This work advocates Eulerian motion representation learning over the current standard Lagrangian optical flow model. Eulerian motion is well captured by using phase, as obtained by decomposing the image through a complex-steerable pyramid. We discuss the gain of Eulerian motion in a set of practical use cases: (i) action recognition, (ii) motion prediction in static images, (iii) motion transfer in static images and, (iv) motion transfer in video. For each task we motivate the phase-based direction and provide a possible approach.
Eulerian motion modeling has shown remarkable results for motion magnification @cite_18 where a phase-based approach significantly improves the quality @cite_4 and broadens its application @cite_2 @cite_3 . A phase-based video interpolation is proposed in @cite_15 and a phase-based optical flow estimation is proposed in @cite_0 . Inspired by the these work, we advocate the use of the Eulerian model as exemplified by phase for learning motion representations.
@cite_18 @cite_4 @cite_3 @cite_0 @cite_2 @cite_15
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The quantitative evaluation of optical flow algorithms by (1994) led to significant advances in performance. The challenges for optical flow algorithms today go beyond the datasets and evaluation methods proposed in that paper. Instead, they center on problems associated with complex natural scenes, including nonrigid motion, real sensor noise, and motion discontinuities. We propose a new set of benchmarks and evaluation methods for the next generation of optical flow algorithms. To that end, we contribute four types of data to test different aspects of optical flow algorithms: (1) sequences with nonrigid motion where the ground-truth flow is determined by tracking hidden fluorescent texture, (2) realistic synthetic sequences, (3) high frame-rate video used to study interpolation error, and (4) modified stereo sequences of static scenes. In addition to the average angular error used by , we compute the absolute flow endpoint error, measures for frame interpolation error, improved statistics, and results at motion discontinuities and in textureless regions. In October 2007, we published the performance of several well-known methods on a preliminary version of our data to establish the current state of the art. We also made the data freely available on the web at http: vision.middlebury.edu flow . Subsequently a number of researchers have uploaded their results to our website and published papers using the data. A significant improvement in performance has already been achieved. In this paper we analyze the results obtained to date and draw a large number of conclusions from them. We introduce a technique to manipulate small movements in videos based on an analysis of motion in complex-valued image pyramids. Phase variations of the coefficients of a complex-valued steerable pyramid over time correspond to motion, and can be temporally processed and amplified to reveal imperceptible motions, or attenuated to remove distracting changes. This processing does not involve the computation of optical flow, and in comparison to the previous Eulerian Video Magnification method it supports larger amplification factors and is significantly less sensitive to noise. These improved capabilities broaden the set of applications for motion processing in videos. We demonstrate the advantages of this approach on synthetic and natural video sequences, and explore applications in scientific analysis, visualization and video enhancement. We tackle the problem of estimating optical flow from a monocular camera in the context of autonomous driving. We build on the observation that the scene is typically composed of a static background, as well as a relatively small number of traffic participants which move rigidly in 3D. We propose to estimate the traffic participants using instance-level segmentation. For each traffic participant, we use the epipolar constraints that govern each independent motion for faster and more accurate estimation. Our second contribution is a new convolutional net that learns to perform flow matching, and is able to estimate the uncertainty of its matches. This is a core element of our flow estimation pipeline. We demonstrate the effectiveness of our approach in the challenging KITTI 2015 flow benchmark, and show that our approach outperforms published approaches by a large margin. We propose a novel approach for optical flow estimation, targeted at large displacements with significant occlusions. It consists of two steps: i) dense matching by edge-preserving interpolation from a sparse set of matches; ii) variational energy minimization initialized with the dense matches. The sparse-to-dense interpolation relies on an appropriate choice of the distance, namely an edge-aware geodesic distance. This distance is tailored to handle occlusions and motion boundaries - two common and difficult issues for optical flow computation. We also propose an approximation scheme for the geodesic distance to allow fast computation without loss of performance. Subsequent to the dense interpolation step, standard one-level variational energy minimization is carried out on the dense matches to obtain the final flow estimation. The proposed approach, called Edge-Preserving Interpolation of Correspondences (EpicFlow) is fast and robust to large displacements. It significantly outperforms the state of the art on MPI-Sintel and performs on par on Kitti and Middlebury.