# Improved Low Complexity Predictor for Block-Based Lossless Image Compression +
## 3 Experimental Results  
We select an experimental dataset from Ref. [9], which contains 5 image categories. Each category has 65 images with a resolution from 4000 to 8000, on average, as shown in Figure 5.  
Figure 4: Mapping function when predicted value = 50. Tables 1-5 show the comparison results of entropy between the proposed method and original MED in full size, 8 \(\times\) 8, 16 \(\times\) 16, and 32 \(\times\) 32. MED without threshold is inferior to MED in a larger size but outperforms MED in several categories when the block size is 8 \(\times\) 8. By examining the dataset, we discovered that MED without threshold has an advantage when the input images are composed of complicated textures. For example, the peacock, leaves, and forest in Figure 5 contain complicated regions, and the MED without a threshold surpasses the MED by an entropy reduction of 0.1 on average. The performance of the 3 \(\times\) 3 matrix is similar to that of the MED without a threshold. It outperforms the MED in the 8 \(\times\) 8 matrix and is inferior with a larger size, but unexpectedly surpasses the MED in full size. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Full Size** & **MED** & **MED Without Threshold** & **3 \(\times\) 3 Ranged Threshold** & **Adaptive Prediction** \\ \hline mountain & 4.9827 & 5.0320 & 4.9255 & 4.8388 \\ \hline capture & 4.0214 & 4.0771 & 3.9514 & 3.8621 \\ \hline street & 5.2816 & 5.4018 & 5.2873 & 5.2097 \\ \hline building & 5.0343 & 5.1060 & 5.0068 & 4.9211 \\ \hline animal & 5.1374 & 5.2777 & 5.1469 & 5.0726 \\ \hline average & 4.8915 & 4.9789 & 4.8636 & 4.7809 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A comparison of the residual entropy of the proposed and other algorithms for full size compression. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**8 \(\times\) 8** & **MED** & **MED Without Threshold** & **3 \(\times\) 3 Ranged Threshold** & **Adaptive Prediction** \\ \hline mountain & 5.1531 & 5.0942 & 5.0779 & 4.9886 \\ \hline capture & 4.2426 & 4.1864 & 4.1765 & 4.0661 \\ \hline street & 5.4400 & 5.4395 & 5.4222 & 5.3343 \\ \hline building & 5.2140 & 5.1805 & 5.1676 & 5.0801 \\ \hline animal & 5.2903 & 5.3060 & 5.2826 & 5.1910 \\ \hline average & 5.0680 & 5.0413 & 5.0254 & 4.9320 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: A comparison of the residual entropy of the proposed and other algorithms for 8 block-based compression. Figure 5: Test image dataset [9]. Adaptive prediction has the lowest entropy in every category and block size. Additionally, the result of 32 \(\times\) 32 is extremely close to that of the full size, which indicates that the time spent is 32/N, determined by sacrificing a few compression rates (CRs), where N is the length of the input image with the same infinite encoder and decoder. Table 5 shows the result of the vertical flip and hybrid flip in different block sizes. The entropy is the original entropy added by the extra bits 1/(square of block size) depending on the flipped block. If the block size is 32 \(\times\) 32, the extra bpp required becomes 1/32/32 = 0.000976. The value is multiplied by 2 if the block is applied with the hybrid flip. Using only one one-direction flip is the most appropriate approach, since the trade-off between the entropy reduction and the extra bits balances the buffer to record growing residues exponentially. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**32 \(\times\) 32** & **MED** & \begin{tabular}{c} **MED Without** \\ **Threshold** \\ \end{tabular} & \
\begin{tabular}{c} **3 \(\times\) 3 Ranged** \\ **Threshold** \\ \end{tabular} &
\begin{tabular}{c} **Adaptive** \\ **Prediction** \\ \end{tabular} \\ \hline mountain & 5.0084 & 5.0290 & 5.0029 & 4.8594 \\ \hline capture & 4.0523 & 4.0775 & 4.0618 & 3.8881 \\ \hline street & 5.3054 & 5.3933 & 5.3653 & 5.2246 \\ \hline building & 5.0631 & 5.1067 & 5.0855 & 4.9448 \\ \hline animal & 5.1591 & 5.2667 & 5.2298 & 5.0854 \\ \hline average & 4.9177 & 4.9746 & 4.9491 & 4.8005 \\ \hline \hline \end{tabular}
\end{table}