A Novel Patch-Based TDA Approach for Computed Tomography Imaging
Dashti A. Ali, Aras T. Asaad, Jacob J. Peoples, Ahmad Bashir Barekzai, Camila Vilela, Hala Khasawneh, Jayasree Chakraborty, Jo\~ao Miranda, Mohammad Hamghalam, Natalie Gangai, Natally Horvat, Richard K. G. Do, Alice C. Wei, Amber L. Simpson

TL;DR
This paper introduces a patch-based topological data analysis method for CT imaging that enhances classification accuracy and reduces computational costs, outperforming traditional cubical complex algorithms.
Contribution
The study presents a novel patch-based persistent homology approach for volumetric CT data, improving performance and efficiency over existing methods.
Findings
Patch-based TDA outperforms cubical complex in accuracy and speed.
Proposed method achieves up to 8% improvement in key metrics.
Python package Patch-TDA facilitates adoption of the new approach.
Abstract
The development of machine learning 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 where 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 3D cubical complex filtration, a method adapted for grid-structured data. However, this approach is subject to poor performance and high computational cost…
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