# Pre-Processing of Inner CCD Image Stitching of the SDGSAT-1 Satellite
## 3 Methodology
### Fine Line-Time Normalization
As shown in Figure 7, the step-points of the actual line-time and designed line-time for each inner CCD image are not synchronous, and the actual line-time randomly changes around the designed line-time. Therefore, the application of the actual line-time rather than the designed line-time is of great significance, and can improve the accuracy of image stitching. Usually, the sub-CCD located in the center or edge of the imaging plane is selected as the reference. For the SDGSAT-1 satellite, the reference image is the raw inner CCD image located on the edge of each camera. For better consistency between adjacent inner CCD images, different fine line-time normalization methods can be applied to resampling all slave images. The misalignment between adjacent inner CCD images caused by the staggered installation is treated as a systematic error, which can be calibrated according to the design of the imaging sensor. After calibration, the start lines of each sub-CCD image are geometrically rectified, as shown in Figure 4c. The line-based line-time normalization method is the finest among all investigated models. Supposing that \(LT_{i}^{\prime}\) is the line-time of the \(i\)th line in the normalized inner CCD image, the corresponding actual line-time of the denormalized inner CCD image is \(LT_{j}\) (where \(j\) is the row index of the denormalized inner CCD image), and \(P_{i}^{\prime}\) and \(P_{j}^{\prime}\) represent the pixel value of the \(i\)th and \(j\)th row in the normalized and denormalized sub-CCD image, respectively. Then, the normalized image can be resampled as follows:  
\[ \begin{split} P_{i}^{\prime}=\frac{LT_{i}^{\prime}-LT_{j}}{LT_{i} ^{\prime}-LT_{i-1}^{\prime}}\cdot P_{2}^{j+\Delta x_{i,j}}+(1-\frac{LT_{i+1}^{ \prime}-LT_{i+1}}{LT_{1}^{i+1}-LT_{1}^{i}})\cdot P_{2}^{j+1+\Delta x_{i,j}},\\ if~{}LT_{1}^{i}~{}<~{}LT_{2}^{j+\Delta x_{i,j}}~{}<LT_{1}^{i+1} \end{split}  \tag{5}\]  
All slave images can be normalized according to Equation (5). After line-based line-time normalization, the pixels of slave images are stretched or compressed or are mixed between adjacent images. However, the relationship with the actual line-time is unchangeable. In particular, Equation (5) can be rewritten as  
\[P_{2}^{i}=P_{2}^{j+\Delta x_{i,j}},~{}if~{}LT_{1}^{i}~{}=~{}LT_{2}^{j+\Delta x _{i,j}} \tag{6}\]  
Therefore, all slave sub-CCD images are refined using the same reference image for consistency. Typically, the resampling of each scan line is time-consuming. According to the statistical results shown in Figures 7 and 8, the actual time intervals between every two scan lines are relatively stable for a brief period. Therefore, a block-based line-time normalization method is introduced based on the actual line-time. The whole dataset is  
Figure 10: Illustration of the fine line-time normalization method: (**a**) sub-CCD image before fine line-time normalization and (**b**) sub-CCD image after fine line-time normalization. divided into several segments according to the step-point. The average imaging frequency in each segment can be obtained as follows:  
\[freq_{i}=\frac{LT_{i+1}-LT_{i}}{R_{i}} \tag{7}\]  
where \(R_{i}\) represents the total number of rows in the \(i\)th segment. A more simplified method is the scene-based line-time normalization method, which is built around the assumption that the line-time is relatively stable in each scene. In this method, only the start-line and end-line of each scene are interpolated. The internal rows are calculated based on the relationship of the average imaging frequency. Therefore, the raw image is resized as a whole.