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arxiv: 2512.12108 · v5 · submitted 2025-12-13 · 💻 cs.CV · cs.LG

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
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Mohammad Hamghalam Natalie Gangai Natally Horvat Richard K. G. Do Alice C. Wei Amber L. Simpson
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Pith reviewed 2026-05-16 23:24 UTC · model grok-4.3

classification 💻 cs.CV cs.LG
keywords topological data analysispersistent homologypatch-basedcomputed tomographymachine learningimage classificationvolumetric imaging
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The pith

Patch-based persistent homology boosts CT scan classification over full-volume methods

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a patch-based method for constructing persistent homology from 3D CT images to extract topological features more efficiently than traditional cubical complexes. By dividing volumes into patches, computing features on each, and aggregating them, the approach aims to maintain discriminative power while lowering computational demands for high-resolution data. Experiments on multiple datasets demonstrate superior performance in machine learning classification tasks compared to both the standard cubical approach and conventional radiomic features. This matters because it could make topological analysis practical for routine medical imaging workflows where full-volume methods are too slow or memory-intensive.

Core claim

The authors claim that their patch-based TDA approach for volumetric CT imaging outperforms the 3D cubical complex filtration and radiomic features in classification tasks. It achieves average improvements of 7.2% accuracy, 3.6% AUC, 2.7% sensitivity, 8.0% specificity, and 7.2% F1 score across datasets, while also reducing computational time. The method is implemented in a provided Python package called Patch-TDA.

What carries the argument

Patch-based persistent homology construction, where the CT volume is divided into smaller patches for independent filtration and feature extraction before aggregation for downstream classification.

Load-bearing premise

Splitting the CT volume into patches and combining their persistent homology features retains enough global topological information to improve or match full-volume analysis for the classification problems studied.

What would settle it

A direct comparison on a new high-resolution CT dataset where global structures like large voids are critical for classification, checking if the patch method still outperforms or if performance drops relative to full cubical filtration.

Figures

Figures reproduced from arXiv: 2512.12108 by Ahmad Bashir Barekzai, Alice C. Wei, Amber L. Simpson, Aras T. Asaad, Camila Vilela, Dashti A. Ali, Hala Khasawneh, Jacob J. Peoples, Jayasree Chakraborty, Jo\~ao Miranda, Mohammad Hamghalam, Natalie Gangai, Natally Horvat, Richard K. G. Do.

Figure 1
Figure 1. Figure 1: Generating persistent barcodes from a sample point cloud. In the far left side, at the beginning, the distance [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Cubical complex filtration and PBs representations in dimension zero and one for a 4x4 grayscale image [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: A summary illustration of the process of cubical complex filtration on a sample 2D image, the ROI of a [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The process of generating a d-dimensional point from a 3D patch of 3×3×3 voxels from a 3D image is demonstrated in part A, and the transformation of a 3D image ROI into a 3D point cloud is visualized in part B. There are different ways to compute PH from a point cloud. In this study, alpha complex filtration [33, 34] is utilized to compute PH in dimensions zero, one and two, corresponding to the number of … view at source ↗
Figure 5
Figure 5. Figure 5: Patch-based TDA pipeline. abdominal CT images, and two in-house datasets. Sample CT slices of different classes of each dataset is illustrated in [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Sample slices of CT images from each dataset are visualized. Sample images of unique classes of each [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original 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 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper introduces a patch-based persistent homology construction for 3D CT volumes as an alternative to full-volume cubical complex filtrations. It claims this yields superior classification performance (average gains of 7.2% accuracy, 3.6% AUC, 2.7% sensitivity, 8.0% specificity, 7.2% F1) over both cubical TDA and radiomic baselines across multiple datasets while lowering computational cost, and releases a Python package Patch-TDA.

Significance. If the reported gains prove robust and stem from effective capture of discriminative topological features without loss of global structure, the work would improve the practicality of TDA for high-resolution medical volumes. The open Patch-TDA package is a clear strength for reproducibility.

