrate & 3.12 & 3.57 & 2.75 & 3.24 & 2.52 & 2.75 \\ \hline \multirow{2}{*}{Tiffany} & PSNR & 38.98 & 38.42 & 37.55 & 37.29 & 36.46 & 36.41 \\  & Bitrate & 1.92 & 2.12 & 1.54 & 1.99 & 1.40 & 1.81 \\ \hline \multirow{2}{*}{Boat} & PSNR & 35.37 & 34.81 & 34.27 & 33.43 & 33.44 & 32.11 \\  & Bitrate & 2.65 & 3.02 & 2.09 & 2.79 & 1.87 & 2.43 \\ \hline \multirow{2}{*}{Stream} & PSNR & 32.98 & 32.69 & 32.53 & 31.14 & 31.46 & 29.69 \\  & Bitrate & 3.07 & 3.45 & 2.73 & 3.18 & 2.39 & 2.75 \\ \hline \multirow{2}{*}{Peppers} & PSNR & 37.11 & 36.38 & 35.71 & 35.23 & 35.03 & 34.16 \\  & Bitrate & 2.28 & 2.64 & 1.77 & 2.45 & 1.65 & 2.20 \\ \hline \multirow{2}{*}{House} & PSNR & 35.32 & 35.06 & 34.82 & 33.52 & 33.99 & 31.86 \\  & Bitrate & 2.28 & 2.52 & 2.00 & 2.35 & 1.80 & 2.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparisons of PSNR and bitrate with block size \(4\times 4\). \(2.20-1.68=0.52\) bpp lower than that of [PERSON] et al. 's method. Comparisons with other images and another set of parameters also reveal similar results, with the exception of the Baboon image. When \(\tau_{1}=8\) and \(d_{\min}=6\) are set, the PSNR of [PERSON] et al. 's method is \(31.40-31.28=0.12\) dB higher than the proposed method. The reason is that under these settings, more blocks are divided into four groups and thus a better image quality is achieved. However, their method requires \(3.57-3.12=0.45\) bpp more than the proposed method. In the performance comparisons with block size \(8\times 8\), the proposed method shows better results for all test images.