Weakly Supervised Segmentation by A Deep Geodesic Prior

Aliasghar Mortazi; Drew A. Torigian; Naji Khosravan; Sila Kurugol; Ulas Bagci

REVIEW 4 major objections 6 minor 12 references

Weakly Supervised Segmentation by A Deep Geodesic Prior

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read A geodesic autoencoder prior added to the loss improves 3D cardiac segmentation under clean and noisy labels by 4.4–6.3 Dice points.

desk verdict A modest but plausible result: geodesic distance maps as an autoencoder shape prior give a few Dice points on noisy cardiac labels; the main weaknesses are missing variance and an unanalyzed domain-shift assumption. read the letter →

arxiv 1908.06498 v1 pith:MSZNSBQQ submitted 2019-08-18 stat.ML cs.CVcs.LG

Aliasghar Mortazi , Naji Khosravan , Drew A. Torigian , Sila Kurugol , Ulas Bagci This is my paper · ORCID

classification stat.MLcs.CVcs.LG MSC 68T0768U10

keywords weaklysupervisedsegmentationgeodesicpriorshapeautoencodercardiacMRInoisylabelsdeeplearning3Dmedicalimage

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 is trying to establish that a learned geodesic shape prior can make deep segmentation networks much less sensitive to weak or noisy labels. Its mechanism is an auxiliary loss: a geodesic autoencoder, trained once to convert geodesic distance maps of the annotated structures back into binary maps, supplies bottleneck features that the segmentor's own probability map is asked to match. On cardiac MRI with expert labels and two levels of simulated boundary noise, this extra term raises average Dice over the same network without the prior by 4.4, 4.6, and 6.3 points. That would matter because expert medical annotations are scarce and expensive, while imperfect labels from non-experts are abundant.

What carries the argument

The central object is the geodesic autoencoder (GAE): an encoder-decoder with a fully connected bottleneck, trained to reconstruct binary label maps from geodesic distance maps computed by fast marching, which solves the Eikonal equation for contour arrival time. The encoder's bottleneck feature vector captures shape and boundary information for each object, and the mean squared error between the features of the segmentor's soft probability map and the features of the geodesic map becomes the auxiliary loss term. This carries the argument because it converts weak boundary information into a shape constraint that is independent of the pixel-level segmentation loss, and because the GAE is frozen during segmentor training so the prior is a fixed geometric guide rather than a learned feature that can drift with the noisy labels.

What would settle it

If the auxiliary loss were replaced by the same mean squared error against features of a permuted or random geodesic map and the Dice scores remained equally high, the reported gains would not be caused by the learned prior; alternatively, one can measure on a validation split how far the segmentor's probability-map features and the geodesic-map features actually are and check whether that distance tracks segmentation error.

Watch

Extended reading notes

Core claim

The paper's central claim is that a deep geodesic prior reduces the adverse effect of weak labels on segmentation accuracy. Concretely, the authors train a geodesic autoencoder (GAE) to map geodesic distance maps of the objects of interest (left ventricle, right ventricle, myocardium) back to their binary maps, and use the GAE's frozen encoder to compute an auxiliary loss between the segmentor's soft probability map and the corresponding geodesic map. The total loss becomes Lseg + Lgae, with Lgae a mean squared error on bottleneck features. On the ACDC cardiac MRI data, the geodesic prior outperforms both the bare segmentor and a binary-map autoencoder prior: average Dice rises from 0.809 to 0.853 with clean labels, from 0.795 to 0.841 with noise level L1, and from 0.775 to 0.838 with noise level L2.

Load-bearing premise

The method's gain depends on the assumption that the bottleneck features extracted from the segmentor's soft probability map are comparable to those extracted from the binary-derived geodesic map, so that forcing them together conveys useful shape information; the paper does not examine how different those two feature distributions are.

