Computation of Homographies
Matthew Harker, Paul L. O'Leary · 2005
A new method for the non-iterative computation of a homography matrix is described. Rearrangement of the equations leads to a block partitioned sparse matrix, facilitating a residualization based on orthogonal matrix projections. This improves the handling of the error structure of the linear system of equations. The vanishing line is treated as the principal component in the estimation process. This estimate is more robust, since the position of the vanishing line depends only on the relative position and orientation of the camera to the observed plane, and is invariant to the structure of the points observed on the plane. A flop-count indicates that the new method is 11 times faster for four point correspondences, and converges to a factor of 5 for a large number of points. Furthermore, a new non-iterative method of treating error in both images is derived. Combining the forward H and reverse G projections in a suitable manner eliminates the systematic bias of the estimation, and the first order error: a strict bound on the error reduction is derived. This can be achieved faster than a classical DLT due to the improved numerical efficiency. Results of Monte-Carlo simulations are presented to verify the performance. 1