A Robust Multilinear Model Learning Framework for 3D Faces

Multilinear models are widely used to represent the statistical variations of 3D human faces as they decouple shape changes due to identity and expression. Existing methods to learn a multilinear face model degrade if not every person is captured in every expression, if face scans are noisy or partially occluded, if expressions are erroneously labeled, or if the vertex correspondence is inaccurate. These limitations impose requirements on the training data that disqualify large amounts of available 3D face data from being usable to learn a multilinear model. To overcome this, we introduce the first framework to robustly learn a multilinear model from 3D face databases with missing data, corrupt data, wrong semantic correspondence, and inaccurate vertex correspondence. To achieve this robustness to erroneous training data, our framework jointly learns a multilinear model and fixes the data. We evaluate our framework on two publicly available 3D face databases, and show that our framework achieves a data completion accuracy that is comparable to state-of-the-art tensor completion methods. Our method reconstructs corrupt data more accurately than state-of-the-art methods, and improves the quality of the learned model significantly for erroneously labeled expressions.