Hierarchical LoG Bayesian Neural Network for Enhanced Aorta Segmentation

Chaoli Wang; Delin An; Jian-Xun Wang; Pan Du; Pengfei Gu

REVIEW 4 major objections 5 minor 37 references

Hierarchical LoG Bayesian Neural Network for Enhanced Aorta Segmentation

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that adding a Bayesian hierarchical Laplacian-of-Gaussian stream to a 3D U-Net lifts aorta and supra-aortic branch segmentation by about 3 Dice points over ten baselines and yields confidence intervals for downstream CFD.

desk verdict Solid, honest architecture paper with real gains on aorta branch segmentation, but the Bayesian/UQ component is presently under-specified and the balanced gate is not fully reproducible; worth refereeing, not ready as is. read the letter →

arxiv 2501.10615 v2 pith:PWBFAAGM submitted 2025-01-18 cs.CV

Delin An , Pan Du , Pengfei Gu , Jian-Xun Wang , Chaoli Wang This is my paper · ORCID

classification cs.CV

keywords aortasegmentationLaplacianofGaussianBayesianneuralnetworkuncertaintyquantificationmultiscalevesselsupra-aorticbranches3DU-NetCTangiography

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 tries to establish that LoGB-Net, a two-stream segmentation model for aortic CT angiography volumes, beats ten existing methods on both the main aorta and the small supra-aortic branches, with the clearest margin on the branches. The first stream is a standard 3D U-Net that captures the whole vessel, and the second stream is a set of five convolutional layers initialized as 3D Laplacian-of-Gaussian kernels at different scales and then trained, which lets the network adapt to vessels of very different radii. A balanced gate rebalances the extreme foreground-to-background ratio, and a Bayesian parameterization of the LoG stream produces per-voxel confidence intervals instead of a single surface. If the claims hold, automated aorta branch segmentation becomes more accurate and downstream hemodynamic simulations get a quantified uncertainty from the segmentation itself.

What carries the argument

The load-bearing object is the hierarchical LoG stream: five 3D convolutional layers of kernel sizes 3, 5, 7, 9, and 11, initialized with discretized 3D Laplacian-of-Gaussian kernels at $\sigma$ values 0.5, 1.0, 1.5, 2.0, and 2.5, and left trainable. This gives the model a self-adaptive multiscale edge detector tuned to vessels of different radii. The balanced gate computes a foreground-to-background ratio $T$; images with $T < \mu$ (here $\mu = 0.15$) enter one queue, images with $T > \mu$ enter another, and when both queues reach capacity $C$ the $2C$ images are concatenated along the channel dimension, forcing each mini-batch to mix foreground-poor and foreground-rich examples. The Bayesian treatment regards the LoG kernel as the prior and the module output as the posterior, maximizes the evidence lower bound (ELBO), and uses a total loss of Dice minus ELBO.

What would settle it

Force the balanced gate to open on every image by setting its queue capacity to one, retrain on the same 34 volumes, and measure SA Dice on the same 16 test volumes; if the score does not fall from 0.927 toward the 0.896 gate-off level, the gate is not carrying the claimed gain.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a two-stream network outperforms every compared method on both aorta regions, with the largest margin on the small supra-aortic branches: SA Dice reaches 0.927 ± 0.011 against Swin-UNETR's 0.896 ± 0.019, and MA Dice reaches 0.937 ± 0.006. The gain is attributed to the LoG stream, whose five convolutional layers (kernel sizes 3, 5, 7, 9, 11) are initialized as 3D Laplacian-of-Gaussian kernels at $\sigma$ values 0.5 to 2.5 and then optimized, so the network enhances vessels of widely different radii without manual scale selection. Bayesian parameterization of that stream gives confidence intervals that widen where boundaries are blurred. The balanced gate is reported as a major contributor: removing it drops SA Dice from 0.927 to 0.896, exactly the level of the strongest attention baseline.

