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REVIEW 3 major objections 6 minor 42 references

Improving Remote Sensing Classification using Topological Data Analysis and Convolutional Neural Networks

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Small CNN plus topological features hits 99.33% on EuroSAT

desk verdict A plausible and clearly written TDA+CNN fusion paper whose within-paper gains look real, but whose headline SOTA claim rests on comparing different EuroSAT test splits and a five-image margin. read the letter →

arxiv 2507.10381 v1 pith:EIFX7GM4 submitted 2025-07-14 cs.CV cs.LG

Aaryam Sharma This is my paper · ORCID
classification cs.CVcs.LG
keywords topologicaldataanalysispersistencehomologyremotesensingsatellitesceneclassificationconvolutionalneuralnetworksfeaturefusionEuroSATRESISC45
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that adding topological data analysis (TDA) features to a small convolutional network lets it classify satellite scenes more accurately than much larger models, on datasets where the discriminative information is a global pattern rather than a local object. It proposes a feature-engineering pipeline that converts each image channel into several filtered cubical complexes, extracts persistence diagrams, and vectorizes them into descriptors that are concatenated with CNN features before the final classifier. The central empirical claim is a 99.33% test accuracy on EuroSAT with a ResNet18 plus TDA, a 1.44-point gain over the same network without TDA and a result the paper says surpasses all previously reported single-model accuracies. On the object-centric RESISC45 dataset the gain is smaller (1.82 points), which the paper interprets as evidence that TDA helps most when the class structure is global and geometric rather than local and texture-based. If correct, the work shows that a relatively simple, interpretable feature source can close the gap between small models and much larger architectures on certain image classification tasks.

What carries the argument

The load-bearing mechanism is the TDA feature-engineering pipeline. Each RGB channel is turned into a filtered cubical complex in four ways: binary thresholding followed by height and radial filtrations, raw grayscale filtration, local entropy filtration with 3x3 and 5x5 kernels, and Sobel-gradient filtration. From each filtered complex the paper computes a persistence diagram in dimension 0, then vectorizes it into Betti curves, bottleneck and Wasserstein amplitudes, landscape amplitudes, heat-kernel amplitudes, and persistence entropy. These per-channel vectors are passed through a 4-layer MLP and concatenated with the features of a ResNet12 or ResNet18 backbone before a 2-layer MLP outputs logits. The pipeline relies on the observation that most 32x32 downsampled images contain very few dimension-1 features, so only H0 persistence is used, and it is implemented with the authors' chosen open-source TDA software.

What would settle it

Run the same ResNet18 plus TDA pipeline several times with different random seeds on the same split, and also on the official or previously used EuroSAT test split; if the accuracy varies by more than about five images across seeds, or drops to 99.2% or below on the prior split, the 'surpasses all single models' claim is not robust, even though the internal 1.44-point gain over the authors' baseline may still hold.

Watch

Extended reading notes

Core claim

The central discovery is that persistence-homology features, computed from multiple filtrations of image channels (binary thresholding followed by height and radial filtrations, grayscale filtration, local entropy filtration, and Sobel-gradient filtration), carry discriminative information that convolutional networks miss, and that simply concatenating these features with the CNN's penultimate representation improves accuracy and accelerates convergence. On EuroSAT, the fused ResNet18 reaches 99.33% test accuracy, surpassing the paper's own ResNet18 baseline by 1.44 percentage points and matching or beating larger single models such as ResNet50 (99.2%) and InternImage-XL (99.24%). On RESISC45, the same fusion raises accuracy by 1.82 points over its baseline. The paper also shows that a 6-layer MLP trained only on the TDA features reaches 92.39% on EuroSAT but only 37.19% on RESISC45, which it reads as evidence that EuroSAT's classes are defined by global geometric structure while RESISC45's are defined by local object details.

Load-bearing premise

The claim that the method sets a new state of the art on EuroSAT depends on the assumption that the authors' 60/20/20 train/validation/test split is comparable to the splits used in the prior papers being compared, even though the exact split was not available and the margin is roughly five test images.

