# Resolving Gas Bubbles Ascending in Liquid Metal from Low-SNR Neutron Radiography Images
## 5 Experimental Validation  
### Stationary Reference Body  
The developed image processing algorithm is first validated by applying it to the images of a stationary reference body described in Section 2.1. Three imaging cases are considered here: neutron flux transmission through the shorter body axis, the longer axis, and the latter with an extra distance from the body to the scintillator. Thus, the SNR of the neutron-transparent spherical cavity within the body progressively decreases for these cases. This is illustrated in Figure 18. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Image Sequence** & **MRIF** & **Algorithm 6** & **Property Filters** & **Total** & **Remainder** \\ \hline Figure 14b & 1.75 & 2.63 & 1.21 & 5.49 & 94.5 \\ Figure 14d & 1.51 & 4.63 & 6.80 & 12.5 & 87.5 \\ Figure 17b & 1.53 & 2.05 & 1.25 & 4.76 & 95.2 \\ Figure 17c & 0.71 & 0.51 & 0.18 & 1.39 & 98.6 \\ Figure 17d & 1.62 & 0.89 & 0.32 & 2.81 & 97.2 \\ \hline \hline \end{tabular}  
* **Algorithm 7:** Post-processing for the output of the image processing code.  
**Input**: Tilt angle (or any other bubble property) values over elevation (or any other independent variable)
* Construct the upper and lower quantile spline envelope (QSE) functions for the input data with the quantile \(q\)
* Sample the QSEs evenly in intervals of \(N_{\text{QSE}}\) points over the independent variable range
* Smooth the QSEs using Gaussian TV filtering
* Designate the data points above the upper and below the lower lower QSEs as outliers and remove from the dataset
* Bin the remaining data points over the independent variable range into bins with size of \(\delta_{\text{b}}\) points
* Compute means and standard deviations for the resulting bins
* Smooth the resulting mean value sequence using Gaussian TV filtering
* **Output**: An averaged curve for the dataset with error bands  
\end{table} 
Table 1: False positive elimination rates (%) over three stages—MRIF, the luminance map-based filter (Algorithm 6) and the object property filter (with respect to the input that each filter received), and the percentage of detection events input to MRIF that were eliminated in total. Figure 18: Static reference body: (**a**) an example radiograph; (**b–d**) normalized images cropped as in (**a**) for neutron flux transmission through the shorter axis, the longer axis, and the latter with an extra distance to the scintillator, respectively; (**e–g**) normalized mean luminance maps for the respective image sequences. Note the color bar to the right. A neutron radiography image of the reference body (slightly inclined) is shown in (a) where one can see the rectangular brass frame (darker) and a circular projection of the spherical void (brighter), as well as the surrounding background due to air. Neutron transmission in the case of (a) is along the shorter of the body axes. In all three imaging cases the images are cropped as indicated in (a). Examples of cropped images of the spherical void within the body with exposure very similar (\(\sim\)1.3\(\times\)) to that for the bubble images (100 FPS, \(\sim\)1.3\(\times\) neutron flux) are shown in (b-d) for the three cases listed above, respectively. The corresponding mean luminance maps shown in (e-g) were obtained by averaging over \(\sim\)5.8 K, \(\sim\)12 K and \(\sim\)9.5 K images (entire recorded sequences), respectively--these averaged images are used to obtain reference shapes. The shapes detected by the image processing code in images like (b-d) are then compared to the reference shapes to compute shape detection error metrics. Note that all images seen in Figure 18 and used for validation are obtained from raw images by pre-processing via Algorithm 2, as with bubble flow images. Note that the images shown in Figure 18 have the image side length to sphere diameter ratios that are very similar to what one has for MRIF IWs.