Principal Geodesic Analysis in the Space of Discrete Shells

Abstract

Important sources of shape variability, such as articulated motion of body models or soft tissue dynamics, are highly nonlinear and are usually superposed on top of rigid body motion which must be factored out. We propose a novel, nonlinear, rigid body motion invariant Principal Geodesic Analysis (PGA) that allows us to analyse this variability, compress large variations based on statistical shape analysis and fit a model to measurements. For given input shape data sets we show how to compute a low dimensional approximating submanifold on the space of discrete shells, making our approach a hybrid between a physical and statistical model. General discrete shells can be projected onto the submanifold and sparsely represented by a small set of coefficients. We demonstrate two specific applications: model-constrained mesh editing and reconstruction of a dense animated mesh from sparse motion capture markers using the statistical knowledge as a prior.

Publication
In Computer Graphics Forum (Proceedings of SGP)
We show how to learn nonlinear, physically plausible modes of shape variation (bottom right) from a set of highly varying training shapes, which can be used for projection onto a low dimensional submanifold and thus sparse representation by a small set of weights. This model can be used to solve problems such as reconstruction of dense body shapes from motion capture markers (top) providing compressed animations for the reconstructed shapes via time sequences of the weights (bottom left) even when the captured data is sparse, noisy and comes from a different body shape.
Avatar
Chao Zhang
Computer Vision Researcher
Avatar
Will Smith
Professor in Computer Vision