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REVIEW 2 major objections 5 minor 35 references

AxoNet: an AI-based tool to count retinal ganglion cell axons

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A neural network trained on rat optic nerves counts axons in rat and monkey tissue, outperforming existing tools.

desk verdict A solid, reproducible axon-counting tool whose rat evaluation split likely inflates the reported advantage; on NHP it is parity, not superiority. read the letter →

arxiv 1908.02919 v1 pith:XJCCWDJK submitted 2019-08-08 q-bio.QM eess.IV

Matthew D. Ritch , Bailey G. Hannon , A. Thomas Read , Andrew J. Feola , Grant A. Cull , Juan Reynaud , John C. Morrison , Claude F. Burgoyne
show 2 more authors
Machelle T. Pardue C. Ross Ethier
This is my paper · ORCID
classification q-bio.QMeess.IV
keywords retinalganglioncellaxonsopticnerveaxoncountingdeeplearningU-Netcountdensityregressionglaucomaautomatedimageanalysis
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 develops AxoNet, a deep learning tool that counts retinal ganglion cell axons in light microscopy images of optic nerve cross sections. Using a U-Net architecture modified to predict a pixelwise axon-count density rather than a segmentation, the network was trained on manually annotated rat optic nerve sub-images and then applied to non-human primate images without retraining. The paper reports that AxoNet outperforms the existing automated tools AxonMaster and AxonJ on both rat and NHP datasets, with mean absolute errors of 4.4 and 17.8 axons per image after bias correction. If these results hold, AxoNet offers a species-general, labor-saving way to quantify glaucomatous optic nerve damage.

What carries the argument

The load-bearing mechanism is count-density regression by a U-Net convolutional network. Instead of segmenting individual axons, the network's final layer uses a ReLU activation to output a pixelwise density map; the axon count for an image is the sum of the density map divided by a learned scaling factor (m=1000). Training minimizes mean squared error between predicted and Gaussian-blurred manual annotation densities, with edge mirroring to avoid border artifacts. Because no hand-crafted features are used, the same network trained on rat data can be applied to monkey images.

What would settle it

Hold out whole optic nerves from training and test AxoNet on sub-images from those nerves; if mean absolute error rises from the reported 4.4 axons per image to the 8.6 level of AxonMaster or higher, the claimed accuracy is an artifact of the random sub-image split.

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Extended reading notes

Core claim

The paper claims that AxoNet, built by adapting the U-Net architecture to regress a pixelwise axon-count density, counts 'normal'-appearing retinal ganglion cell axons in light-microscopy optic nerve images with near-manual accuracy in rats (mean absolute error 4.4 axons per 12x12 µm sub-image after linear bias correction) and transfers to non-human primate images without retraining (R²=0.945 against semi-automated manual counts). On both datasets it outperforms the existing automated tools AxonMaster and AxonJ by mean absolute error, regression R², and Bland-Altman limits of agreement.

Load-bearing premise

The reported rat accuracy assumes that randomly splitting sub-images into training and test sets keeps test images independent, even though all 1,474 sub-images come from only 27 optic nerves, so images from the same nerve can appear in both sets.

Editorial extensions

If this is right

  • AxoNet can replace fully manual axon counting in rat and NHP glaucoma studies, cutting analysis time to about 15 minutes per full nerve versus hours of manual counting.
  • A rat-trained model works on monkey images, so the method does not require species-specific retraining to move between mammalian models.
  • Because the network outputs a count density map rather than a segmentation, it can be extended to quantify other optic nerve features such as glial processes and nuclei.
  • The reported 84% success rate for AxoNet counts falling within the 95% confidence interval of manual counters means automated counts are typically indistinguishable from a human counter within inter-observer variability.
  • Full nerve counts around 80,000 'normal' axons in healthy rat nerves are consistent with published manual counts, validating the tool at the whole-nerve scale.

Reading between the lines

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

  • A nerve-level validation study would determine whether the R²=0.901 rat result reflects true generalization to unseen tissue or memorization of the 27 source nerves.
  • The same count-density approach could be retrained on transmission electron microscopy images to address the known ~30% underestimation of light microscopy counts.
  • AxoNet's counts describe 'normal-appearing' axons, so it should not be read as a measure of total surviving retinal ganglion cells without checking how many abnormal-looking axons still function.
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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

2 major / 5 minor

Summary. The paper presents AxoNet, a U-Net-based convolutional neural network that predicts pixelwise axon count density in light-microscopy images of optic nerve cross sections; the predicted density is integrated and divided by a learned scaling factor to produce an axon count. The network is trained on 1,474 manually annotated rat optic nerve sub-images drawn from 27 nerves of 14 rats, and is then applied without retraining to a separate non-human primate (NHP) dataset previously used to validate AxonMaster. The authors compare AxoNet against AxonMaster and AxonJ on both datasets, using linear bias-correction equations fitted on validation subsets, and report R², mean absolute error, and Bland-Altman limits of agreement. The central claims are that AxoNet outperforms the existing tools on both the rat and NHP datasets, and that it is robust to tissue damage, image quality, and species.

