  Learning based representation has become the key to the success of many
computer vision systems. While many 3D representations have been proposed, it
is still an unaddressed problem how to represent a dynamically changing 3D
object. In this paper, we introduce a compositional representation for 4D
captures, i.e. a deforming 3D object over a temporal span, that disentangles
shape, initial state, and motion respectively. Each component is represented by
a latent code via a trained encoder. To model the motion, a neural Ordinary
Differential Equation (ODE) is trained to update the initial state conditioned
on the learned motion code, and a decoder takes the shape code and the updated
state code to reconstruct the 3D model at each time stamp. To this end, we
propose an Identity Exchange Training (IET) strategy to encourage the network
to learn effectively decoupling each component. Extensive experiments
demonstrate that the proposed method outperforms existing state-of-the-art deep
learning based methods on 4D reconstruction, and significantly improves on
various tasks, including motion transfer and completion.
