Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentation

2024-11-05

arXiv.org

AI Summary

Existing image segmentation methods predominantly rely on pixel-wise losses (e.g., Dice), neglecting topological consistency; mainstream topology-aware approaches either lack rigorous theoretical guarantees or suffer from high computational cost and poor generalizability. Method: We propose the first differentiable, lightweight, and formally guaranteed topology-preserving framework: (i) we introduce and optimize a strict homotopy equivalence metric; (ii) we construct a differentiable component graph based on connected components, enabling local neighborhood-sensitive topological modeling and loss computation; (iii) we employ graph neural networks for feature aggregation and homotopy classification to enforce homotopy equivalence between predictions and ground truth. Contribution/Results: Our method achieves state-of-the-art performance on diverse multi-class medical and natural image segmentation benchmarks. It significantly improves topological accuracy and accelerates topological loss computation by 5× compared to persistent homology–based methods.

Technology Category

• Computer Vision: Segmentation
• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust topological guarantees, are limited to specific use cases, or impose high computational costs. In this work, we propose a novel, graph-based framework for topologically accurate image segmentation that is both computationally efficient and generally applicable. Our method constructs a component graph that fully encodes the topological information of both the prediction and ground truth, allowing us to efficiently identify topologically critical regions and aggregate a loss based on local neighborhood information. Furthermore, we introduce a strict topological metric capturing the homotopy equivalence between the union and intersection of prediction-label pairs. We formally prove the topological guarantees of our approach and empirically validate its effectiveness on binary and multi-class datasets. Our loss demonstrates state-of-the-art performance with up to fivefold faster loss computation compared to persistent homology methods.

Problem

• Ensures topological accuracy in image segmentation tasks
• Addresses inefficiency in existing topology-aware methods
• Provides robust topological guarantees with computational efficiency

Innovation

• Graph-based framework for topology preservation
• Component graph encoding topological information
• Strict homotopy equivalence metric