This thesis researches techniques for modelling static facial expressions, as well as the dynamics of continuous facial motion. We demonstrate how static and dynamic properties of facial expressions can be represented within a linear and nonlinear context, respectively. These two representations do not act in isolation, but are mutually reinforcing in conceding a cohesive framework for the analysis, animation, and manipulation of expressive faces. We derive a basis for the linear space of expressions through Principal Components Analysis (PCA). We introduce and formalize the notion of "expression manifolds", manifolds residing in PCA space that model motion dynamics for semantically similar expressions. We then integrate these manifolds into an animation workflow by performing Nonlinear Dimensionality Reduction (NLDR) on the expression manifolds. This operation yields expression maps that encode a wealth of information relating to complex facial dynamics, in a low dimensional space that is intuitive to navigate and efficient to manage.

This thesis researches techniques for modelling static facial expressions, as well as the dynamics of continuous facial motion. We demonstrate how static and dynamic properties of facial expressions can be represented within a linear and nonlinear context, respectively. These two representations do not act in isolation, but are mutually reinforcing in conceding a cohesive framework for the analysis, animation, and manipulation of expressive faces. We derive a basis for the linear space of expressions through Principal Components Analysis (PCA). We introduce and formalize the notion of "expression manifolds", manifolds residing in PCA space that model motion dynamics for semantically similar expressions. We then integrate these manifolds into an animation workflow by performing Nonlinear Dimensionality Reduction (NLDR) on the expression manifolds. This operation yields expression maps that encode a wealth of information relating to complex facial dynamics, in a low dimensional space that is intuitive to navigate and efficient to manage.