## Solving the Mean Field Approximation in the Level Set Framework via the Logarithm of Odds

We describe the Active Mean Fields algorithm, a new approach for estimating the posterior probability of compartments in images. Conventional likelihood models are combined with a curve length prior on boundaries, and an approximate posterior distribution on labels is sought via the mean field approach. Optimizing the resulting estimator by gradient descent leads to a level set style algorithm where the level set functions are the logarithm of odds encoding of the posterior label probabilities in an unconstrained linear vector space. Applications with more than two labels are easily accommodated. The label assignment is accomplished by the Maximum /A Posteriori/ rule, so there are no problems of "overlap'' or "vacuum". We test the method on synthetic images with additive noise. In addition, we segment a magnetic resonance scan into the major brain compartments and subcortical structures.