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arxiv: 2606.21608 · v1 · pith:EXAY43ZZnew · submitted 2026-06-19 · 💻 cs.CV · q-bio.QM

CurvSegFlow: Time-Conditioned Flow Matching for Robust Segmentation of Curvilinear Structures in Noisy Biomedical Images

Sidi Mohamed Sid'El Moctar , Achraf Ait Laydi , Alexandre Beber , Marcus Braun , Zdenek Lansky , Yousef El Mourabit , Helene Bouvrais This is my paper

Pith reviewed 2026-06-26 14:39 UTC · model grok-4.3

classification 💻 cs.CV q-bio.QM
keywords curvilinear segmentationflow matchingbiomedical imagingmicrotubule segmentationretinal vessel segmentationnoisy imagesiterative refinementvelocity field
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The pith

Time-conditioned flow matching refines noisy initial masks into accurate curvilinear segmentations through a learned velocity field.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that segmentation of thin curvilinear structures can be modeled as a continuous refinement process driven by a time-conditioned velocity field rather than a single forward pass. This matters because single-pass networks frequently break thin filaments or produce disconnected outputs when noise is high and crossings are dense, as occurs in cytoskeletal microscopy. The model uses a U-Net backbone augmented with temporal embeddings and a triple-term loss to learn the velocity field that guides progressive correction from an initial noisy mask toward the target structure. Experiments across synthetic and real microtubule images plus public retinal, corneal, and coronary datasets show gains in precision and continuity, especially at low signal-to-noise ratios, without requiring architecture changes per modality. If the claim holds, flow-based iterative refinement supplies a general route to more stable results on elongated biomedical structures.

Core claim

CurvSegFlow models segmentation as a dynamic process in which a learned velocity field, conditioned on a time parameter, progressively transforms a noisy initialization into the target curvilinear mask. A U-Net backbone supplied with temporal embeddings and trained under a triple-term loss produces the velocity field that drives this refinement across stages. The resulting framework is evaluated on multiple synthetic and real microtubule datasets together with public benchmarks of retinal vessels, corneal nerves, and coronary arteries, where it delivers competitive or superior performance with particular gains in structural continuity under low signal-to-noise conditions.

What carries the argument

time-conditioned flow matching, which defines a velocity field that maps a noisy initial mask to the target segmentation over a continuous time interval

If this is right

  • The method produces consistent gains in precision and structural continuity on microtubule, retinal vessel, corneal nerve, and coronary artery images.
  • Iterative refinement reduces fragmentation at filament crossings and under low signal-to-noise ratios.
  • The same architecture generalizes across imaging modalities without modification.
  • Gradual error correction improves continuity of thin structures that single-pass predictors typically break.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same flow-matching formulation could be tested on other elongated structures such as neuronal processes or plant vasculature without retraining the core components.
  • Because the velocity field operates continuously in time, the approach might support progressive refinement of live or time-lapse sequences where an initial guess improves as more frames arrive.
  • If the learned velocity field truly encodes general error-correction dynamics, the framework may lower the volume of labeled data needed by allowing the model to correct its own early mistakes.

Load-bearing premise

A U-Net backbone with temporal embeddings and a triple-term loss can learn a velocity field that reliably corrects errors across refinement stages without any dataset-specific post-hoc tuning.

What would settle it

Performance on a new dataset with previously unseen noise statistics falls below standard single-pass baselines unless the model receives additional fine-tuning or architectural adjustment.

Figures

Figures reproduced from arXiv: 2606.21608 by Achraf Ait Laydi, Alexandre Beber, Helene Bouvrais, Marcus Braun, Sidi Mohamed Sid'El Moctar, Yousef El Mourabit, Zdenek Lansky.

