  Recently, variational methods were successfully applied for computing the
optical flow in gray and RGB-valued image sequences. A crucial assumption in
these models is that pixel-values do not change under transformations.
Nowadays, modern image acquisition techniques such as electron backscatter
tomography (EBSD), which is used in material sciences, can capture images with
values in nonlinear spaces. Here, the image values belong to the quotient space
$\text{SO}(3)/ \mathcal S$ of the special orthogonal group modulo the discrete
symmetry group of the crystal. For such data, the assumption that pixel-values
remain unchanged under transformations appears to be no longer valid. Hence, we
propose a variational model for determining the optical flow in
$\text{SO}(3)/\mathcal S$-valued image sequences, taking the dependence of
pixel-values on the transformation into account. More precisely, the data is
transformed according to the rotation part in the polar decomposition of the
Jacobian of the transformation. To model non-smooth transformations without
obtaining so-called staircasing effects, we propose to use a total generalized
variation like prior. Then, we prove existence of a minimizer for our model and
explain how it can be discretized and minimized by a primal-dual algorithm.
Numerical examples illustrate the performance of our method.