Editorial extensions

If this is right

Medical segmentation models can be trained on inexpert or automatically generated annotations and still approach the accuracy of models trained on expert labels, as long as a geodesic shape prior is available.
The relative benefit of the prior grows with label noise, from 4.4 Dice points on clean labels to 6.3 Dice points on the noisier level, suggesting shape priors matter most exactly where supervision is weakest.
The geodesic representation is more effective than a binary-map autoencoder prior, so the choice of how the shape is encoded into the prior is part of the performance.
At test time only the segmentor runs; the geodesic autoencoder is needed only during training, so the accuracy gain does not add inference cost.
The method is stated to be generic, meaning any 3D multi-object segmentation problem could in principle use the same geodesic-prior loss.

Reading between the lines

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

The reported gains come from a single cardiac MRI dataset with simulated label noise; a natural next test would be whether the same prior helps with real inexpert annotations and other anatomies, where the noise structure may differ.
Because the geodesic map is derived from the same labels used for supervision, the prior may act mainly as a regularizer that suppresses boundary errors; comparing the method against other strong regularizers such as conditional random fields or adversarial losses would clarify the source of the gain.
The mechanism could be validated more directly by monitoring the feature distance Lgae during training: if the segmentor's probability-map features quickly collapse to the geodesic-map features even when the probability map is wrong, the loss may be pulling the wrong shape, which would be especially visible on donut-shaped objects like the myocardium.
The idea could be adapted to weaker supervision than noisy full masks, such as scribbles or bounding boxes, by defining the geodesic map from those available cues; that would test how much of the prior lives in the distance representation rather than in the full label.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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 —

You should know up front: this is a solid incremental paper, not a breakthrough. The new bit is using fast-marching geodesic distance maps as the input to an autoencoder shape prior, then using the encoder's bottleneck features as an auxiliary loss for a 3D segmentation network. Oktay et al. used binary maps, Zotti et al. used atlases; the geodesic encoding is new, and the comparison against a binary-prior baseline gives it real content. The method is coherent, and the experiments cover two noise levels plus clean labels, with both Dice and Hausdorff reported. The gains are a few points, which is plausible for a regularizer of this kind.

The soft spots are about evidence quality, not design. First, no error bars, no significance tests, and no per-case breakdown, so a 0.004 average Dice difference (expert labels: 0.853 vs 0.849) could be noise. Second, in the L2 row the geodesic prior (0.838) exceeds the paper's own 'Upper boundary' (0.831). That column is just the Dice of the noisy labels against clean ground truth; exceeding it is what a regularizer should do, but the paper doesn't explain the seeming contradiction. Third, the load-bearing assumption in Eq. (3) is that the frozen GAE encoder, trained on geodesic maps, produces meaningful embeddings for the segmentor's soft probability maps. The stress-test note is right: nothing guarantees that Encgae(Pi) lives in a region where distance to Encgae(Gi) tracks shape dissimilarity. That said, the binary-prior baseline has exactly the same domain shift and the geodesic version beats it, so the empirical case for the prior is not empty. The paper would be stronger with an ablation swapping Lgae for a generic feature-matching loss, and with a sentence acknowledging the shift.

Bottom line: the central claim — that a learned geodesic prior helps with noisy labels — holds up as a plausible, modest result. The missing variance and the unanalyzed domain shift keep it from being fully convincing, but it deserves a proper peer-review round rather than a desk reject. I'd send it to review, ask for error bars, a direct comparison with the atlas prior of Zotti et al., and an ablation isolating the geodesic encoding.

Referee Report

4 major / 6 minor

Summary. The manuscript proposes a weakly supervised segmentation framework for 3D cardiac MRI. A geodesic autoencoder (GAE) is first trained to reconstruct binary labels from geodesic distance maps; its encoder is then frozen and used in an auxiliary feature-matching loss Lgae(Encgae(Pi), Encgae(Gi)) that encourages the segmentor's softmax output to share bottleneck features with the label-derived geodesic maps. Experiments on the ACDC dataset with clean labels and two synthetic noise levels (L1, L2) report Dice improvements of 4.4%, 4.6%, and 6.3% over the segmentor trained without the prior, and the method also outperforms a binary-map AE variant. The authors conclude that the geodesic prior improves robustness to weak labels.

