## 2 Materials and Methods
### Rough Mosaic of Adjacent Frames Based on SIFT  
The accuracy of geometric correction of images based on attitude and position is not high because the accuracy of attitude measurement and position measurement of aviation platforms is limited, and geometric mosaic processing needs to be carried out according to the overlapping area between adjacent images. Wide-field aerial scanning image takes the same time to scan, during which the platform movement causes systematic and local deformation of the image. In order to effectively eliminate the overall and local deformation of the image, it is necessary to process the whole image and local image deformation according to the image in the overlapping area. The transformation of whole adjacent images is realized by extracting the homonymous points through SIFT and calculating the translation, scale, and rotation parameters. The SIFT feature was proposed by [PERSON] et al. in 2004 and has been successfully applied in the field of computer vision [PERSON] et al. (2004). In the field of remote sensing image processing, scholars have conducted a lot of improvement research by using the excellent characteristics of SIFT. The SIFT method can effectively extract the local features of the image, some extreme points in the scale space, and it has strong adaptability to the brightness, translation, rotation, and scale change of the image. The feature descriptors of the feature points are extracted from the images around the feature points so that the feature descriptors can be matched. The main steps of the SIFT method include the formation of scale space and downsampled images, the detection of extreme points in scale space, the accurate positioning of feature points, the generation of directional parameters of feature points, and the formation of feature point descriptors. We use the approximate geometric overlapping relationship between two adjacent images to clip the image blocks from the previous image and the corresponding image blocks from the next image, then extract SIFT feature points, and then extract the best homonymous point pair according to the ratio relationship between the nearest neighbor  
Figure 3: Block rectification of infrared image. and the next neighbor and the bi-directional matching strategy. The basic principle is shown in Figure 4, while Figure 5 shows a pair of best homonymous-matched point pairs extracted from two adjacent overlapping areas. A pair of best-matched point pairs are extracted from the left and right sides of the image, and then these two points are taken as control points. Considering that the main geometric deformations of two adjacent images are caused by translation, scale, and rotation, the geometric transformation parameters between the two images can be calculated according to the extracted two pairs of point pairs. The specific calculation formula is as follows:  
\[ \begin{bmatrix}k_{1}\\ k_{2}\\ d_{x}\\ d_{y}\end{bmatrix} = \begin{bmatrix}x_{1}&y_{1}&1&0\\ -y_{1}&x_{1}&0&1\\ x_{2}&y_{2}&1&0\\ -y_{2}&x_{2}&0&1\end{bmatrix} ^{-1}\cdot \begin{bmatrix}u_{1}\\ v_{1}\\ u_{2}\\ v_{2}\end{bmatrix}  \tag{3}\]  
where \(k_{1}\), \(k_{2}\), \(d_{x}\), and \(d_{y}\) are the four parameters to be calculated, \((x_{1},y_{1})\) indicates the image coordinates of homonymous point \(P_{1}\) in the current image, \((u_{1},v_{1})\) indicates the image coordinates of homonymous point \(P_{1}\) in the previous image, \((x_{2},y_{2})\) indicates the image coordinates of homonymous point \(P_{2}\) in the current image, and \((u_{2},v_{2})\) indicates the image coordinates of homonymous point \(P_{2}\) in the previous image. The image with the same position as the previous one can be obtained using the calculated scale, translation, and rotation parameters to resample the current image. The coordinate transformation processing of the current image is calculated according to the following formula:  
\[\left\{ \begin{array}{rl}u=k_{1}x+k_{2}y+d_{x}\\ v=-k_{2}x+k_{1}y+d_{y}\end{array} \right.