Improved Vessel Segmentation with Symmetric Rotation-Equivariant U-Net

Jiazhen Zhang; John A. Onofrey; Nicha C. Dvornek; Yuexi Du

REVIEW 3 major objections 5 minor 1 cited by

Improved Vessel Segmentation with Symmetric Rotation-Equivariant U-Net

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that replacing standard convolutions with symmetric rotation-equivariant kernels makes a U-Net segment retinal vessels accurately on rotated inputs while using 0.12M parameters, about 1.7% of a 6.97M-parameter…

desk verdict A plausible plug-in for rotation-robust U-Net segmentation, but the headline performance margins are within the noise floor and need a proper evaluation before they carry weight. read the letter →

arxiv 2501.14592 v1 pith:GH6Z7ZRW submitted 2025-01-24 eess.IV cs.CVcs.LG

Jiazhen Zhang , Yuexi Du , Nicha C. Dvornek , John A. Onofrey This is my paper · ORCID

classification eess.IVcs.CVcs.LG

keywords retinalvesselsegmentationrotationequivariancesymmetricconvolutionkernelU-Netparameterefficiencyfundusimagingsemanticconvolutionalneuralnetworks

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 a U-Net whose ordinary convolution kernels are replaced by symmetric rotation-equivariant kernels can segment retinal vessels accurately even when test images are rotated, while using far fewer trainable parameters than standard or state-of-the-art networks. On the DRIVE dataset, the proposed SRE U-Net reports the best accuracy, specificity, IoU, Dice, and AUC among the compared methods, and it outperforms a 6.97M-parameter state-of-the-art segmentation network using only 1.7% of that parameter count. The core idea is that rotational equivariance can be built directly into a standard segmentation architecture through a cheap kernel constraint, rather than through large group-convolution or steerable-filter stacks. If the paper is right, rotation-robust segmentation becomes practical in data- and compute-limited clinical settings, where image orientation is often inconsistent or unknown.

What carries the argument

The load-bearing object is the symmetric rotation-equivariant convolution kernel (SRE-Conv kernel). It partitions a $k \times k$ kernel into $b = \lfloor k/2 \rfloor + 2$ concentric bands; a binary index matrix $I$ assigns each kernel entry to one band, and the kernel is reconstructed as $\psi(\Theta_i \cdot I)$, where $\Theta_i$ holds only $b$ trainable values per channel. This construction forces the kernel to be centrally symmetric, which makes the convolution commute with 90-degree rotations and reflections and, the paper argues, generalizes to finer rotations through the learned band structure. Two architectural choices complete the mechanism: every convolution in the encoder and decoder is replaced with SRE-Conv, and decoder upsampling uses linear interpolation instead of trainable strided up-convolution, because strided up-convolution would break equivariance under rotation.

What would settle it

Train a comparison U-Net with the identical architecture and kernel-size schedule as SRE U-Net but standard asymmetric convolutions, matched for parameter count, and evaluate both on the DRIVE test set rotated in 1-degree steps. If the standard network matches SRE U-Net's Dice and AUC under rotation, the symmetric kernel is not what carries the reported robustness.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that applying SRE-Conv, a convolution kernel constrained to be centrally symmetric and encoded by a small number of band parameters, throughout a U-Net yields a segmentation model that is rotation- and reflection-equivariant in its feature maps and stays accurate when inputs are rotated by small angles (1 to 5 degrees) as well as by 90 degrees. In the reported experiments, the SRE U-Net (0.12M parameters) attains the highest averaged accuracy (0.9600), specificity (0.9870), IoU (0.6795), Dice (0.8087), and AUC (0.9767) among U-Net, Group U-Net, ES U-Net, FR U-Net, and Frangi baselines, with FR U-Net slightly ahead on sensitivity. The authors take this as evidence that symmetric kernels give the network both parameter efficiency and rotational robustness, and that the SRE kernel can serve as a drop-in replacement for the convolution layers in segmentation backbones.

Load-bearing premise

The central claim rests on the assumption that the improved accuracy and rotation stability come from the symmetric kernel's equivariance, rather than from the smaller model, the two-downsampling architecture, the interpolation upsampling, or from configuring kernel sizes on the test set.

