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.

Visual repetition is ubiquitous in our world. It appears in human activity (sports, cooking), animal behavior (a bee’s waggle dance), natural phenomena (leaves in the wind) and in urban environments (flashing lights). Estimating visual repetition from realistic video is challenging as periodic motion is rarely perfectly static and stationary . To better deal with realistic video, we elevate the static and stationary assumptions often made by existing work. Our spatiotemporal filtering approach, established on the theory of periodic motion, effectively handles a wide variety of appearances and requires no learning. Starting from motion in 3D we derive three periodic motion types by decomposition of the motion field into its fundamental components. In addition, three temporal motion continuities emerge from the field’s temporal dynamics. For the 2D perception of 3D motion we consider the viewpoint relative to the motion; what follows are 18 cases of recurrent motion perception. To estimate repetition under all circumstances, our theory implies constructing a mixture of differential motion maps: \(\mathbf {F}\) , \({\varvec{\nabla }}\mathbf {F}\) , \({\varvec{\nabla }}{\varvec{\cdot }} \mathbf {F}\) and \({\varvec{\nabla }}{\varvec{\times }} \mathbf {F}\) . We temporally convolve the motion maps with wavelet filters to estimate repetitive dynamics. Our method is able to spatially segment repetitive motion directly from the temporal filter responses densely computed over the motion maps. For experimental verification of our claims, we use our novel dataset for repetition estimation, better-reflecting reality with non-static and non-stationary repetitive motion. On the task of repetition counting, we obtain favorable results compared to a deep learning alternative.

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 Ftand its differentials ΔFt, Δ·Ftand Δ×Ftover 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.