Dimensions of Motion: Learning to Predict a Subspace of Optical Flow from a Single Image.

We introduce the problem of predicting, from a single video frame, a low-dimensional subspace of optical flow which includes the actual instantaneous optical flow. We show how several natural scene assumptions allow us to identify an appropriate flow subspace via a set of basis flow fields parameterized by disparity and a representation of object instances. The flow subspace, together with a novel loss function, can be used for the tasks of predicting monocular depth or predicting depth plus an object instance embedding. This provides a new approach to learning these tasks in an unsupervised fashion using monocular input video without requiring camera intrinsics or poses.