Metric constraints described in Sect. 4 are closely related with theory of self-calibration, that is, recovering Euclidean structure of motion and shape without knowledge of intrinsic camera parameters.
In the context of self-calibration for perspective cameras, 
in
(25) represents the absolute
quadric[14] described with respect to the
Euclidean coordinate frame. The absolute quadric is a virtual plane
quadric invariant under rigid motion. If the intrinsic parameters are
unknown but fixed to a constant value 
through camera
movement, (25) becomes
where
is the absolute quadric represented with respect to the projective
coordinate frame and 
is its
projection onto each image. Equation (27) means
the invariance of the image of the absolute quadric and can be solved
for 
and 
from three or more
views[14]. Self-calibration for perspective
cameras with varying intrinsic parameters is also possible based on a
similar formulation[8].
Self-calibration problem under affine projections is discussed in [9].
