Manifold-based constraints for operations in face space

• We decompose statistical face models into identity and distinctiveness subspaces.
• The identity subspace forms a hyperspherical manifold that we validate empirically.
• The manifold provides non-linear alternatives to warping and averaging.
• We use the manifold to constrain optimisation-based model fitting.
• This outperforms two existing algorithms on over- and under-constrained problems.

In this paper, we constrain faces to points on a manifold within the parameter space of a linear statistical model. The manifold is the subspace of faces which have maximally likely distinctiveness and different points correspond to unique identities. We provide a detailed empirical validation for the chosen manifold. We show how the Log and Exponential maps for a hyperspherical manifold can be used to replace linear operations such as warping and averaging with operations on this manifold. Finally, we use the manifold to develop a new method for fitting a statistical face shape model to data, which is both robust (avoids overfitting) and overcomes model dominance (is not susceptible to local minima close to the mean face). We provide experimental results for fitting a dense 3D morphable face model to data using two different objective functions (one underconstrained and one with many local minima). Our method outperforms generic nonlinear optimisers based on the BFGS Quasi-Newton method and the Levenberg–Marquardt algorithm when fitting using the Basel Face Model.