26 February 2008 MCMC curve sampling and geometric conditional simulation
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Abstract
We present an algorithm to generate samples from probability distributions on the space of curves. Traditional curve evolution methods use gradient descent to find a local minimum of a specified energy functional. Here, we view the energy functional as a negative log probability distribution and sample from it using a Markov chain Monte Carlo (MCMC) algorithm. We define a proposal distribution by generating smooth perturbations to the normal of the curve, update the curve using level-set methods, and show how to compute the transition probabilities to ensure that we compute samples from the posterior. We demonstrate the benefits of sampling methods (such as robustness to local minima, better characterization of multi-modal distributions, and access to some measures of estimation error) on medical and geophysical applications. We then use our sampling framework to construct a novel semi-automatic segmentation approach which takes in partial user segmentations and conditionally simulates the unknown portion of the curve. This allows us to dramatically lower the estimation variance in low-SNR and ill-posed problems.
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Ayres Fan, John W. Fisher, Jonathan Kane, Alan S. Willsky, "MCMC curve sampling and geometric conditional simulation", Proc. SPIE 6814, Computational Imaging VI, 681407 (26 February 2008); doi: 10.1117/12.778608; https://doi.org/10.1117/12.778608
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