Instability of Projective Reconstruction of Dynamic Scenes near Critical Configurations

In the context of multiple view geometry in any dimension, we compute the minimum number of views necessary for projective reconstruction of both the set of cameras and of scenes. Within a unified approach to critical configurations and their loci, the paper focuses on the case of dynamic scenes of multiple bodies traveling along parallel straight-line trajectories with constant velocities, in the framework of higher dimensional projections introduced by Shashua and Wolf. Critical loci in this case are explicitly determined. A stratification of the resulting locus in terms of fixed common velocities is presented and leveraged to show, via a number of simulated experiments, instability of the reconstruction near critical configurations.