Let be an affine camera motion
obtained by factoring the measurement matrix. Then
is related to the ``true'' motion
described with respect to the
Euclidean coordinate frame by (9). Our goal here
is to obtain the affine transformation
(up to an arbitrary
rotation) in (9) with which affine descriptions
of
motion and shape are corrected to Euclidean ones
.
Let two 3-vectors and
denote two rows of
. Then, for each affine camera
model introduced in §2.2, the affine
transformation
is determined as follows;
Let and
be two elements of
. Then, eliminating
from
(19), we obtain
which gives 2F linear homogeneous equations in terms of 6 elements of
the 33 symmetric matrix
. If three or
more views are available, we can obtain a least-squares solution
determined up to a scale as a solution of the ordinary eigenvalue
problem. Once
is determined,
is
recovered through, for instance, Cholesky decomposition.
and the affine transformation is determined as a
least-squares solution of the following equations:
and is recovered by solving, in the
least-squares sense,