Inbetweening auto-animation via Fokker-Planck dynamics and thresholding

TL;DR

This paper introduces EDDA, an equilibrium-driven deformation algorithm based on Fokker-Planck dynamics, for simulating inbetweening transformations across various image types and complex processes with stability and convergence guarantees.

Contribution

The paper presents a novel equilibrium-driven deformation algorithm utilizing Fokker-Planck dynamics on manifolds, enabling efficient and stable inbetweening transformations with a thresholding scheme for finite-time convergence.

Findings

Successfully applied to facial aging, COVID-19 progression, and continental evolution.

Demonstrates stability, positivity, and mass conservation in transformations.

Achieves finite-time convergence with the adapted thresholding scheme.

Abstract

We propose an equilibrium-driven deformation algorithm (EDDA) to simulate the inbetweening transformations starting from an initial image to an equilibrium image, which covers images varying from a greyscale type to a colorful type on plane or manifold. The algorithm is based on Fokker-Planck dynamics on manifold, which automatically cooperates positivity, unconditional stability, mass conservation law, exponentially convergence and also the manifold structure suggested by dataset. The thresholding scheme is adapted for the sharp interface dynamics and is used to achieve the finite time convergence. Using EDDA, three challenging examples, (I) facial aging process, (II) coronavirus disease 2019 (COVID-19) invading/treatment process, and (III) continental evolution process are conducted efficiently.