# Accurate Tracking Algorithm for Cluster Targets in Multispectral Infrared Images
## 3 Methods
### Construction of the Target Observation Model
Under the control of the numerical model, in the case of multi-channel infrared images, the complex background will cause a change in the optical flow field value. For this purpose, we set a random variable (\(G\)) of the infrared image, which can be expressed as:  
\[G=\left\{g_{1},g_{2},\ldots,g_{n}\right\} \tag{21}\]  
where \(g_{n}\) represents the pixel variance in the infrared image. Corresponding to the pixel sampling points of a single image, the probability density of individual pixel sampling points is calculated using Gaussian distribution probability, which can be expressed as:  
\[\rho(x_{t})=\sum_{i=1}^{n}w_{i}\cdot\tau \tag{22}\]where \(w_{i}\) represents the pixel sampling point parameters and \(\tau\) represents random variable parameters. After setting the membership time parameter of the Gaussian distribution, we set the new pixel parameter \(X_{t}\) and control the deviation of the model mean value to \(e\). At this time, the matching parameter relationship of weak and small target features in the infrared image can be expressed as:  
\[\frac{|X_{t}-u_{i,t-1}|}{\rho(x_{t})}<e \tag{23}\]  
where \(u_{i,t-1}\) represents the distribution parameters of the matching pixels. When the infrared image conforms to the numerical relationship of the calculation Formula (24), the background pixel is defined as the foreground, and the weights are updated according to the above parameters. Using the traditional algorithm, if the background is dynamically changing in this process, upon the weight update, the target feature pixels and background interference pixels will be infinitely copied and amplified to form interference or they will not be copied and will be eliminated, resulting in noise amplification or target loss. The improved algorithm has better adaptability. With the optimal setting of the threshold value in resampling, the particle weight of the particle at a certain moment is only related to the probability distribution of the measurement noise, and the change in the target characteristic pixels will not be disturbed by the dynamic change in the background, thus enabling the effective realization of the high-precision identification and tracking of weak targets. After updating and normalizing the pixel model, the final dim and small target features of the infrared image can be represented as follows:  
Figure 3:0  
where \(\alpha\) represents the normalization parameter and \(M_{k,t}\) represents the infrared image pixel matching parameter. \(\alpha\) parameter normalization is carried out using resampling and the selection of an optimized proposed distribution \(q(y|x)\). This is because, in traditional SIS [22], there is a problem of weight degradation, i.e., in the iterative process, the weights of the particles become increasingly smaller or increasingly less even, which results in an excessively large sample variance for the approximation of a distribution caused by the high-dimensional space. The higher the dimensionality, the higher the increase in the required sample size. The resampling will result in a new number of particle replications, and particles with large weights will be replicated multiple times, while particles with small weights will be replicated less often or eliminated, thus achieving idealized parameter normalization. Using the infrared image weak target features defined above, the multi-channel weak target feature constraint relationship is constructed. The overall flow that constitutes the proposed algorithm in this paper is shown in Figure 4, based on the preceding discussion of the methods used. The original multi-target images and the images annotated using Labelme software form the training set and are trained into a PigNet model using the PigNet network built previously. The infrared image subspace is then established for the adjacent frames of the acquired multi-target image set, and the high-dimensional input image is projected onto the subspace to remove redundant information and obtain the original image feature information.