Wassersplines for Neural Vector Field‐Controlled Animation

Abstract

Much of computer‐generated animation is created by manipulating meshes with rigs. While this approach works well for animating articulated objects like animals, it has limited flexibility for animating less structured free‐form objects. We introduce Wassersplines, a novel trajectory inference method for animating unstructured densities based on recent advances in continuous normalizing flows and optimal transport. The key idea is to train a neurally‐parameterized velocity field that represents the motion between keyframes. Trajectories are then computed by advecting keyframes through the velocity field. We solve an additional Wasserstein barycenter interpolation problem to guarantee strict adherence to keyframes. Our tool can stylize trajectories through a variety of PDE‐based regularizers to create different visual effects. We demonstrate our tool on various keyframe interpolation problems to produce temporally‐coherent animations without meshing or rigging.

A survey of Optimal Transport for Computer Graphics and Computer Vision

“…However it is extremely powerful at modeling unstructured data evolution. Zhang et al [ZSS22] propose to interpolate unstructured freeform objects between user‐provided keyframes by combining optimal transport with Continuous Normalizing Flows (CNF) [CRBD18]. Here, the Sinkhorn divergence is used to replace the Kullback‐Leibler divergence in the CNF framework.…”