Significance. If the performance claims hold, AxoNet would be a practically useful, openly available tool for a labor-intensive neuroscience assay, and the count-density approach is a sensible alternative to per-axon segmentation. The paper's strengths are real: the code and training data are released, the tool is packaged as an ImageJ/Fiji plugin, the training procedure is described in enough detail to reproduce, the scaling-factor procedure in Eqs. (2)-(3) is an internal optimization device that is divided out of the final count and does not force agreement, and the limitation to 'normal'-appearing axons is explicitly disclosed. The main risk to the rat claim is the image-level rather than nerve-level split of the training/validation/testing data; the main risk to the NHP claim is that the reported statistics do not support the word 'outperformed.' These are load-bearing because the abstract and conclusion rest on them.

major comments (2)
  1. [II.A.3-II.A.4, II.B] The rat evaluation split is at the level of individual 12×12 µm sub-images, not at the level of optic nerves or animals, even though the 1,474 sub-images were sampled from only 27 nerves belonging to 14 rats. Because sub-images from the same nerve (and often the same animal) appear in both training and testing, the fully convolutional network can exploit nerve-specific staining intensity, section thickness, tissue processing, and damage level. This makes the reported rat test results (R²=0.901, MAE=4.4, and the claim that only AxoNet's limits of agreement fall within the manual-count threshold in Fig. 6) potentially inflated. The authors should re-evaluate with whole nerves (or whole animals) held out, for example via nested cross-validation over nerves, and report the range of performance across folds. The same image-level split is used for the NHP dataset, so the NHP comparisons may also be optimistic.
  2. [Abstract and III.B] The abstract states that AxoNet 'outperformed the existing tools on both the rat and NHP optic nerve datasets,' but the NHP results in Section III.B do not support this. AxoNet's NHP MAE was 17.8 versus AxonMaster's 18.2 with p=0.976 (not significant), and R² was 0.945 versus 0.938, with 'comparable limits of agreement.' At best, AxoNet ties with AxonMaster on the NHP dataset. The abstract and any summary statements should be revised to say that AxoNet performed comparably to AxonMaster on NHP and better than AxonMaster and AxonJ on rat, pending the nerve-level split analysis requested above.
minor comments (5)
  1. [Fig. 10 caption] The caption for Figure 10 says 'Each data point is a single sub-image from the rat testing subset,' but the figure shows the NHP testing subset; this should be corrected.
  2. [Fig. 4 caption] The caption for Figure 4 says 'Each data point is obtained from a single sub-image from the rat testing subset,' but the figure and the text indicate that the data are from the validation subset; this discrepancy should be fixed.
  3. [II.D.2] There is a typo: 'Kuskal-Wallis' should be 'Kruskal-Wallis.'
  4. [II.C.2] The sentence 'This including image mirroring and rotation...' should read 'This included image mirroring and rotation...'
  5. [II.B] The NHP dataset is not quantified in this manuscript (number of images, number of animals, selection procedure); since the split-level concern also applies there, the authors should provide these details or a clear reference to where they are reported.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: AxoNet's test evaluation is independent of its training targets, and the cited prior work is an external benchmark rather than a load-bearing premise.

full rationale

AxoNet's central claim is an empirical comparison: the network is trained on manually annotated axon count density maps, and its predicted summed density is evaluated on a held-out test subset against manual counts. The density scaling factor m is explicitly divided out in Eq. 3, so it does not force the reported counts. The linear bias correction (Eqs. 4-5) is fitted on the validation subset and then applied to the testing subset, so the test-set R2 and mean absolute error are not optimized by construction on the test images. The NHP benchmark and the AxonMaster baseline come from Reynaud et al., a prior paper with overlapping authors, but the comparison target is the semi-automated manual counts from that dataset, not an unverified claim imported from that paper; thus the self-citation is not load-bearing. The U-Net and count-density ideas are cited to external sources (Ronnenberger et al., Lempitsky et al.), not to the authors' own prior work. The only substantive concern is that the rat dataset was randomly split at the sub-image level rather than at the nerve or animal level, so images from the same optic nerve may appear in both training and testing; this is a potential independence/validation flaw that could inflate the reported rat accuracy, but it is not a circularity of the derivation. No predicted quantity is defined in terms of the target by construction, and no fitted parameter is renamed as a prediction. Therefore no circular step is present.

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

AxoNet is an empirical regressor whose main components are data, architecture, and calibration rather than a derivation. The key assumptions are the definition of normal axon, the use of manual counts as truth, the validity of the Gaussian density target, and the independence of the random image split. No new physical or biological entities are introduced.