Load-bearing premise

The load-bearing premise is that the balanced gate can be implemented as described—two queues of unspecified capacity $C$ that concatenate $2C$ images once full—and also works at inference time on a single volume, because the paper attributes a roughly 3-point SA Dice gain to this gate yet gives no inference-time procedure.

Editorial extensions

If this is right

Supra-aortic branch segmentation improves by roughly 3 Dice points over the strongest attention baseline, with the largest visual gains on small-radius vessels that other methods miss.
The Bayesian LoG stream turns segmentation into a distribution: ten forward passes yield confidence intervals, and intervals widen on blurred boundaries, giving analysts a spatial map of where the prediction is reliable.
Removing the balanced gate drops SA Dice to 0.896, the same level as Swin-UNETR, indicating that foreground-background rebalancing contributes most of the branch-class gain.
CFD simulations on nine sampled segmentations show measurable flow variations, so the uncertainty intervals propagate into hemodynamic quantities such as velocity, pressure, and wall shear stress.
The added computational cost is modest at 48.88 GFLOPS, between UNETR's 41.19 and far below nnU-Net's 412.65, so the accuracy gain is not bought with an impractical model.

Reading between the lines

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

The same two-stream recipe—a coarse segmentation encoder plus a trainable multiscale edge-filter stream—should transfer to other branching vessel trees such as coronary, cerebral, and pulmonary vessels, where the root-to-branch diameter ratio is similarly large.
A per-image foreground-fraction reweighting, instead of a queue that must fill before any batch is formed, might recover most of the balanced gate's effect while remaining well-defined at inference time.
The gate's queue capacity is never stated and its inference-time operation is not described, so the reported 3-point contribution of the gate cannot yet be reproduced from the paper alone; a concrete gate specification is the natural next step.
The widened confidence intervals on blurred boundaries suggest the model could serve as a pre-CFD reliability screen, flagging regions where a single reconstructed aortic surface would be misleading.

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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

Colleague,

The thing to know: this is a legitimate empirical paper, not a shell. The authors combine a regular 3D U-Net with a hierarchical trainable LoG stream, add a balanced gate, and report a ~3% Dice gain over ten baselines on supra-aortic branch segmentation, with five random seeds and two public datasets. The ablation shows each component contributes, and the code is linked. The segmentation result itself is plausible and should be taken seriously.

What is actually new: the specific design of a five-scale trainable LoG stream with a foreground/background balancing gate for aorta segmentation. That is a modest but useful contribution. The experimental comparison is also better than the field average: ten baselines, consistent training, standard deviations reported.

The soft spots are real and clustered in the Bayesian part, which the stress-test note names correctly. Section 3 writes a Bayes rule, says theta = argmax(ELBO), and calls the LoG kernel a prior and the module output a posterior, but no ELBO is ever defined: no variational family, no KL term, no posterior predictive, no sampling procedure for the "ten Bayesian inferences." The confidence intervals are shown visually and used in a CFD illustration, but never checked against held-out annotations for coverage or calibration. So the "reliable confidence intervals" claim is currently asserted, not demonstrated. That is the load-bearing weak point because it is the paper's main novelty beyond the architecture.

The balanced gate is under-specified too: queue capacity C is never given, and inference-time behavior is unclear since images are concatenated in groups of 2C during training but inference is presumably per-volume. This is a genuine reproducibility gap, but smaller than the UQ one: the released code could pin it down. The abstract's "at least a 3% gain" also overreaches slightly: the gain over Swin-UNETR is about 3.1% on SA but 2.8% on MA, and no significance test backs the "at least" phrasing.

Bottom line: the architecture and main segmentation result probably hold up. The Bayesian/UQ story needs a full rewrite: specify the inference procedure, report calibration, and temper the claims until then. The gate needs its capacity and inference protocol stated. None of this is fatal; all of it is addressable.

Recommendation: yes, send it to peer review. A serious referee can force the authors to produce the missing derivations and calibration experiments. The paper deserves referee time, but it should not be accepted in its current form.

