# Optical Flow-Based Fast Motion Parameters Estimation for Affine Motion Compensation
## 4 Experimental Results
### Comparison with the State of The Art
When comparing with the proposed method, the gradient approach offers a better encoding for a limited cost in encoding time but we believe we have a lot of margin left in optimizations. On some videos, like Blue Sky and Station the efficiency of the proposed method is very close to the existing state of the art, with a increase in time halved compared to [PERSON] et al. If there are time constraints, the proposed method can offer superior encoding to HM and close to state of the art while maintaining the encoding time low. In two sequences, Fungus Zoom and Twilight scene, the efficiency is higher than [PERSON] et al., but fails to attain the efficient from the gradient approach using 3 parameters. However, it beats the gradient approach using 4 parameters in the Fungus Zoom case, as the additional unused parameter (rotation being almost inexistent) incurs a coding cost overhead. Two sequences are very challenging for our proposed method. Tractor was previously mentioned for the limited accuracy for motion estimation, and when compared to the state of the art the effects of the limited accuracy in model estimation are significant. Figure 2 illustrates only one aspect of the challenges in encoding this sequence. Rotating wheel is difficult because of the black background, that optical flow is unable to track, making areas at the edge of the rotating objects hard to estimate. However, as it is a very artificial sequence that is unlikely to appear in more common sequences, we do not believe optimizing for this specific sequence to be sensible. We can see that while the proposed method does not achieve an efficiency as high as the existing state of the art, it is able to encode in a much faster time, so if time is limited, it could be preferable to use the proposed method as the best compromise between speed and efficiency. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Proposed** & **Tsutake [10]** & **Gradient [9]** & **Gradient 3-Parameter** \\ \hline Encoding Efficiency & & & & \\ Encoding Speed (affine motion) & & & & \\ Encoding Speed (translation) & & & & \\ Hardware implementation & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Overview of Advantages and Disadvantages of Each Method. \(\bigcirc\) marks when the method is effective, \(\bigtriangleup\) when it is acceptable, and \(\times\) when it is inadequate for this aspect. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Sequence Name**} & \multicolumn{2}{c}{**Proposed**} & \multicolumn{2}{c}{**Tsutake [10]**} & \multicolumn{2}{c}{**Gradient [9]**} & \multicolumn{2}{c}{**Gradient 3-Parameter**} \\ \cline{2-9}  & **BD-R[\%]** & **AT[\%]** & **BD-R[\%]** & **\(\Delta\)T[\%]** & **BD-R[\%]** & **\(\Delta\)T[\%]** & **BD-R[\%]** & **\(\Delta\)T[\%]** \\ \hline Station & \(-23.68\) & \(13.25\) & \(-24.76\) & \(24.60\) & \(-25.62\) & \(12.81\) & \(-24.61\) & \(22.22\) \\ Fountain & \(-0.15\) & \(5.10\) & \(-0.16\) & \(16.20\) & \(-0.24\) & \(10.49\) & \(-0.17\) & \(10.07\) \\ Fungus Zoom & \(-16.42\) & \(19.92\) & \(-16.37\) & \(26.70\) & \(-15.23\) & \(17.35\) & \(-16.64\) & \(23.15\) \\ Rotating Disk & \(-23.74\) & \(10.01\) & \(-26.77\) & \(20.42\) & \(-29.28\) & \(11.24\) & \(-27.28\) & \(17.06\) \\ Blue Sky & \(-4.69\) & \(8.93\) & \(-5.13\) & \(19.18\) & \(-5.52\) & \(9.23\) & \(-5.78\) & \(15.52\) \\ Tractor & \(-3.38\) & \(5.79\) & \(-4.59\) & \(15.24\) & \(-4.82\) & \(7.68\) & \(-4.09\) & \(11.94\) \\ Twilight Scene & \(-0.42\) & \(10.65\) & \(-0.39\) & \(20.48\) & \(-0.51\) & \(10.15\) & \(-0.65\) & \(16.43\) \\ \hline Average & \(-10.35\) & \(10.52\) & \(-11.17\) & \(20.40\) & \(-11.61\) & \(11.28\) & \(-11.32\) & \(16.62\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of Coding Efficiency and Encoding Speed.