free parameters (4)
  • Gaussian blur sigma and filter size = sigma = 8 px; filter size = 33 px
    Chosen empirically in Methods II.A.3 to spread annotation points over the axon; this defines the density target that the network learns.
  • Density scaling factor m = 1000
    Determined during hyperparameter optimization; multiplies the ground truth density in the loss and is divided out of predictions, affecting training dynamics but not the final count in a perfect fit.
  • Training hyperparameters = learning rate = 1e-4; 500 epochs; 100 steps/epoch; batch size = 1; dropout rate = 0.5
    Selected by validation performance on the rat dataset; these choices affect convergence and generalization.
  • Network architecture modifications = filter count halved; ReLU final layer; same padding; input resized to 192x192 and padded to 224x224
    Iteratively developed against the validation set; these choices trade off model capacity, speed, and accuracy.
assumptions (4)
  • domain assumption Manual counts are the gold standard for axon quantification.
    All ground truth and evaluation metrics are defined relative to manual annotations by trained counters; if manual counts are biased, AxoNet's accuracy is defined against that bias.
  • domain assumption Only normal-appearing axons, defined as having an intact continuous myelin sheath, homogenous light interior, and no obvious swelling or shrinkage, are counted.
    This restricts the central claim; damaged or abnormal axons are excluded, so the tool does not measure total axon number in diseased tissue.
  • domain assumption Sub-images randomly split into training, validation, and testing are independent observations.
    Sub-images were randomly selected from 27 nerves and split at image level; images from the same nerve may be correlated or overlapping, so this independence assumption is likely violated and can inflate test performance.
  • ad hoc to paper A Gaussian blur with sigma = 8 and filter size 33 converts point annotations into a valid continuous count density.
    The blur parameters were chosen empirically rather than derived, and the resulting density is the training target for the network.

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Cite this review

Pith. "Pith review of AxoNet: an AI-based tool to count retinal ganglion cell axons." pith.science (2026). https://pith.science/paper/XJCCWDJK

@misc{pith2026190802919,
  author       = {Pith},
  title        = {Pith review of: AxoNet: an AI-based tool to count retinal ganglion cell axons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XJCCWDJK}},
  note         = {Machine review of arXiv:1908.02919}
}
read the original abstract

Goal: In this work, we develop a robust, extensible tool to automatically and accurately count retinal ganglion cell axons in images of optic nerve tissue from various animal models of glaucoma. Methods: The U-Net convolutional neural network architecture was adapted to learn pixelwise axon count density estimates, which were then integrated over the image area to determine axon counts. The tool, termed AxoNet, was trained and evaluated using a dataset containing images of optic nerve regions randomly selected from complete cross sections of intact rat optic nerves and manually annotated for axon count and location. Both control and damaged optic nerves were used. This rat-trained network was then applied to a separate dataset of non-human primate (NHP) optic nerve images. AxoNet was then compared to two existing automated axon counting tools, AxonMaster and AxonJ, using both datasets. Results: AxoNet outperformed the existing tools on both the rat and NHP optic nerve datasets as judged by mean absolute error, R2 values when regressing automated vs. manual counts, and Bland-Altman analysis. Conclusion: The proposed tool allows for accurate quantification of axon numbers as a measure of glaucomatous damage. AxoNet is robust to variations in optic nerve tissue damage extent, image quality, and species of mammal. Significance: The deep learning method does not rely on hand-crafted image features for axon recognition. Therefore, this approach is not species-specific and can be extended to quantify additional optic nerve features. It will aid evaluation of optic nerve changes in glaucoma and potentially other neurodegenerative diseases.

Figures

Figures reproduced from arXiv: 1908.02919 by the authors.

Figure 1
Figure 1. Rat Dataset Image Variety. A representative set of images from the rat optic nerve image dataset is shown. These images include a range of nerve health, variations in sample processing quality, and in image acquisition contrast and quality [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Histogram of Manual Count Variability for Rat Dataset. Variability between counters is expressed as the coefficient of variation (standard deviation of the manual count divided by the mean of the manual count for each image). The median coefficient of variation was 0.12, indicating good general agreement between manual counters [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. U-Net Architecture. A visual representation of our adapted U-Net convolutional neural network architecture, with the encoding branch on the left and the decoding branch on the right. Each box represents the output array of one of the network’s convolutions, which are represented by colored arrows. The bold numbers to the left of the boxes indicate the row and column sizes of the feature array at those layers. The nu… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Comparison between automated and manual axon counts for the rat validation subset. Comparisons are shown for AxoNet (A), AxonMaster (B) and AxonJ (C). Each data point is obtained from a single sub-image from the rat testing subset. The regression relationships between …
Figure 5
Figure 5. Figure 5: Comparison between corrected automated and manual axon counts for the rat testing subset. Comparisons are shown for AxoNet (A), AxonMaster (B) and AxonJ (C). Each data point is obtained from a single sub-image from the rat testing subset. Mean absolute value predicted …
Figure 6
Figure 6. Figure 6: Comparison of error distribution for the rat testing subset. Differences between rat testing subset MC and corrected AC are plotted against manual counts for AxoNet (A), AxonMaster (B) and AxonJ (C) as Bland-Altman plots. Each data point is a single sub-image from the …
Figure 7
Figure 7. Figure 7: Visualization of AxoNet Performance. The images from the rat testing subset which produced the smallest (top) and greatest (bottom) difference between AxoNet predicted and ground truth manual axon count are shown in the left column. The corresponding manually annotated…
Figure 8
Figure 8. Figure 8: Comparison between automated and manual axon counts for the NHP validation subset. Comparisons are shown for AxoNet (A), AxonMaster (B) and AxonJ (C). Each data point is obtained from a single sub-image from the NHP testing subset. The regression relationships between …

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