Editorial extensions

If this is right

Retinal vessel segmentation can become rotation-robust without the memory overhead of group convolution: SRE U-Net uses 0.12M parameters versus 1.92M for Group U-Net and 0.72M for ES U-Net in the comparison.
Because the SRE kernel is designed as a drop-in replacement for standard convolutions, the same equivariance benefit could transfer to other U-Net-based segmentation tasks where object orientation is arbitrary.
A smaller, cheaper segmentation model makes rotation-equivariant learning usable in settings with limited training data or GPU memory.
The reported stability under small rotations implies fewer inconsistent predictions when clinical fundus images are acquired at slightly different angles.

Reading between the lines

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

The exact equivariance guarantee holds for grid-preserving rotations such as 90 degrees and reflections; the observed robustness to continuous 1-to-5-degree rotations is an empirical property that likely depends on the band structure, interpolation, and data augmentation together, not on a proven symmetry for arbitrary angles.
A cleaner test of the kernel's contribution would hold every architectural choice fixed and vary only kernel symmetry; the paper changes downsampling depth and upsampling method at the same time, so part of the gain may come from those changes rather than the symmetric kernel alone.
The same kernel could be evaluated on histopathology or other orientation-agnostic imaging where vessels and tissue structures appear at arbitrary angles; a public multi-dataset benchmark would show whether the parameter-efficiency advantage persists outside DRIVE.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: SRE U-Net is a clean, plausible application of the authors' own SRE-Conv kernel to segmentation, and the parameter-efficiency story is real—0.12M parameters versus 6.97M for FR U-Net is a big difference, not a rounding error. What is not established is the headline performance claim. The Dice gaps driving "surpasses" are 0.001 to 0.01 on a 20-image test set, with no error bars and no significance testing. The kernel-size configuration was chosen by looking at Dice on the same test set used for the final numbers. That is test-set tuning, and the gaps are within the noise floor. I think the reader's strongest concern lands.

The paper does several things well. It makes a sensible architectural choice: two downsamplings reduce parameters, and linear-interpolation upsampling instead of trainable up-convolution is the right way to preserve equivariance through the decoder. The benchmarking includes reasonable baselines, a range of metrics, and a qualitative consistency check under 90-degree and 45-degree rotation. The code link is a positive, though I did not run it and cannot verify the reported numbers from the repo alone.

The soft spots are real and load-bearing for the headline claims. First, no repeated runs, error bars, or statistical tests appear anywhere. With 20 test images, a per-image Dice SD of 0.05–0.1 puts the standard error around 0.01–0.02; the SRE U-Net versus FR U-Net differences at 0 and ±5 degrees are smaller than that. So "significantly surpasses" is not supported. Second, the ablation in Table 2 selects k=[9,7,5] by maximizing Dice on the test set, and that same configuration then produces the paper's main results. That is optimistic selection, not a fair evaluation. Third, the small-angle robustness story is underspecified: the kernel's exact equivariance is for grid-preserving rotations like 90 degrees and reflections, while the continuous 1–5 degree results are empirical and confounded by nearest-neighbor resampling. The paper never isolates the SRE kernel's contribution from the other architectural changes, so we do not know how much of the gain is the kernel rather than the smaller network or the interpolation upsampling.

None of this makes the central idea wrong. A parameter-efficient radially symmetric convolution kernel is a sensible plug-in for medical segmentation, and the qualitative rotation consistency is visible. But the empirical case needs a validation split for the ablation, error bars with significance tests on the rotated test set, and an explicit statement about what exact equivariance the kernel does and does not provide.

Who is this for? People working on rotation-robust medical image segmentation and small-model equivariant CNNs. I would not desk-reject it, but I would send it to peer review with a strong request for proper statistical evaluation. As it stands, the contribution is promising but the reported margins are not yet credible.

Referee Report

3 major / 5 minor

Summary. The manuscript proposes SRE U-Net, a U-Net variant in which all convolution kernels are replaced by symmetric rotation-equivariant (SRE) kernels with a small number of trainable parameters, two downsampling stages, and linear-interpolation upsampling. The authors evaluate the method on the DRIVE retinal vessel segmentation dataset, using both original test images and images rotated in 1-degree increments within +/-5 degrees, and compare against standard U-Net, Group U-Net, ES U-Net, FR U-Net, and the Frangi filter. They report that SRE U-Net achieves the best accuracy, specificity, IoU, Dice, and AUC while using only 0.12M parameters, and they claim that it surpasses the state-of-the-art FR U-Net while using 1.7% of its trainable parameters. The paper also includes an ablation over kernel sizes and qualitative difference maps.

