A Novel Patch-Based TDA Approach for Computed Tomography Imaging

Abstract

The development of machine learning (ML) models based on computed tomography (CT) imaging has been a major focus due to the promise that imaging holds for diagnosis, staging, and prognostication. These models often rely on the extraction of hand-crafted features, incorporating robust feature engineering improves the performance of these models. Topological data analysis (TDA), based on the mathematical field of algebraic topology, focuses on data from a topological perspective, extracting deeper insight and higher dimensional structures. Persistent homology (PH), a fundamental tool in TDA, extracts topological features such as connected components, cycles, and voids. 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 is subject to poor performance and high computational cost with higher resolution CT images. This study introduces a novel patch-based PH construction approach tailored for volumetric CT imaging data that improves performance and reduces computational time. This study conducts a series of systematic experiments to comprehensively analyze the performance of the proposed method with various parameters and benchmarks against the 3D cubical complex algorithm and radiomic features. Our results highlight the dominance of the patch-based TDA approach in terms of both classification performance and computational time. The proposed approach outperformed the cubical complex method and radiomic features, achieving average improvement of 7.2%, 3.6%, 2.7%, 8.0%, and 7.2% 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.

Reproductions