Best, [You]

Referee Report

4 major / 5 minor

Summary. The paper proposes LoGB-Net, a dual-stream 3D aorta segmentation architecture consisting of a regular 3D U-Net stream and a hierarchical Laplacian-of-Gaussian (LoG) stream with a so-called Bayesian parameterization and a balanced gate for foreground-background rebalancing. The method is evaluated on two CTA datasets against ten baselines, with a five-seed comparison reporting Dice, ASD, and Hausdorff distances. The authors claim that LoGB-Net outperforms all baselines, especially on supra-aortic branches (about 3 percentage points higher Dice than Swin-UNETR), and that the Bayesian LoG module provides confidence intervals for segmentation, illustrated on boundary-clarity variations and used to propagate uncertainty into CFD simulations.

Significance. If the claims hold, the paper addresses a genuine clinical need: automated, accurate segmentation of small aortic branches and uncertainty quantification for downstream hemodynamic simulation. The experimental setup is a real, multi-seed comparison against a wide range of modern baselines on two public datasets, and the code is released, which are clear strengths. The ablation study (Table 2) gives initial evidence that each proposed component contributes to the reported performance. However, the Bayesian/UQ component, which is load-bearing for the paper's central 'reliable confidence intervals' claim, is under-specified: no variational objective, inference procedure, or calibration evaluation is provided, and the balanced gate's capacity and inference-time behavior are not defined. The paper's contribution is therefore only partially supported at present.

major comments (4)

[Section 3, 'Bayesian method and balanced gate'] The ELBO is named but never defined. The text writes 'θ = argmax(ELBO)' and 'L = Dice − ELBO', but no variational family, no KL divergence term, and no posterior predictive distribution are given. The sentence 'treating the LoG kernel as the prior distribution and the module's output as the posterior' appears to conflate a kernel initialization with a distribution over parameters. This makes the Bayesian claim unverifiable and the confidence intervals in Section 4 unsupported. Please provide the full variational objective, the exact inference procedure (e.g., Monte Carlo dropout, mean-field variational inference, or sampling from an approximate posterior), and the mechanism by which the 'ten Bayesian inferences' in the UQ paragraph are generated.
[Section 3, 'Balanced gate'] The queue capacity C is never specified, and the inference-time behavior of the gate is undefined. The text says that when counters c1 and c2 reach capacity C, the 2C images are concatenated along the channel dimension and the regular stream is initiated. At test time, volumes are processed individually; it is unclear whether the gate buffers images across the test set or is disabled during inference. This is load-bearing because Table 2 shows that removing the gate reduces SA Dice from 0.927 to 0.896. Please specify the value of C, the training dynamics when the queues are not full, and precisely how a single test volume is handled. If the gate is not applied at inference, the reported gains may be an artifact of batch-level rebalancing rather than a deployable architectural feature.
[Section 4, 'UQ' and abstract] The claim of 'reliable confidence intervals' is asserted but not demonstrated. The confidence intervals are said to come from 'ten Bayesian inferences', yet no sampling method, posterior approximation, or number of stochastic forward passes is described. The only evaluations are visual (Figure 2) and a CFD illustration (Figure 4), which do not constitute calibration evidence. Please report a coverage or calibration metric on held-out volumes, such as the fraction of ground-truth voxels falling within the confidence interval or an expected calibration error, and specify exactly how the ten inferences are generated.
[Abstract and Section 4, Table 1] The abstract claims 'at least a 3% gain in the Dice coefficient over state-of-the-art methods across multiple volumes.' Table 1 shows a 3.1 percentage-point SA Dice gain over Swin-UNETR, but the MA gain over Swin-UNETR is 2.8 points (0.937 vs. 0.909), and the gain over UNETR++ on MA is 3.0 points (0.937 vs. 0.907). The 'at least 3%' claim is therefore not uniformly true across regions and baselines. Please qualify the claim (e.g., 'up to 3%' or specify the best baseline for each region) so that it matches the reported numbers.

minor comments (5)