Editorial extensions

If this is right

  • If the EuroSAT result is correct, a ResNet18 with roughly 11M parameters can outperform vision models tens to hundreds of times larger, so model scale is not the only route to accuracy on global-structure image datasets.
  • The fused models reach high accuracy in far fewer epochs than the plain ResNets, so adding TDA features acts as a form of acceleration as well as a final accuracy boost.
  • Because a TDA-only MLP reaches 92.39% on EuroSAT, the paper implies that pure topological information, without any learned visual features, already captures most of the class structure on that dataset.
  • On RESISC45 the TDA features help the ResNet18 but hurt the small ResNet12, so the benefit of the method is conditional on the dataset relying on global rather than local discriminative features.
  • Since the same fixed split ratio and experimental setup are used across all of the authors' experiments, the internal comparisons against the paper's own baselines are consistent and reproducible in principle.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The margin that establishes the new state of the art on EuroSAT is 99.33% versus 99.24%, which is roughly five test images out of 5400; reproducing the exact test split used by the earlier papers is needed before the ranking over prior single models can be treated as settled.
  • The pipeline downsamples images to 32x32 before computing TDA, which likely discards fine topological detail; running the same feature extraction on larger crops, as the paper lists as future work, could change the RESISC45 results.
  • A natural ablation that the paper does not report is which of the six TDA descriptors carries the gain; testing each descriptor alone could make the method cheaper and more interpretable.
  • The same feature-fusion recipe could be transferred to other domains with global structure, such as medical whole-slide images or aerial scenes, where CNN texture bias is also a known limitation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript proposes a topological data analysis (TDA) feature-engineering pipeline for remote sensing scene classification. The pipeline computes persistence diagrams from several filtrations on 32x32 downsampled images (binary threshold followed by height/radial, grayscale, local entropy, and Sobel gradient filtrations), vectorizes the diagrams with Betti curves, persistence amplitudes, landscapes, heat kernels, and persistence entropy, and feeds the resulting features through an MLP whose output is concatenated with ResNet features. Experiments on EuroSAT and RESISC45 with ResNet12 and ResNet18 report 99.33% EuroSAT accuracy for ResNet18+TDA, a 1.44% gain over the paper's own ResNet18 baseline, and a 1.82% gain on RESISC45; a TDA-only MLP reaches 92.39% on EuroSAT. The abstract further claims that 99.33% is a new state-of-the-art single-model accuracy on EuroSAT, surpassing larger architectures such as ResNet50 and InternImage-XL.

Significance. The contribution is potentially useful: the TDA feature extraction recipe is described in detail, the mathematical background is standard but clearly presented, and the paper honestly acknowledges limitations such as heavy downsampling and increased inference cost. If the empirical gains are reproducible, the work provides evidence that TDA features can complement small CNNs on remote sensing classification and can speed up convergence. The main value is empirical rather than theoretical. However, the headline state-of-the-art claim is not yet supported by the evidence as presented, because the EuroSAT comparison is made across different random splits and without uncertainty estimates. With a reframed contribution as 'TDA improves our own baseline and is competitive with prior published accuracies,' the paper could be publishable after revision.

