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554 C. Aligning T wo Images in a Panoramic Mosaic
after the camera and the world coordinate frame of reference have been ro-
tated slightly, it will appear in image I
i
to lie at p
where
p
= Rp, (C.12)
where R is a 3 × 3 rotation matrix. For a pinhole camera of focal length f ,
we have x = F p and x
= Fp
where
F =
⎡
⎣
f 00
0 f 0
001
⎤
⎦
.
If we know x then we can write (up to an arbitrary scale factor) p = F
−1
x.
Using Equation (C.12), one obtains the homography
x
= FRF
−1
x. (C.13)
The rotation R may be specified in a number of different ways, one
of which defines an axis of rotation and an angle of rotation around that
axis. Appendix A gave an expression ...