Significance. If the reported effects are reproducible, the work is a useful contribution to the line of work on shape-prior regularization for medical image segmentation, offering a concrete way to encode multi-object shape information in a 3D network. The design is coherent: a fixed GAE with a feature-matching loss is a simple and computationally cheap auxiliary objective, and the comparison against a binary AE baseline is the right control for the choice of geodesic over binary maps. The main limitations are experimental: no variance/significance information, an unexplained exceedance of the 'Upper boundary' under L2 noise, and no analysis of the domain shift between binary-derived geodesic maps and soft probability maps. The core mechanism is therefore not yet established.

major comments (4)

[Table 1, Inexpert Labels (L2) rows] The reported Dice values for Geodesic Prior (LV 0.873, RV 0.831, MYO 0.809; average 0.838) are all higher than the corresponding 'Upper boundary' values (0.869, 0.824, 0.801; average 0.831). Because the upper boundary is defined as the Dice of the noisy training labels against the clean ground truth, a model trained on those labels would not be expected to exceed it. The authors should explain this anomaly or justify why the comparison is meaningful; as written, it undermines the main claim of improved accuracy under noise.
[Section 2.2, Eq. (3)] The auxiliary loss feeds the segmentor's continuous probability map Pi through Encgae, yet Encgae was trained exclusively on geodesic maps Gi generated from binary labels. Geodesic maps are distance transforms with a large dynamic range and sharp boundaries, while Pi is a softmax output in [0,1]. The paper provides no analysis showing that Encgae(Pi) lies in the feature regime where distances to Encgae(Gi) reflect shape dissimilarity, and no ablation isolates the geodesic encoder from a generic feature-matching regularizer (e.g., replacing Encgae with a randomly initialized frozen encoder, or applying the same loss directly to Pi). Without such evidence, the reported gains may not be attributable to the geodesic prior mechanism.
[Section 2.2 and Fig. 1] The 'prior' is learned from the same labels (clean or noisy) that supervise the segmentor. For the L1 and L2 conditions, the GAE's geodesic inputs and reconstruction targets are generated from the corrupted labels, so the auxiliary loss inherits the same label noise. Calling this a shape prior is therefore not justified. The authors should either reframe the contribution as a learned feature-matching regularizer or provide evidence that the GAE recovers clean shape statistics despite noisy inputs.
[Experiments, Table 1] No variance, confidence intervals, or statistical tests are reported. The average Dice differences between Geodesic Prior and Seg.Net are 0.044, 0.046, and 0.063, but with a single trained model per condition and no error bars, these differences may not be robust. The authors should report means and standard deviations over multiple runs, or provide per-volume significance testing on the 50 test volumes.

minor comments (6)

[Section 2.2] The text 'LV, RV, Mayo' should read 'LV, RV, Myo'.
[Section 2.2] The notation Lrecons appears in the GAE training description while Lrecon is used earlier; please unify.
[Conclusion] The conclusion states the approach 'outperforms the state-of-the-art methods,' but no comparison to state-of-the-art segmentation methods is included in Table 1; this overstates the results.
[Implementation Details] The sentence 'we used 80 MR images for training, the 20 images were used as validation' needs a conjunction or period and should clarify whether these counts refer to volumes or 2D slices.
[Equation (4)] Equation (4) writes 'F(x)|ΔT(x)| = 1' but the surrounding text discusses the gradient of T; please replace ΔT with ∇T for clarity.
[Section 2.2] The bottleneck dimension Lfeat of the GAE is never specified numerically; please report it for reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the geodesic prior is an auxiliary regularizer learned from training labels and evaluated on held-out test data.

