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Next: Affine-to-Euclidean calibration Up: Analysis of the Previous: Ambiguity

Particular forms of

  For any motion, the relation eq:ambiguity implies that the form of is :

where commutes with .

When the rotation component of the displacement is performed around an axis parallel to the basis axes of the camera, takes special forms :

If the rotation axis is parallel to the horizontal axis of the camera : eq:Sx Q=(

) and S S_x (


If the rotation axis is parallel to the vertical axis of the camera :

In practice, r is often negligible in comparison with k and we can consider that : eq:Sy S S_y (


Finally, if the rotation axis is orthogonal to the image plane, is the identity and : eq:Sz S S_z (


We can observe that, in these 3 cases, the structure of is independent of any ambiguity in the real Jordan decomposition. It will be shown later that these cases correspond to critical motions for affine-to-Euclidean calibration.

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