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REVIEW 5 major objections 4 minor 34 references

Cracks in concrete

T0 review · 5 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

Pith's one-line read The paper argues a Riesz-transform network can segment cracks in 3D concrete CT images as well as a fine-tuned 3D U-Net, with 7,153 trainable parameters.

desk verdict A promising 3D RieszNet for crack segmentation, but the central comparison lacks a training protocol and is not reproducible as written. read the letter →

arxiv 2501.18376 v1 pith:JFNPGMZT submitted 2025-01-30 cs.CV eess.IVstat.AP

classification cs.CVeess.IVstat.AP
keywords cracksegmentationconcreteRiesztransformscaleequivariance3DU-Netcomputedtomographysynthetictrainingdatadeeplearning
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

This paper argues that a neural network whose encoder uses Riesz transforms instead of learned convolutions can segment cracks in 3D computed-tomography images of concrete as reliably as a fine-tuned 3D U-Net, while needing only about 7,153 trainable parameters. The authors show that cracks have strongly varying thickness, so the segmentation method should be invariant to scale changes, and they build that invariance into the RieszNet architecture directly. On 15 synthetic images with multiscale Voronoi-model cracks, RieszNet reaches a mean F1 of 0.872 at zero tolerance, close to the fine-tuned U-Net's 0.897, and it keeps a recall of 0.805 on the hardest image where the U-Net drops to 0.046. The paper also details how to generate semi-synthetic training data by embedding simulated crack surfaces into real CT images of crack-free concrete.

What carries the argument

The load-bearing object is the Riesz transform, defined in d dimensions by a singular integral, which commutes with scaling: $R_j(L_a f)=L_a(R_j f)$. A Riesz layer forms each output channel as a learned linear combination of first- and second-order Riesz transforms of the input channels. Stacked with batch normalization and ReLU activation, these layers replace the convolutional encoder, so the network inherits approximate scale equivariance without image pyramids or fine-tuning on multiscale data. The other machinery is the synthetic-data pipeline: cracks modeled as minimum-weight surfaces in 3D Voronoi diagrams, with thickness varied by adaptive dilation, embedded into real CT images of crack-free concrete.

What would settle it

Segment a set of real CT concrete volumes with manually annotated crack ground truth using the same trained RieszNet and fine-tuned U-Net, and compare their F1 at zero tolerance: if RieszNet's recall or F1 falls below the U-Net baseline on real cracks, the claim that it competes with the fine-tuned U-Net on realistic data is refuted.

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Extended reading notes

Core claim

The central claim is that a network whose layers combine first- and second-order Riesz transforms instead of learned convolutions is naturally scale-equivariant and therefore suited to segmenting cracks whose thickness varies from 1 to 20 voxels. On a test set of 15 synthetic multiscale-crack images, the three-layer RieszNet achieves a mean F1 of 0.872 at zero tolerance, close to the fine-tuned 3D U-Net's 0.897 and slightly above the multiscale U-Net's 0.869, while using only 7,153 trainable parameters. On the hardest image, its recall remains 0.805 where the fine-tuned U-Net drops to 0.046. The paper argues this makes RieszNet a promising alternative to CNN-based segmentation whenever scale invariance is a natural requirement and annotated training data are scarce.

Load-bearing premise

The quantitative comparison assumes that cracks generated by the authors' Voronoi surface model, embedded in real CT backgrounds, behave like real cracks; if these synthetic images do not predict real-crack performance, the comparison only holds for synthetic data.

Editorial extensions

If this is right

  • RieszNet can segment cracks of widely varying thickness without dedicated multiscale processing or fine-tuning on multiscale data.
  • A 7,153-parameter network can reach U-Net-level performance, which is valuable when annotated training data are scarce.
  • The synthetic Voronoi-based crack model with adaptive dilation produces training data on which deep networks generalize to multiscale cracks, at least within the synthetic domain.
  • The class-imbalance weighting scheme used for the U-Net training transfers to the RieszNet training setup.

Reading between the lines

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

  • If RieszNet's scale equivariance holds as strongly as the synthetic results suggest, the same architecture could segment other thin, dark lower-dimensional structures in 3D images, such as fibers, platelets, or biological sheets, without retuning the scale range.
  • A direct test of the paper's central claim would be to train RieszNet on synthetic cracks and evaluate on a set of real CT cracks with voxel-level annotations; the paper only shows real-crack images without quantitative ground truth, so this transfer remains the open question it flags.
  • The tiny parameter count suggests RieszNet may be suitable for 4D in-situ crack-evolution analysis, where many time steps must be processed and manual annotation is infeasible.
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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

5 major / 4 minor

Summary. The paper addresses 3D segmentation of cracks in concrete CT images. It describes a semi-synthetic data-generation pipeline based on fractional Brownian surfaces and Voronoi minimum-weight surfaces with adaptive dilation, trains 3D U-Net baselines, and introduces RieszNet, a scale-equivariant network built from Riesz transforms with 7,153 trainable parameters. The central empirical claim, based on 15 synthetic multiscale-crack test images in Table 1, is that RieszNet competes with a fine-tuned 3D U-Net (mean F1 0.872 vs 0.897 at tolerance 0) and is substantially more robust on the hardest image (recall 0.805 vs 0.046). The paper also shows qualitative segmentation results on real concrete and on fiber-reinforced concrete.

