Inserting the Past in Video Sequences 
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let frame i have an image constant ci and a rotation matrix Ri(<|>j). Besides, as the panoramic image had a considerable upwards 
rotation (Op about the horizontal X-axis, a constant downward shift y 0 of the principal point of the “video camera” was also 
introduced in order to compensate for “lowering” the view of the frames due to neglecting the upward rotation of the panoramic 
image. 
panoramic image 
interior orientation 
and rotational matrix 
of image 1 
Cn X 0l , y 0 i, 
interior orientation 
and rotational matrix 
of panoramic image 
Cp, x oP- УоР- Rp 
interior orientation 
and rotational matrix 
of image n 
C|i- X on , Уоп? *^n 
Figure 10: Basic scheme of frame generation from the final panoramic image 
If the image coordinates of the panoramic image, referred to its principal point, are denoted by xp, yp and the corresponding image 
coordinates of frame i by Xj, y t then they are related to each other through the following transformation: 
Xp 
X i 
У p 
~ c p 
= kR P Rj 
>’/ - >’o 
~ C i 
Scale factor k can be eliminated by dividing the two first equations with the third. From the resulting two equations we can find the 
projection of the four comers of each frame onto the panoramic image. The area thus defined on the latter is subsequently rectified to 
produce the final image content of the frame. The first and last frames of the final sequence, along with the corresponding areas of 
the panoramic image from which they have been resampled, are seen in Fig. 11. 
Figure 11. Below: first (left) and last (right) frame of the sequence. Above: corresponding areas on the panoramic image.