Hausdorff Distance Constraint for Multi-surface Segmentation

It is well known that multi-surface segmentation can be cast as a multi-labeling problem. Different segments may belong to the same semantic object which may impose various inter-segment constraints [1]. In medical applications, there are a lot of scenarios where upper bounds on the Hausdorff distances between subsequent surfaces are known. We show that incorporating these priors into multi-surface segmentation is potentially NP-hard. To cope with this problem we develop a submodularsupermodular procedure that converges to a locally optimal solution well-approximating the problem. While we cannot guarantee global optimality, only feasible solutions are considered during the optimization process. Empirically, we get useful solutions for many challenging medical applications including MRI and ultrasound images.