# A Dynamic Measurement System Based on Adaptive Clustering and Multi-Classifier
## 3 Materials and Methods
### Multi-Feature Offline Classification Model  
One of the fundamental tasks in the offline phase of deep learning is the training of the sample set. Prior to this training, it is typically essential to normalize the features across each dimension to the same range and to remove correlations among different features. As the diversity of samples grows, so too does the complexity and number of features. The refueling drogue in aerial refueling is a multi-skeletal, umbrella-shaped structure that changes in appearance during different stages of the refueling process. Notably, during the docking stage, the refueling drogue may transition from a frontal view to a side view; however, this side-view phase is relatively brief, typically encompassing only one or two rounds of sample collection. Consequently, this paper employs three data augmentation techniques to broaden the receptive field in the higher-dimensional layers. The goal is to enhance the representation of datasets in the training set that have small sample sizes but high feature distinctiveness. The detection performance of targets at varying scales is positively correlated with the expansion rate, indicating that a larger receptive field leads to improved detection performance for larger objects, while a smaller receptive field is more suitable for detecting smaller objects. The preprocessed samples adequately meet the required dimensions for training; however, due to their substantial size and high complexity, the weights derived from training demonstrate substantial missed and false detections during actual tests on the smallest distant target. Conversely, for the closest large target, significant changes in appearance and anchor points occur due to the locking state of the refueling drogue, with its position at the side of the camera often causing severe shaking of the detection frame and a marked reduction in accuracy. This paper introduces a feature responder that accentuates various drogue features within the training set and employs a K-means clustering algorithm to facilitate adaptive classification of the same target training set using multi-object classifiers. A continuous Fourier transform is applied to the positive samples of the annotated drogue region in the dataset, translating image information from the spatial domain to the frequency domain. In this domain, higher frequencies indicate a faster rate of change in the original signal, while lower frequencies imply that the original signal is smoother. Therefore, abrupt changes in the image are primarily a combination of edge information from the refueling drogue and noise; meanwhile, the slowly changing parts of the image, which represent the contour details, can be effectively distinguished using high- and low-pass filters. The Fourier transform \(F(u,v)\) of a two-dimensional continuous function f(x, y) is defined as in Equation (1):  
\[F(u,v)=\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f(x,y)e^{-j2\pi(ux+vy)}d_{x }d_{y} \tag{1}\]  
where \(f(x,y)\) is a two-dimensional signal, \(F(u,v)\) is the transformed frequency domain representation, \(u\) and \(v\) are frequency variables, and \(d_{x}\), and \(d_{y}\) represent the number of rows and columns of the signal, respectively. Based on the feature information captured by the feature responder, the majority of the sample features can be adaptively segmented into three categories using the K-means algorithm: far-range, medium-range, and close-range drogues. Depending on various pre-selection boxes and feature responses, the training set is automatically categorized into large, medium, and small drogue subsets. The model incorporates a pyramid structure, where pre-selection boxes of different sizes are allocated to corresponding feature layers. The characteristic response values of the refueling drogue during aerial refueling are illustrated in Figure 1.  
In the illustration, red indicates the normalized distance, while blue denotes the feature response value.