An N-Point Linear Solver for Line and Motion Estimation with Event
  Cameras
Ling Gao Daniel Gehrig Hang Su Davide Scaramuzza Laurent Kneip
Event cameras respond primarily to edges--formed by strong gradients--and are
thus particularly well-suited for line-based motion estimation. Recent work has
shown that events generated by a single line each satisfy a polynomial
constraint which describes a manifold in the space-time volume. Multiple such
constraints can be solved simultaneously to recover the partial linear velocity
and line parameters. In this work, we show that, with a suitable line
parametrization, this system of constraints is actually linear in the unknowns,
which allows us to design a novel linear solver. Unlike existing solvers, our
linear solver (i) is fast and numerically stable since it does not rely on
expensive root finding, (ii) can solve both minimal and overdetermined systems
with more than 5 events, and (iii) admits the characterization of all
degenerate cases and multiple solutions. The found line parameters are
singularity-free and have a fixed scale, which eliminates the need for
auxiliary constraints typically encountered in previous work. To recover the
full linear camera velocity we fuse observations from multiple lines with a
novel velocity averaging scheme that relies on a geometrically-motivated
residual, and thus solves the problem more efficiently than previous schemes
which minimize an algebraic residual. Extensive experiments in synthetic and
real-world settings demonstrate that our method surpasses the previous work in
numerical stability, and operates over 600 times faster.