Significance. If the RieszNet result is reproducible, it is significant: the parameter count is three orders of magnitude smaller than the 3D U-Net, and the better worst-case recall on the difficult synthetic image is a practically relevant advantage in a setting where annotated training data are scarce. The Voronoi-based crack generator with locally varying thickness is a useful contribution that goes beyond fixed-width fractional Brownian surfaces. The paper is also commendably honest about limits: Section 7 explicitly states that generalization to unseen concrete formulations is an open challenge, and the real-crack results in Table 3 are only qualitative. However, the empirical support for the central competitiveness claim is thin and incompletely documented, so the significance currently rests on a promising but not yet fully verified result.

major comments (5)
  1. [Section 5.4 / Table 1] The RieszNet evaluation is not reproducible because the training protocol is never given. Section 5.3 describes the architecture and parameter count, but Section 5.4 only states that three approaches were tested on 15 images. The paper does not specify the training set size, the train/validation/test split, the patch size, the loss function, the optimizer, the learning rate schedule, the number of epochs, or the threshold used to binarize the sigmoid output. This contrasts with the detailed protocols provided for the 3D U-Net baselines in Sections 4.3 and 5.2. Without this information, the Table 1 comparison could be confounded by unstated training choices or by threshold selection on the test images, and the central claim that RieszNet 'can compete with 3D U-Net' cannot be verified.
  2. [Section 5.4 / Table 1] The evidence for the central claim consists of only 15 synthetic test images, with no error bars, confidence intervals, or significance tests. At tolerance 0 the mean F1 difference between RieszNet (0.872) and the fine-tuned 3D U-Net (0.897) is small relative to the per-image variation (RieszNet's minimum F1 is 0.773 on image 10, while the fine-tuned U-Net's minimum is 0.088 on image 7). The claim of competitiveness would be much better supported by reporting per-image results, bootstrap intervals, or a paired test, or by explicitly labeling the result as a case study on a limited benchmark.
  3. [Section 5.3] The paper states that the Riesz network imposes scale invariance, but the actual layer composition is batch normalization, a Riesz layer, and ReLU. Batch normalization and ReLU do not commute with scaling, so the network is at best approximately scale-invariant. The paper should either soften the claim to approximate scale invariance or provide empirical evidence (e.g., segmentation performance across crack widths from 1 to 20 voxels) showing that the intended invariance is preserved in practice. This is load-bearing because the motivation for RieszNet, and the expected improvement over U-Net on multiscale cracks, rests on this property.
  4. [Section 7 / Table 3] The paper explicitly acknowledges that generalization to unseen concrete formulations is an open challenge, and the real-crack results in Table 3 are shown only as images with no quantitative ground truth. The synthetic test data come from the authors' own Voronoi-based generator, and the RieszNet architecture was also developed by the same group; this creates a validity burden for the claim that the synthetic benchmark predicts real performance. The paper should either add quantitative real-image evaluation with ground truth, or clearly state that the real-crack demonstrations are qualitative and that the competitiveness claim is restricted to the synthetic benchmark.
  5. [Section 4.2 / Section 5.4] The number of Voronoi-based multiscale crack images is not stated explicitly. Section 5.2 says five such images are used for fine-tuning and Section 5.4 refers to 'the remaining 15 images', which implies a total of 20, but Section 4.2 only gives the count of 60 for the fixed-width crack images. This omission is part of the missing evaluation protocol and should be corrected so that the reader can understand the full data split.
minor comments (4)
  1. [Section 4.1] The sentence defining p0 and p1 says 'the proportion of background (class 0) and crack pixels (class 0)' — the crack class should be class 1, not class 0.
  2. [Figure 3 caption] The caption refers to a 'Bernoulli random walk with parameter' without specifying the parameter; it should say 'with parameter p' and give its value or range.
  3. [Section 5.2] The fine-tuning description says the U-Net is 'further train[ed] on five of these multiscale crack images', but it is not stated how many epochs, what learning rate, or whether the same augmentation as in Section 4.3 was used; this makes the fine-tuning baseline less reproducible than the original U-Net training.
  4. [General] There is no statement about code or data availability; given that the paper introduces a new network and a new synthetic data generator, a statement about releasing code and the generated test images would substantially improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the RieszNet comparison is an empirical benchmark on held-out generated test images, not a derivation that folds its inputs into its outputs.

