Although existing medical image segmentation methods provide impressive pixel-wise accuracy, they often neglect topological correctness, making their segmentations unusable for many downstream tasks. One option is to retrain such models whilst including a topology-driven loss component. However, this is computationally expensive and often impractical. A better solution would be to have a versatile plug-and-play topology refinement method that is compatible with any domain-specific segmentation pipeline. Directly training a post-processing model to mitigate topological errors often fails as such models tend to be biased towards the topological errors of a target segmentation network. The diversity of these errors is confined to the information provided by a labelled training set, which is especially problematic for small datasets. Our method solves this problem by training a model-agnostic topology refinement network with synthetic segmentations that cover a wide variety of topological errors. Inspired by the Stone-Weierstrass theorem, we synthesize topology-perturbation masks with randomly sampled coefficients of orthogonal polynomial bases, which ensures a complete and unbiased representation. Practically, we verified the efficiency and effectiveness of our methods as being compatible with multiple families of polynomial bases, and show evidence that our universal plug-and-play topology refinement network outperforms both existing topology-driven learning-based and post-processing methods. We also show that combining our method with learning-based models provides an effortless add-on, which can further improve the performance of existing approaches.

本研究解决了现有医疗图像分割方法在像素精度高的同时，常常忽视拓扑正确性的问题。提出了一种与特定分割流程兼容的通用拓扑细化方法，通过合成涵盖多种拓扑错误的分割图像，显著提高了拓扑修复的效率和效果，最终证明该方法能够超越现有的基于拓扑学习的和后处理的方法。

医疗图像分割的通用拓扑细化与多项式特征合成