Significance. If the empirical claims were established, the paper would provide a useful plug-in convolution kernel that improves rotation robustness and parameter efficiency for segmentation: reducing from 0.48M parameters for the U-Net baseline to 0.12M and from 6.97M for FR U-Net to 0.12M is striking, and the code is made publicly available. The use of a public benchmark, multiple metrics, and a rotation-based test protocol are strengths. However, the central quantitative claims are not currently supported: the kernel configuration is selected on the same test set used for the final evaluation, no error bars or significance tests are reported, and the headline differences are smaller than the likely noise floor. The 90-degree equivariance is also a design consequence of the kernel construction rather than an independently discovered property. The direction is plausible, but the reported margins need substantially stronger evidence.

major comments (3)

[Sec. 3.4, Table 2] The kernel configuration k=[9,7,5] is selected by maximizing Dice on the same rotated test set used for the final evaluation: Table 2 reports Dice averaged over +/-5 degrees of 0.8064 for [9,7,5] versus 0.7960 for [7,7,7], and the selected configuration is labelled 'Proposed'. Because the test set contains only 20 images and no error bars are given, this test-set-based model selection makes the final headline numbers optimistically biased. The configuration choice should be made on a held-out validation set, or the authors should report nested cross-validation; without this, the reported margins cannot be taken at face value.
[Sec. 3.2, Table 1] No error bars, repeated runs, or statistical significance tests are reported. The decisive comparisons are very small: at 0 degrees, SRE U-Net Dice is 0.8087 versus 0.8079 for FR U-Net and 0.7998 for U-Net; at +/-5 degrees, the values are 0.8046 versus 0.8027 and 0.7947, respectively. With n=20 test images and per-image Dice variability typical of this dataset, the standard error of the mean is on the order of 0.01-0.02, so the claimed 'significantly surpasses' and 'best across most metrics' are not established. The authors should provide per-image metric distributions, multiple training seeds, or statistical significance tests for the differences.
[Sec. 2.1, Eq. (1); Sec. 3.2] The strict rotation-equivariance claim is broader than the construction supports. The SRE kernel is invariant under grid-preserving rotations and reflections, such as 90-degree rotations, by construction of the bands, but the paper's central evidence includes continuous small-angle rotations (1 to 5 degrees) where exact equivariance does not follow from Eq. (1). No analytical statement is given for small angles, and the experiments do not isolate the kernel's contribution from the architectural changes (two downsampling stages, linear-interpolation upsampling) or from the kernel-size selection. Please either narrow the equivariance claim to the discrete symmetry group or add an analytical or carefully controlled empirical argument for small-angle robustness.

minor comments (5)

[Title, Sec. 2] The title contains a typo: 'EQUIV ARIANT' should be 'EQUIVARIANT'.
[Sec. 2.2] Please clarify whether the standard U-Net baseline and the other equivariant baselines also use two downsampling stages and linear-interpolation upsampling; the text says 'same architecture' but the original U-Net uses transposed convolutions, so the comparison is otherwise not architecture-matched.
[Fig. 3] The reported MSE values need a precise definition (mean over pixels, normalized, or image-level) and the qualitative result is shown for one image; a quantitative aggregate over the full test set would be more informative.
[Sec. 2.1, Eq. (1)] The band-index construction would be clearer if the dimensions of the binary index matrix I and the reshaping operator psi were defined explicitly in the text; Fig. 1 partially provides this, but the notation in Eq. (1) is otherwise ambiguous.
[Sec. 4] The claim that SRE-Conv can be 'easily integrated into other existing segmentation frameworks' is speculative and should be framed as future work rather than an established result.

