Apathy is the Root of all Expressions

In this paper, we present a new statistical model for human faces. Our approach is built upon a tensor factorisation model that allows controlled estimation, morphing and transfer of new facial shapes and expressions. We propose a direct parametrisation and regularisation for person and expression related terms so that the training database is well utilised. In contrast to existing works we are the first to reveal that the expression subspace is star shaped. This stems from the fact that increasing the strength of an expression approximately forms a linear trajectory in the expression subspace, and all these linear trajectories intersect in a single point which corresponds to the point of no expression or the point of apathy. After centring our analysis to this point, we then demonstrate how the dimensionality of the expression subspace can be further reduced by projection pursuit with the help of the fourth-order moment tensor. The results show that our method is able to achieve convincing separation of the person specific and expression subspaces as well as flexible, natural modelling of facial expressions for wide variety of human faces. By the proposed approach, one can morph between different persons and different expressions even if they do not exist in the database. In contrast to the state-of-the-art, the morphing works without causing strong deformations. In the application of expression classification, the results are also better.