## 2 Materials and Methods
### Fine Splicing of Local Matching  
[PERSON], [PERSON] et al. proposed a fine stitching algorithm based on Wallis smoothing and distance weight enhancement [13]. [PERSON], [PERSON] et al. proposed a remote sensing image matching method based on Non-Subsampled Contourlet Transform (NSCT) and Speed Up Robust Features (SURF) [14]. [PERSON], [PERSON] et al. proposed a new method for accurately stitching airborne images acquired from multiple sensor imagers [15]. [PERSON], [PERSON] et al. proposed an adaptive multi-view and real-time image mosaic method based on the combination of grayscale and feature [16]. [PERSON], [PERSON] et al. proposed an automatic panoramic image mosaic algorithm using invariant features [17]. [PERSON], [PERSON] et al. proposed an adaptive and as natural as possible image stitching algorithm [18]. [PERSON], [PERSON] et al. proposed a high-resolution automatic image stitching algorithm for construction sites based on UAV images [19]. [PERSON], [PERSON] et al. described a method for registering and mosaicking based on multicamera images [20]. [PERSON], [PERSON] et al. introduced a UAV image stitching algorithm based on mesh-guided deformation and ground constraint, which can achieve precise registration and acquire ideal stitching effect [21]. [PERSON], [PERSON] et al. proposed a spatially-varying deformation method that uses multiple local transformation matrices to reduce the image alignment error and reduce the image projection distortion and improve the perspective of non-overlapping regions of the stitched image [22]. The scale and rotation relationship between the images is basically the same because the time interval between two adjacent images is short, and the whole geometric deformation is basically eliminated after geometric correction. Therefore, a normalized cross-correlation matching algorithm can be used to extract a large number of homonymous points in the overlapping image area. A normalized cross-correlation coefficient is a standardized covariance function that indicates the similarity between two functions. If the correlation coefficient reaches 1, it means that the two functions are completely the same; otherwise, the correlation coefficient is less than 1. For the discrete infrared image, its calculation formula is as follows:  
\[C(u,v)=\frac{\sum\limits_{x}\sum\limits_{y}\left[T(x,y)-\mu_{T}\right]\left[I( x-u,y-v)-\mu_{I(u,v)}\right]}{\sqrt{\sum\limits_{x}\sum\limits_{y}\left[T(x,y)- \mu_{T}\right]^{2}}\sum\limits_{x}\sum\limits_{y}\left[I(x,y)-\mu_{I(u,v)} \right]^{2}} \tag{5}\]  
where \(T\) represents the template image and \(I\) represents the image to be registered, \(\mu_{T}\) represents the mean value of the template, \(\mu_{I}\) represents the mean value of the image to be registered, and the image chip to be registered is used for matching in the reference image, and the position with the largest normalized correlation coefficient is the required matching point. According to the coordinates of two adjacent matched points, coordinate adjustment is carried out on the scanning direction (column direction) of the current image, and the formula of column direction adjustment is as follows:  
\[C_{new}=\frac{(Y_{k}-Y_{k-1})}{(y_{k}-y_{k-1})}(C_{old}-y_{k-1})+Y_{k-1} \tag{6}\]  
where \(Y_{k}\) represents the previous column coordinate of a \(k\)th-matched point, \(Y_{k-1}\) represents the previous column coordinate of a \(k-1\)th-matched point, \(y_{k}\) represents the current column coordinate of a \(k-1\)th-matched point, \(C_{old}\) represents the original column coordinate of the current frame, \(C_{new}\) represents the adjusted column coordinate of the current frame, and \(k\) represents the serial number of matched points. After obtaining the best-matching position, the adjacent images are locally resampled according to the scanning direction so that the adjacent images with more accurate positions are obtained. Finally, the geometric stitching of the two images can be completed by stitching according to the geometric position.