# Optical Flow-Based Fast Motion Parameters Estimation for Affine Motion Compensation
## 4 Experimental Results
### Comparison of Variants of the Proposed Method  
We evaluated the encoding time and coding efficiency effects of our proposed model prediction, affine mode skip and fast parameter estimation. We compare three variants of the proposed method. The differences between the variants are presented in Table 3.  
Figure 1: Distribution of the affine parameter (quantization levels) in the Rotating Disk sequence for accurately and incorrectly predicted transform models. Table 4 shows the results of the three variants. While the fast estimation variant is able to achieve the fastest encoding, this comes at the cost of greatly reduced efficiency. If more time is available, on of the other two methods is preferable, as they are able to achieve a better efficiency for a little more time. On some more complex sequences like Tractor, while the encoding speed increases significantly with the fast estimation method, the efficiency is more affected. This sequence is very challenging and the optical flow scaling fails to work on the wheels because of the fast rotation. While optical flow can estimate with some accuracy the motion for the first reference picture, the scaling does not work. As the wheel follows a rotational symmetry, in most cases the correct motion vector does not represent the real movement of the wheel. It will match a similar part of the wheel that has moved less compared to the current picture. Figure 2 illustrates this. There are two interesting results for the method using variance to skip affine mode, Twilight Scene and Fungus Zoom, where the efficiency increases with checking the affine mode less often. This happens because the Rate Distortion Optimization (RDO) process is not perfect. While we do not \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sequence Name**} & \multicolumn{2}{c}{**Model Prediction**} & \multicolumn{2}{c}{**Model + Skip**} & \multicolumn{2}{c}{**Fast Estimation**} \\ \cline{2-6}  & BD-R[\%] & \(\Delta\)**T[\%]** & **BD-R[\%]** & \(\Delta\)**T[\%]** & **BD-R[\%]** & \(\Delta\)**T[\%]** \\ \hline Station & \(-23.75\) & \(14.54\) & \(-23.68\) & \(13.25\) & \(-18.03\) & \(14.32\) \\ Fountain & \(-0.15\) & \(7.38\) & \(-0.15\) & \(5.10\) & \(-0.10\) & \(5.28\) \\ Fungus Zoom & \(-16.18\) & \(19.77\) & \(-16.42\) & \(19.92\) & \(-11.38\) & \(16.77\) \\ Rotating Disk & \(-24.07\) & \(10.23\) & \(-23.74\) & \(10.01\) & \(-13.22\) & \(6.98\) \\ Blue Sky & \(-4.74\) & \(8.78\) & \(-4.69\) & \(8.93\) & \(-3.76\) & \(5.90\) \\ Tractor & \(-3.71\) & \(8.44\) & \(-3.38\) & \(5.79\) & \(-1.66\) & \(5.79\) \\ Twilight Scene & \(-0.26\) & \(11.05\) & \(-0.42\) & \(10.65\) & \(-0.27\) & \(8.01\) \\ \hline Average & \(-10.41\) & \(11.46\) & \(-10.35\) & \(10.52\) & \(-6.92\) & \(9.01\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of Coding Efficiency and Encoding Speed of the Proposed Method Variants. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method Name**} & \multicolumn{2}{c}{**Affine Model**} & \multirow{2}{*}{**Affine Skip**} & \multicolumn{2}{c}{**Fast Parameter**} \\  & & **Prediction** & **Affine Skip** & **Refinement** \\ \hline Model prediction & \(\checkmark\) & \(\times\) & \(\times\) \\ Model + Skip & \(\checkmark\) & \(\checkmark\) & \(\times\) \\ Fast estimation & \(\checkmark\) & \(\checkmark\) & \(\checkmark\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Overview of proposed method variants. Figure 2: Three frames extracted from the Tractor sequence: (**a**) Current picture (POC N), wheel angle \(136\); (**b**) reference picture 0 (POC N-1), wheel angle \(132\); (**c**) reference picture 1 (POC N-4), wheel angle \(118\).