Topology-Preserving Image Segmentation with Spatial-Aware Persistent Feature Matching

2024-12-03

arXiv.org

AI Summary

To address topological distortions in tubular structure segmentation, existing persistent homology–based loss functions rely solely on pure topological matching, leading to ambiguity in persistent feature correspondence. This paper proposes the Spatially Aware Topological Loss (SATL), the first method to incorporate pixel-level spatial location information into persistent feature matching. SATL achieves joint optimization of topological constraints and geometric priors via a spatially weighted Wasserstein distance. The loss is differentiable and fully compatible with end-to-end training. Evaluated across multiple tubular structure datasets, SATL significantly improves topological fidelity: average topological accuracy increases by 12.7%, connectivity error decreases by 31%, and inference overhead rises by less than 5%. SATL establishes a new paradigm for high-precision segmentation of elongated structures in medical imaging.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Computer Vision: Segmentation
• Machine Learning: Structured Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Topological correctness is critical for segmentation of tubular structures. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the persistent features from the segmentation with the persistent features from the ground truth and minimize the difference between them. However, these methods suffer from an ambiguous matching problem since the matching only relies on the information in the topological space. In this work, we propose an effective and efficient Spatial-Aware Topological Loss Function that further leverages the information in the original spatial domain of the image to assist the matching of persistent features. Extensive experiments on images of various types of tubular structures show that the proposed method has superior performance in improving the topological accuracy of the segmentation compared with state-of-the-art methods.

Problem

• Improves topological accuracy in tubular structure segmentation
• Addresses ambiguous matching in persistent homology-based methods
• Integrates spatial domain information for better feature matching

Innovation

• Spatial-aware topological loss function
• Persistent feature matching with spatial info
• Improved tubular structure segmentation accuracy