Locally rigid globally non-rigid surface registration

We present a novel non-rigid surface registration method that achieves high accuracy and matches characteristic features without manual intervention. The key insight is to consider the entire shape as a collection of local structures that individually undergo rigid transformations to collectively deform the global structure. We realize this locally rigid but globally non-rigid surface registration with a newly derived dual-grid Free-form Deformation (FFD) framework. We first represent the source and target shapes with their signed distance fields (SDF). We then superimpose a sampling grid onto a conventional FFD grid that is dual to the control points. Each control point is then iteratively translated by a rigid transformation that minimizes the difference between two SDFs within the corresponding sampling region. The translated control points then interpolate the embedding space within the FFD grid and determine the overall deformation. The experimental results clearly demonstrate that our method is capable of overcoming the difficulty of preserving and matching local features.