# An Analytic Transform Kernel Derivation Method for Video Codecs
## 3 Experimental Results and Analysis
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{13}{c}{**CoT [118]**} & \multicolumn{1}{c}{**Unified Matrix [20]**} & \multicolumn{1}{c}{**Error [21]**} & \multicolumn{1}{c}{**Error [22]**} & \multicolumn{1}{c}{**Error [23]**} & \multicolumn{1}{c}{**Error [24]**} & \multicolumn{1}{c}{**Error [25]**} & \multicolumn{1}{c}{**Error [26]**} & \multicolumn{1}{c}{**Error [27]**} & \multicolumn{1}{c}{**Error [28]**} & \multicolumn{1}{c}{**Error [29]**} & \multicolumn{1}{c}{**Error [30]**} & \multicolumn{1}{c}{**Error [31]**} & \multicolumn{1}{c}{**Error [32]**} & \multicolumn{1}{c}{**Error [33]**} & \multicolumn{1}{c}{**Error [34]**} & \multicolumn{1}{c}{**Error [35]**} & \multicolumn{1}{c}{**Error [36]**} & \multicolumn{1}{c}{**Error [37]**} & \multicolumn{1}{c}{**Error [38]**} & \multicolumn{1}{c}{**Error [39]**} & \multicolumn{1}{c}{**Error [31]**} & \multicolumn{1}{c}{**Error [32]**} & \multicolumn{1}{c}{**Error [30]**} & \multicolumn{1}{c}{**Error [31]**} & \multicolumn{1}{c}{**Error [32]**} & \multicolumn{1}{c}{**Error [33]**} & \multicolumn{1}{c}{**Error [34]**} & \multicolumn{1}{c}{**Error [35]**} & \multicolumn{1}{c}{**Error [36]**} & \multicolumn{1}{c}{**Error [37]**} & \multicolumn{1}{c}{**Error [38]**} & \multicolumn{1}{c}{**Error [39]**} & \multicolumn{1}{c}{**Error [39]**} & \multicolumn{1}{c}{**Error [38] \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{13}{c}{**COT [18]**} & \multicolumn{13}{c}{**Unified Matrix [20]**} & \multicolumn{13}{c}{**TAF [22]**} & \multicolumn{13}{c}{**Proposed Method**} \\ \cline{2-13} \multicolumn{1}{c}{} & **Y** & **U** & **V** & **EncT** & **DeT** & **Y** & **U** & **V** & **EncT** & **DeT** & **Y** & **U** & **V** & **EncT** & **DeT** & **Y** & **U** & **V** & **EncT** & **DeT** \\ \hline Class B & \(-0.015\) & \(-0.203\) & \(0.078\) & \(100\) & \(100\) & \(0.148\) & \(0.016\) & \(0.326\) & \(98\) & \(96\) & \(0.048\) & \(-0.169\) & \(0.118\) & \(100\) & \(101\) & \(-0.010\) & \(-0.291\) & \(-0.420\) & \(100\) & \(100\) \\ Class C & \(0.015\) & \(0.437\) & \(0.174\) & \(99\) & \(96\) & \(0.148\) & \(0.341\) & \(0.388\) & \(98\) & \(96\) & \(0.013\) & \(-0.009\) & \(0.214\) & \(100\) & \(100\) & \(0.060\) & \(0.211\) & \(0.100\) & \(100\) & \(100\) \\ Class D & \(0.016\) & \(0.202\) & \(0.078\) & \(104\) & \(102\) & \(0.057\) & \(0.054\) & \(-0.170\) & \(98\) & \(57\) & \(-0.035\) & \(0.208\) & \(-0.171\) & \(100\) & \(100\) & \(-0.030\) & \(0.081\) & \(-0.210\) & \(101\) & \(100\) \\ Class E & \(0.098\) & \(1.063\) & \(0.158\) & \(102\) & \(98\) & \(0.156\) & \(0.832\) & \(-0.355\) & \(96\) & \(80\) & \(0.019\) & \(1.000\) & \(102\) & \(100\) & \(99\) & \(-0.020\) & \(0.540\) & \(-0.510\) & \(101\) & \(100\) \\
**Overall** & **0.023** & **0.302** & **0.130** & **100** & **59** & **0.166** & **0.323** & **0.177** & **97** & **95** & **0.030** & **0.177** & **0.161** & **100** & **100** & **0.000** & **0.079** & \(-0.270\) & **101** & **100** \\ \multicolumn{13}{c}{**Unif. \({}^{*}\)**} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of the overall simulation results for the derivation of transform kernels with the proposed method (LDB).