  We argue that the time derivative in a fixed coordinate frame may not be the
most appropriate measure of time regularity of an optical flow field. Instead,
for a given velocity field $v$ we consider the convective acceleration $v_t +
\nabla v v$ which describes the acceleration of objects moving according to
$v$. Consequently we investigate the suitability of the nonconvex functional
$\|v_t + \nabla v v\|^2_{L^2}$ as a regularization term for optical flow. We
demonstrate that this term acts as both a spatial and a temporal regularizer
and has an intrinsic edge-preserving property. We incorporate it into a
contrast invariant and time-regularized variant of the Horn-Schunck functional,
prove existence of minimizers and verify experimentally that it addresses some
of the problems of basic quadratic models. For the minimization we use an
iterative scheme that approximates the original nonlinear problem with a
sequence of linear ones. We believe that the convective acceleration may be
gainfully introduced in a variety of optical flow models.
