Long-Term Human Video Generation of Multiple Futures Using Poses

Predicting future human behavior from an input human video is a useful task for applications such as autonomous driving and robotics. While most previous works predict a single future, multiple futures with different behavior can potentially occur. Moreover, if the predicted future is too short (e.g., less than one second), it may not be fully usable by a human or other systems. In this paper, we propose a novel method for future human pose prediction capable of predicting multiple long-term futures. This makes the predictions more suitable for real applications. Also, from the input video and the predicted human behavior, we generate future videos. First, from an input human video, we generate sequences of future human poses (i.e., the image coordinates of their body-joints) via adversarial learning. Adversarial learning suffers from mode collapse, which makes it difficult to generate a variety of multiple poses. We solve this problem by utilizing two additional inputs to the generator to make the outputs diverse, namely, a latent code (to reflect various behaviors) and an attraction point (to reflect various trajectories). In addition, we generate long-term future human poses using a novel approach based on unidimensional convolutional neural networks. Last, we generate an output video based on the generated poses for visualization. We evaluate the generated future poses and videos using three criteria (i.e., realism, diversity and accuracy), and show that our proposed method outperforms other state-of-the-art works

Defect Dynamics for Spiral Chaos in Rayleigh-Benard Convection

A theory of the novel spiral chaos state recently observed in Rayleigh-Benard convection is proposed in terms of the importance of invasive defects i.e defects that through their intrinsic dynamics expand to take over the system. The motion of the spiral defects is shown to be dominated by wave vector frustration, rather than a rotational motion driven by a vertical vorticity field. This leads to a continuum of spiral frequencies, and a spiral may rotate in either sense depending on the wave vector of its local environment. Results of extensive numerical work on equations modelling the convection system provide some confirmation of these ideas.Comment: Revtex (15 pages) with 4 encoded Postscript figures appende

Integral Human Pose Regression

State-of-the-art human pose estimation methods are based on heat map representation. In spite of the good performance, the representation has a few issues in nature, such as not differentiable and quantization error. This work shows that a simple integral operation relates and unifies the heat map representation and joint regression, thus avoiding the above issues. It is differentiable, efficient, and compatible with any heat map based methods. Its effectiveness is convincingly validated via comprehensive ablation experiments under various settings, specifically on 3D pose estimation, for the first time

Exploiting temporal information for 3D pose estimation

In this work, we address the problem of 3D human pose estimation from a sequence of 2D human poses. Although the recent success of deep networks has led many state-of-the-art methods for 3D pose estimation to train deep networks end-to-end to predict from images directly, the top-performing approaches have shown the effectiveness of dividing the task of 3D pose estimation into two steps: using a state-of-the-art 2D pose estimator to estimate the 2D pose from images and then mapping them into 3D space. They also showed that a low-dimensional representation like 2D locations of a set of joints can be discriminative enough to estimate 3D pose with high accuracy. However, estimation of 3D pose for individual frames leads to temporally incoherent estimates due to independent error in each frame causing jitter. Therefore, in this work we utilize the temporal information across a sequence of 2D joint locations to estimate a sequence of 3D poses. We designed a sequence-to-sequence network composed of layer-normalized LSTM units with shortcut connections connecting the input to the output on the decoder side and imposed temporal smoothness constraint during training. We found that the knowledge of temporal consistency improves the best reported result on Human3.6M dataset by approximately $12.2\%$ and helps our network to recover temporally consistent 3D poses over a sequence of images even when the 2D pose detector fails

KP solitons in shallow water

The main purpose of the paper is to provide a survey of our recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. The classification is based on the far-field patterns of the solutions which consist of a finite number of line-solitons. Each soliton solution is then defined by a point of the totally non-negative Grassmann variety which can be parametrized by a unique derangement of the symmetric group of permutations. Our study also includes certain numerical stability problems of those soliton solutions. Numerical simulations of the initial value problems indicate that certain class of initial waves asymptotically approach to these exact solutions of the KP equation. We then discuss an application of our theory to the Mach reflection problem in shallow water. This problem describes the resonant interaction of solitary waves appearing in the reflection of an obliquely incident wave onto a vertical wall, and it predicts an extra-ordinary four-fold amplification of the wave at the wall. There are several numerical studies confirming the prediction, but all indicate disagreements with the KP theory. Contrary to those previous numerical studies, we find that the KP theory actually provides an excellent model to describe the Mach reflection phenomena when the higher order corrections are included to the quasi-two dimensional approximation. We also present laboratory experiments of the Mach reflection recently carried out by Yeh and his colleagues, and show how precisely the KP theory predicts this wave behavior.Comment: 50 pages, 25 figure

Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems

In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one parameter family of exact solutions, which include as special cases the Toda lattice solutions as well as the Whitham's solutions in the Newell's model. Our solutions can be used to describe temporal-spatial density patterns observed in the optimal velocity model for traffic flow.Comment: Latex, 13 pages, 1 figur

On a Camassa-Holm type equation with two dependent variables

We consider a generalization of the Camassa Holm (CH) equation with two dependent variables, called CH2, introduced by Liu and Zhang. We briefly provide an alternative derivation of it based on the theory of Hamiltonian structures on (the dual of) a Lie Algebra. The Lie Algebra here involved is the same algebra underlying the NLS hierarchy. We study the structural properties of the CH2 hierarchy within the bihamiltonian theory of integrable PDEs, and provide its Lax representation. Then we explicitly discuss how to construct classes of solutions, both of peakon and of algebro-geometrical type. We finally sketch the construction of a class of singular solutions, defined by setting to zero one of the two dependent variables.Comment: 22 pages, 2 figures. A few typos correcte

Solvable Optimal Velocity Models and Asymptotic Trajectory

In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established congested flow obtained in a numerical simulation shows a remarkable repetitive property such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except a time delay $T$. This leads to a global pattern formation in time development of vehicles' motion, and gives rise to a closed trajectory on $\Delta x$-$v$ (headway-velocity) plane connecting congested and free flow points. To obtain the closed trajectory analytically, we propose a new approach to the pattern formation, which makes it possible to reduce the coupled car following equations to a single difference-differential equation (Rondo equation). To demonstrate our approach, we employ a class of linear models which are exactly solvable. We also introduce the concept of ``asymptotic trajectory'' to determine $T$ and $v_B$ (the backward velocity of the pattern), the global parameters associated with vehicles' collective motion in a congested flow, in terms of parameters such as the sensitivity $a$, which appeared in the original coupled equations.Comment: 25 pages, 15 eps figures, LaTe

New way to achieve chaotic synchronization in spatially extended systems

We study the spatio-temporal behavior of simple coupled map lattices with periodic boundary conditions. The local dynamics is governed by two maps, namely, the sine circle map and the logistic map respectively. It is found that even though the spatial behavior is irregular for the regularly coupled (nearest neighbor coupling) system, the spatially synchronized (chaotic synchronization) as well as periodic solution may be obtained by the introduction of three long range couplings at the cost of three nearest neighbor couplings.Comment: 5 pages (revtex), 7 figures (eps, included

Cavitation induced by explosion in a model of ideal fluid

We discuss the problem of an explosion in the cubic-quintic superfluid model, in relation to some experimental observations. We show numerically that an explosion in such a model might induce a cavitation bubble for large enough energy. This gives a consistent view for rebound bubbles in superfluid and we indentify the loss of energy between the successive rebounds as radiated waves. We compute self-similar solution of the explosion for the early stage, when no bubbles have been nucleated. The solution also gives the wave number of the excitations emitted through the shock wave.Comment: 21 pages,13 figures, other comment