An Efficient Minimal Solution for Infinitesimal Camera Motion

Given five motion vectors observed in a calibrated camera, what is the rotational and translational velocity of the camera? This problem is the infinitesimal motion analogue to the five-point relative orientation problem, which has previously been solved through the derivation of a tenth-degree polynomial and extraction of its roots. Here, we present the first efficient solution to the infinitesimal version of the problem. The solution is faster than its finite counterpart. In our experiments, we investigate over which range of motions and scene distances the infinitesimal approximation is valid and show that the infinitesimal approximation works well in applications such as camera tracking.