# Method for Detecting Underwater Microbubbles Using Dual-Mode Fusion of Laser Polarization
## 2 Dual-Mode Fusion Detection Mechanism
### Dual-Mode Fusion Discrimination
Finally, we averaged the dynamic normalized grayscale received by the CCD camera for a selection of n cases to obtain Equation (18):  
\[\sigma_{1}^{2}(a,b,N_{num},D_{s})=\frac{1}{n}\sum_{i=1}^{n}\frac{-(a-b)^{2}( \frac{\overline{s}N_{num}\omega{D_{s}}^{2}}{N_{max}})^{2}+(a-b)^{2}(\frac{ \overline{s}N_{num}\omega{D_{s}}^{2}}{N_{max}})}{(a-b)^{2}(\frac{\overline{s} N_{num}\omega{D_{s}}^{2}}{N_{max}}  
suspension contains many plankton, which have the ability to absorb the polarized light formed by the \"polarization artifacts\", they and the bubble have a similar degree of polarization, even after polarization recognition, and there are still a significant portion of errors for bubble size and number remaining in the distribution statistics. This brings errors to the statistics of bubble size and number distribution.  
We test the effectiveness of our polarization image fusion algorithm by introducing the bubble detection rate (\(DR\)) with a multi-frame detection standard deviation (\(S^{2}\)). The detection rate and standard deviation equations are shown below:  
\[DR=\frac{C_{f}}{C_{T}} \tag{19}\]  
Figure 8: Bubble image under partial conditions. (**a**) Real shot image of bubbles generated by electrolytic molybdenum wire. (**b**) Bubble image after fusion processing in the box selection. Figure 9: Bubble handling count results. where \(C_{f}\) is the actual bubble detection value and \(C_{T}\) is the theoretical value of the bubble generated in that case. \[S^{2}=[(D_{1}-\overline{D})^{2}+\dots(D_{n}-\overline{D})^{2}]/n \tag{20}\]  
where \(D_{n}\) is the nth frame bubble size and \(\overline{D}\) is the average of the bubble sizes in that case. Meanwhile, in order to verify the reliability and accuracy of the polarization fusion algorithm, we use several common polarization image processing methods to detect and process the bubble images in the same case, and compare their binarization results as well, which are measured by the detection rate and variance mentioned above. The comparison results are shown in Figure 10 and Table 1 below. Figure 10 illustrates how the established algorithms can be used to finish bubble recognition. However, [PERSON]'s and [PERSON]'s methods depend on the extraction of stable background regions to some extent, so under the high-turbidity suspended particle flow field, the processed images all have large shadow regions, and are disturbed by dynamic background light, and the light intensity is uneven, so the images are blurred. As a result, the variance of multi-frame detection is larger and the error recognition rate is higher. However, compared with [PERSON]'s method, [PERSON]'s algorithm has strong adaptability in background selection and correction, so [PERSON]'s method has a higher value in the bubble detection rate. [PERSON]'s method does not rely on prior knowledge and assumptions, so it has strong ability in background scattering. Meanwhile, the contour of bubble recognition is clear, the image shadows are less, the multi-frame detection variance is low, and the error recognition rate is low. However, due to the existence of multiple objects with polarization characteristics in the image, the algorithm struggles to achieve uniformity in recognition, so its threshold of descattering is high. Some of the bubble particles with weak light intensity are filtered out, which makes the detection rate of this method low. Our method not only achieves image enhancement by weighted fusion of polarized and unpolarized images, but also homogenizes the brightness of the overall image and strengthens the bubble edge contour \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **[PERSON]’s [22]** & **[PERSON]’s [23]** & **[PERSON]’s [11]** & **Our** \\ \hline Detection rate & 75.6\% & 84.7\% & 81.2\% & 95.3\% \\ \(S^{2}\) & 0.364 & 0.205 & 0.064 & 0.051 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of results under different treatments.