[Section 3, 'Algorithm Description'] The numbered pipeline steps are not fully consistent with the preceding description: step (2) says the gate 'initiate[s] the regular stream', while steps (3)-(4) describe concatenating the regular and LoG stream outputs into an ASPP module. Please clarify the exact data flow, including where the LoG stream's mean output enters the concatenation.
[Section 3, 'Hierarchical LoG module'] The equation for T = Σ f_i / Σ b_j does not define what f_i and b_j are (foreground/background voxel counts? intensities?), and the text says the threshold μ is 'determined statistically by calculating the mean of the foreground-to-background ratio for the SA' but does not say over which training images or how the value 0.15 was obtained. Please provide a precise definition and the computation procedure, and consider reporting sensitivity to μ.
[Figure 1 caption] The caption states that the Bayesian segmentation results' blue, red, and green lines represent the upper bound, mean, and lower bound, but the figure itself does not label which color is which in the displayed image. Please add a legend or clarify in the text.
[Table 2] The row label 'L−LoG(L(0))' is slightly confusing; it would be clearer to state explicitly that L(0) denotes the regular-stream-only baseline without any LoG stream, and to order the columns consistently with the text describing the ablation.
[Section 2, 'Related Work'] The UQ-related related work is thin, citing only one variational-inference segmentation paper. Please include representative probabilistic segmentation methods (e.g., PHiSeg, probabilistic U-Net, or MC-dropout approaches) to better position the contribution against the existing UQ literature.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the segmentation claims rest on an independent train/test comparison; the underspecified Bayesian/UQ component is a validity gap, not a circular derivation.

full rationale

The paper's reported Dice/ASD/Hausdorff gains come from training LoGB-Net on a 34-volume training set and evaluating on a separate 16-volume test set, with five random seeds and external baselines trained under the same protocol; no test-set quantity is used as a fitted input. The initial LoG sigma values and the balanced-gate threshold µ=0.15 are training-time hyperparameters, not renamed predictions. The Bayesian/UQ section does not define an ELBO, a variational family, or a sampling procedure, and the confidence intervals are never calibration-tested; however, that is missing support and an underspecified claim, not a case of a result being equivalent to its inputs by construction. The only self-citations (refs. [12] and [16]) are ordinary related-work mentions and are not load-bearing. No circular step can be quoted with a specific equation-to-equation reduction, so the appropriate finding is no significant circularity.

Assumptions & free parameters 3 free parameters · 3 assumptions · 2 invented entities

The central claims rest on two new architectural components (the hierarchical LoG stream and the balanced gate) and on a re-framing of the LoG module as Bayesian. The components are only validated in the paper's own experiments, the gate has an unspecified capacity, and the Bayesian formulation is asserted without the mathematical steps that would make it a verifiable inference procedure.

free parameters (3)

Balanced gate threshold mu = 0.15
Set in Section 3 as the mean foreground-to-background ratio for the SA, used to route images into queues Q1 and Q2. This is fitted to training data rather than derived, and its transfer to the MA and to unseen datasets is assumed.
Queue capacity C = not specified
The balanced gate concatenates 2C images along the channel dimension, but the paper never states the value of C, leaving the pipeline under-specified and not reproducible as described.
Initial LoG sigma values = 0.5 to 2.5 (five values)
Section 3 says the five LoG layers are initialized with sigma values from 0.5 to 2.5 and these initial values are 'optimized to achieve the best lumen boundaries', a manual choice tied to the target vessel scales.

assumptions (3)

ad hoc to paper The LoG kernel can serve as the prior and the module output as the posterior in a valid Bayesian neural network.
Section 3 states p(theta|D)=p(D|theta)p(theta)/p(D) and theta=argmax(ELBO) without specifying the variational family, the prior, or the inference algorithm. This framing is unique to this paper and is not backed by a derivation.
domain assumption A single scalar foreground-to-background ratio threshold characterizes both MA and SA across both datasets.
The balanced gate uses one mu=0.15 for all training volumes, but the paper gives no evidence that the foreground-to-background ratio distribution is unimodal or consistent between the two public datasets.
domain assumption Resampling to 0.8x0.8x0.3 spacing and cropping into 64x64x64 blocks preserves the clinically relevant vessel structures.
Section 4 applies MONAI's Spacingd to all volumes. This assumes no important anatomical information is lost and that the two datasets are comparable after resampling, which is not tested explicitly.

