Topology-Preserving Deep Image Segmentation
This addresses the issue of broken connections in fine-scale structures for segmentation tasks, with incremental improvements in topology preservation.
The paper tackles the problem of topological errors in image segmentation by proposing a differentiable loss function that enforces correct topology, achieving better performance on Betti number error and other topology-relevant metrics across natural and biomedical datasets.
Segmentation algorithms are prone to make topological errors on fine-scale structures, 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 we incorporate it 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 superiorly on other topology-relevant metrics, e.g., the Adjusted Rand Index and the Variation of Information. We illustrate the effectiveness of the proposed method on a broad spectrum of natural and biomedical datasets.