|Stochastic Systems Group|
Geometric Conditional Simulation
Ayres C. Fan
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 review our basic Markov Chain Monte Carlo (MCMC)-based curve sampling algorithm, and describe some extensions to our basic approach. In particular, we explore the use of partial user information in the sampling process to perform conditional simulation, and how we can use it to create semi-automatic segmentation algorithms. These methods are useful to constrain the range of possible answers in problems with very low SNR or with ill-posed probability distributions. We also construct and sample from a hybrid 2D/3D formulation where individual slices are viewed as being nodes in a Markov chain. Results are demonstrated on thalamus segmentation and geophysical gravity inversion applications.
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