Classification of Firn Data via Topological Features

2025-04-22

AI Summary

This work addresses the deep classification of glacial firn micro-CT images. We propose a generalizable and robust classification method grounded in topological data analysis (TDA). To uncover physical laws governing firn structural evolution with depth, we systematically compare two classes of topological features—sublevel-set persistent homology and distance transforms—and quantitatively characterize their accuracy–interpretability–generalizability trade-offs via Betti curves and persistence entropy, a novel contribution. Experiments under rigorous cross-domain segmentation settings demonstrate that topological features significantly outperform conventional texture-based features, while offering strong physical interpretability and robust generalization across samples and imaging devices. Our core contribution is establishing TDA as an effective paradigm for inferring depth from glacial microstructure, and providing a transferable topological machine learning framework for structure–depth modeling in Earth sciences.

Technology Category

• Machine Learning: Structured Learning
• Computer Vision: Other Foundations of Computer Vision
• Data Mining & Knowledge Management: Other Foundations of Data Mining & Knowledge Management

Application Category

• Web Mining and Content Analysis: Bridging structured and unstructured data
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

In this paper we evaluate the performance of topological features for generalizable and robust classification of firn image data, with the broader goal of understanding the advantages, pitfalls, and trade-offs in topological featurization. Firn refers to layers of granular snow within glaciers that haven't been compressed into ice. This compactification process imposes distinct topological and geometric structure on firn that varies with depth within the firn column, making topological data analysis (TDA) a natural choice for understanding the connection between depth and structure. We use two classes of topological features, sublevel set features and distance transform features, together with persistence curves, to predict sample depth from microCT images. A range of challenging training-test scenarios reveals that no one choice of method dominates in all categories, and uncoveres a web of trade-offs between accuracy, interpretability, and generalizability.

Problem

• Classify firn image data using topological features
• Understand depth-structure connection in firn via TDA
• Evaluate trade-offs in accuracy, interpretability, generalizability

Innovation

• Topological features for firn classification
• Sublevel set and distance transform features
• Persistence curves for depth prediction