# Resolving Gas Bubbles Ascending in Liquid Metal from Low-SNR Neutron Radiography Images
## 4 Performance Analysis
### Mrif
Figure 9: Updating a first segment estimate using the local filter (Algorithm 5): (**a**) first estimate in an IW; (**b**) original pre-processed image projected onto the IW; (**c**) SSCF output projection onto the IW (Algorithm 3); (**d**) mean-filtered SSCF output; (**e**) gradient filter output; (**f**) Chan–Vese segmentation output; (**g**) edges extracted via erosion and thinning; (**h**) updated local segment for the IW. Segment filling and cleanup are similar to what is done in Algorithm 3.  
noise structure in the background that resembles a bubble. However, as seen in (d,e), MRIF successfully removes all false-positives and artefacts while improving the shape estimates. An even more difficult case is seen in Figure 12 where very large segments appear. The largest one in the upper part of (c) has occluded two of the four bubbles visible in (a,b). This is also an instance where the crop correction (17) is significant for remapping the updated segments onto the FOV (16). MRIF successfully resolves bubbles from the first estimates, as seen in (d-f). Notice the segment in the bottom-left part of (e,f)--its luminance map contains background only, so it will be later eliminated by Algorithm 6. To see how MRIF iteratively resolves cases like the above two examples, consider Figure 13 where the updates for the first segment estimates are shown for MRIF iterations. One can see in (e3) that the SNR and CNR are even worse than in the cases shown in Figures 11 and 12. The largest segment seen in (e1,a1) is first resolved into two bubbles (b1) and then each bubble is interrogated once more, obtaining more precise shapes. The bottom-most segment in (e1) requires the most MRIF iterations--the first two, (b3) and (c3), remove portions of the artefact that had obscured the bubble, and the last iteration (d) updates the resolved shape. The resulting bubble shapes are then mapped onto the FOV as indicated in (b-e). Figure 11: An example of segmentation improvement by MRIF: (a) horizontally cropped pre-processed image—note the very low CNR in the upper half of the image; (b) global SCTMM filtering result; (c) first segment estimates; (d) updated segments output by MRIF; (e) output segment overlays for (a). Note that the top- and bottom-most segments from (c) are not present in (d,e)—this is the correct behaviour, since one can visually see in (a,b) that the corresponding bubbles are partially outside of the FOV, and thus are not eligible for analysis. Figure 12: Another example of MRIF resolving initially occluded and incorrectly detected segments. Sub-figures (**a**–**d**,**f**) correspond to Figure 11a–**e**, respectively, and (**e**) shows the MRIF output overlays for the global filter output. The false positive in the bottom-left corner of (**d**–**f**) that survived MRIF interrogation will be eliminated by Algorithm 6, since it corresponds to background (**e**). Figure 13: An illustration of the iterative interrogation process for an image with one of the worst overall SNR values, where \(R\) is the MRIF recursion depth. Sub-figures (**a**–**d**) show \(R\) running 0 through 3 for the segments detected at each depth. Sub-figure (**e**) displays (1) the initial segments, (2) MRIF output and (3) output overlays for the original image. Converged segments are flagged with green ticked boxes. Colored frames in (**e2**) correspond to (**b2**), (**c1**–**2**,**d**) via respective colors. Orange frames in (**e1**) indicate the IWs at \(R=1\): note the high aspect ratio of the topmost IW—its virtual counterpart is significantly out-of-bounds and therefore considerable crop correction (17) is assigned to properly map (**c1**–**2**) onto the FOV. Here it is important to reiterate that the performance of MRIF strongly depends on the user-defined IW scaling factor \(s\) (8) and the critical IW length scale ratio \(\varepsilon\) for the latest and the (potential) next recursion iterations. Specifically, the \(\chi=s/\varepsilon\) ratio is of interest--we suggest \(\chi\geq 1\) in general.