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.