  We present a progressive 3D registration framework that is a highly-efficient
variant of classical non-rigid Iterative Closest Points (N-ICP). Since it uses
the Laplace-Beltrami operator for deformation regularisation, we view the
overall process as Laplacian ICP (L-ICP). This exploits a `small deformation
per iteration' assumption and is progressively coarse-to-fine, employing an
increasingly flexible deformation model, an increasing number of correspondence
sets, and increasingly sophisticated correspondence estimation. Correspondence
matching is only permitted within predefined vertex subsets derived from
domain-specific feature extractors. Additionally, we present a new benchmark
and a pair of evaluation metrics for 3D non-rigid registration, based on
annotation transfer. We use this to evaluate our framework on a
publicly-available dataset of 3D human head scans (Headspace). The method is
robust and only requires a small fraction of the computation time compared to
the most popular classical approach, yet has comparable registration
performance.
