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.
A plethora of phenomena exhibit motions that are too small to be well perceived by the naked eye and require computational amplification to be revealed [Liu et al. 2005; Wu et al. 2012]. In Lagrangian approaches to motion magnification [Liu et al. 2005; Wang et al. 2006], motion is computed explicitly and the frames of the video are warped according to the magnified velocity vectors. Motion estimation, however, remains a challenging and computationally-intensive task, and errors in the estimated motions are often visible in the results. Recently-proposed Eulerian approaches eliminate the need for costly flow computation, and process the video separately in space and time. Eulerian video processing was used by [Fuchs et al. 2010] to dampen temporal aliasing of motion in videos, while [Wu et al. 2012] use it to reveal small color changes and subtle motions. Unfortunately, linear Eulerian video magnification [Wu et al. 2012] supports only small magnification factors at high spatial frequencies.
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