Identity-Expression Ambiguity in 3D Morphable Face Models

3D Morphable Models are a class of generative models commonly used to model faces. They are typically applied to ill-posed problems such as 3D reconstruction from 2D data. Several ambiguities in this problem's image formation process have been studied explicitly. We demonstrate that non-orthogonality of the variation in identity and expression can cause identity-expression ambiguity in 3D Morphable Models, and that in practice expression and identity are far from orthogonal and can explain each other surprisingly well. Whilst previously reported ambiguities only arise in an inverse rendering setting, identity-expression ambiguity emerges in the 3D shape generation process itself. We demonstrate this effect with 3D shapes directly as well as through an inverse rendering task, and use two popular models built from high quality 3D scans as well as a model built from a large collection of 2D images and videos. We explore this issue's implications for inverse rendering and observe that it cannot be resolved by a purely statistical prior on identity and expression deformations.