Recently, it was proven empirically that facial expressions can be modelled as isometries, that is, geodesic distances on the facial surface were shown to be significantly less sensitive to facial expressions compared to Euclidean ones. Based on this assumption, the 3DFACE face recognition system was built. The system efficiently computes expression invariant signatures based on isometry-invariant representation of the facial surface. One of the crucial steps in the recognition system was embedding of the face geometric structure into a Euclidean (flat) space. Here, we propose to replace the flat embedding by a spherical one to construct isometric invariant representations of the facial image. We refer to these new invariants as spherical canonical images. Compared to its Euclidean counterpart, spherical embedding leads to notably smaller metric distortion. We demonstrate experimentally that representations with lower embedding error lead to better recognition. In order to efficiently compute the invariants we introduce a dissimilarity measure between the spherical canonical images based on the spherical harmonic transform.