Topology-Preserving Deep Image Segmentation

TL;DR

This paper introduces a deep learning segmentation method that preserves topological features by using a novel differentiable loss function, improving accuracy on topological metrics across various datasets.

Contribution

A new topology-preserving loss function for deep segmentation that ensures topological correctness during end-to-end training.

Findings

Significantly reduces Betti number errors in segmentation.

Outperforms existing methods on topology-related metrics.

Effective on natural and biomedical datasets.

Abstract

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.