A Bayesian formulation of graph-cut surface estimation with global shape priors

In this paper, we propose a formulation of graph-cut segmentation that relies on a generative image model by incorporating both local and global shape priors. With surface estimation, rather than pixel classification, we cast the segmentation problem as a maximum a posteriori estimation from the image intensities via a cut through a multi-layer three-dimensional mesh model that preserves the topology of the shape class of interest. Methods that rely on local optimization techniques and/or local shape penalties, e.g., smoothness, have been proven to be ineffective to address challenging segmentation problems, such as noisy/ill-defined boundaries and irregular shapes. On the other hand, our method relies on graph cuts as well as a new formulation to estimate shape parameters in a closed form that provides a global updates-based optimization strategy. We demonstrate our formulation on synthetic datasets as well as the left atrial wall segmentation from late-gadolinium enhancement MRI, which is useful in atrial fibrillation to identify fibrosis, but presents local contrast and noise within the wall.