# Resolving Gas Bubbles Ascending in Liquid Metal from Low-SNR Neutron Radiography Images
## 5 Experimental Validation
### Error Analysis
To verify this, we also observe how \(S_{\Delta}\) changes for shapes with significant deformities detected (rarely) for stationary body images when ground truth masks (Figure 18e-f) are replaced with fits using (19)--this is in agreement with the above idealized estimate rather well, yielding \(S_{\Delta}\) differences \(\in(4;5\%)\). If this adjustment is applied to Figure 28a,c,e, the observations are consistent with the results for the stationary reference body, and the local filter \(S_{\Delta}\) values come out to about \(\sim 10\%\) at distribution peaks (versus \(\sim\)8% for Figure 24c), excluding one of the cases in Figure 28e (light green curves). To reiterate, \(\delta S\), \(\delta r\) and \(\delta c\) are unaffected by (19) by their definitions. Figure 27: Frame pair velocimetry (magnitude) for the moving body (Figure 22): (**a**) velocity over sequential frames for all recorded image sequences with oscillations filtered out for visual clarity; (**b**) velocity for one of the image sequences with oscillations shown. (**a1**) shows the first 500 frames in (**a**). Gaussian TV filtering was used for (**a,b**) with the regularization parameters set to 5 (150 iterations) and 0.5, respectively. Here the \(\delta r\) distributions again conform to \(\delta S\). \(\delta c\) is negligible for all cases and, as seen in Figure 29, \(\|\delta x,\delta y\|\) is such that the asphericity of the detected shapes in within acceptable bounds. Turning to Figure 29 and recalling that with (19) \(\delta x\) and \(\delta y\) are correlated with the sphericity of the detected shapes, notice that the errors are anisotropic in all cases. The greater component \(\delta x\) corresponds to the main direction of motion. Importantly, this anisotropy is also observed when inspecting the shape/reference difference masks for the local and global filters, where the largest contributions to \(S_{\Delta}\) are at the shape sides in the \(-x\) and \(x\) directions which are the pendulum (Figure 22) oscillation directions. Since \(S_{\Delta}\) and \(\delta S\) maxima for the global filters were not included in Figure 28 for visual clarity, and to quantify error dispersion, Figures 30 and 31 show these quantities explicitly for all three test groups and for both global and local filters, while shape detections with \(S_{\Delta}\) and \(\delta S\) values close to the values indicated in Figures 30b and 31b are very rare, it is important that the local filter can significantly improve the quality of detected shapes even in these instances. Figure 28: Smooth normalized \(S_{\Delta}\) (**a**,**c**,**e**) and \(\delta S\) (**b**,**d**,**f**) histograms for the cases with a moving body (pendulum): neutron flux transmission along the (**a**,**b**) smaller axis, (**c**,**d**) larger axis and (**e**,**f**) the latter with the addition of synthetic image artefacts. Note the legend in the upper-right corner of (**a**) indicating the results for the global and local filtering. Colors indicate different imaging instances. \(S_{\Delta}^{+}\) is the correction for the reference mask fitting bias (red arrows). Figure 30: (**a**) Mean and (**b**) maximum \(S_{\Delta}\) values for the cases with a moving reference body. The results for the global and local filtering are represented with matte and glossy bars, respectively. The standard deviations for the mean values in (**a**) are indicated by the red (global) and black (local) error bars. Note the color legend in the upper-left corner of (**a**) indicating the three different test groups considered in Figures 28 and 29. Figure 29: Smooth normalized \(\delta x\) (**a**,**c**,**e**) and \(\delta y\) (**b**,**d**,**f**) histograms for the cases with the moving body: neutron flux transmission along the (**a**,**b**) smaller axis, (**c**,**d**) larger axis and (**e**,**f**) the latter with the addition of synthetic image artefacts. The effects of motion blur can be assessed more quantitatively and directly--consider Figure 32 where \(S_{\Delta}\) is plotted as a time series for two of the processed image sequences.