Deformable geometric models fit very naturally into the context of Bayesian analysis. The prior probability of boundary shapes is taken to proportional to the negative exponential of the deformation energy of the boundary. This probabilistic interpretation is demonstrated using a Markov-Chain Monte-Carlo (MCMC) technique, which permits one to generate configurations drawn from 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. The maximum a posteriori reconstruction is obtained by minimizing the minus-log-posterior, a process that is facilitated through the use of adjoint differentiation, which is incorporated as a standard capability in the Bayes Inference Engine. 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.
Keywords: tomographic reconstruction, Bayesian uncertainty estimation, deformable models, Markov Chain Monte Carlo, Bayes Inference Engine (BIE), hard truth method
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