full rationale

The paper's central claim is empirical: adding Lgae(Encgae(Pi), Encgae(Gi)) to the segmentation loss improves Dice score. This is evaluated on the held-out ACDC test set (Section 3), not on the training labels used to fit the GAE. The GAE is trained once on geodesic maps Gi=Fgeo(Bi) derived from training labels and then fixed; its encoder features are used only as an auxiliary training signal in Eq. (3). This is supervised regularization, not a prediction of a fitted quantity. There is no self-definitional step: Pi is not defined in terms of Bi, and Gi is not defined in terms of Pi. The learned prior is not independent of the training labels, but that is a modeling limitation (the prior may partly inherit label noise), not circularity; the binary-prior baseline and the external ACDC benchmark provide independent evidence for the mechanism. Self-citations in the related work are not load-bearing: the proposed GAE is novel and does not rest on an unverified uniqueness theorem or ansatz imported from the authors' prior work. The domain-shift concern about Encgae(Pi) versus Encgae(Gi) is a correctness or robustness risk, not circularity, because the auxiliary loss is not equivalent to the segmentation loss by construction. The conclusion's acknowledged limitation about synthetic noise concerns external validity, not circular reasoning. No circular step is exhibited, so the score is 0.

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

The central claim depends on four design choices and assumptions that are not independently established: architecture hyperparameters, the synthetic noise levels, the mapping from distance maps to shapes, and the transfer of GAE features to soft probability maps. No new physical entities are posited.

free parameters (4)

GAE bottleneck feature dimension L_feat = not reported
The length of the encoded feature vector is a free design choice that controls how much shape information the prior can carry; the paper never states its value (Section 2, Eq. 2).
Network growth rate and initial filter count = 16
Chosen 'for an optimal performance after extensive explorations' on the validation set (Section 2.1), so the reported gains include tuning to the validation data.
Synthetic noise levels L1 and L2 = unspecified
The erosion, salt-pepper, and filling operations are described qualitatively (Section 3), but the exact magnitudes of L1 and L2 noise are not given, making the central noisy-label results hard to reproduce or compare.
CRF post-processing parameters = not reported
Conditional Random Field post-processing is mentioned in Section 3 without parameters; it is part of the reported final Dice values.

assumptions (4)

domain assumption Expert ACDC annotations are accurate ground truth for validation
All metrics are computed against these annotations; if they contain errors, the reported Dice and Hausdorff values are shifted.
domain assumption Synthetic boundary noise reproduces inexpert annotation behavior
Section 3 generates weak labels by eroding, adding salt-pepper noise, and refilling; the conclusion explicitly acknowledges that real inexpert annotations were not obtained due to data-sharing regulations.
ad hoc to paper Geodesic maps computed with unit speed and the chosen zero-level sets capture useful shape prior information
This is the paper's central modeling hypothesis (Section 2.2), assumed rather than derived or benchmarked.
ad hoc to paper Features from a GAE trained on binary-derived geodesic maps remain meaningful for continuous probability maps of the segmentor
Equation 3 evaluates Encgae(Pi) and compares it with Encgae(Gi), but the GAE never saw soft probability maps during training.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Weakly Supervised Segmentation by A Deep Geodesic Prior." pith.science (2026). https://pith.science/paper/MSZNSBQQ

@misc{pith2026190806498,
  author       = {Pith},
  title        = {Pith review of: Weakly Supervised Segmentation by A Deep Geodesic Prior},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MSZNSBQQ}},
  note         = {Machine review of arXiv:1908.06498}
}

read the original abstract

The performance of the state-of-the-art image segmentation methods heavily relies on the high-quality annotations, which are not easily affordable, particularly for medical data. To alleviate this limitation, in this study, we propose a weakly supervised image segmentation method based on a deep geodesic prior. We hypothesize that integration of this prior information can reduce the adverse effects of weak labels in segmentation accuracy. Our proposed algorithm is based on a prior information, extracted from an auto-encoder, trained to map objects geodesic maps to their corresponding binary maps. The obtained information is then used as an extra term in the loss function of the segmentor. In order to show efficacy of the proposed strategy, we have experimented segmentation of cardiac substructures with clean and two levels of noisy labels (L1, L2). Our experiments showed that the proposed algorithm boosted the performance of baseline deep learning-based segmentation for both clean and noisy labels by 4.4%, 4.6%(L1), and 6.3%(L2) in dice score, respectively. We also showed that the proposed method was more robust in the presence of high-level noise due to the existence of shape priors.

