Topology Optimization in Medical Image Segmentation With Fast χ Euler Characteristic

Area of Science:

• Medical Imaging
• Computer Vision
• Computational Topology

Background:

• Deep learning excels in medical image segmentation using metrics like Dice score and IoU.
• However, fully automatic methods struggle with clinical accuracy, especially for topological constraints like continuous boundaries.
• Topological correctness (e.g., genus) is often critical in medical image segmentation, sometimes more than pixel-wise accuracy.

Purpose of the Study:

• To develop a computationally efficient, topology-aware medical image segmentation approach.
• To address the limitations of existing persistent homology (PH)-based methods in high-dimensional data.
• To improve the clinical acceptability of deep learning segmentation by ensuring topological correctness.

Main Methods:

• Proposed a novel, fast Euler Characteristic (χ) computation for 2D and 3D medical image segmentation.
• Introduced a topological violation map to identify regions with χ errors in segmentation predictions.
• Developed a topology-aware correction network to refine segmentation results using these violation maps.

Main Results:

• The proposed method significantly enhances topological correctness in segmentation.
• Pixel-wise segmentation accuracy is preserved during the topological refinement process.
• Experiments on 2D and 3D datasets demonstrate the effectiveness and speed of the Euler Characteristic-based approach.

Conclusions:

• The Euler Characteristic (χ) offers a computationally efficient alternative to persistent homology for topology-aware segmentation.
• The developed method successfully refines segmentation to meet topological constraints without sacrificing pixel accuracy.
• This approach holds promise for improving the clinical utility of deep learning in medical image analysis.