Topology Optimization in Medical Image Segmentation with Fast Euler Characteristic

2025-07-31

AI Summary

Medical image segmentation often yields clinically unacceptable errors—such as disconnected boundaries or non-closed surfaces—because conventional metrics (e.g., Dice) ignore topological fidelity. Existing persistent homology (PH)-based topological-aware methods suffer from high computational complexity, hindering their application to 3D medical images. To address this, we propose a fast Euler characteristic (EC)-driven topological-aware segmentation framework. First, EC is introduced as an efficient topological metric with linear computational complexity—its first use in medical image segmentation. Second, a Topological Violation Map is designed to precisely localize topological inconsistencies. Third, a plug-and-play correction network enables end-to-end topological optimization. Evaluated on both 2D and 3D medical datasets, our method significantly improves topological correctness—including accuracy in the number of connected components and holes—while preserving pixel-level segmentation performance, outperforming PH-based approaches.

Technology Category

• Computer Vision: Segmentation
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

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.

Problem

• Improves topological accuracy in medical image segmentation
• Addresses high computational complexity in topology-aware methods
• Ensures clinically acceptable segmentation with correct topology

Innovation

• Fast Euler Characteristic computation for topology
• Topological violation map highlights error regions
• Topology-aware correction network refines segmentation