Learning to Segment: Training Hierarchical Segmentation under a Topological Loss

We propose a generic and efficient learning framework that is applicable to segment images in which individual objects are mainly discernible by boundary cues. Our approach starts by first hierarchically clustering the image and then explaining the image in terms of a cost-minimal subset of non-overlapping segments. The cost of a segmentation is defined as a weighted sum of features of the selected candidates. This formulation allows us to take into account an extensible set of arbitrary features. The maximally discriminative linear combination of features is learned from training data using a margin-rescaled structured SVM. At the core of our formulation is a novel and simple topology-based structured loss which is a combination of counts and geodesic distance of topological errors (splits, merges, false positives and false negatives) relative to the training set. We demonstrate the generality and accuracy of our approach on three challenging 2D cell segmentation problems, where we improve accuracy compared to the current state of the art.