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 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. Self-calibration for perspective cameras with varying intrinsic parameters is also possible based on a similar formulation.
Self-calibration problem under affine projections is discussed in .