|Stochastic Systems Group|
Level-set MCMC Curve Sampling
Traditional curve evolution algorithms are optimization based: an energy functional is defined and gradient descent is used to find a local minimum. This approach can be problematic if there are many local minima which are not close to the global minimum or there is inherently a multi-modal distribution. Additionally, while these algorithms give a single answer, there is no notion of uncertainty of the estimate. In this talk we describe a Markov Chain Monte Carlo (MCMC) approach to sampling from a probability distribution on curves. MCMC sampling methods allow one to asymptotically generate samples from a target probability distribution by actually sampling from a proposal distribution and accepting or rejecting a sample according to a decision rule. We detail a sampling method based on a continuous level-set based curve evolution formulation. We discuss techniques we use to achieve "approximate" detailed balance to have asymptotic convergence. We demonstrate results on a variety of synthetic and real images from the medical and geological fields.
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