# Vehicle Speed Estimation Based on 3D ConvNets and Non-Local Blocks
## 4 Experiments and Analysis
### 3D ConvNets and Non-Local Neural Networks
#### 4.3.2 Adding Optical Flow Information  
Optical flow is the observed motion pattern of objects, surfaces, and edges in a visual scene caused by relative motion between an observer and a scene [37; 38]. It can also be defined as apparent velocity of brightness patterns in an image. As optical flow reflects the velocity of pixel points, and the velocity of a vehicle is closely related to that of all the pixel points comprising the vehicle, optical flow information is a logical and useful additional input to our model.  
As show in Table 4, we experiment with various input resolutions of \(56\times 56\), \(112\times 112\), \(224\times 224\) on IR(2+1)D50, corresponding to the original video frames resized to \(64\times 64\), \(128\times 128\), \(256\times 256\), respectively. Because the last pooling layer is Adaptive Pooling, the network produces the same sized output for different input sizes. From Table 4, we inspect that input size of \(56\times 56\) gives the highest MAE and MSE. That is because resizing images too small causes a loss of useful information. As the input size grows, the information in input accordingly increases. So that error measure consistently decreases as the input size increases. However, increase in input size also brings redundant information, which causes increase in error measures. Thus, the marginal improvement diminishes as the input size increases due to this tradeoff.  
Experimental results in Table 4 suggest that input size and form have a significant impact on the performance of the model. Here, \"cat\" means that RGB images and optical flow images are concatenated together as input. Table 4 shows the model results for three input forms in three rows. More specifically, the first row corresponds to the RGB images sequence used as the input; the second corresponds to optical flow images as the input; the third corresponds to \"cat\" as input. It can be seen that optical flow input gives significantly better results than that of RGB input, everything else equal. Clearly, optical flow information is more suitable an input form for our model in vehicle speed estimation problem. One explanation for this observation is since optical flow reflects the motion of pixel points, it incorporates more useful vehicle speed information.  
An interesting observation is that in the video action classification problem, RGB input outperforms optical flow [14]. In contrast, the results are reverse in the vehicle speed estimation problem. Problems differ in terms of structure. It is crucial to propose a fitting solution supported by a deep understanding and consideration of the particular structure of the problem of interest.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Input**} & \multicolumn{2}{c}{\(\mathbf{56\times 56}\)} & \multicolumn{2}{c}{\(\mathbf{112\times 112}\)} & \multicolumn{2}{c}{\(\mathbf{224\times 224}\)} \\  & **MAE** & **MSE** & **MAE** & **MSE** & **MAE** & **MSE** \\ \hline RGB & 3.99 & 28.91 & 3.80 & 25.87 & 3.76 & 25.80 \\ Optical flow & 3.60 & 23.39 & 3.16 & 18.15 & 3.02 & 17.35 \\ cat & 3.50 & 21.60 & 3.08 & 17.92 & 3.01 & 17.24 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Influence of different input on the IR(2+1)D50.