  We propose to view non-rigid surface registration as a probabilistic
inference problem. Given a target surface, we estimate the posterior
distribution of surface registrations. We demonstrate how the posterior
distribution can be used to build shape models that generalize better and show
how to visualize the uncertainty in the established correspondence.
Furthermore, in a reconstruction task, we show how to estimate the posterior
distribution of missing data without assuming a fixed point-to-point
correspondence.
  We introduce the closest-point proposal for the Metropolis-Hastings
algorithm. Our proposal overcomes the limitation of slow convergence compared
to a random-walk strategy. As the algorithm decouples inference from modeling
the posterior using a propose-and-verify scheme, we show how to choose
different distance measures for the likelihood model.
  All presented results are fully reproducible using publicly available data
and our open-source implementation of the registration framework.
