Dashti A. Ali | Searcharxiv

arXiv2026

A Novel Patch-Based TDA Approach for Computed Tomography Imaging

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 with higher resolution images. This study introduces a novel patch-based PH construction approach designed for volumetric CT imaging data that improves performance and reduces computational time. This study conducts a series of experiments to comprehensively analyze the performance of the proposed method and benchmarks against the 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.

cs.CV↗

arXiv2025

Comparing the Effects of Persistence Barcodes Aggregation and Feature Concatenation on Medical Imaging

In medical image analysis, feature engineering plays an important role in the design and performance of machine learning models. Persistent homology (PH), from the field of topological data analysis (TDA), demonstrates robustness and stability to data perturbations and addresses the limitation from traditional feature extraction approaches where a small change in input results in a large change in feature representation. Using PH, we store persistent topological and geometrical features in the form of the persistence barcode whereby large bars represent global topological features and small bars encapsulate geometrical information of the data. When multiple barcodes are computed from 2D or 3D medical images, two approaches can be used to construct the final topological feature vector in each dimension: aggregating persistence barcodes followed by featurization or concatenating topological feature vectors derived from each barcode. In this study, we conduct a comprehensive analysis across diverse medical imaging datasets to compare the effects of the two aforementioned approaches on the performance of classification models. The results of this analysis indicate that feature concatenation preserves detailed topological information from individual barcodes, yields better classification performance and is therefore a preferred approach when conducting similar experiments.

cs.CV↗