## 2 Related Work
### Capsule Network  
Within the domain of NIR target tracking, the selection of features is important [48; 49]. These features not only describe multiple attributes of the target object, such as shape and texture, but also they are related to the precision and stability of the tracking process. To further improve the tracking performance, capsule features [42] show their unique advantages. Capsule features not only capture the features of the object, but also emphasise the mutual and dependency relationships between different layers of capsules. However, traditional capsule networks focus on the capture of spatial features and ignore spectral information when extracting features. Spectral information, as unique to NIR [30] imaging technology, contains rich material clues that are conducive to accurate identification and tracking of targets. Therefore, by fusing spectral information with capsule features, the characteristicsof the target object can be comprehensively depicted and provide a richer and more reliable basis for predicting the target location. This fusion strategy is expected to significantly enhance the performance of NIR target tracking systems.  
The capsule network architecture comprises a dual-component framework: an encoder-decoder structure. The encoder incorporates sequential feature transformation stages, including convolutional operations for low-level feature extraction, primary capsule formation via initialization layers, and hierarchical capsule transformations through dynamic routing mechanisms. Conversely, the decoder implements a reconstruction module containing three-tier fully connected layers for dimensional mapping. Crucially, the network employs dynamic routing algorithms to propagate capsule activations between hierarchical levels, establishing iterative agreement processes that ensure context-aware feature propagation from lower to higher capsule tiers. The dynamic routing protocol is as follows: The feature vector is subjected to a squashing operation such that its length is between 0 and 1. The squashing function [40] is denoted as:  
\[V_{j} =\text{squash}\big{(}S_{j}\big{)}= \frac{\big{\|}S_{j}\big{\|}^{2}}{1+\big{\|}S_{j}\big{\|}^{2}}\frac{S _{j}}{\big{\|}S_{j}\big{\|}} \tag{1}\]  
where \(V_{j}\) denote the output produced by capsule \(j\), \(S_{j}\) represent its total received input, and \(\big{\|}\big{\|}\) denotes the magnitude of a vector. The prediction of the \(i\)-th capsule output vector \(u_{i}\) in layer \(l\) for the \(j\)-th capsule in layer \(l+1\) is represented as:  
\[u_{j|i} = W_{ij}u_{i} \tag{2}\]  
where \(u_{j|i}\) denotes the predicted output of the \(i\)-th capsule of feature capsule in layer \(l\) to the \(i\)-th capsule in layer \(l+1\), \(u^{i}\) denotes the output vector of the \(i\)-th capsule of feature capsule in layer \(l\) after similarity processing, and \(W_{ij}\) denotes the transformation containing the learning relation of the \(i\)-th capsule of feature capsule in layer \(l\) to the \(i\)-th capsule in layer \(l+1\). The aggregated input to capsule \(j\) in layer \(l+1\) is obtained by computing a weighted sum of the predictions made by all capsules in the preceding layer:  
\[S_{j} = \sum_{i}C_{ij}u_{j|i} \tag{3}\]  
where \(S_{j}\) represents the aggregated input received by capsule \(j\), and \(C_{ij}\) refers to the dynamic coupling weight linking capsule \(i\) in the previous layer to capsule \(j\) in the subsequent layer. The symbol \(\sum\) indicates the operation of summation. The coupling coefficients are normalised using the softmax function during the iteration process:  
\[C_{ij} = \text{softmax}\big{(}b_{ij}\big{)} \tag{4}\]  
where \(b_{ij}\) is the initial weight and \(C_{ij}\) is the coupling coefficient.