Modelling Character Motions on Infinite-Dimensional Manifolds

TL;DR

This paper introduces a mathematical framework using infinite-dimensional manifolds to analyze, interpolate, and cluster character animations, improving the handling of cyclic motions and motion retrieval in computer animation.

Contribution

It formulates character motions as points on infinite-dimensional Hilbert manifolds, enabling new methods for animation analysis, interpolation, artifact removal, and clustering.

Findings

Effective removal of visual artifacts in cyclic animations.

Stable interpolation between different animations.

Successful clustering of large motion capture datasets.

Abstract

In this article, we will formulate a mathematical framework that allows us to treat character animations as points on infinite dimensional Hilbert manifolds. Constructing geodesic paths between animations on those manifolds allows us to derive a distance function to measure similarities of different motions. This approach is derived from the field of geometric shape analysis, where such formalisms have been used to facilitate object recognition tasks. Analogously to the idea of shape spaces, we construct motion spaces consisting of equivalence classes of animations under reparametrizations. Especially cyclic motions can be represented elegantly in this framework. We demonstrate the suitability of this approach in multiple applications in the field of computer animation. First, we show how visual artifacts in cyclic animations can be removed by applying a computationally efficient manifold projection method. We next highlight how geodesic paths can be used to calculate interpolations between various animations in a computationally stable way. Finally, we show how the same mathematical framework can be used to perform cluster analysis on large motion capture databases, which can be used for or as part of motion retrieval problems.