Real-World Repetition Estimation by Div, Grad and Curl

We consider the problem of estimating repetition in video, such as performing push-ups, cutting a melon or playing violin. Existing work shows good results under the assumption of static and stationary periodicity. As realistic video is rarely perfectly static and stationary, the often preferred Fourier-based measurements is inapt. Instead, we adopt the wavelet transform to better handle non-static and non-stationary video dynamics. From the flow field and its differentials, we derive three fundamental motion types and three motion continuities of intrinsic periodicity in 3D. On top of this, the 2D perception of 3D periodicity considers two extreme viewpoints. What follows are 18 fundamental cases of recurrent perception in 2D. In practice, to deal with the variety of repetitive appearance, our theory implies measuring time-varying flow and its differentials (gradient, divergence and curl) over segmented foreground motion. For experiments, we introduce the new QUVA Repetition dataset, reflecting reality by including non-static and non-stationary videos. On the task of counting repetitions in video, we obtain favorable results compared to a deep learning alternative

Cloth in the Wind: A Case Study of Physical Measurement through Simulation

For many of the physical phenomena around us, we have developed sophisticated models explaining their behavior. Nevertheless, measuring physical properties from visual observations is challenging due to the high number of causally underlying physical parameters -- including material properties and external forces. In this paper, we propose to measure latent physical properties for cloth in the wind without ever having seen a real example before. Our solution is an iterative refinement procedure with simulation at its core. The algorithm gradually updates the physical model parameters by running a simulation of the observed phenomenon and comparing the current simulation to a real-world observation. The correspondence is measured using an embedding function that maps physically similar examples to nearby points. We consider a case study of cloth in the wind, with curling flags as our leading example -- a seemingly simple phenomena but physically highly involved. Based on the physics of cloth and its visual manifestation, we propose an instantiation of the embedding function. For this mapping, modeled as a deep network, we introduce a spectral layer that decomposes a video volume into its temporal spectral power and corresponding frequencies. Our experiments demonstrate that the proposed method compares favorably to prior work on the task of measuring cloth material properties and external wind force from a real-world video.Comment: CVPR 2020. arXiv admin note: substantial text overlap with arXiv:1910.0786