  Based on previous work we extend a primal-dual semi-smooth Newton method for
minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of
bounded variations by adaptivity in a finite element setting. For automatically
generating an adaptive grid we introduce indicators based on a-posteriori error
estimates. Further we discuss data interpolation methods on unstructured grids
in the context of image processing and present a pixel-based interpolation
method. For the computation of optical flow we derive an adaptive finite
element coarse-to-fine scheme for resolving large displacements. The
coarse-to-fine scheme speeds-up the computing time tremendously.
