Virtual Image Generation from the Linear Array Image


With the linear array images, on the other hand, each scan line has its own nadir point and iso-centre. Therefore, there are as many nadir points and iso-centres as the number of the scan lines. Fig.2, visualizes different geometry of these two classes of images.


Fig.2. (a) Relief displacement in a single-projection image,
(b) Relief displacement in a multi-projection image.


With a flat terrain, in the absence of tilt displacement, the geometry of single and multi-projection images is identical, since the relief displacements of the pixels are equal. However, in a non-flat terrain as indicated in Fig.2., the two classes of images have different displacement patterns. To generate a virtual single-projection image, relief variation on the ground must be taken into consideration, without which the single-projection image can not be generated. Fig.3. depicts graphically the simplified relationship of the virtual single-projection image and the linear array image.


Fig.3. Virtual image generated from the scan lines using a digital elevation model.


Assuming that the approximate satellite trajectory is known, pixels of the scan lines can be transferred to the object space via collinearity condition equations. This is performed by a forward intersection of the collinearity equation with the DEM surface using the following relations:



where XA, YA, ZA are the object coordinates of the pixels; R1,…,R3 are the direction cosines of the orientation angles of the scan lines; x is a vector containing the 3d scan line coordinates of each pixel. XC, YC and ZC are the 3d position of the projection centre of each scan line estimated via the approximate satellite trajectory. To evaluate equation 1, the rotation matrix is considered to be an identity matrix and the height values (i.e. ZA), is extracted from the available DEM. Having transferred the pixels to the object space, an inverse transformation given by equation 2 is employed to transfer the points in the object space into the virtual single projection plane:



where x, y, f, are the 3d coordinates of the pixels with respect to the virtual camera projection centre coordinate system; M is the rotation matrix of the virtual camera; and X is given by:



where Xc, …, Zc are the 3d coordinate of the virtual camera projection centre with respect to the object space coordinate system. The values for the exterior and interior orientation parameters of the virtual camera can be assigned arbitrarily. However, to acquire a virtual image with the same resolution as the linear array image, the virtual camera focal length should be equal to the focal length of the linear array imaging camera. Each transferred pixel to the virtual plane has its own grey value. An off-line grey value interpolation is then carried out to generate the final virtual image. To avoid the off-line grey shade interpolation, the whole process described above can be performed in a reverse order. That is, a 2d out put array is constructed in the virtual image plane. By reverse transformation these pixels are first transferred to the object space and then to the linear array scan lines and simultaneously a density value is resampled and assigned to the out put pixels. This latter approach is implemented in the present project. Fig.4. shows a simulated stereo-virtual image generated from an ETM+ satellite image and a DEM. Note that in this simulated stereo-pair, the satellite trajectory and the off-nadir viewing angle for the stereo-pair is assigned arbitrarily.

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