We study the problem of identifying shapes in point clouds that
have been corrupted by clutter and observation noise. Taking an
analysis-by-synthesis approach, we simulate high-probability
configurations from models learnt from the training data to
evaluate a given configuration. To facilitate simulations, we
develop statistical models for sources of (nuisance) variability:
(i) shape variations within classes, (ii) variability in sampling
curves, (iii) pose variability, (iv) observation noise, and (v)
points introduced by background clutter. The variability in
sampling curves is represented by positive diffeomorphisms of a
unit circle and we derive probability models on these functions
using their square-root forms and the Fisher-Rao metric. Using a
Monte Carlo approach, we simulate configurations using a joint
prior on the shape-sample space and compare them to the data using
a likelihood function. Average likelihoods of simulated
configurations lead to estimates of posterior probabilities of
different classes and, hence, Bayesian classification.