Thomas Brox - Andrés Bruhn - Nils Papenberg - Joachim Weickert
Variational formulations of the optic flow estimation problem have several
advantages. Firstly, they lead to a sound model where one clearly has to
formulate the model assumptions. Secondly, variational methods give access
to the long experience of numerical mathematics in solving partly difficult
optimisation problems.
Here we show a variational approach that integrates several concepts that
are important for accurate optic flow estimation, such as smoothness constraints
that permit piecewise smooth results [1,9,14,16,19],
robust data fidelity terms where outliers are penalised less severely [5,6],
coarse-to-fine strategies [3,6,12] and a non-linearised model
[14,2] to tackle large displacements, and spatio-temporal smoothness
constraints [13,5,20,10] that ameliorate the results by simply
using the information of an additional dimension. Furthermore, the grey value
constancy assumption, which is the basic assumption in optical flow estimation,
is extended by a gradient constancy assumption [18,17]. This makes
the method more robust against illumination changes.
As the variational model leads to a highly nonlinear optimisation problem,
a well-elaborated minimisation scheme becomes necessary. In order to really
find the minimiser of the original nonlinear model, all linearisations are
consequently postponed to the numerical scheme. While linearisations in the model
would immediately compromise the overall performance of the system, linearisations
in the numerical scheme can help to improve convergence to the global minimum.
The description of the optic flow estimation method given here is based on the paper High accuracy optical flow estimation based on a theory of warping [7].