Topology Optimization in Medical Image Segmentation with Fast χ Euler Characteristic

Li L, Ma Q, Oyang C, Paetzold JC, Rueckert D, Kainz B (2025)

Publication Type: Journal article

Publication year: 2025

Journal

IEEE Transactions on Medical Imaging Institute of Electrical and Electronics Engineers (IEEE)

DOI: 10.1109/TMI.2025.3589495

Abstract

Deep learning-based medical image segmentation techniques have shown promising results when evaluated based on conventional metrics such as the Dice score or Intersection-over-Union. However, these fully automatic methods often fail to meet clinically acceptable accuracy, especially when topological constraints should be observed, e.g., continuous boundaries or closed surfaces. In medical image segmentation, the correctness of a segmentation in terms of the required topological genus sometimes is even more important than the pixel-wise accuracy. Existing topology-aware approaches commonly estimate and constrain the topological structure via the concept of persistent homology (PH). However, these methods are difficult to implement for high dimensional data due to their polynomial computational complexity. To overcome this problem, we propose a novel and fast approach for topology-aware segmentation based on the Euler Characteristic (χ). First, we propose a fast formulation for χ computation in both 2D and 3D. The scalar χ error between the prediction and ground-truth serves as the topological evaluation metric. Then we estimate the spatial topology correctness of any segmentation network via a so-called topological violation map, i.e., a detailed map that highlights regions with χ errors. Finally, the segmentation results from the arbitrary network are refined based on the topological violation maps by a topology-aware correction network. Our experiments are conducted on both 2D and 3D datasets and show that our method can significantly improve topological correctness while preserving pixel-wise segmentation accuracy.

Authors with CRIS profile

Bernhard Kainz

Involved external institutions

Imperial College London / The Imperial College of Science, Technology and Medicine GB United Kingdom (GB)

How to cite

APA:

Li, L., Ma, Q., Oyang, C., Paetzold, J.C., Rueckert, D., & Kainz, B. (2025). Topology Optimization in Medical Image Segmentation with Fast χ Euler Characteristic. IEEE Transactions on Medical Imaging. https://doi.org/10.1109/TMI.2025.3589495

MLA:

Li, Liu, et al. "Topology Optimization in Medical Image Segmentation with Fast χ Euler Characteristic." IEEE Transactions on Medical Imaging (2025).

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