major comments (3)
  1. [Section 4 and Section 6, Table 1] The central state-of-the-art claim is undermined by a split mismatch. The paper states in Section 4 that 'the exact same splits were not available for EuroSAT,' yet Section 6 and the abstract compare the authors' 99.33% accuracy on a random 60/20/20 split with 99.24% for InternImage-XL and 99.2% for ResNet50 from other papers' splits. On a roughly 5,400-image test set, the margin is about five images, so the ranking could easily change with a different split. Please evaluate on the original benchmark splits, report multiple-seed means with confidence intervals, or explicitly qualify the claim as holding on the authors' own split rather than as a universal state-of-the-art result.
  2. [Section 5 and Figure 4] The threshold-selection protocol is underspecified. The text says that class-wise color intensity distributions were examined to choose binary thresholds, but it does not state whether this examination was restricted to the training split. If class statistics computed on the full dataset were used to select thresholds, test information would leak into feature construction and the reported accuracies would be optimistically biased. Please specify a train-only selection procedure, or demonstrate that the final accuracy is insensitive to the particular thresholds chosen.
  3. [Section 6, Tables 1 and 2] All reported accuracies are single runs with no random seeds, standard deviations, or error bars. The claimed improvements of 1.44% on EuroSAT and 1.82% on RESISC45 may be within run-to-run variation for the small models used. Please report results over at least three to five seeds with mean and standard deviation, and ideally paired comparisons between the baseline and TDA-augmented models, so that the reader can assess whether the gains are statistically meaningful.
minor comments (6)
  1. [Section 2, Related Works] The sentence 'They achieved achieved an accuracy for ResNet50 on RESISC45 of 96.83%' contains a duplicated word and should be corrected.
  2. [Section 5, Experiment Setup] The paper says the exact ResNet18 training parameters 'can be found in our config file in our code,' but the code is not yet released. Please include the key hyperparameters (learning rate schedule, batch size, weight decay, data augmentation) in the manuscript or supplement.
  3. [Section 3.3.4, Eq. (13)] The landscape distance formula is missing the integration variable in the display; the expression should specify integration with respect to x and the domain of each landscape layer.
  4. [Tables 1 and 2] The rows quoted from prior work use different pretraining protocols, model sizes, and evaluation splits. A footnote clarifying that these numbers are quoted from their original papers and are not directly comparable to the authors' split would help avoid misleading readers.
  5. [Section 4, Datasets] The sentence 'These datasets are of the perfect size' is informal; consider rewording to describe the trade-off between computational feasibility and information content.
  6. [Figure 4 caption] The caption mentions 'error bars' but does not define what they represent; please state whether they are standard deviations, standard errors, or another quantity.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reasoning found: the accuracy gains are measured outcomes, not derived from fitted inputs or self-citation.

full rationale

The paper's central claims are empirical: adding TDA features to ResNet18 improves EuroSAT accuracy from 97.89% to 99.33% and RESISC45 accuracy from 91.40% to 93.22%. These numbers are reported from trained models on test sets, not derived from the definitions of the TDA features or from any fitted parameter being renamed as a prediction. The TDA pipeline itself (filtrations, persistence diagrams, amplitudes) is defined independently of the final accuracy; the choice of hyperparameters and thresholds is presented as experimental selection (e.g., 'From our experimentation, it was found that in most images, there are very few dimension 1 features'). This is model selection, not circularity. The comparison to prior state-of-the-art numbers is potentially undermined by split mismatch — the paper states 'the exact same splits were not available for EuroSAT' — but that is an external-validity or benchmarking concern, not a circular-derivation concern. The only self-referential element is the acknowledgment of a professor and the use of giotto-tda, which is cited as a software tool and is not load-bearing for any mathematical derivation. No equation or algorithm step reduces to its own output. Therefore the paper is self-contained with respect to circularity, and the derivation chain is independent of the results it reports.

Assumptions & free parameters 7 free parameters · 4 assumptions · 0 invented entities

The central empirical claim depends on several unstated choices: the threshold set, the choice to keep only H0, the amplitude hyperparameters, and the 32x32 downsampling. None of these are evaluated with ablations or error bars, and the split comparability with prior SOTA numbers is unverified.