invented entities (2)

Balanced gate with queues Q1 and Q2
purpose: Rebalance the foreground-to-background ratio by grouping images with small and large foreground regions and concatenating pairs of batches.
The gate is introduced by this paper, and its benefit is shown only in the paper's own ablation (L-Gate row of Table 2). No external validation or theoretical analysis supports it.
Hierarchical LoG stream with trainable kernels
purpose: Enhance multiscale vessel features by learning Laplacian-of-Gaussian kernels at five scales.
This module is the central architectural novelty, but its contribution is evidenced only by the paper's own ablation and qualitative results, not by independent replication or a formal property.

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Cite this review

Pith. "Pith review of Hierarchical LoG Bayesian Neural Network for Enhanced Aorta Segmentation." pith.science (2026). https://pith.science/paper/PWBFAAGM

@misc{pith2026250110615,
  author       = {Pith},
  title        = {Pith review of: Hierarchical LoG Bayesian Neural Network for Enhanced Aorta Segmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PWBFAAGM}},
  note         = {Machine review of arXiv:2501.10615}
}

read the original abstract

Accurate segmentation of the aorta and its associated arch branches is crucial for diagnosing aortic diseases. While deep learning techniques have significantly improved aorta segmentation, they remain challenging due to the intricate multiscale structure and the complexity of the surrounding tissues. This paper presents a novel approach for enhancing aorta segmentation using a Bayesian neural network-based hierarchical Laplacian of Gaussian (LoG) model. Our model consists of a 3D U-Net stream and a hierarchical LoG stream: the former provides an initial aorta segmentation, and the latter enhances blood vessel detection across varying scales by learning suitable LoG kernels, enabling self-adaptive handling of different parts of the aorta vessels with significant scale differences. We employ a Bayesian method to parameterize the LoG stream and provide confidence intervals for the segmentation results, ensuring robustness and reliability of the prediction for vascular medical image analysts. Experimental results show that our model can accurately segment main and supra-aortic vessels, yielding at least a 3% gain in the Dice coefficient over state-of-the-art methods across multiple volumes drawn from two aorta datasets, and can provide reliable confidence intervals for different parts of the aorta. The code is available at https://github.com/adlsn/LoGBNet.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Hierarchical LoG Bayesian Neural Network for Enhanced Aorta Segmentation

INTRODUCTION Semantic segmentation is a crucial research direction in deep learning technologies, extensively applied in medical im- age processing. It finds wide-ranging applications in organ segmentation, lesion detection, tumor segmentation, and ves- sel segmentation. Vessel segmentation includes coronary artery, aorta, and pulmonary artery segmentatio...

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Semi-automatic methods in- volve manual lumen boundary and centerline annotation, achieving good performance but are labor-intensive

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We propose a hier- archical LoG module to address these issues and enhance aorta segmentation

LOGB-NET Multiscale aortic vessels require attention to the overall structure and local details, and the imbalanced foreground- background ratio complicates training. We propose a hier- archical LoG module to address these issues and enhance aorta segmentation. Our framework (Figure 1) comprises regular and LoG streams. The regular stream employs a 3D U-N...

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Two datasets were used: the first is from [23], and the second is the Aortic Ves- sel Tree (A VT) CTA dataset [24]

EXPERIMENTS Datasets, network training, and metrics. Two datasets were used: the first is from [23], and the second is the Aortic Ves- sel Tree (A VT) CTA dataset [24]. The training set contains 34 volumes (24 from the first, 10 from the second), and the testing set has 16 volumes (8 from each). V olumes were re- sampled using MONAI’s Spacingd function to...

