## 3 Proposed Algorithm
### Spectral Information Position Prediction  
A capsule network has higher computational complexity when dealing with HSI because it processes each feature into vectors for output. Searching within the predicted search box in the next frame can reduce computational complexity and locate the target area more accurately than searching the entire image range. It enhances tracking performance in terms of both responsiveness and precision. When the target is moving fast or the shape changes suddenly, the traditional strategy of fixing center of the search frame may lead to loss of the target. Predicting the position of the search frame in the next frame can better cope with these challenges and maintain stable tracking.  
Using the capsule network to predict the frame at time \(t\) and the adjacent frame at time \(t\)\(-\)1, where the target is located at \(p_{t}\) and \(p_{t-1}\), respectively.  
\[p_{t} = (x_{t},y_{t}) \tag{28}\]  
where \(p_{t}\) denotes the position of the target center at \(t\)-th frame, \(x_{t}\) indicates the horizontal coordinate of the target at frame \(t\), and \(y_{t}\) represents the vertical coordinate.  
\[p_{t-1} = (x_{t-1},y_{t-1}) \tag{29}\]  
where \(p_{t-1}\) indicates the center position of target at the \((t\)\(-\)1)-th frame, \(x_{t-1}\) refers to its horizontal coordinate, and \(y_{t-1}\) corresponds to the vertical one.  
In the case where relying only on the target center position to estimate the search center position in the subsequent frame may lead to a large error, we therefore approach the representation of the target by adding spectral information. When selecting the region  
The spectral curve difference \(f\) is calculated from \(C^{t}\) and \(C^{t-1}\) as:  
\[f=\int_{1}^{B}\Big{[}C^{t}-C^{t-1}\Big{]}^{2}dx \tag{35}\]  
where \(f\) denotes the spectral curve differernce. If this value of \(f\) is closer to 0, we can assume that \(C^{t}\) and \(C^{t-1}\) are more similar on the band interval. In practice, due to the precision limitations of numerical calculations, we cannot directly obtain the case where the value of \(f\) is exactly equal to 0. Therefore, if the value of \(f\) is less than some very small positive number, we consider the two functions to be similar.  
The spectral curve difference \(f\) determines whether the objects in the frames \(t\) and \(t-1\) exhibit similarity. This is specifically achieved as follows:  
\[S_{t\to t-1} = \begin{cases}Yes&\text{if }f<\varepsilon\\ Update&\text{if }f\geq\varepsilon\end{cases} \tag{36}\]  
where \(S_{t\to t-1}\) represents whether two objects are similar, and \(\varepsilon\) is the spectral positive number. Below the spectral positive number, it is similar and judged to be the same object, and the next position prediction is performed. If it is not an object, the information from the previous frame is updated into the Section 3.1 for subsequent tracking. Position prediction is performed as follows:  
\[P_{pre} = p_{t}+\Delta p \tag{37}\]  
where \(P_{pre}\) represents the centre of the search area. The location of the next frame is used as the centre point of the search area to select the search area for tracking the next frame.