Topology Optimization in Medical Image Segmentation with Fast Euler Characteristic

TL;DR

This paper introduces a fast Euler Characteristic-based method for topology-aware medical image segmentation, improving topological correctness without sacrificing pixel accuracy, especially useful for clinical applications requiring topological constraints.

Contribution

The paper presents a novel, computationally efficient approach using Euler Characteristic for topology-aware segmentation, overcoming the complexity of persistent homology methods.

Findings

Significantly improves topological correctness of segmentations

Maintains high pixel-wise segmentation accuracy

Effective in both 2D and 3D medical imaging datasets

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 ($\chi$). First, we propose a fast formulation for $\chi$ computation in both 2D and 3D. The scalar $\chi$ 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 $\chi$ 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.