The selection of an optical flow method is mostly a choice from among accuracy, efficiency and ease of implementation. While variational approaches tend to be more accurate than local parametric methods, much algorithmic effort and expertise is often required to obtain comparable efficiency with the latter. Through the exploitation of natural motion statistics, the estimation of optical flow from local parametric models yields a good alternative. We show that learned, linear, parametric models capture specific higher order relations between neighboring flow vectors and, thus, allow for complex, spatio-temporal motion patterns despite a simple and efficient implementation. The method comes with an inherent confidence measure, and the motion models can easily be adapted to specific applications with typical motion patterns by choice of training data. The proposed approach can be understood as a generalization of the original structure tensor approach to the incorporation of arbitrary lin...