Deformation Based 3D Facial Expression Representation

We propose a deformation based representation for analyzing expressions from 3D faces. A point cloud of a 3D face is decomposed into an ordered deformable set of curves that start from a fixed point. Subsequently, a mapping function is defined to identify the set of curves with an element of a high dimensional matrix Lie group, specifically the direct product of SE(3). Representing 3D faces as an element of a high dimensional Lie group has two main advantages. First, using the group structure, facial expressions can be decoupled from a neutral face. Second, an underlying non-linear facial expression manifold can be captured with the Lie group and mapped to a linear space, Lie algebra of the group. This opens up the possibility of classifying facial expressions with linear models without compromising the underlying manifold. Alternatively, linear combinations of linearised facial expressions can be mapped back from the Lie algebra to the Lie group. The approach is tested on the BU-3DFE and the Bosphorus datasets. The results show that the proposed approach performed comparably, on the BU-3DFE dataset, without using features or extensive landmark points

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

International audienceWe 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