Figures

Figures reproduced from arXiv: 1908.06498 by the authors.

**Figure 1.** The proposed framework has two main components: (1) segmentation network: assigns a class label to each pixel, and, (2) AE which learns a prior from geodesic maps. Green arrows show the flow of training of the segmentor and red arrows show the flow of training of GAE. Note that in test phase only segmentor is used. Also, the in our method the noisy annotations are used for whole training process. F eatgae contains h… view at source ↗

**Figure 2.** Dense Block (DB) content. C: concatenation operation, BN : Batch normalization, LReLu: Leaky ReLu activation, and 3D conv: 3D convolution with a 3 × 3 × 3 filter. We extend fully convolutional dense nets, called Tiramisu [5], from 2D to fully 3D. The details of the adapted network are shown in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Generating noisy labels. Binary images went through a two-step process of adding pepper noise and filling inside object which makes the boundaries inaccurate. Generating noisy labels: The current annotations at ES and ED in ACDC dataset are considered as expert annotations (as clearly defined by the challenge organizers). Usually, the inexpert annotations include some under-segmentation and/or over-segmentation.… view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

12 extracted references · 9 canonical work pages

[1]

http://www.who.int/mediacentre/factsheets/ fs317/en/ (2007), [Online; accessed 30-June-2017]

Cardiovascular Diseases (cvds). http://www.who.int/mediacentre/factsheets/ fs317/en/ (2007), [Online; accessed 30-June-2017]

work page 2007
[2]

arXiv preprint arXiv:1511.00561 (2015)

Badrinarayanan, V., Kendall, A., Cipolla, R.: Segnet: A deep convolu- tional encoder-decoder architecture for image segmentation. arXiv preprint arXiv:1511.00561 (2015)

arXiv 2015
[3]

Bernard, O., Lalande, A., Zotti, C., Cervenansky, F., Yang, X., Heng, P.A., Cetin, I., Lekadir, K., Camara, O., Ballester, M.A.G., et al.: Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: Is the problem solved? IEEE transactions on medical imaging 37(11), 2514–2525 (2018)

work page 2018
[4]

In: CVPR

Huang, G., Liu, Z., Van Der Maaten, L., Weinberger, K.Q.: Densely connected convolutional networks. In: CVPR. vol. 1, p. 3 (2017)

work page 2017
[5]

In: Com- puter Vision and Pattern Recognition Workshops (CVPRW), 2017 IEEE Confer- ence on

J´ egou, S., Drozdzal, M., Vazquez, D., Romero, A., Bengio, Y.: The one hundred layers tiramisu: Fully convolutional densenets for semantic segmentation. In: Com- puter Vision and Pattern Recognition Workshops (CVPRW), 2017 IEEE Confer- ence on. pp. 1175–1183. IEEE (2017)

work page 2017
[6]

In: Pattern Recognition (ICPR), 2010 20th International Conference on

Kurugol, S., Ozay, N., Dy, J.G., Sharp, G.C., Brooks, D.H.: Locally deformable shape model to improve 3d level set based esophagus segmentation. In: Pattern Recognition (ICPR), 2010 20th International Conference on. IEEE (2010)

work page 2010
[7]

MIDL Conference, ArXiv preprint arXiv:1804.04241 (2018)

LaLonde, R., Bagci, U.: Capsules for object segmentation. MIDL Conference, ArXiv preprint arXiv:1804.04241 (2018)

arXiv 2018
[8]

In: Iberoamerican Congress on Pattern Recognition

Lim, P.H., Bagci, U., Bai, L.: A new prior shape model for level set segmentation. In: Iberoamerican Congress on Pattern Recognition. pp. 125–132. Springer (2011)

work page 2011

Show all 12 references

[9]

IEEE transactions on medical imaging 37(2), 384–395 (2018)

Oktay, O., Ferrante, E., Kamnitsas, K., Heinrich, M., Bai, W., Caballero, J., Cook, S.A., de Marvao, A., Dawes, T., ORegan, D.P., et al.: Anatomically constrained neural networks (acnns): application to cardiac image enhancement and segmen- tation. IEEE transactions on medical...

