Estimation of Riemannian Metric in a High-Dimensional Facial Expression Space from Low-Dimensional Subspaces

To determine the Riemannian metric tensor in the psychophysical space of facial expression images demands a large amount of psychophysical experiments and coping with observation noise. We propose a new algorithm to estimate high dimensional Riemannian metric tensor of facial expression spaces using ellipse/ellipsoid fitting in low dimensional subspaces. The proposal based on conformality between different cross-sections of a hyperellipsoid with low dimensional affine subspaces and a method to find the conformality factor. We evaluate the proposed algorithms using artificial discrimination data containing noise, comparing the least square and maximal likelihood fitting, and show that they are noise robust and data efficient. The method is then applied to construct 10D facial expression spaces.