# An Enhanced Adaptive Block Truncation Coding with Edge Quantization Scheme +
## 4 Experiment and Comparison
### Discussion
For Scheme B-I, the value in \(R_{0}\) is \(\sum_{i=1}^{7}(b_{i}\times 2^{i})\), while the values in \(R_{1}\) and \(R_{2}\) are \(\sum_{i=1}^{7}(b_{i}\times 2^{i-1})\) (note: \(R_{0}\), \(R_{1}\) and \(R_{2}\) use the following quantization ranges: \(R_{0}:(r_{7},r_{6},\ldots,r_{1})=(128\ 64\ 32\ 16\ 8\ 4\ 2)\), \(R_{1}:(r_{7},r_{6},\ldots,r_{1})=(64\ 32\ 16\ 8\ 4\ 2\ 1)\), \(R_{2}:(r_{7},r_{6},\ldots,r_{1})=(64\ 32\ 16\ 8\ 4\ 2\ 1)\). From the above description, Scheme A and Scheme B have almost the same execution time as the original ABTC-EQ. However, for Scheme C, we use four clusters. Thus, we need to use \(k\)-means clustering algorithm to subdivide a \((k\times k)\)-pixel block into four clusters. Running a fixed number \(t\) of iterations of the standard algorithm takes \(O(t\times c\times k^{2})\) for \(k^{2}\) pixels in a block, where \(c\) is the number of clusters. The original ABTC-EQ and Scheme C use \(c=3\) and 4, respectively. The proposed Scheme C uses four clusters and the quantization ranges in Equation (14). As described above the quantization approach has almost the same execution time as the original ABTC-EQ, but subdividing more clusters in every block for Scheme C is slightly greater than ABTC-EQ (note: time complexity order of clustering is \(O(t\times c\times k^{2})\). **(4) Appropriate Way Using Our Schemes:**  
Our goal is for consumers to understand and appropriately use application scenarios for the three proposed ABTC-EQ schemes. To clearly describe their respective application scenarios, we create a radar chart to illustrate the multiple performances (the number of clusters, the PSNR of a recovered image, and the size of compressed file) and the variations among all the schemes (Scheme A, Scheme B-I\(\sim\)IV, and Scheme C). The values of PSNR and CR are adopted from Table 1 using the test image Lena and the block size \(4\times 4\) pixels. From Figure 3, we conclude the following results showing how to appropriately use Scheme A, Scheme B-I\(\sim\)B-IV, and Scheme C to develop their specialties according to  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\mathcal{P}_{r}\)} & \multicolumn{3}{c}{**Scheme A**} & \multicolumn{3}{c}{**Scheme B-I**} & \multicolumn{3}{c}{**Scheme B-II**} & \multicolumn{3}{c}{**Scheme B-III**} & \multicolumn{3}{c}{**Scheme B-IV**} & \multicolumn{3}{c}{**(AMBTC-EQ)**} \\  & \multicolumn{3}{c}{**k =4**} & \multicolumn{3}{c}{**k =4**} & \multicolumn{3}{c}{**k = 4**} & \multicolumn{3}{c}{**k = 6**} & \multicolumn{3}{c}{**k = 8**} & \multicolumn{3}{c}{**k = 4**} & \multicolumn{3}{c}{**k = 8**} & \multicolumn{3}{c}{**k = 4**} & \multicolumn{3}{c}{**k = 8**} & \multicolumn{3}{c}{**k = 4**} & \multicolumn{3}{c}{**k = 6**} & \multicolumn{3}{c}{**k = 8**} & \multicolumn{3}{c}{**k = 4**} & \multicolumn{3}{c}{**k = 6**} & \multicolumn{3}{c}{**k = 8**} \\ \hline
0.05 & 3.77 & 5.27 & 6.13 & 3.79 & 5.29 & 6.14 & 3.81 & 5.30 & 6.15 & 3.82 & 5.32 & 6.16 & 3.84 & 5.53 & 6.17 & 3.74 & 5.22 & 6.05 \\
0.10 & 3.67 & 5.12 & 5.95 & 3.70 & 5.15 & 5.97 & 3.74 & 5.18 & 5.99 & 3.77 & 5.21 & 6.01 & 3.80 & 5.24 & 6.03 & 3.62 & 5.02 & 5.80 \\
0.15 & 3.58 & 4.98 & 5.78 & 3.62 & 5.02 & 5.81 & 3.67 & 5.06 & 5.84 & 3.72 & 5.10 & 5.87 & 3.76 & 5.14 & 5.90 applications. Because Scheme A has the same PSNR as ABTC-EQ, if we want to obtain a good PSNR along with a good CR, we should choose Scheme A. On the other hand, Scheme C has a very high PSNR. Therefore, if we want to have a significant improvement in PSNR, we may choose Scheme C, which still has the same CR as ABTC-EQ. For the application that a high CR is a requirement, we may use Scheme B to trade off the PSNR for the CR.