Uncertainties in Bayesian geometric models

Deformable geometric models fit very naturally into the context of Bayesian analysis. The prior probability of boundary shapes as taken to proportional to the negative exponential of the deformation energy used to control the boundary. This probabilistic interpretation is demonstrated using a Markov-Chain Monte-Carlo (MCMC) technique, which permits one to generate configurations that populate the prior. One of many uses for deformable models is to solve ill-posed tomographic reconstruction problems, which we demonstrate by reconstructing a two-dimensional object from two orthogonal noisy projections. We show how MCMC samples drawn from the posterior can be used to estimate uncertainties in the location of the edge of the reconstructed object.