  We present \emph{SPHEAR}, an accurate, differentiable parametric statistical
3D human head model, enabled by a novel 3D registration method based on
spherical embeddings. We shift the paradigm away from the classical Non-Rigid
Registration methods, which operate under various surface priors, increasing
reconstruction fidelity and minimizing required human intervention.
Additionally, SPHEAR is a \emph{complete} model that allows not only to sample
diverse synthetic head shapes and facial expressions, but also gaze directions,
high-resolution color textures, surface normal maps, and hair cuts represented
in detail, as strands. SPHEAR can be used for automatic realistic visual data
generation, semantic annotation, and general reconstruction tasks. Compared to
state-of-the-art approaches, our components are fast and memory efficient, and
experiments support the validity of our design choices and the accuracy of
registration, reconstruction and generation techniques.
