# Resolving Gas Bubbles Ascending in Liquid Metal from Low-SNR Neutron Radiography Images
## 5 Experimental Validation
### Error Analysis
Moving on to the moving reference body imaging, the results of these tests are shown in Figures 27-32. Figure 27 shows the pendulum (and reference void) velocity dynamics over consecutive frames for all imaging series. The [20; 40] cm/s range of expected bubble velocities (Section 2.3) is covered by the performed measurements, as seen in (a) and (a1), where the obtained velocity range is [5; 70] cm/s. Importantly, in addition to shorter and longer axis transmission tests, we also used purposefully inappropriate texture synthesis and outlier removal settings in Algorithm 8 to generate three sets of data with synthetic image edge artefacts (luminance similar to the void regions) and single pixels with luminance exceeding the image maximum by an order of magnitude (greatly  
Figure 26: Static reference body: smooth normalized \(\|\delta x,\delta y\|\) histograms for neutron flux transmission along the (**a**) smaller axis, (**b**) larger axis and (**c**) larger axis with an extra 1 cm distance between the scintillator and the body. Note that here \(\delta x\approx\delta y\) for all instances, which is why they are not plotted individually. reduced image CNR) to see how the filters perform. Consider Figure 28 where \(S_{\Delta}\) and \(\delta S\) distributions are shown for the three test groups. As before, the global filter performance in terms of both \(S_{\Delta}\) and \(\delta S\) progressively decreases as the transmission axis length is increased and then image artefacts are introduced to the data from the longer axis transmission measurements. Notice that the \(S_{\Delta}\) and \(\delta S\) values in Figure 28 are in all cases greater than in the static body cases (Figures 24-26). This is clear enough to be seen visually, as histogram peaks in (a,b) are just under \(\lesssim 15\%\) errors for the global filter output, while only being just under \(\lesssim\)8% in the worst case for \(S_{\Delta}\) in Figure 24c. However, this is exactly where the local filter makes a radical difference--observe in Figure 28a,c,e that the dispersion, maxima, minima and means of \(S_{\Delta}\) are greatly reduced. Similarly good performance is seen in (b,d,f) in terms of \(\delta S\). Notice that the changes in the local filter error distributions as image quality gets worse from (a,b) to (e,f) are consistent with what is seen for static body imaging in Figures 24 and 25. Another important point here is that two of the shorter axis transmission instances (Figure 28a,b) and one from the longer axis groups (Figure 28c,d) are with an extra 1 cm body-to-scintillator distance (2 mm by default)--however, in this case the differences are not significant enough to warrant attention. This likely stems from the fact a large fraction of errors is due to motion blur, especially during the pendulum deceleration stage, which is within the first 300-500 imaging frames (Figure 27). It is also very clear from Figure 28e,f that introducing additional image artefacts considerably degrades the global filter performance. The local filter, again, greatly improves the quality of detected shapes, but, of course, also produces greater errors as opposed to what is seen in (c) and (d). One must remember that \(S_{\Delta}\) is reduced by (19). To estimate the reduction, consider that if the centers of two circles with equal radii are displaced by a factor \(k\leq 2\) of the radius of either, the relative area of their difference is \(S_{\Delta}(k)=1-(2/\pi)\arccos(k/2)+(k/\pi)\sqrt{1-k^{2}/4}\). Assuming the worst-case scenario where mask fitting via (19) \"improves\" the position of the detected shape by the peak \(\|\delta x,\delta y\|\) value in Figure 26c, \(k\sim 8\%\), the \(S_{\Delta}\) underestimation comes out to \(S_{\Delta}^{+}\sim 5\%\).