# Resolving Gas Bubbles Ascending in Liquid Metal from Low-SNR Neutron Radiography Images
## 4 Performance Analysis
### Mrif  
The first segment estimator could have been enough for bubble shape extraction, when tuned appropriately, if not for the fact that the image considered in Figures 6-8 is one of the better examples in terms of noise and artefacts present, i.e., a considerable portion of the images captured in our experiments are of a much poorer quality. Not only are the obtained shapes often imprecise or deformed, they can at times be decidedly non-physical--one such example is show in Figure 9, where in (a) a segment is shown that looks like two bubbles that are in the process of merging. Such events are not expected at the flow rate for which this image was acquired, therefore Figure 9a shows an obvious artefact. The bottom-right corner of (b) contains closely packed high-luminance spots which likely have been combined and merged with the bubble region in the upper-left corner. However, once MRIF targets the segment and the local filter is applied to the SSCF output projected onto the segment IW (c) in stages (d-h), the artefact is no longer present and a single bubble is correctly resolved. In addition to such artefacts, since the global filter was tuned to maximize the odds of detecting bubbles in the FOV, there are cases where detected segments are false positives. Two instances of such segments interrogated by MRIF are shown in Figure 10. In (a) one can see that the local filter has revealed that there is indeed no segment contained within the IW. However, interrogating the false positives in an IW might on occasion produce segments yet again, as in (b), where the gradient filter stage (b4) generated a structure that resembles a bubble edge halo. It was then segmented and, through edge cleanup, transformed into a segment that seems eligible--but simply overlaying it over the original image projected onto the IW, one can see that this is not the case. However, MRIF effectively performs a two-factor false-positive check, and in such cases the luminance map-based filter (Algorithm 6) serves as a backup. Once the global SCTMM output is projected onto the IW and SCTMM is applied to the resulting image (b9), one can see that the segment overlay contains only background, and thus this false positive will be eliminated since it has \(\langle I\rangle\cdot\text{max}(I)<\eta\). Figure 8: The effect of filtering stages on bubble signal versus noise and background: (**a**) pseudo-3D shaded relief plots of strips taken from Figure 6a–f (sub-figures 1–6, respectively) containing bubbles and background in between; (**b**) mean luminance profiles over image strips (1–4) in the direction indicated by a blue dashed arrow in (**a**) for pre-processed, PM-, TV- and SSCF-filtered images; (**c**) mean luminance profiles for SSCF-, SCTMM- and gradient-filtered strips (4–6). Note that all luminance profiles in (**b**,**c**) have been normalized for direct comparison. An example containing several instances of false positives, under-resolved shapes and bubble regions merged with noise patterns is shown in Figure 11. Notice that the image quality, even visually, is much worse than in Figures 6-8. The artefacts in the upper part of the image stem from lower CNR in (b), whereas one of the bottom artefacts comes from a  
Figure 10: Instances of false positives revealed by MRIF with (**a**) no local segments found and (**b**) an artefact (purple outline) that will be eliminated later by Algorithm 6 based on the segment luminance map. Sub-figures (1–9) in (**a**,**b**) are: (1) is the original image projected onto an IW; (2–7) are the respective local filtering stages (Figure 9c–h); (8) is (1) with detected edge overlays; (9) is SCTMM applied to (2).