A Fully Projective Error Model for Visual Reconstruction

Measurement uncertainty is a recurrent concern in visual reconstruction. Image formation and 3D structure recovery are essentially projective processes that do not quite fit into the classical framework of affine least squares, so intrinsically projective error models must be developed. This paper describes initial theoretical work on a fully projective generalization of affine least squares. The result is simple and projectively natural and works for a wide variety of projective objects (points, lines, hyperplanes, and so on). The affine theory is contained as a special case, and there is also a canonical probabilistic interpretation along the lines of the classical leastsquares/Gaussian/approximate log-likelihood connection. Standard linear algebra often suffices for practical calculations.