Abstract

It is well known that multi-surface segmentation can be cast as a multi-labeling problem. Different segments may belong to the same semantic ob ject 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 submodular- supermodular procedure that converges to a locally optimal solution well-approximating the problem. While we cannot guarantee global op- timality, only feasible solutions are considered during the optimization process. Empirically, we get useful solutions for many challenging medi- cal applications including MRI and ultrasound images.