major comments (3)
  1. [Methods] Methods section on patch-based filtration: the aggregation step for per-patch persistence diagrams (concatenation, pooling, or other summary) is not specified in sufficient detail to determine whether generators spanning patch boundaries are retained. In CT data, diagnostically relevant structures such as vessel trees or tumor margins routinely cross patch boundaries, so the homology of the union is not a simple function of the per-patch homologies; this directly affects whether the claimed superiority over single 3D cubical filtration can be attributed to topology rather than to other factors.
  2. [Results] Results section reporting performance: average improvements are stated without statistical significance tests, confidence intervals, or per-dataset breakdowns with standard deviations. In addition, the number of datasets, cross-validation protocol, and classifier details are not provided, so it is impossible to assess whether the 7.2% accuracy gain is reliable or driven by particular data splits.
  3. [Experiments] Experiments section: patch size is listed as a free parameter yet no ablation or sensitivity analysis on its value is shown, nor is any complexity analysis or wall-clock timing table provided to substantiate the computational-time claim relative to full cubical filtration.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'across all datasets' is used without naming the datasets or their sizes, which should be stated for immediate context.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped us identify areas for improvement in clarity and rigor. We address each major comment point by point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Methods] Methods section on patch-based filtration: the aggregation step for per-patch persistence diagrams (concatenation, pooling, or other summary) is not specified in sufficient detail to determine whether generators spanning patch boundaries are retained. In CT data, diagnostically relevant structures such as vessel trees or tumor margins routinely cross patch boundaries, so the homology of the union is not a simple function of the per-patch homologies; this directly affects whether the claimed superiority over single 3D cubical filtration can be attributed to topology rather than to other factors.

    Authors: We thank the referee for highlighting this critical aspect of the method. The aggregation in our approach consists of computing persistence diagrams independently on each patch and then concatenating the resulting diagrams (birth-death pairs across all dimensions) into a single high-dimensional feature vector per volume. We will revise the Methods section to include a precise algorithmic description, pseudocode, and explicit statement of this concatenation procedure. We acknowledge that boundary-crossing generators are not guaranteed to be preserved exactly as in a global filtration; however, the empirical superiority suggests that the local topological features captured remain highly informative for the classification tasks. We will add a short discussion of this approximation and its potential mitigation via overlapping patches in future work. revision: yes

  2. Referee: [Results] Results section reporting performance: average improvements are stated without statistical significance tests, confidence intervals, or per-dataset breakdowns with standard deviations. In addition, the number of datasets, cross-validation protocol, and classifier details are not provided, so it is impossible to assess whether the 7.2% accuracy gain is reliable or driven by particular data splits.

    Authors: We agree that the current reporting lacks the necessary statistical detail. In the revision we will expand the Results section with a table showing per-dataset performance (accuracy, AUC, sensitivity, specificity, F1) as mean ± standard deviation across cross-validation folds, together with 95% confidence intervals. We will also report p-values from paired statistical tests (e.g., Wilcoxon signed-rank or t-tests) against the baselines. The revised text will explicitly state the number of datasets, the cross-validation protocol (stratified 5-fold), and the classifier (random forest with default hyperparameters after grid search). revision: yes

  3. Referee: [Experiments] Experiments section: patch size is listed as a free parameter yet no ablation or sensitivity analysis on its value is shown, nor is any complexity analysis or wall-clock timing table provided to substantiate the computational-time claim relative to full cubical filtration.

    Authors: We will add a dedicated ablation subsection that evaluates classification performance for patch sizes 16³, 32³, and 64³ voxels, reporting the resulting metrics for each choice. We will also include a complexity analysis paragraph deriving the expected runtime scaling and a new table of measured wall-clock times (in seconds) for the patch-based pipeline versus the full-volume cubical filtration on the same hardware and datasets, thereby substantiating the claimed computational advantage. revision: yes

Circularity Check

0 steps flagged

No circularity: algorithmic reformulation with independent empirical validation

full rationale

The paper introduces a patch-based persistent homology construction for 3D CT volumes as a direct algorithmic alternative to full-volume cubical filtration, motivated by computational cost and resolution issues. All reported performance metrics (accuracy, AUC, etc.) arise from standard supervised classification benchmarks on held-out data against two external baselines (cubical complex and radiomics). No equations, fitted parameters, or self-citations are shown that would make any claimed improvement equivalent to its own inputs by construction. The derivation chain consists of a practical change in filtration construction followed by independent empirical testing, rendering the result self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on standard persistent homology definitions and the assumption that patch-wise computation yields equivalent or superior features for downstream classification; no new physical entities or ad-hoc constants are introduced.

free parameters (1)
  • patch size
    Determines granularity of local topology extraction; value must be chosen to balance speed and feature fidelity but is not numerically specified in the abstract.
axioms (1)
  • standard math Persistent homology extracts stable topological features (connected components, cycles, voids) from filtered simplicial or cubical complexes.
    Invoked as the foundation for both the baseline cubical method and the proposed patch approach.

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Reference graph

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