# Method for Detecting Underwater Microbubbles Using Dual-Mode Fusion of Laser Polarization
## 2 Dual-Mode Fusion Detection Mechanism
### Image Fusion and Feature Extraction  
In this section, we propose a polarization scattering-weighted fusion imaging method for turbid water bubbles. We consider the effect of bubble number density on the detection transmission; according to the literature [18], we can know that with an increase in bubble number density, the Mie scattering probability of the laser and the bubble group increases not only single scattering but also multiple scattering probability, which leads to an increase in the scintillation factor. Therefore, in order to accurately measure the fluctuation value of the bubble density on the scintillation factor, the key is to accurately identify and count the number of bubbles in the laser detection channel. Due to the large number of stray particles in the water, the coexistence of bright bubbles and dark bubbles occurs easily in the traditional active illumination imaging and particle velocimetry (PIV) methods due to the limitation of illumination methods and mutual blockage [19]. It is difficult  
Figure 4: Bubble group receding polarizability results with different size and number distributions. to accurately identify the bubble particles by the grayscale-based identification method, while using polarization imaging, it is difficult to unify the bubble polarization due to the severe receding effect caused by the bubble's own stray particles. At the same time, due to the movement of the bubbles, the background polarization changes significantly, so the coexistence of bright and dark bubbles still occurs on the image, making it difficult to accurately locate and identify them so as to better determine the number of bubbles and identify the bubble targets. A literature review [20], which suggests using the fusion of polarized and unpolarized pictures to discriminate and determine the likelihood, is cited in this paper. One way to describe the fused image is as follows:  
\[I_{fused}(x,y)=a(x,y)I_{P}(x,y)+b(x,y)I_{nP}(x,y) \tag{6}\]  
where \(I_{fused}(x,y)\) is the fused image, \(I_{P}(x,y)\) is the polarized image, \(I_{nP}(x,y)\) is the unpolarized image, and \(a(x,y)\), \(b(x,y)\) are the weights of the polarized image and the unpolarized image, respectively. The calculation of the weights of \(a(x,y)\), \(b(x,y)\) are determined by the polarization change of the polarized image, which can be specifically characterized as follows:  
\[\left\{ \begin{array}{l}a(x,y)=\frac{P_{D}(x,y)}{P_{D}}\\ b(x,y)=\frac{\overline{P_{D}}}{P_{D}(x,y)}\end{array} \right. \tag{7}\]  
where \(P_{D}(x,y)\) is the line polarization of a point in the polarized image and \(\overline{P_{D}}\) is the average polarization of the polarized image, taking into account that when \(P_{D}(x,y)\) is too small it will make the weight \(b(x,y)\) too large, making the image appear as an oversaturated point, an overexposure phenomenon, which will affect the subsequent judgment, so the weights will be modified to the following:  
\[\left\{ \begin{array}{l}a(x,y)=\frac{P_{D}(x,y)}{\overline{P_{D}}}\\ b(x,y)=\frac{\overline{P_{D}}}{P_{D}(x,y)+\theta}\end{array} \right. \tag{8}\]  
\(\theta\) is a correction parameter ranging from 0 to 1, which is adjusted according to the background and impurity content of the water body, and is measured to be around 0.104 in clear water, 0.226 in coastal water, and 0.486 in port water, and in order to ensure the quality of the fused images, the correction function \(\theta\) should not be higher than 0.5. The polarization fusion image mechanism is shown in Figure 5 below:  
Figure 5: Polarization image fusion mechanism.