A comprehensive statistical framework for elastic shape analysis of 3D faces

Abstract

We develop a comprehensive statistical framework for analyzing shapes of 3D faces. In particular, we adapt a recent elastic shape analysis framework to the case of hemispherical surfaces, and explore its use in a number of processing applications. This framework provides a parameterization-invariant, elastic Riemannian metric, which allows the development of mathematically rigorous tools for statistical analysis. Specifically, this paper describes methods for registration, comparison and deformation, averaging, computation of covariance and summarization of variability using principal component analysis, random sampling from generative shape models, symmetry analysis, and expression and identity classification. An important aspect of this work is that all tasks are preformed under a unified metric, which has a natural interpretation in terms of bending and stretching of one 3D face to align it with another. We use a subset of the BU-3DFE face dataset, which contains varying magnitudes of expression.