  Recovering the camera motion and scene geometry from visual data is a
fundamental problem in the field of computer vision. Its success in standard
vision is attributed to the maturity of feature extraction, data association
and multi-view geometry. The recent emergence of neuromorphic event-based
cameras places great demands on approaches that use raw event data as input to
solve this fundamental problem.Existing state-of-the-art solutions typically
infer implicitly data association by iteratively reversing the event data
generation process. However, the nonlinear nature of these methods limits their
applicability in real-time tasks, and the constant-motion assumption leads to
unstable results under agile motion. To this end, we rethink the problem
formulation in a way that aligns better with the differential working principle
of event cameras.We show that the event-based normal flow can be used, via the
proposed geometric error term, as an alternative to the full flow in solving a
family of geometric problems that involve instantaneous first-order kinematics
and scene geometry. Furthermore, we develop a fast linear solver and a
continuous-time nonlinear solver on top of the proposed geometric error
term.Experiments on both synthetic and real data show the superiority of our
linear solver in terms of accuracy and efficiency, and indicate its
complementary feature as an initialization method for existing nonlinear
solvers. Besides, our continuous-time non-linear solver exhibits exceptional
capability in accommodating sudden variations in motion since it does not rely
on the constant-motion assumption.
