## 4 Experiments
### Subpixel Accuracy  
We investigated the appropriateness of the traditional 3-point Gaussian sub-pixel accuracy in the context of estimating bee motions to determine whether the correlation matrices generated Gaussian curves. We randomly selected several consecutive image pairs from our dataset. For each selected image pair, the image size was \(160\times 120\) and the interrogation window size was \(12\) with a \(50\%\) overlap. To simplify visualization, we selected only the image pairs with a singly bee moving. Figure 6 shows a sample image pair with the moving bee selected by the green box and the corresponding vectors generated by DPIV.  
We computed the correlation matrices for all motion vectors and visualized them with 3D plots, as shown in Figure 7. Each 3D plot in Figure 7 corresponds to a vector in the vector map of Figure 6. Specifically, the first 3D plot in the first row (Figure 7a) corresponds to the first (left) vector in the first row of the vector map in Figure 6c; the second 3D plot in the first row (Figure 7b) corresponds to the second (right) vector in the first row of the vector map in Figure 6c; the first 3D plot in the second row (Figure 7c) corresponds to the first vector in the the second row of Figure 6c; the second 3D plot in the second row (Figure 7d) corresponds to the second vector in the second row of the vector map in Figure 6c; the first 3D plot in the third row (Figure 7e) corresponds to the first vector in the third row of the vector map in Figure 6c; and the second 3D plot in the third row (Figure 7f) corresponds to the second vector in the third row of the vector map in Figure 6c. Since the vectors in the first row are small, we scaled the plots to better visualize the corresponding distribution (see Figure 8). Another sample image pair with the corresponding DPIV vectors and plots are given in Figures 11 and 12 in Appendix A.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**DTW vs. Video** & **HT\_Vid.mp4** & **MT\_Vid.mp4** & **LT\_Vid.mp4** & **NT\_Vid.mp4** \\ \hline \(DTW(C_{1}^{*},C_{3}^{*})\) & 20.75 & 21.71 & 15.36 & 10.53 \\ \(DTW(C_{2}^{*},C_{3}^{*})\) & 22.02 & 22.19 & 18.13 & 6.47 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Omnidirectional traffic curve comparison: \(C_{1}^{*}\) is DPIV; \(C_{2}^{*}\) is MOG2/VGG16; and \(C_{3}^{*}\) is Human Count (ground truth).  
By analyzing such 3D plots of correlation vectors of two consecutive images with single bees moving, we concluded that all correlation maps follow Gaussian distribution. We also observed that not all plots have distinct peaks. For example, the first plot in the second row in Figure 7 has a distinct peak while the first plot of the third row has no distinct peaks. Therefore, the traditional three-point Gaussian sub-pixel accuracy method can be used to determine better peaks in such cases. Another observation we made is that the middle vectors tend to have larger magnitudes than the vectors in the higher and lower rows. This observation seems to indicate that the body of the bee, as a whole, causes maximum motion and, as a consequence, it is reasonable to treat whole bees as tracers. The bee body parts such as wings, thorax, and legs result in smaller motions or are not detected at all.  
Figure 6: Two consecutive video frames, Frame 1 and Frame 2 with a single moving bee and corresponding DPIV motion vectors.  
Figure 7: 3D plots of correlation matrices for the motion vectors in Figure 6c. Each row in the figure corresponds to each row in the vector plot of Figure 6c.