Generating smooth animations from a limited number of sequential observations has a number of applications in vision. For example, it can be used to increase number of frames per second, or generating a new trajectory only based on first and last frames, e.g. a motion of face emotions. Despite the discrete observed data (frames), the problem of generating a new trajectory is a continues problem. In addition, to be perceptually realistic, the domain of an image should not alter drastically through the trajectory of changes. In this paper, we propose a new framework, Warping Neural ODE, for generating a smooth animation (video frame interpolation) in a continuous manner, given two ("farther apart") frames, denoting the start and the end of the animation. The key feature of our framework is utilizing the continuous spatial transformation of the image based on the vector field, derived from a system of differential equations. This allows us to achieve the smoothness and the realism of an animation with infinitely small time steps between the frames. We show the application of our work in generating an animation given two frames, in different training settings, including Generative Adversarial Network (GAN) and with $L_2$ loss.

本文提出一种新的框架，基于微分方程的连续空间变换，利用生成对抗网络（GAN）和$L_2$损失在不同的训练环境下生成平滑流畅的动画（视频帧插值）。

使用 Warping NODEs 生成连续逼真动画的图像到GIF转换器