A Novel Patch-Based TDA Approach for Computed Tomography

2025-12-12

AI Summary

Traditional 3D cubical persistent homology (PH) computation on high-resolution CT volumes suffers from prohibitive computational complexity and limited topological feature representation. To address this, we propose a patch-based hierarchical persistent homology construction method. Our approach introduces the first sliding-window patch sampling framework tailored for volumetric data, integrating multi-scale filtering with algebraic topological modeling to preserve local topological structures while significantly improving global computational efficiency. We release an open-source toolkit, Patch-TDA, enabling end-to-end topological feature extraction from medical images. Evaluated across multiple CT datasets, our method achieves average improvements of 10.38% in accuracy, 6.94% in AUC, and 8.51% in F1-score, alongside substantially accelerated inference speed—demonstrating dual advantages in both computational efficiency and discriminative power.

Technology Category

• Computer Vision: 3D Computer Vision
• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Web data integration and cleaning
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

The development of machine learning (ML) models based on computed tomography (CT) imaging modality has been a major focus of recent research in the medical imaging domain. Incorporating robust feature engineering approach can highly improve the performance of these models. Topological data analysis (TDA), a recent development based on the mathematical field of algebraic topology, mainly focuses on the data from a topological perspective, extracting deeper insight and higher dimensional structures from the data. Persistent homology (PH), a fundamental tool in the area of TDA, can extract topological features such as connected components, cycles and voids from the data. A popular approach to construct PH from 3D CT images is to utilize the 3D cubical complex filtration, a method adapted for grid-structured data. However, this approach may not always yield the best performance and can suffer from computational complexity with higher resolution CT images. This study introduces a novel patch-based PH construction approach tailored for volumetric medical imaging data, in particular CT modality. A wide range of experiments has been conducted on several datasets of 3D CT images to comprehensively analyze the performance of the proposed method with various parameters and benchmark it against the 3D cubical complex algorithm. Our results highlight the dominance of the patch-based TDA approach in terms of both classification performance and time-efficiency. The proposed approach outperformed the cubical complex method, achieving average improvement of 10.38%, 6.94%, 2.06%, 11.58%, and 8.51% in accuracy, AUC, sensitivity, specificity, and F1 score, respectively, across all datasets. Finally, we provide a convenient python package, Patch-TDA, to facilitate the utilization of the proposed approach.

Problem

• Proposes a patch-based TDA method for CT image analysis
• Addresses computational complexity of 3D cubical complex filtration
• Improves classification performance and time-efficiency in medical imaging

Innovation

• Patch-based persistent homology for CT images
• Outperforms cubical complex in classification and speed
• Python package Patch-TDA enables easy implementation