Robust Segmentation via Topology Violation Detection and Feature Synthesis

Despite recent progress of deep learning-based medical image segmentation techniques, fully automatic results often fail to meet clinically acceptable accuracy, especially when topological constraints should be observed, e.g., closed surfaces. Although modern image segmentation methods show promising results when evaluated based on conventional metrics such as the Dice score or Intersection-over-Union, these metrics do not reflect the correctness of a segmentation in terms of a required topological genus. Existing approaches estimate and constrain the topological structure via persistent homology (PH). However, these methods are not computationally efficient as calculating PH is not differentiable. To overcome this problem, we propose a novel approach for topological constraints based on the multi-scale Euler Characteristic (EC). To mitigate computational complexity, we propose a fast formulation for the EC that can inform the learning process of arbitrary segmentation networks via topological violation maps. Topological performance is further facilitated through a corrective convolutional network block. Our experiments on two datasets show that our method can significantly improve topological correctness.