## 4 Experiments
### Interrogation Window Sizes  
We used a single bee as a tracer. However, a single bee motion generates multiple motion vectors, because multiple bee parts (wings, thorax, legs, etc.) are moving simultaneously, which may be captured in interrogation windows. We executed additional experiments with our algorithm to evaluate its performance with different image and interrogation window sizes. Specifically, we experimented with three image sizes: \(160\times 120\), \(320\times 240\), and \(640\times 480\). For each image size, we manually calculated the bee size in pixels. For \(160\times 120\) images, the average bee size was equal to \(8\times 8\) pixels; for \(320\times 240\) images, the average bee size was equal to \(16\times 16\); and for images \(640\times 480\), the average bee size was equal to \(32\times 32\). For each image size and bee size, we tested different sizes of interrogation windows (i.e., smaller than the bee size, equal to the bee size, and larger than the bee size) with different amounts of interrogation window overlap. We made no attempt to improve the quality of the data or reduce the uncertainty of particle displacement, because the system should work out-of-the-box in the field on inexpensive, off-the-shelf hardware for beekeepers and apiary scientists worldwide to afford it. To remove the spurious vectors, we calculated the signal to noise (SNR) ratio for each generated correlation matrix. The SNR was calculated by finding the highest peak (\(p_{1}\)) and the second highest peak (\(p_{2}\)) in the correlation matrix and then computing SNR as their ratio (i.e., \(SNR=p_{1}/p_{2}\)). If the SNR values were less than a given threshold (0.05 in our case), the corresponding vectors were considered spurious and removed. Such vectors were replaced by the weighted average of the neighboring vectors. We used a kernel size (\(K\)) of 2 and a local mean to assign the weights with the formula \(1/((2K+1)^{2}-1)\). We used a maximum iteration limit of 15 and a tolerance of 0.001 to replace the spurious vectors. Table 4 gives the results of our experiments with different interrogation window sizes on \(640\times 480\) image frames in the high-traffic video \(HT\_Vid.mp4\). The last two columns give the dynamic time warping (DTW) results. Tables for the other image sizes and videos (Tables 14-15) are given in the Appendix A. As these tables show, the best similarity with the ground truth was achieved when the interrogation window was twice the size of the bee or higher for all three image sizes and an interrogation window overlap of 30% or higher. Figure 8: Scaled 3D map for the correlation matrices of Figure 6(a),b respectively. In the course of our investigation, we discovered that in some videos there were bees which flew very fast. Figure 9 gives the first and last frames (Frames 1 and 7, respectively) in a seven-frame sequence from a high bee traffic video. Table A3 in the Appendix A gives all the frames in the sequence. In Figure 9, a fast moving bee is delineated in each frame by a green polygon. The bee is moving right to left. The coordinates of the green dot (a single pixel) in each polygon are x = 507.0, y = 1782.0 in Frame 1 and x = 660.0, y = 151.5 in Frame 7. The pixel displacements of the green dot for this sequence are as follows: 220.9 pixels between Frames 1 and 2 (first displacement); 218.5 pixels between Frames 2 and 3 (second displacement); 247.6 pixels between Frames 3 and 4 (third displacement); 329.7 pixels between Frames 4 and 5 (fourth displacement); 347.6 pixels between Frames 5 and 6 (fifth displacement); and 303.1 pixels between Frames 6 and 7 (sixth displacement). The total pixel displacement of the green dot between Frames 1 and 7 is 1667.4 pixels. The average pixel displacement per frame is 277.9 pixels. The pi camera used in our investigation is not sufficiently powerful to capture all such displacements. In our system, the maximum pixel displacement per frame is set to 40 pixels, which represents the maximum velocity that our system can currently handle.