Moving Forward in Structure From Motion

It is well-known that forward motion induces a large number of local minima in the instantaneous least-squares reprojection error. This is caused in part by singularities in the error landscape around the forward direction, and presents a challenge in using existing algorithms for structure-from-motion in autonomous navigation applications. In this paper we prove that imposing a bound on the reconstructed depth of the scene makes the least-squares re-projection error continuous. This has implications for autonomous navigation, as it suggests simple modifications for existing algorithms to minimize the effects of local minima in forward translation.