Auxiliary Maximum Likelihood Estimation for Noisy Point Cloud Registration

Abstract

We establish first a theoretical foundation for the use of Gromov-Hausdorff (GH) distance for point set registration with homeomorphic deformation maps perturbed by Gaussian noise. We then present a probabilistic, deformable registration framework. At the core of the framework is a highly efficient iterative algorithm with guaranteed convergence to a local minimum of the GH-based objective function. The framework has two other key components - a multi-scale stochastic shape descriptor and a data compression scheme. We also present an experimental comparison between our method and two existing influential methods on non-rigid motion between digital anthropomorphic phantoms extracted from physical data of multiple individuals.