We use a simple yet powerful higher-order conditional ran- dom eld (CRF) to model optical ow. It consists of a standard photo- consistency cost and a prior on ane motions both modeled in terms of higher-order potential functions. Reasoning jointly over a large set of unknown variables provides more reliable motion estimates and a robust matching criterion. One of the main contributions is that unlike previous region-based methods, we omit the assumption of constant ow. Instead, we consider local ane warps whose likelihood energy can be computed exactly without approximations. This results in a tractable, so-called, higher-order likelihood function. We realize this idea by employing tri- angulation meshes which immensely reduce the complexity of the prob- lem. Optimization is performed by hierarchical QPBO moves and an adaptive mesh renement strategy. Experiments show that we achieve high-quality motion elds on several data sets including the Middlebury optical ow database.