Machine Learning and Topological Analysis Identify COVID-19 in Lung Scans

A mathematical imaging framework combining topological data analysis with supervised machine learning algorithms has achieved an accuracy rate of 97.5 percent and an area under the receiver operating characteristic curve exceeding 0.99 in detecting COVID-19 from axial chest computed tomography scans. In an experimental evaluation reported by researchers Rabih Assaf, Abbas Rammal, Alban Goupil, Mohammad Kacim, and Valeriu Vrabie, persistent homology was applied to extract multi-scale structural descriptors of lung parenchyma, which were subsequently supplied to various automated classification architectures. The resulting experimental outcomes established that a Random Forest classifier attained a peak classification accuracy of 97.51 percent at a thirty percent testing split, while a Support Vector Machine utilizing a radial basis function kernel achieved the highest overall area under the curve value of 0.992495. By systematically capturing intrinsic geometric and homological structures within chest scans rather than depending exclusively on raw pixel intensity matrices or traditional localized pixel statistics, this analytical configuration demonstrates an automated diagnostic methodology capable of identifying viral pulmonary alterations across complex radiological datasets.

The clinical motivation outlined in the investigation centers on the persistent vulnerabilities of established pathogenic diagnostic procedures alongside the operational challenges posed by global viral dissemination. While pathogenic laboratory examinations such as reverse transcription polymerase chain reaction testing remain the prevailing diagnostic standard for severe acute respiratory syndrome coronavirus 2, they carry notable operational limitations including processing turnaround delays and documented frequencies of false-negative outcomes. Conventional molecular tests identify viral genetic sequences directly from respiratory specimens, whereas rapid antigen screenings identify viral surface proteins at lower sensitivity, and serological examinations identify host antibody production but cannot diagnose acute phase illnesses. Consequently, chest radiography and computed tomography imaging modalities serve as vital adjunctive diagnostic pathways capable of highlighting pulmonary damage patterns, including ground-glass opacities, lung consolidations, and fine reticular anomalies that perturb the anatomical architecture of healthy lung tissue. To resolve these radiological challenges rapidly without overwhelming clinical facilities, the researchers formulated an automated computational pipeline designed to process high-dimensional radiological data, discern infection-induced structural alterations, and provide consistent classification without relying on subjective human observation.

To capture high-dimensional geometric arrangements that evade classical statistical distributions, the proposed technique introduces concepts grounded in algebraic topology through topological data analysis. Unlike traditional geometrical models that simplify shapes into rudimentary cell complexes and lose fine quantitative information, topological data analysis extracts coarse-scale, global, and nonlinear structural invariants from spatial datasets. In this radiological implementation, two-dimensional grayscale lung slice images are formally converted into topological cubical complexes, designated as pixels complexes, wherein individual image pixels function as zero-dimensional vertices or zero-cells. Spatial connections between horizontally or vertically adjacent pixels differing by a single spatial unit coordinate are mapped as unit-length edges or one-cells, and the bounded regions enclosed by four perimeter edges are defined as unit squares or two-cells. This formal construction yields an integrated algebraic structure that simultaneously encapsulates discrete numerical pixel intensities alongside their exact spatial neighborhoods, generating a rigorous geometric baseline from which multi-scale topological features can be consistently measured across diverse radiological densities.

Within the algebraic structure of the constructed pixels complex, formal linear combinations of k-cells are organized into k-chains with coefficients belonging to the binary finite field of integers modulo two. The aggregate set of these k-chains constitutes a sequence of chain groups interconnected by boundary operators that map k-dimensional chains directly into boundary chains of dimension k minus one. The mathematical integrity of this system relies on the fundamental topological condition establishing that the composition of successive boundary operators yields zero for every dimension, meaning that the boundary of a boundary is identically empty. Elements whose boundaries evaluate to zero constitute the k-th cycle subgroup, representing closed loops or voids that encircle spatial cavities without enclosing solid matter. Concurrently, elements formed by taking the boundary of higher-dimensional chains constitute the k-th boundary subgroup. Because the boundary subgroup forms a proper subset of the cycle subgroup, algebraic quotient groups designated as homology groups are formed by factoring cycle groups by their boundary groups. These quotient groups isolate persistent structural cavities, such as zero-dimensional connected components and one-dimensional enclosing loops, while mathematically discarding trivial boundaries.

Because single static evaluations of homology groups fail to capture the evolutionary trajectory of spatial features across brightness gradients, the researchers instituted an intensity-driven filtration scheme to compute persistent homology. Under this ordering protocol, zero-cells inherit values directly corresponding to image pixel intensities, whereas each higher-dimensional k-cell is systematically assigned the maximum intensity exhibited among the lower-dimensional cells forming its immediate boundary. As a numerical threshold parameter advances monotonically, a nested sequence of expanding subcomplexes emerges, spanning from the empty set through the entire image complex. Throughout this sequential expansion, topological cavities emerge at specific birth thresholds and eventually terminate or merge into higher-dimensional structures at subsequent death thresholds. The lifespan of any topological class is computed as the quantitative difference between its destruction level and creation level, with prolonged lifespans designating stable, prominent structural properties of pulmonary tissue and brief lifespans representing radiological image noise. These multidimensional birth and death coordinates are summarized through persistence diagrams and persistence barcodes, calculated programmatically utilizing the Persistent Homology Algorithm Toolbox.

