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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Our goal is to reveal temporal variations in videos that are difficult or impossible to see with the naked eye and display them in an indicative manner. Our method, which we call Eulerian Video Magnification, takes a standard video sequence as input, and applies spatial decomposition, followed by temporal filtering to the frames. The resulting signal is then amplified to reveal hidden information. Using our method, we are able to visualize the flow of blood as it fills the face and also to amplify and reveal small motions. Our technique can run in real time to show phenomena occurring at the temporal frequencies selected by the user. 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 introduce a new technique for estimating the optical flow field, starting from image sequences. As suggested by Fleet and Jepson (1990), we track contours of constant phase over time, since these are more robust to variations in lighting conditions and deviations from pure translation than contours of constant amplitude. Our phase-based approach proceeds in three stages. First, the image sequence is spatially filtered using a bank of quadrature pairs of Gabor filters, and the temporal phase gradient is computed, yielding estimates of the velocity component in directions orthogonal to the filter pairs' orientations. Second, a component velocity is rejected if the corresponding filter pair's phase information is not linear over a given time span. Third, the remaining component velocities at a single spatial location are combined and a recurrent neural network is used to derive the full velocity. We test our approach on several image sequences, both synthetic and realistic. Video cameras offer the unique capability of collecting high density spatial data from a distant scene of interest. They can be employed as remote monitoring or inspection sensors for structures because of their commonplace availability, simplicity, and potentially low cost. An issue is that video data is difficult to interpret into a format familiar to engineers such as displacement. A methodology called motion magnification has been developed for visualizing exaggerated versions of small displacements with an extension of the methodology to obtain the optical flow to measure displacements. In this paper, these methods are extended to modal identification in structures and the measurement of structural vibrations. Camera-based measurements of displacement are compared against laser vibrometer and accelerometer measurements for verification. The methodology is demonstrated on simple structures, a cantilever beam and a pipe, to identify and visualize the operational deflection shapes. Suggestions for applications of this methodology and challenges in real-world implementation are given. Standard approaches to computing interpolated (in-between) frames in a video sequence require accurate pixel correspondences between images e.g. using optical flow. We present an efficient alternative by leveraging recent developments in phase-based methods that represent motion in the phase shift of individual pixels. This concept allows in-between images to be generated by simple per-pixel phase modification, without the need for any form of explicit correspondence estimation. Up until now, such methods have been limited in the range of motion that can be interpolated, which fundamentally restricts their usefulness. In order to reduce these limitations, we introduce a novel, bounded phase shift correction method that combines phase information across the levels of a multi-scale pyramid. Additionally, we propose extensions for phase-based image synthesis that yield smoother transitions between the interpolated images. Our approach avoids expensive global optimization typical of optical flow methods, and is both simple to implement and easy to parallelize. This allows us to interpolate frames at a fraction of the computational cost of traditional optical flow-based solutions, while achieving similar quality and in some cases even superior results. Our method fails gracefully in difficult interpolation settings, e.g., significant appearance changes, where flow-based methods often introduce serious visual artifacts. Due to its efficiency, our method is especially well suited for frame interpolation and retiming of high resolution, high frame rate video.