# A Full-Spectrum Registration Method for Zhuhai-1 Satellite Hyperspectral Imagery
## 3 Methods
### Absolute Registration
#### 3.2.2 Affine Transformation Relationship Transfer Strategy  
The affine transformation relationship for adjacent bands can be transferred to perform registration for all other bands after a spectral band is selected as the reference band. The criteria for reference band selection is that the band should represent the texture characteristics of ground objects and have high contrast. The reference band can be chosen by analyzing the signal-to-noise ratio and range of spectral bands. Generally, the middle or red band is selected as the reference band. There are two situations in the registration process, including the registration of bands that are adjacent and non-adjacent to the reference band. In the first case, the differential correction method based on dense Delaunay triangulation is directly used for registration. In the second case, the registration of non-adjacent bands is completed by combining the transferred affine transformation relationship of adjacent bands with a differential correction from dense Delaunay triangulation. Figure 7 displays a schematic diagram of full-spectrum registration. In the figure, the reference image is Band 1. The solid circle points in Figure 7a,b are the matching point pairs in Band 1 and Band 2. The diamond-shaped points in Figure 7b,c are the matching point pairs in Band 2 and Band 3. The quadrangular points in Figure 7d are the matching point pairs in Band N-1 and Band N. The dotted circle points in Figure 7c,d are the matching points (solid circle points) in (b) in Band 3 and Band N.  
The registration steps for Band 1 and Band 2 are described below. Step 1: The matching points in Band 1 (the solid circled points in Figure 7a) are used to construct a dense Delaunay triangulation D1. Step 2: The affine transformation coefficients are calculated using Equation (15). This is based on the three vertices of the small triangle in D1 (the red solid triangle vertices), and the corresponding matching points in Band 2 (the red dashed triangle vertices in Figure 7b). Step 3: An affine transformation is performed on the internal points of the small triangles in D1. The correct coordinates are calculated for the internal points in Band 2. Nearest neighbor interpolation, bilinear, or bicubic interpolation is then used to calculate new pixel values. Step 4: Steps (2) and (3) are repeated until all triangle calculations are complete. Figure 6: Delaunay triangulation. (**a**) Reference band (subset). (**b**) Band to be registered (subset). Figure 7: Full-spectrum registration diagram. The registration of Band 3 and Band 1 can be used as an example. The following steps describe registration in the second case. Step 1: The matching points for Band 2 and Band 3 (the diamond point in Figure 7b) are used to construct a dense Delaunay triangulation D2. Step 2: Equation (15) is used to calculate the affine transformation coefficients. This calculation is based on the small triangle vertices in D2 (the red diamond points), and the corresponding matching points in Band 3 (the red diamond points in Figure 7c). Step 3: The coordinates for the matching points between Band 1 and Band 2 (the red solid circle point in Figure 7b) are calculated for Band 3 (the red dashed circle point in Figure 7c) based on the affine transformation relationship. Step 4: Steps (2) and (3) are repeated until all the matching points in Band 1 and Band 2 (the solid circle point in Figure 7b) are calculated for Band 3 (the dotted circle point in Figure 7c). Based on the above steps, the coordinates of the matching points for Band 1 and Band 2 are derived in Band 3 using the transfer strategy based on the affine transformation relationship between adjacent bands. Thus, Band 3 can be regarded as being adjacent to Band 1. The registration of Band 3 can then be performed using the differential correction method based on dense Delaunay triangulation.