A New Bayesian Approach to Global Optimization on Parametrized Surfaces in $$\mathbb {R}^{3}$$

This work introduces a new Riemannian optimization method for registering open parameterized surfaces with a constrained global optimization approach. The proposed formulation leads to a rigorous theoretic foundation and guarantees the existence and the uniqueness of a global solution. We also propose a new Bayesian clustering approach where local distributions of surfaces are modeled with spherical Gaussian processes. The maximization of the posterior density is performed with Hamiltonian dynamics which provide a natural and computationally efficient spherical Hamiltonian Monte Carlo sampling. Experimental results demonstrate the efficiency of the proposed method.