# Resolving Gas Bubbles Ascending in Liquid Metal from Low-SNR Neutron Radiography Images
## 4 Performance Analysis
### Results for Existing and New Data  
Aside from the examples shown in Sections 4.1 and 4.2, it is also of interest how the developed approach performs for entire image sequences in terms of bubble detection density in the FOV and the physicality of obtained results, i.e., bubble trajectory and shape properties. Figures 14-16 demonstrate the differences in performance for the preceding image processing pipeline [8; 43] and the methodology presented here. Figure 14: The locations of bubbles detected in the FOV for a sequence of 3000 images (30 s) at a 100 sccm flow rate for the model system from [8; 43] (Section 2.1, horizontal inlet): no applied MF, (**a**) previous and (**b**) current image processing code; applied \(\sim\)265 mT horizontal MF, (**c**) previous and (**d**) current image processing code. Bubble locations are marked with dots color-coded in the chronological order of appearance. Note the color legend in (**d**): imaging starts at 0 and ends at 1. The red-tinted areas indicate the blind zones of the previously used image processing code. All sub-figures are to scale. One can clearly see in Figure 14 that the new version of the image processing code outperforms the previous version by completely avoiding the blind zones in the lower part of the FOV for both image sequences. Notice also that bubble tracks visible in (b) are much more coherent than in (a). Figure 15, in turn, shows that with the new methods one can now clearly resolve the classical S-shaped mean trajectory cluster formed by zigzag trajectories, as seen in (c,d), as opposed to (a,b) where a significant portion of the events is missing. The deflection bias in the \(x>0\) direction in (c,d) is determined by the horizontal inlet releasing gas in that direction. Another point of interest are the tilt angle dynamics resolved in [8] versus the current results--this is showcased in Figure 16. Three things are important to note here: first, as a consequence of the blind zone elimination, the new curves extend all the way through the FOV; second, the average trends yielded by both approaches indicate that the previously used code indeed resolved the dynamics without unacceptable inaccuracy; third, the error bands are considerably narrower about the averaged curves for the present results. The latter is especially true for the case with applied MF shown in (b) where the SNR was much lower then in the image sequence corresponding to (a). This indicates that the new approach indeed yields significant improvement not just in bubble detection, but also in shape boundary resolution. The experimentally obtained results in [8] were in a rather good agreement with performed simulations, meaning one thus has an indirect yet significant validation of the presented approach. The developed approach was also applied to the newly acquired data to ensure consistency in the code output across different experimental campaigns--one instance of  
Figure 16: Bubble tilt angle versus elevation (averaged curves and error bands) over the FOV bottom for (**a**) the case with no applied MF (Figure 14a,b) and (**b**) applied horizontal \(\sim\)265 mT MF (Figure 14c,d), both cases at a 100 sccm flow rate. Orange indicates the previous paper [8] and the current results are shown in gray. The tilt angle definition is shown in the bottom-right corner of (**a**). Figure 15: Normalized bubble detection density histograms with \((dx,dy)=(2,4)\) mm bins color-coded by detection counts: (**a,b**) the case in Figure 14a with (**a**) all bins and (**b**) bins with 3+ detections shown; (**c,d**) the case in Figure 14b with (**c**) all bins and (**d**) bins with 4+ detections shown. Note the color legend to the right of (**d**). the new results is shown in Figure 17. Again, the bubbles are resolved over the entire FOV for all three cases shown. An in-depth physical analysis of the bubble dynamics is beyond the scope of this paper and is reserved for a follow-up article.