Acceleration of Non-Rigid Point Set Registration With Downsampling and Gaussian Process Regression

Non-rigid point set registration is the process of transforming a shape represented as a point set into a shape matching another shape. In this paper, we propose an acceleration method for solving non-rigid point set registration problems. We accelerate non-rigid registration by dividing it into three steps: i) downsampling of point sets; ii) non-rigid registration of downsampled point sets; and iii) interpolation of shape deformation vectors corresponding to points removed during downsampling. To register downsampled point sets, we use a registration algorithm based on a prior distribution, called motion coherence prior. Using the same prior, we derive an interpolation method interpreted as Gaussian process regression. Through numerical experiments, we demonstrate that our algorithm registers point sets containing over ten million points. We also show that our algorithm reduces computing time more radically than a state-of-the-art acceleration algorithm.