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CONCLUSIONS AND FUTURE WORK We have presented LoGB-Net, a hierarchical, Bayesian- optimized LoG segmentation model for enhanced aorta seg- mentation. Combining a regular stream for overall structure with a LoG stream for local details, LoGB-Net enhances SA detection, addresses foreground-background imbalance, and improves robustness by providing the UQ co...

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Ethical approval was not required, as confirmed by the licenses attached to the open- access datasets

COMPLIANCE WITH ETHICAL STANDARDS This research study was conducted retrospectively using hu- man subject data made available in open access by two pub- licly available datasets [23, 24]. Ethical approval was not required, as confirmed by the licenses attached to the open- access datasets

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The au- thors would like to thank the anonymous reviewers for their insightful comments

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A tensorial approach to computational continuum mechanics using object- oriented techniques,

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Pith tools

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

[1] [1]

Hierarchical LoG Bayesian Neural Network for Enhanced Aorta Segmentation

INTRODUCTION Semantic segmentation is a crucial research direction in deep learning technologies, extensively applied in medical im- age processing. It finds wide-ranging applications in organ segmentation, lesion detection, tumor segmentation, and ves- sel segmentation. Vessel segmentation includes coronary artery, aorta, and pulmonary artery segmentatio...

work page Pith review arXiv 2025

[2] [2]

Semi-automatic methods in- volve manual lumen boundary and centerline annotation, achieving good performance but are labor-intensive

RELA TED WORK Medical image semantic segmentation methods are semi- automatic and automatic [8]. Semi-automatic methods in- volve manual lumen boundary and centerline annotation, achieving good performance but are labor-intensive. SimVas- cular [4] reduces manual effort by combining centerline and lumen edge for segmentation but still requires annotations...

work page

[3] [3]

We propose a hier- archical LoG module to address these issues and enhance aorta segmentation

LOGB-NET Multiscale aortic vessels require attention to the overall structure and local details, and the imbalanced foreground- background ratio complicates training. We propose a hier- archical LoG module to address these issues and enhance aorta segmentation. Our framework (Figure 1) comprises regular and LoG streams. The regular stream employs a 3D U-N...

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[4] [4]

Two datasets were used: the first is from [23], and the second is the Aortic Ves- sel Tree (A VT) CTA dataset [24]

EXPERIMENTS Datasets, network training, and metrics. Two datasets were used: the first is from [23], and the second is the Aortic Ves- sel Tree (A VT) CTA dataset [24]. The training set contains 34 volumes (24 from the first, 10 from the second), and the testing set has 16 volumes (8 from each). V olumes were re- sampled using MONAI’s Spacingd function to...

work page

[5] [5]

CONCLUSIONS AND FUTURE WORK We have presented LoGB-Net, a hierarchical, Bayesian- optimized LoG segmentation model for enhanced aorta seg- mentation. Combining a regular stream for overall structure with a LoG stream for local details, LoGB-Net enhances SA detection, addresses foreground-background imbalance, and improves robustness by providing the UQ co...

work page

[6] [6]

Ethical approval was not required, as confirmed by the licenses attached to the open- access datasets

COMPLIANCE WITH ETHICAL STANDARDS This research study was conducted retrospectively using hu- man subject data made available in open access by two pub- licly available datasets [23, 24]. Ethical approval was not required, as confirmed by the licenses attached to the open- access datasets

work page

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The au- thors would like to thank the anonymous reviewers for their insightful comments

ACKNOWLEDGMENTS This research was supported in part by NSF grants IIS- 1955395, OAC-2047127, IIS-2101696, OAC-2104158, and IIS-2401144, and NIH grant 1R01HL177814-01. The au- thors would like to thank the anonymous reviewers for their insightful comments

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U-Net: Convolu- tional networks for biomedical image segmentation,

O. Ronneberger, P. Fischer, and T. Brox, “U-Net: Convolu- tional networks for biomedical image segmentation,” in Proc. MICCAI, 2015, pp. 234–241

work page 2015