Circularity Check

1 steps flagged · score 6.0 of 10

Headline Dice advantage is a test-set-selected maximum rather than an independent prediction

fitted input called prediction [Sec. 3.1 (Experimental Settings); Sec. 3.2 (Table 1); Sec. 3.4 (Table 2)]
"We implement our SRE U-net using SRE-Conv with sizes k=[9,7,5] at each layer (ablation studies in Sec. 3.4 justify our model architecture). ... Table 2. SRE-Conv Ablation Studies. Model performance using different kernel size configurations ... Dice are averaged across rotation angles in the test set. ... [9, 7, 5](Proposed) 0.12M 0.8064"

The same ±5° rotated DRIVE test set is used both to select the kernel configuration and to report the final evaluation. Table 2's Dice values are averaged over the test set, and the [9,7,5] row is the highest of the four configurations; the paper labels it 'Proposed'. Table 1 then reports this selected configuration as SRE U-Net's performance (Dice 0.8046 at ±5°, 0.8087 at 0°) and bases the headline conclusion on it: 'surpasses the performance of the SoTA segmentation method [20] ... using only 1.7% of the trainable parameters.' Thus the reported advantage is not an independent prediction of the method; it is the result of optimizing the model selector on the same evaluation data.

full rationale

The DRIVE segmentation experiments themselves are externally measured: test images, ground-truth labels, and baseline methods are independent of the paper's construction, so the core benchmarking is not circular by construction. The SRE-Conv kernel is taken from an overlapping-author preprint ([18], Du and Onofrey), but Eq. (1) and the binary index matrix make the central-symmetry construction explicit, so the exact 90°/reflection equivariance is a direct design property rather than a self-citation-dependent result. However, the paper's central empirical claim—that SRE U-Net 'significantly surpasses' baselines and the SoTA method with 1.7% of parameters—is partially circular because the [9,7,5] kernel configuration was selected by maximizing Dice on the same rotated test set used for the final comparison. The reported gap (e.g., 0.8046 vs 0.8027 for FR U-Net at ±5°) is also within a plausible noise floor for 20 test images, but that is a statistical-correctness concern rather than a circularity concern. The load-bearing circular step is the test-set-based model selection: the headline numbers are selected maxima, not independent predictions.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper's own contribution is architectural application, so its correct behavior depends on the SRE kernel definition, the band-matrix construction, and the labeling of the test set; there are no newly invented physical entities.

free parameters (3)

Kernel size configuration per layer = [9,7,5]
Chosen after evaluating four configurations (Table 2) on the same DRIVE test set used for the headline results, so it is a test-set-selected architectural hyperparameter.
Number of downsampling stages = 2
Hand-selected in Sec 3.1 to compress the model; not ablated, yet the paper credits the architecture's parameter efficiency partly to this choice.
Training epochs = 6000
Hand-set without a validation-based stopping criterion; on a 20-image training set this risks overfitting and affects the comparison.

assumptions (4)

domain assumption The SRE-Conv kernel defined by Eq. 1 with the binary band matrix I is rotation- and reflection-equivariant.
The paper inherits this result from the authors' prior work (ref 18) and does not prove it here; the entire method rests on this property.
domain assumption All deep-learning baselines were trained under the same hyperparameters, augmentation, and architecture with only the equivariant layers changed, so differences in Table 1 are attributable to the kernel.
Stated in Sec 3.1 but no training curves, config files, or seed analysis are provided to verify comparable training.
domain assumption The DRIVE test set of 20 images and the binary vessel labels are reliable enough to rank methods on the reported metrics.
Used without independent annotation review or confidence intervals; a 20-image test set is small for detecting the small metric differences in Table 1.
ad hoc to paper Nearest-neighbor resampling of rotated test images does not introduce a bias favoring any particular method.
The rotation protocol (Sec 3.1) is chosen to avoid interpolation artifacts, but no experiment compares resampling schemes or verifies that the equivariant method is not preferentially helped.

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Cite this review

Pith. "Pith review of Improved Vessel Segmentation with Symmetric Rotation-Equivariant U-Net." pith.science (2026). https://pith.science/paper/GH6Z7ZRW

