## 2 Methods
### Multi-Feature Fusion  
A corner is one of the most important local features in object detection owing to its strong invariance to rotation, scale and illumination variation. In this paper, corners are extracted by the Harris operator [6], which is a popular corner detection algorithm that can be divided into the following steps. 1. Calculate the gray gradient in the \(X\) direction (denoted as \(I_{x}\)) and \(Y\) (denoted as \(I_{y}\)) direction of the image \(I\), then filter the \(I_{x}^{2},I_{x}^{2}\times I_{y}^{2},I_{y}^{2}\) with a Gaussian window. 2. The covariance matrix \(M\) of the object pixel is denoted as below: \[M=\left[ \begin{array}{cc}I_{x}^{2}&I_{x}I_{y}\\ I_{x}I_{y}&I_{y}^{2}\end{array} \right],\] (2)  
Figure 1: Overview framework of multi-feature fusion with rotating anchors generation mechanism for oriented aircraft detection. The proposed framework based on FFN, fuses multi-scale features from different CNN layers and integrates Harris corner features which extracted from binarized feature maps of FPN. (3) The value of corner response \(R\) of each pixel in the image can be calculated by:  
\[R=Det(M)-k(Tr(M))^{2}, \tag{3}\]  
where _Det(M)_ represents the matrix determinant of \(M\), _Tr(M)_ is the trace of \(M\), the \(k\) is empirical constant which generally take the value 0.04-0.06. The local non-maximum suppression of \(R\) is carried out. That is, retain the points whose values are the local maximum and greater than the threshold \(T\), reset the values of the other points to zero. These non-zero points are corners. Threshold \(T\) is generally \(10^{-2}\) times of the global maximum response value, and the smaller the \(T\) value is, the more corner points are retained. As shown in Figure 2, the measure \(R\) with a large positive value indicates the presence of a corner; \(R\) with a large negative value indicates an edge; a small absolute value \(|R|\) indicates a flat area. Different levels of features provide more information for accurate object detection. For the diversity scales of the aircraft, the feature pyramid network fuses the low-level and high-level features, providing rich spatial location and high-level semantic information. The feature pyramid network integrates the Harris corner features from different layers, which well expresses the aircraft salient feature for accurate aircraft detection. The network architecture consists of two parts: a bottom-up network, a top-down network and horizontal connection, as shown in Figure 1. The bottom-up feed forward network {C1, C2, C3, C4, C5} is composed of the output of the last convolutional layer in each residual block in the ResNet network. Since C1 and C2 need to take up a lot of memory, then remove them, and the step size of the convolutional layer is set to [8; 16; 32] respectively. The feature map generated by each layer of the network has the characteristics of resolution decreasing layer by layer and semantic information enhancing while location information weakens layer by layer. Therefore, in the top-down network, up-sampling and level connection are used to generate features {P3, P4, P5} containing rich information. P5 is obtained by using a \(1\times 1\) convolutional layer to reduce the channel of C5, and then adding a \(3\times 3\) convolution to obtain the first layer network P5 of the FPN. P4 is obtained by fusing the rough feature map obtained from C4 and the feature map obtained from P5 and adding \(3\times 3\) convolution to eliminate the aliasing effect of up sampling, so as with P3. In contrast to the traditional FPN, the model introduces two more layers with small scales in order to improve the detection accuracy of obvious objects with significant structures, which are demoted as P6 and P7. P6 is obtained by performing convolution with a \(3\times 3\) kernel and the step size of 2, taking C5 as the input. P7 is obtained by adding RELU activation and a step size of 2, \(3\times 3\) convolution operation based on P6.