Three algorithms for 2-image and 2-image structure from motion

Abstract

We describe three approaches to 2-image and 2-image structure from motion. First, we present a new approximation to the least-squares image-reprojection error for 2 images. It depends only on the motion unknowns and is much more accurate than previous approximations such as the (weighted) coplanarity, especially for forward camera motions. We use this error to compute tight, rigorous upper and lower bounds on the true error and to study its properties experimentally. We demonstrate that the true error has many local minima for forward motions even when the motion is large. We propose and experimentally test a second approach, which is potentially more robust than bundle adjustment. Last, we describe algorithms for 2 images that reconstruct from the measured 2D affine deformations of image patches.