@misc{pith2026250114592,
  author       = {Pith},
  title        = {Pith review of: Improved Vessel Segmentation with Symmetric Rotation-Equivariant U-Net},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GH6Z7ZRW}},
  note         = {Machine review of arXiv:2501.14592}
}

read the original abstract

Automated segmentation plays a pivotal role in medical image analysis and computer-assisted interventions. Despite the promising performance of existing methods based on convolutional neural networks (CNNs), they neglect useful equivariant properties for images, such as rotational and reflection equivariance. This limitation can decrease performance and lead to inconsistent predictions, especially in applications like vessel segmentation where explicit orientation is absent. While existing equivariant learning approaches attempt to mitigate these issues, they substantially increase learning cost, model size, or both. To overcome these challenges, we propose a novel application of an efficient symmetric rotation-equivariant (SRE) convolutional (SRE-Conv) kernel implementation to the U-Net architecture, to learn rotation and reflection-equivariant features, while also reducing the model size dramatically. We validate the effectiveness of our method through improved segmentation performance on retina vessel fundus imaging. Our proposed SRE U-Net not only significantly surpasses standard U-Net in handling rotated images, but also outperforms existing equivariant learning methods and does so with a reduced number of trainable parameters and smaller memory cost. The code is available at https://github.com/OnofreyLab/sre_conv_segm_isbi2025.

Discussion (0). Continue with ORCID to comment.

Forward citations

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Works this paper leans on

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Improved Vessel Segmentation with Symmetric Rotation-Equivariant U-Net

INTRODUCTION Segmentation is a fundamental task in medical imaging anal- ysis that involves identifying and delineating regions of inter- est, such as organs, lesions, and tissues. Accurate segmenta- tion is essential for many clinical applications, including dis- ease diagnosis, treatment planning, and monitoring of disease © 2025 IEEE. Personal use of t...

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Improved Vessel Segmentation with Symmetric Rotation-Equivariant U-Net

INTRODUCTION Segmentation is a fundamental task in medical imaging anal- ysis that involves identifying and delineating regions of inter- est, such as organs, lesions, and tissues. Accurate segmenta- tion is essential for many clinical applications, including dis- ease diagnosis, treatment planning, and monitoring of disease © 2025 IEEE. Personal use of t...

work page Pith review arXiv 2025

[2] [2]

Symmetric Rotation-Equivariant (SRE) Convolution CNNs are equivariant with respect to translation

METHODS 2.1. Symmetric Rotation-Equivariant (SRE) Convolution CNNs are equivariant with respect to translation. This means that translating the input to a convolutional layer will result in translating the output by the same amount. To achieve rota- tional equivariance, we apply SRE-Conv kernels [18], which parameterize the kernels to be centrally symmetr...

work page

[3] [3]

Experimental Setup Dataset: We evaluate using the public retina vessel DRIVE dataset [19], which consists of 40 2D RGB fundus images with paired binary vessel segmentation labels

EXPERIMENTS AND RESULTS 3.1. Experimental Setup Dataset: We evaluate using the public retina vessel DRIVE dataset [19], which consists of 40 2D RGB fundus images with paired binary vessel segmentation labels. We partition the dataset into equal halves for training and testing. Baselines Comparison: We choose the standard U-Net [1] with the same architectu...

work page

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We integrate this kernel into the standard U-Net framework to learn rotation- and reflection-equivariant segmentation features, while also reducing the model size

DISCUSSION AND CONCLUSION In this work, we present a novel application of an efficient symmetric rotation-equivariant convolution (SRE-Conv) ker- nel to the task of semantic segmentation. We integrate this kernel into the standard U-Net framework to learn rotation- and reflection-equivariant segmentation features, while also reducing the model size. The e...

work page

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U-net: Convolutional networks for biomedical image segmentation,

Olaf Ronneberger, Philipp Fischer, and Thomas Brox, “U-net: Convolutional networks for biomedical image segmentation,” in MICCAI. Springer, 2015, pp. 234– 241

work page 2015

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Learning calibrated medi- cal image segmentation via multi-rater agreement mod- eling,

Wei Ji, Yefeng Zheng, et al., “Learning calibrated medi- cal image segmentation via multi-rater agreement mod- eling,” in IEEE CVPR, 2021, pp. 12341–12351

work page 2021

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nnu- net: a self-configuring method for deep learning-based biomedical image segmentation,

Fabian Isensee, Klaus H Maier-Hein, et al., “nnu- net: a self-configuring method for deep learning-based biomedical image segmentation,” Nature methods, vol. 18, no. 2, pp. 203–211, 2021

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Atlas-based semantic segmentation of prostate zones,

Jiazhen Zhang, John A Onofrey, et al., “Atlas-based semantic segmentation of prostate zones,” in MICCAI. Springer, 2022, pp. 570–579

work page 2022