Shell PCA: Statistical Shape Modelling in Shell Space

Chao Zhang, Behrend Heeren, Martin Rumpf, William A. P. Smith; Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2015, pp. 1671-1679

In this paper we describe how to perform Principal Components Analysis in "shell space". Thin shells are a physical model for surfaces with non-zero thickness whose deformation dissipates elastic energy. Thin shells, or their discrete counterparts, can be considered to reside in a shell space in which the notion of distance is given by the elastic energy required to deform one shape into another. It is in this setting that we show how to perform statistical analysis of a set of shapes (meshes in dense correspondence), providing a hybrid between physical and statistical shape modelling. The resulting models are better able to capture non-linear deformations, for example resulting from articulated motion, even when training data is very sparse compared to the dimensionality of the observation space.