free parameters (7)
  • Binary threshold set = not specified
    Thresholds for binary height/radial filtrations were selected after inspecting per-class mean intensities (Fig. 4); the actual values are not listed and may have been chosen on all data.
  • Height filtration directions = 4 cardinal directions
    Hand-selected; other directions (e.g., diagonals) are not tested.
  • Radial filtration centers = 4 quadrant centers (8,8),(8,24),(24,8),(24,24) on 32x32
    Determined by the quadrant structure; no sensitivity analysis given.
  • Local entropy kernel sizes = 3x3 and 5x5
    Two kernel sizes chosen without justification or ablation.
  • Homological dimension limit = H0 only
    H1 was dropped after observing few features 'from experimentation'; this could discard signal.
  • Amplitude hyperparameters (p,q,t) = not specified
    Bottleneck, Wasserstein, landscape and heat-kernel amplitudes depend on p, q, t and discretization; values are not reported.
  • ResNet18 training hyperparameters = in unreleased config file
    Learning rate and other settings are not stated in the paper.
assumptions (4)
  • standard math Persistence diagrams of filtered cubical complexes are stable and meaningful descriptors of image structure.
    Standard TDA stability theorems, referenced through [20]; used throughout the pipeline.
  • domain assumption Downsampling images to 32x32 preserves the global topological features relevant to classification.
    All TDA features are computed on 32x32 images; the authors acknowledge in Section 8 that this loses granularity, especially for RESISC45.
  • ad hoc to paper Threshold statistics can be computed from class intensity distributions without leaking test information.
    Section 3.1.1 and Figure 4 use per-class intensity distributions, but the paper does not state they were computed only on the training split.
  • domain assumption EuroSAT classes are better separated by global geometry, while RESISC45 is dominated by local object features.
    This assumption explains the differing gains and guides the interpretation; it is supported post hoc by the TDA-MLP accuracy contrast.

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Cite this review

Pith. "Pith review of Improving Remote Sensing Classification using Topological Data Analysis and Convolutional Neural Networks." pith.science (2026). https://pith.science/paper/EIFX7GM4

@misc{pith2026250710381,
  author       = {Pith},
  title        = {Pith review of: Improving Remote Sensing Classification using Topological Data Analysis and Convolutional Neural Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EIFX7GM4}},
  note         = {Machine review of arXiv:2507.10381}
}
read the original abstract

Topological data analysis (TDA) is a relatively new field that is gaining rapid adoption due to its robustness and ability to effectively describe complex datasets by quantifying geometric information. In imaging contexts, TDA typically models data as filtered cubical complexes from which we can extract discriminative features using persistence homology. Meanwhile, convolutional neural networks (CNNs) have been shown to be biased towards texture based local features. To address this limitation, we propose a TDA feature engineering pipeline and a simple method to integrate topological features with deep learning models on remote sensing classification. Our method improves the performance of a ResNet18 model on the EuroSAT dataset by 1.44% achieving 99.33% accuracy, which surpasses all previously reported single-model accuracies, including those with larger architectures, such as ResNet50 (2x larger) and XL Vision Transformers (197x larger). We additionally show that our method's accuracy is 1.82% higher than our ResNet18 baseline on the RESISC45 dataset. To our knowledge, this is the first application of TDA features in satellite scene classification with deep learning. This demonstrates that TDA features can be integrated with deep learning models, even on datasets without explicit topological structures, thereby increasing the applicability of TDA. A clean implementation of our method will be made publicly available upon publication.

Figures

Figures reproduced from arXiv: 2507.10381 by the authors.

Figure 1
Figure 1. Combining TDA and ResNet features via concatena [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. ABDC is a cube ((0,0,0),(e, f, e)). For the x-coordinate, the bottom face is AB and the top face is CD. For z-coordinate the faces are correspondingly AC and BD. ABDC, all faces and vertices, together form a cubical complex. A filtered cubical complex C is a collection of cubical com￾plices {Ct}t∈R such that ∀t ≤ s ∈ R, we have Ct ⊆ Cs. An N1 ×N2 × ··· ×ND grid complex is a cubical complex with top dimensional cubes… view at source ↗
Figure 3
Figure 3. The TDA pipeline in full. A specific image channel is selected, then passed through each of the filtrations. Before the radial or [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Mean color intensity per class for each EuroSAT category. Some classes such as forests can be seen on average, to have very low [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: An example of the pipeline of local entropy filtration is shown. Starting from the top left panel to the bottom right, we have (1) the [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: Sample images from the EuroSAT and RESISC45 datasets. EuroSAT images capture land use patterns such as forest or industrial [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: Accumulated training accuracy as the training epoch in [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Validation accuracy as the number of epochs increases [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.