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We present a progressive 3D registration framework that is a highly-efficientvariant of classical non-rigid Iterative Closest Points (N-ICP). Since it usesthe Laplace-Beltrami operator for deformation regularisation, we view theoverall process as Laplacian ICP (L-ICP). This exploits a `small deformationper iteration' assumption and is progressively coarse-to-fine, employing anincreasingly flexible deformation model, an increasing number of correspondencesets, and increasingly sophisticated correspondence estimation. Correspondencematching is only permitted within predefined vertex subsets derived fromdomain-specific feature extractors. Additionally, we present a new benchmarkand a pair of evaluation metrics for 3D non-rigid registration, based onannotation transfer. We use this to evaluate our framework on apublicly-available dataset of 3D human head scans (Headspace). The method isrobust and only requires a small fraction of the computation time compared tothe most popular classical approach, yet has comparable registrationperformance.

Laplacian ICP for Progressive Registration of 3D Human Head Meshes