# Hybrid Encoding Scheme for AMBTC Compressed Images Using Ternary Representation Technique
## 4 Experimental Results
### The Performance of the Proposed Method
#### 4.1.2 Performance Comparison of Various \(\tau_{1}\)  
The parameter \(\tau_{1}\) controls the number of smooth and complex blocks. The number of complex blocks decreases as \(\tau_{1}\) increases. To see the distribution of flat, smooth, and complex blocks of a test image, we take the Lena image as an example to illustrate their distribution by varying \(\tau_{1}\). Figure 6a-d shows the distributions of blocks when \(\tau_{1}=8\), \(16\), \(32\), and \(64\) are set. The block sizes in these figures are \(8\times 8\) and \(\tau_{0}=4\). In this figure, the blue squares, red dots, and black cross marks represent flat, smooth, and complex blocks, respectively. Because the same \(\tau_{0}\) is applied, it can be seen that the number of blue squares (flat blocks) is the same in Figure 6a-d. However, as \(\tau_{1}\) increases, the red dots increase and black cross marks decrease. The reason is that an increase in \(\tau_{1}\) leads more blocks to be categorized as smooth. It can also be inferred that a better image quality can be achieved at a smaller \(\tau_{1}\) but the bitrate will be higher because more blocks are deemed to be complex. Note that in the proposed method, more bits are required to represent a complex block than a smooth block. Figure 5: The gain of PSNR when the quantized value adjustment (QA) technique is applied. Tables 4 and 5 show the PSNR and bitrate for all of the test images under various \(\tau_{1}\) with block size \(4\times 4\) and \(8\times 8\), respectively. In this experiment, \(\tau_{0}=4\), \(\gamma=64\), and \(k=256\) are set. We also list the PSNR and bitrate of the standard AMBTC method as a comparison. Note that the bitrates of the AMBTC with block size \(4\times 4\) and \(8\times 8\) are \(2.0\) and \(1.25\) bpp, respectively. As seen in Tables 4 and 5, the PSNR of block size \(8\times 8\) is lower than that of block size \(4\times 4\). For example, when \(\tau_{1}=16\), the PSNR of the Lena image of block sizes \(4\times 4\) and \(8\times 8\) are \(34.73\) and \(31.91\) dB, respectively. However, the former requires \(1.68-1.02=0.66\) more bits per pixel than the latter. In addition, the experiments also reveal the fact that a large \(\tau_{1}\) effectively reduces the bitrate at the expense of image quality. On the contrary, a small \(\tau_{1}\) provides better image quality, but requires more bitrate. This result is expected because a small \(\tau_{1}\) increases the number of complex blocks and, therefore, the bitrate, however, the image quality also increases. Figure 6: Distribution of flat, smooth and complex blocks. Figure 7 shows the bitrate-PSNR curves of each of the eight test images by varying the threshold \(\tau_{1}\) from 8 to 64. The figure shows that for all of the test images, the PSNR increases as the bitrate increases. Moreover, the figure also reveals that smooth images, such as Tiffany or Jet, have a better compression efficiency than those of complex images, such as Stream or Baboon. The reason is that a smooth block not only requires less bits to record its compressed code but also provides better reconstructed quality. Because the smooth images naturally possess more smooth blocks than complex blocks, their bitrate-PSNR curves are higher than those of complex ones.