This paper addresses the weighted orthogonal Procrustes problem of matching stochastically perturbed point clouds, formulated as an optimization problem with a closed-form solution. A novel uncertainty characterization of the solution of this problem is proposed resorting to perturbation theory concepts, which admits arbitrary transformations between point clouds and individual covariance and cross-covariance matrices for the points of each cloud. The method is thoroughly validated through extensive Monte Carlo simulations, and particularly interesting cases where nonlinearities may arise are further analyzed.
['Pedro Lourenço', 'Bruno Joao Nogueira Guerreiro', 'Pedro Tiago Martins Batista', 'Paulo Jorge Ramalho Oliveira', 'Carlos Silvestre']
Uncertainty characterization of the orthogonal Procrustes problem with arbitrary covariance matrices