# Pre-Processing of Inner CCD Image Stitching of the SDGSAT-1 Satellite
## 3 Methodology
### Traditional Line-Time Normalization  
The multi-level integration method is usually applied in TDI-CCD sensors for the collection of sufficient echo energy, which can produce images with very high resolution. Therefore, the combination of multiple inner CCD images can achieve earth observation with a wide swath and high ground resolution. For the SDGSAT-1, eight inner CCDs are placed in a staggered arrangement on two substrates at regular intervals, as shown in Figure 4a. The projections of different inner CCDs are discontinuous, leading to misalignments between adjacent raw inner CCD images. Figure 4b,c illustrates the imaging mode of multiple CCD sensors and its projections in object-space. To meet the requirements of mapping applications, it is critical to obtain imagery with high geometric stitching accuracy [3; 27]. Figure 3: Work-flow of the proposed method. Figure 5a,b show the rigorous model for processing multiple CCD images in object-space and image-space, respectively. Traditionally, a homogenous CCD line is produced based on the relationships between adjacent chips in object-space. Supposing that \(p_{1}(x_{1},y_{1})\) and \(p_{2}(x_{2},y_{2})\) are corresponding image-space points of the same object \(P(X,Y,Z)\) in inner CCD image 1 and image 2; we can derive the translations between this two inner CCD images as follows:  
\[ \begin{bmatrix}X\\ Y\\ Z\end{bmatrix}  = \begin{bmatrix}X_{S1}\\ Y_{S1}\\ Z_{S1}\end{bmatrix} +R_{1}\cdot \begin{bmatrix}x_{1}\\ y_{1}\\ -f\end{bmatrix}  \tag{1}\] \[ \begin{bmatrix}X\\ Y\\ Z\end{bmatrix}  = \begin{bmatrix}X_{S2}\\ Y_{S2}\\ Z_{S2}\end{bmatrix} +R_{2}\cdot \begin{bmatrix}x_{2}\\ y_{2}\\ -f\end{bmatrix} \]  
where \((X_{S1},Y_{S1},Z_{S1})\) and \((X_{S2},Y_{S2},Z_{S2})\) are the GPS antenna centers of different inner CCD sensors and \(R_{1}\) and \(R_{2}\) are the translation matrixes. With the help of ground control information and constraints between adjacent inner CCDs, the internal and external geometric parameters can be calibrated. After that, an equivalent rigorous model can be established by projecting all inner CCD images into a pseudo-imaging plane. In contrast, the image-space method produces stitched images without considering the relationships in object-space. For a single object \(P\) on the ground, the projected points in different inner CCD images may differ from each other due to the staggered installation. Supposing that \(P_{1}\) and \(P_{2}\) in Figure 5b are the corresponding  
Figure 4: Illustration of imaging principles of multiple CCD stitching [28]: (**a**) imaging principle of multiple CCD in focal plane, (**b**) imaging Mode, and (**c**) projections. image-space projections of the same object, adjacent inner CCD images can be stitched with an affine transformation model based on the designed line-time. The scaling difference is caused by the misalignment in the sampling rate of each inner CCD during imaging, while staggered installation leads to the offsets. To produce a seamless stitched image, both the scale and offset parameters should be calibrated carefully. The determination of scale parameters of different inner CCD images is closely related to the line-time during flight. Traditionally, a designed line-time is used for the normalization of image-space coordinates. The sampling rate, which is usually considered as the reciprocal of the line-time, remains unchanged for a certain period, as shown in Figure 6a. Therefore, the track dataset is separated into several parts; the imaging period of each CCD can be represented as follows:  
\[ \begin{cases}T_{s}=T_{0}\;,\\ T_{e}=T_{0}+\Sigma_{j=1}^{n}(le_{j}-ls_{j})\cdot t_{j}\end{cases}  \tag{2}\]  
where \(T_{s}\) (\(T_{0}\)) and \(T_{e}\) represent the start and end time of the whole dataset, \(n\) is the number of segments separated by the step-points of the whole dataset, \(ls\) and \(le\) are the start and end line indexes in the \(j\)th segment, and \(t_{j}\) is the corresponding designed sampling rate.