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Resolution of eq:kkt

As we have seen previously, given an infinite homography between the images of the same camera, it is possible to calculate its real Jordan decomposition and hence a matrix such that . Then, it was shown that should satisfy eq:kkt. The calibration process consists of solving this equation which can be written as a system of 6 equations with 7 unknowns (a, k, , , r, and ) :


It is clear that this system cannot be solved just as it is (there is one unknown too many). We must either consider a constraint on one unknown, or add equations from several motions (with non parallel rotation axes).

If we want to calibrate with a single motion or with planar motions (where all rotation axes are parallel), a constraint on the internal parameters must be imposed. Commonly used constraints are either or r=0.

Bob Fisher
Mon Dec 7 13:48:06 GMT 1998