From the persistent homology computations and standard image properties, the investigators engineered a compact vector comprising eight numerical features extracted from each processed lung computed tomography image. These eight quantitative descriptors encompass the mean lifespan and standard deviation of zero-dimensional homology cycles, the mean lifespan and standard deviation of one-dimensional homology cycles, the zero-dimensional persistent entropy, the one-dimensional persistent entropy, alongside the overall mean and standard deviation of image pixel intensities. Persistent entropy quantifies the structural diversity of the topological landscape by evaluating the normalized ratio of individual cycle lifespans against the aggregate sum of all lifespans through a logarithmic entropy formulation. These computed descriptors were then provided to five supervised machine learning models: Decision Trees as a logic-based classifier requiring no prior distributional assumptions, Random Forest as an ensemble tree model, Support Vector Machines utilizing a radial basis function kernel, Gaussian Naive Bayes reflecting conditional predictor probabilities, and Logistic Regression representing linear statistical modeling.

The experimental dataset comprised eight hundred axial chest computed tomography scans collected in equal balance, consisting of four hundred images from confirmed COVID-19 patients and four hundred scans from healthy individuals without viral abnormalities. To eliminate radiological confounders and extraneous non-pulmonary anatomical structures, the team deployed an image preprocessing sequence beginning with spatial resizing that standardized all heterogeneous scans to dimensions of 128 by 128 pixels. The images were subsequently converted to a 256-level grayscale colormap and normalized to floating-point numerical values within a zero-to-one range. To amplify radiological contrast between the lung parenchyma and surrounding thoracic elements such as ribs, soft tissues, blood vessels, and cardiac structures, gamma correction contrast enhancement was implemented using a gamma parameter value of three, notably omitting artificial noise-reduction filters. Lung segmentation was subsequently performed by executing binary and triangle thresholding for normal scans alongside Otsu thresholding for COVID-19 scans, followed by mask generation to eliminate out-lung artifacts while retaining purely pulmonary parenchymal regions.

Model training and evaluation were carried out using varying train-test dataset splits alongside k-fold cross-validation frameworks to verify predictive stability across unseen samples. The cross-validation protocol partitioned the processed imagery across multiple fold configurations including three, four, five, and ten folds, iteratively utilizing each partitioned subset for validation while remaining subsets served for model fitting. In baseline single-split evaluations, the Decision Tree classifier recorded an overall accuracy of 93.75 percent, an F1 score of 0.94, and an area under the curve of 0.93812 at a twenty percent testing split, demonstrating mean cross-validation accuracy of 91.72 percent with a standard deviation of 1.31 percent. The Logistic Regression model achieved a peak accuracy of 85.42 percent at a thirty percent testing split with an average area under the curve of 0.945505 and a cross-validation mean accuracy of 83.86 percent with a standard deviation of 1.03 percent. The Naive Bayes classifier demonstrated lower relative efficacy, recording an average accuracy of 84.09 percent, an F1 score of 0.8559, an area under the curve of 0.948845, and a cross-validation mean accuracy of 84.11 percent with a standard deviation of 1.64 percent across fold evaluations.

The Random Forest and Support Vector Machine models demonstrated the highest performance across all quantitative evaluation metrics. The Random Forest classifier attained an accuracy of 97.51 percent at a thirty percent testing split, sustaining an area under the receiver operating characteristic curve above 0.99 across all testing sizes, alongside a cross-validation accuracy mean of 96.34 percent and a standard deviation of 0.72 percent across folds. The Support Vector Machine recorded a peak accuracy of 96.25 percent at a thirty percent testing split and established the highest area under the curve value among all models at 0.992495, maintaining a cross-validation accuracy mean of 94.51 percent with a standard deviation of 0.95 percent. The investigators noted that the Random Forest architecture derived stability from averaging decision trees to curtail prediction variance, while the Support Vector Machine benefited from mapping the linear algebraic formulations of homological features into higher-dimensional kernel space, distinctly separating pathological patterns from normal parenchymal variations.

To rigorously verify the diagnostic necessity of the topological features, the authors executed ablation trials comparing performance when removing either topological or statistical descriptors from the models. When the identical classifiers were trained using solely the two basic pixel statistics of mean and standard deviation, maximum accuracy dropped to 94.7 percent and area under the curve reached 0.97328. Conversely, training on the six persistent homology features alone without pixel statistics yielded a maximum accuracy of 85.4 percent and an area under the curve of 0.86519, confirming that combining homological descriptors with statistical metrics achieves optimal predictive capability. External validation on a separate independent computed tomography dataset corroborated this performance, with the Support Vector Machine reaching 94.5 percent accuracy with an area under the curve of 0.93 and the Random Forest reaching 93.8 percent accuracy with an area under the curve of 0.94. Benchmarking against convolutional neural networks with three and four layers coupled to the classifiers demonstrated comparable peak accuracies between 92.3 and 95.7 percent, while remaining computationally distinct. The authors explicitly emphasize several operational limitations, noting that clinical variability in image quality, scanner equipment, motion artifacts, and low slice resolution could degrade classification performance in actual medical deployments, while persistent homology values lack the intuitive visual interpretability of traditional clinical biomarkers, necessitating expanded validation across diverse thoracic imaging formats and patient prognostic trajectories before clinical implementation.

Subject of Research: Topological data analysis and machine learning for COVID-19 detection in chest CT scans

Article Title: Topological data analysis and machine learning for COVID-19 detection in CT scan lung images

Article References: Assaf, R., Rammal, A., Goupil, A., Kacim, M., & Vrabie, V. (2025). Topological data analysis and machine learning for COVID-19 detection in CT scan lung images. BMC Biomedical Engineering, 7(1), Article 4. https://doi.org/10.1186/s42490-025-00089-1

Image Credits: AI Generated

DOI: 10.1186/s42490-025-00089-1

Keywords: Topological Data Analysis, Persistent Homology, Machine Learning, COVID-19 Detection, Computed Tomography, Random Forest Classifier, Support Vector Machine, Medical Imaging, Cubical Complexes, Image Preprocessing, Topological, data