# Tracking Method of GM-APD LiDAR Based on Adaptive Fusion of Intensity Image and Point Cloud
## 2 Intensity Image KCF Target Tracking Method Based on the Muti-Feature Fusion
### KCF Tracking Algorithm Based on Muti-Feature Fusion
#### 2.2.2 Fourier Descriptor Feature  
The Fourier descriptor is an example of the application of Fourier theory in shape analysis, whose basic idea is to describe the shape of the target in the frequency domain by using the Fourier transform of the target boundary curve [19]. The Fourier descriptor has invariance in translation, rotation and scale with an excellent performance in image classification.  
The Fourier descriptor can be computed as follows:  
Step 1: The tracking region image captured as input is converted into a binary image which will be normalized by the Gamma correction method.  
Step 2: Canny edge detection algorithm is used to extract the contour point set \(\{(x_{i},y_{i})|i=1,2,\cdots,m\}\) of the target to be tracked;  
Step 3: Calculate coordinates of the central point \((\overline{x},\overline{y})\) of the contour:  
\[\begin{cases}\overline{x}=\sum\limits_{i=1}^{m}x_{i}\\ \overline{y}=\sum\limits_{i=1}^{m}y_{i}\end{cases} \tag{16}\]  
Step 4: Convert a cartesian point to a polar point. Taking \((\overline{x},\overline{y})\) as the pole of the polar coordinate system, the rectangular coordinate \(\{(x_{i},y_{i})|i=1,2,\cdots,m\}\) of the contour point is converted to the corresponding polar coordinate \(\{(r_{i},\theta_{i})|i=1,2,\cdots,m\}\).  
\[\begin{cases}r_{i}=\sqrt{\left(x_{i}-\overline{x}\right)^{2}+\left(y_{i}- \overline{y}\right)^{2}}\\ \theta_{i}=\tan^{-1}\frac{y_{i}-\overline{y}}{x_{i}-\overline{x}}\end{cases} \tag{17}\]  
where \(r_{i}(i=1,2,\cdots,m)\) is the distance from the contour point to the center point. \(r_{i}(i=1,2,\cdots,m)\) is sorted in ascending order to obtain the distance sequence from each contour point to the center point, denoted as \(D=[r_{1},r_{2},\cdots,r_{m}]\).  
Step 5: The distance sequence is transformed by fast Fourier transform.  
\[F(k)=\frac{1}{m}\sum\limits_{i=0}^{m-1}D(i)e^{-\frac{j2\pi ik}{m}k}=0,1,\cdots,m-1 \tag{18}\]  
where after transformation, \(F(0)\) in the boundary sequence represents the DC component, which cannot reflect the shape difference between different images. Therefore, we get rid of it and keep the rest. Finally, the Fourier descriptor is expressed as follows:  
\[F_{D}=\Bigg{\{}\frac{F(2)}{F(1)},\frac{F(3)}{F(1)},\cdots,\frac{F(m-1)}{F(1)} \Bigg{\}} \tag{19}\]The Fourier descriptor is mainly based on frequency domain information and can capture periodic changes in images, while HOG feature mainly focuses on spatial gradient information. By fusing these two features, the frequency domain and spatial domain information can be comprehensively used to provide a more comprehensive target description. The Fourier descriptor has a certain robustness to the illumination change, because it represents the image through the frequency domain information. In a battlefield, lighting conditions can be constantly changing, and the introduction of the Fourier descriptor helps to reduce sensitivity to light. In this paper, serial fusion of HOG feature and the Fourier descriptor is implemented to improve the robustness of KCF tracking algorithm.