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Ayres C. Fan

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Proceedings Article | 26 February 2008 Paper

MCMC curve sampling and geometric conditional simulation

Ayres Fan, John Fisher, Jonathan Kane, Alan Willsky

Proceedings Volume 6814, 681407 (2008) https://doi.org/10.1117/12.778608

KEYWORDS: Image segmentation, Monte Carlo methods, Prostate, Signal to noise ratio, Algorithm development, Computer simulations, Error analysis, Statistical modeling, Rectum, Fluctuations and noise

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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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