Current methods for computing optical flow are based on a four-step pipeline. The goal of the first step is finding point correspondences between two consecutive images. The aim of the second step is filtering problematic or even false correspondences. The purpose of the third step-inpainting, is filling in the missing information from the neighborhood. The final step refines the obtained dense flow field using a variational approach. Up to now, there was little research that deals with the inpainting step and no work if a variational approach could improve the inpainting step. A common technique for the final step of the optical flow pipeline is minimizing an energy functional. In contrast, this thesis uses the minimization of an energy function for the inpainting step, which is also, the focus of this thesis. The inpainting energy functional consists of a similarity term and a smoothness term. For the smoothness term several possible extensions are proposed, that incorporate image information and enable an anisotropic smoothing behavior. Finally, all extensions are compared with each other and with the results from EpicFlow (Revaud et al., 2015).