2018
[10]

In: International Conference on Medical image computing and computer-assisted intervention

Ronneberger, O., Fischer, P., Brox, T.: U-net: Convolutional networks for biomedi- cal image segmentation. In: International Conference on Medical image computing and computer-assisted intervention. pp. 234–241. Springer (2015)

2015
[11]

Journal of graphics tools 9(1), 23–34 (2004)

Telea, A.: An image inpainting technique based on the fast marching method. Journal of graphics tools 9(1), 23–34 (2004)

2004
[12]

IEEE journal of biomedical and health informatics (2018)

Zotti, C., Luo, Z., Lalande, A., Jodoin, P.M.: Convolutional neural network with shape prior applied to cardiac mri segmentation. IEEE journal of biomedical and health informatics (2018)

2018

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

http://www.who.int/mediacentre/factsheets/ fs317/en/ (2007), [Online; accessed 30-June-2017]

Cardiovascular Diseases (cvds). http://www.who.int/mediacentre/factsheets/ fs317/en/ (2007), [Online; accessed 30-June-2017]

work page 2007

[2] [2]

arXiv preprint arXiv:1511.00561 (2015)

Badrinarayanan, V., Kendall, A., Cipolla, R.: Segnet: A deep convolu- tional encoder-decoder architecture for image segmentation. arXiv preprint arXiv:1511.00561 (2015)

arXiv 2015

[3] [3]

Bernard, O., Lalande, A., Zotti, C., Cervenansky, F., Yang, X., Heng, P.A., Cetin, I., Lekadir, K., Camara, O., Ballester, M.A.G., et al.: Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: Is the problem solved? IEEE transactions on medical imaging 37(11), 2514–2525 (2018)

work page 2018

[4] [4]

In: CVPR

Huang, G., Liu, Z., Van Der Maaten, L., Weinberger, K.Q.: Densely connected convolutional networks. In: CVPR. vol. 1, p. 3 (2017)

work page 2017

[5] [5]

In: Com- puter Vision and Pattern Recognition Workshops (CVPRW), 2017 IEEE Confer- ence on

J´ egou, S., Drozdzal, M., Vazquez, D., Romero, A., Bengio, Y.: The one hundred layers tiramisu: Fully convolutional densenets for semantic segmentation. In: Com- puter Vision and Pattern Recognition Workshops (CVPRW), 2017 IEEE Confer- ence on. pp. 1175–1183. IEEE (2017)

work page 2017

[6] [6]

In: Pattern Recognition (ICPR), 2010 20th International Conference on

Kurugol, S., Ozay, N., Dy, J.G., Sharp, G.C., Brooks, D.H.: Locally deformable shape model to improve 3d level set based esophagus segmentation. In: Pattern Recognition (ICPR), 2010 20th International Conference on. IEEE (2010)

work page 2010

[7] [7]

MIDL Conference, ArXiv preprint arXiv:1804.04241 (2018)

LaLonde, R., Bagci, U.: Capsules for object segmentation. MIDL Conference, ArXiv preprint arXiv:1804.04241 (2018)

arXiv 2018

[8] [8]

In: Iberoamerican Congress on Pattern Recognition

Lim, P.H., Bagci, U., Bai, L.: A new prior shape model for level set segmentation. In: Iberoamerican Congress on Pattern Recognition. pp. 125–132. Springer (2011)

work page 2011