# Near-Space Wide-Area and High-Resolution Imaging System Design and Implementation
## 2 Wide-Area and High-Resolution System Design
### Photoelectric Sphere and Swing Imaging Design  
The design of the photoelectric sphere adopts a two axis and two frame stable system structure, and the high-resolution camera is loaded into the pitch frame. The design of the photoelectric platform adopts a spherical structure. On the one hand, the aerodynamic resistance of the spherical structure is smaller than that of other structures (plate, square, diamond, etc.) under the same conditions (same speed, same windward area); on the other hand, the product has good symmetry. During flight, when the azimuth and pitch frames move, the changes in their angular positions cause small changes in the driving torque, making system control easy to implement; thirdly, under certain conditions of stable platform rotation space, the internal space contained by the sphere is larger than that of other structures, and its load-bearing capacity is strong. The installation of the high-resolution camera in the photoelectric sphere is shown in Figure 14.  
In the process of wide-area high-resolution imaging, the high-resolution camera operates in telephoto mode, with a photoelectric sphere azimuth angle of \(90^{\circ}\)--perpendicular to the flight direction--and an initial pitch angle of \(-90^{\circ}\), indicating ground imaging. The pitch direction of the photoelectric sphere provides different imaging fields of view for high-resolution cameras to take photos through steeper motions, as shown in Figure 15. Due to the very slow flight speed of high-altitude balloons, which is about \(10\) m/s, there is no need to consider the image shift in the direction of flight when performing swing imaging. Figure 14: The installation of the high-resolution camera in the photoelectric sphere. Figure 15: Mode of photoelectric sphere and high-resolution camera. Due to the significant distortion caused by large angle squint, in order to reduce the level of image distortion, the sweep width coverage is 33.3\({}^{\circ}\), the step angle is 3.5\({}^{\circ}\), and the overlap rate in the span direction is 35%. The optical axis roll angle of each image frame in a single scanning cycle is uniformly distributed within the width range, and the values are shown in Table 4.  
The SIFT algorithm is very robust in complex geometric images and radiative conditions and is currently the most commonly used registration algorithm. The process of SIFT is mainly divided into four stages: feature point detection, key point localization, direction allocation, and feature point description. Firstly, the scale space of the image is constructed by establishing a Difference of Gaussians (DOG) pyramid to extract feature points and obtain the first layer image through Gaussian blur. \[L(x,y,\sigma)=G(x,y,\sigma)\times I(x,y) \tag{6}\]  
\(I(x,y)\) is the original image, and \(G(x,y,\sigma)\) is the Gaussian kernel, while \((x,y)\) are the pixel coordinates, and \(\sigma\) is the scale factor, wherein the larger the \(\sigma\), the clearer the image contour, and the smaller the \(\sigma\), the more obvious the image details. The Gaussian kernel function is:  
\[G(x,y,\sigma)=\frac{1}{2\pi\sigma}e^{-\frac{x^{2}+y^{2}}{2\sigma^{2}}} \tag{7}\]  
The difference of Gaussians pyramid performs the DOG operation between two adjacent layers of images, which is shown as:  
\[D(x,y,\sigma)=[G(x,y,k\sigma)-G(x,y,\sigma)]\times I(x,y)=L(x,y,k\sigma)-L(x,y,\sigma) \tag{8}\]  
When locating key points, it is necessary to filter out low-contrast extreme points and edge responses. It is necessary to obtain a 2 \(\times\) 2 Hessian matrix by taking the derivative of the Gaussian convolution formula. \[H= \begin{bmatrix}D_{xx}&D_{xy}\\ D_{yx}&D_{yy}\end{bmatrix}  \tag{9}\]  
The direction matching of feature points mainly estimates the direction of neighboring pixels of key points through the grayscale histogram of the image.