Topology-Preserving Deep Image Segmentation

Segmentation algorithms are prone to make topological errors on fine-scale struc- tures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss function that enforces a segmentation to have the same topology as the ground truth, i.e.,having the same Betti number. The proposed topology-preserving loss function is differentiable and can be incorporated into end-to-end training of a deep neural network. Our method achieves much better performance on the Betti number error, which directly accounts for the topological correctness. It also performs superior on other topology-relevant metrics, e.g., the Adjusted Rand Index and the Variation of Information, without sacrificing per-pixel accuracy. We illustrate the effectiveness of the proposed method on a broad spectrum of natural and biomedical datasets.