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Affine calibration of a
Euclidean calibration of a plane
An Euclidean transformation leaves
invariant as a set.
Consequently, under any Euclidean transformation, there are two points on
which are fixed. These are called the
circular points
,
with coordinates
and
To see that they are fixed under Euclidean transformations
(Similarly for
)
The conic
is dual to the the circular points. In Euclidean terms it is given by
The conic
is fixed under actions of any Euclidean transformation.
is the null vector of
. This is because
.
For lines
and
with normals parallel to
and
respectively, in Euclidean geometry the angle between them is given as
Projectively, this is given as
Thus the projective (
) and the affine (
) components are completely determined by the image of
, but the similarity component is undetermined.
Once
is known metric calibration of a plane is possible. Writing the
SVD
of
as
is the rectifying projectivity up to a similarity.
can be computed from five independent angle consrtaints on a plane.
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Affine calibration of a
Subhashis Banerjee 2008-01-20