Project Image MCMC Sampling over Shapes
We present a method for sampling from the posterior distribution of implicitly defined segmentations conditioned on the observed image. Segmentation is often formulated as an energy minimization or statistical inference problem in which either the optimal or most probable configuration is the goal. Exponentiating the negative energy functional provides a Bayesian interpretation in which the solutions are equivalent. Sampling methods enable evaluation of distribution properties that characterize the solution space via the computation of marginal event probabilities. We develop a Metropolis-Hastings sampling algorithm over level-sets which improves upon previous methods by allowing for topological changes (if desired) while simultaneously decreasing computational times by orders of magnitude.

People Involved: Jason Chang, John W. Fisher III
\(
\newcommand{\sizeof}[1] { \left\vert #1 \right\vert } \newcommand{\curve} { \mathcal{C} } \newcommand{\levelset}[1] { \varphi^{\left( #1 \right)} } \newcommand{\hatlevelset}[1] { \hat\varphi^{\left( #1 \right)} } \newcommand{\indicator}[1] { 1{\hskip -2.5 pt}\hbox{I}_{\left\{ #1 \right\}} } \newcommand{\KL}[2] { D\left(#1 \Vert #2\right) } \newcommand{\pplus}[1] { p_X^+\left(x_{#1}\right) } \newcommand{\pminus}[1] { p_X^-\left(x_{#1}\right) } \newcommand{\plabel}[2] { p_X^{#2}\left(x_{#1}\right) } \newcommand{\red}[1] {% \color{red}{#1}\color{black}% } \newcommand{\expected}[2] { \mathbf{E}_{#1}\left[ #2 \right] } \newcommand{\highlight}[1] {% \hl{#1}% }
\)

Comparison to Other Sampling Algorithms

The following movie shows the convergence speed gains by using the BFPS algorithm of (Chang et al. 2011). We note that the more recent GIMH algorithm is even faster than BFPS.



The following movies show one sample path of each sampling algorithm.

[Fan 2007][Chen 2009]BFPS