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

Image2Gif: Generating Continuous Realistic Animations with Warping NODEs

Deep Convolutional Neural Networks (DCNN) have been proven to be effective
for various computer vision problems. In this work, we demonstrate its
effectiveness on a continuous object orientation estimation task, which
requires prediction of 0 to 360 degrees orientation of the objects. We do so by
proposing and comparing three continuous orientation prediction approaches
designed for the DCNNs. The first two approaches work by representing an
orientation as a point on a unit circle and minimizing either L2 loss or
angular difference loss. The third method works by first converting the
continuous orientation estimation task into a set of discrete orientation
estimation tasks and then converting the discrete orientation outputs back to
the continuous orientation using a mean-shift algorithm. By evaluating on a
vehicle orientation estimation task and a pedestrian orientation estimation
task, we demonstrate that the discretization-based approach not only works
better than the other two approaches but also achieves state-of-the-art
performance. We also demonstrate that finding an appropriate feature
representation is critical to achieve a good performance when adapting a DCNN
trained for an image recognition task.

本文研究使用深度卷积神经网络来解决连续物体方位估计任务，并通过比较三种连续方位估计方法的效果证明，将连续方位估计任务转化为离散方位估计任务并使用均值漂移算法将离散方位估计结果转化回连续方位，其中基于离散化的方法不仅性能更好，而且达到了最先进水平。同时，文章也说明了在适应图像识别任务的深度卷积神经网络中，寻找合适的特征表示是获得良好性能的关键。