Bayesian tensor approach for 3-D face modeling

Effectively modeling a collection of three-dimensional (3-D) faces is an important task in various applications, especially facial expression-driven ones, e.g., expression generation, retargeting, and synthesis. These 3-D faces naturally form a set of second-order tensors-one modality for identity and the other for expression. The number of these second-order tensors is three times of that of the vertices for 3-D face modeling. As for algorithms, Bayesian data modeling, which is a natural data analysis tool, has been widely applied with great success; however, it works only for vector data. Therefore, there is a gap between tensor-based representation and vector-based data analysis tools. Aiming at bridging this gap and generalizing conventional statistical tools over tensors, this paper proposes a decoupled probabilistic algorithm, which is named Bayesian tensor analysis (BTA). Theoretically, BTA can automatically and suitably determine dimensionality for different modalities of tensor data. With BTA, a collection of 3-D faces can be well modeled. Empirical studies on expression retargeting also justify the advantages of BTA.