We present a novel framework for motion segmentation that combines the concepts of layer-based methods and feature-based motion estimation. We estimate the initial correspondences by comparing vectors of filter outputs at interest points, from which we compute candidate scene relations via random sampling of minimal subsets of correspondences. We achieve a dense, piecewise smooth assignment of pixels to motion layers using a fast approximate graphcut algorithm based on a Markov random field formulation. We demonstrate our approach on image pairs containing large inter-frame motion and partial occlusion. The approach is efficient and it successfully segments scenes with inter-frame disparities previously beyond the scope of layer-based motion segmentation methods. We also present an extension that accounts for the case of non-planar motion, in which we use our planar motion segmentation results as an initialization for a regularized Thin Plate Spline fit. In addition, we present applications of our method to automatic object removal and to structure from motion.