full rationale

No step in the paper's argument reduces by construction to its own inputs. The central quantitative claim in Table 1 is an empirical comparison on 15 held-out multiscale Voronoi-crack images; the ground-truth labels are produced by the Section 4.2 construction (Dijkstra paths on weighted Voronoi facets, integer-program minimum-weight surfaces, and adaptive dilation), and there is no indication that RieszNet parameters were fitted to those 15 test images. The Riesz layer is defined directly in Eqs. (1)-(2), and the scale-equivariance identity R_j(L_a(f))(x)=L_a(R_j(f))(x) is quoted from the classical Riesz-transform literature (Unser and Van De Ville [32]), so the architecture does not rest solely on the self-citation to Barisin et al. [4]. The fine-tuned 3D U-Net is trained on five multiscale images from the same generator and tested on the remaining 15; that is a normal train/test split rather than a fitted-input-called-prediction pattern. The paper's own stated limitations, such as in Section 7 that 'generalization to unseen concrete formulations' remains an open challenge and in Section 5.4 the omission of the RieszNet training protocol, are reproducibility and external-validity concerns, not circularity. No equation is equivalent to another by definition, and no load-bearing conclusion is forced by a self-citation chain.

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

The central claim depends on the synthetic data generator (both the Voronoi model and the fractional Brownian model), the Riesz transform scale equivariance, and the unverified assumption that batch norm and ReLU keep the network effectively scale invariant. No new physical entities are introduced.

free parameters (4)
  • Hurst index H for fractional Brownian crack surfaces = 0.97 (in Figure 3 example)
    Controls the roughness of synthetic cracks; value chosen by hand, not fitted to outcome, but shapes the training distribution.
  • Bernoulli parameter p for adaptive dilation = not specified
    Controls the local thickness variation of Voronoi-based synthetic cracks in Section 4.2; value not reported, affecting the realism and difficulty of the test data.
  • Evaluation tolerance = 0 and 1 voxel
    Results are reported with tolerance 0 and 1; this is a hand-chosen evaluation parameter that changes the scores.
  • RieszNet architecture channel widths = (1,16,16,32,1)
    Network depth and width chosen by the authors; 7,153 trainable parameters are learned, but the architecture itself is a free design choice.
assumptions (4)
  • standard math Scale equivariance of the Riesz transform
    The Riesz transform commutes with dilation, which is the mathematical basis for the RieszNet's scale invariance (Section 5.3).
  • ad hoc to paper Batch normalization and ReLU preserve scale invariance sufficiently for the network to generalize across crack widths
    The paper assumes that adding batch norm and ReLU to Riesz layers does not destroy the scale-equivariance property in a way that matters for segmentation; no formal analysis is given.
  • domain assumption Voronoi minimum-weight surfaces adequately model real crack geometry
    The quantitative test set uses synthetic cracks from the Voronoi model (Sections 4.2 and 5.4); the paper's own discussion in Section 7 flags generalization to real cracks as open.
  • domain assumption Cracks are air-filled and have gray values similar to pores
    The synthetic training data assigns crack gray values based on pore gray values (Section 4.2); this assumes real cracks have the same contrast behavior in CT.

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Cite this review

Pith. "Pith review of Cracks in concrete." pith.science (2026). https://pith.science/paper/JFNPGMZT

@misc{pith2026250118376,
  author       = {Pith},
  title        = {Pith review of: Cracks in concrete},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JFNPGMZT}},
  note         = {Machine review of arXiv:2501.18376}
}
read the original abstract

Finding and properly segmenting cracks in images of concrete is a challenging task. Cracks are thin and rough and being air filled do yield a very weak contrast in 3D images obtained by computed tomography. Enhancing and segmenting dark lower-dimensional structures is already demanding. The heterogeneous concrete matrix and the size of the images further increase the complexity. ML methods have proven to solve difficult segmentation problems when trained on enough and well annotated data. However, so far, there is not much 3D image data of cracks available at all, let alone annotated. Interactive annotation is error-prone as humans can easily tell cats from dogs or roads without from roads with cars but have a hard time deciding whether a thin and dark structure seen in a 2D slice continues in the next one. Training networks by synthetic, simulated images is an elegant way out, bears however its own challenges. In this contribution, we describe how to generate semi-synthetic image data to train CNN like the well known 3D U-Net or random forests for segmenting cracks in 3D images of concrete. The thickness of real cracks varies widely, both, within one crack as well as from crack to crack in the same sample. The segmentation method should therefore be invariant with respect to scale changes. We introduce the so-called RieszNet, designed for exactly this purpose. Finally, we discuss how to generalize the ML crack segmentation methods to other concrete types.

Figures

Figures reproduced from arXiv: 2501.18376 by the authors.

Figure 1
Figure 1. Example of a crack in concrete as they appear in optical images. Small cutout [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Examples of cracks in concrete as they appear in CT images. 2D slices from [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Examples of simulated cracks in 256 × 256 × 256 voxel images. Left: two fractional Brownian surfaces, both widened to constant thickness 3 pixels and with Hurst index 0.97. Right: a minimal surface from a spatial Voronoi tessellation, width varying according to a Bernoulli random walk with parameter. Top: volume render￾ings. Bottom: 2D slices of the 3D images of the cracks superimposed on CT images of high performan… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Examples of segmentation results for fiber reinforced concrete. The 3D U [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]

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Reference graph

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