Figure 1
Figure 1. Figure 1: Diversity of curvilinear structures and imaging modalities across the studied datasets.(Top row) Exemplar images, and (bottom row) their corresponding annotations. From the left to right: MicSim_FluoMT-Simple, MicSim_FluoMT-Complex, SynthMT, MicReal_FluoMT, Revised Higaki 2024, IRM_InVitroMT, DRIVE, CHASEDB1, CORN-1, and ARCADE fields, beginning with a noisy initialization and guided by a dual-loss control… view at source ↗
Figure 2
Figure 2. Figure 2: An overview of the proposed CurvSegFlow model [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Time-conditioned U-Net architecture of CurvSegFlow The network architecture is based on a time-conditioned U-Net (Ho et al., 2020) as shown in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The attention gate connections. Each gate takes two inputs: a gating signal 𝑔 from the decoder and a feature map 𝑥 from the encoder. Both signals are projected to a lower-dimensional space using 1×1 convolutions and normalized. They are then combined and passed through a non-linear activation followed by a sigmoid function to produce an attention map 𝛼 ∈ (0, 1)𝐻×𝑊 . The encoder features are scaled as: ̃𝑥 =… view at source ↗
Figure 5
Figure 5. Figure 5: Segmentation on the MicSim_FluoMT-Simple dataset: (a) Test image, (b) Ground truth, and (c-e) composite predictions from (c) CurvSegFlow, (d) U-Net++, and (e) nnU-Net, where true positives are shown in yellow, false positives in red, and false negatives in green. AUC-PR = 0.9808. Despite being trained on only 100 im￾ages, CurvSegFlow outperformed the foundation models re￾ported in the SynthMT study (Kodden… view at source ↗
Figure 6
Figure 6. Figure 6: Segmentation on the MicSim_FluoMT-Complex dataset: (a) Test image, (b) Ground truth, and (c-e) composite predictions from (c) CurvSegFlow, (d) U-Net++, and (e) nnU-Net, where true positives are shown in yellow, false positives in red, and false negatives in green [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Segmentation on the SynthMT dataset: (a) Test image, (b) Ground truth, and (c) the predictions from CurvSegFlow. for this task, where missing thin or low-intensity filaments is more detrimental than producing a small number of extra detections, notably since these additional detections might be missing annotations. CurvSegFlow also achieved a competitive MCC compared to nnU-Net and U-Net++, and outperforme… view at source ↗
Figure 8
Figure 8. Figure 8: Segmentation on the MicReal_FluoMT dataset: (a) Test image, (b) Ground truth, and (c-e) predictions from (c) CurvSegFlow, (d) U-Net++, and (e) nnU-Net [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Segmentation on the revised Higaki 2024 dataset: (a) Test image, (b) Ground truth, and (c-e) predictions from (c) CurvSegFlow, (d) Synseg, and (e) nnU-Net [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Segmentation on the IRM_InVitroMT dataset: (a,b) Test images: (a) raw, (b) Contrast-enhanced, (c) Ground truths, (d) predictions from CurvSegFlow, and (e) composites, where true positives are shown in yellow, false positives in red, and false negatives in green. : Preprint submitted to Elsevier Page 10 of 19 [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Segmentation on the DRIVE dataset: (a) Test image, (b) Ground truth, and (c-e) predictions from (c) CurvSegFlow, (d) CAR-Unet, and (e) U-Net. gates aligns with the nature of curvilinear structures. In biomedical images such as retinal fundus photographs, corneal nerve maps, or fluorescence microscopy images of microtubules, the structures of interest are thin, elongated, and occupy a small fraction of the… view at source ↗
Figure 12
Figure 12. Figure 12: Segmentation on the CHASE_DB1 dataset: (a) Test image, (b) Ground truth, and (c-e) predictions from (c) CurvSegFlow, (d) CAR-Unet, and (e) ARU-net. the impact of different loss function combinations on the DRIVE dataset. Using MSE alone led to a collapse in seg￾mentation performance, despite a high precision, indicating that the model predicted predominantly background pixels and failed to capture vessel … view at source ↗
Figure 13
Figure 13. Figure 13: Segmentation on the CORN1 dataset: (a) Test image, (b) Ground truth, and (c-d) predictions from (c) CurvSegFlow, and (d) U-Net [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Segmentation on the ARCADE dataset: (a) Test image, (b) Ground truth, and (c) prediction from CurvSegFlow [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: CurvSegFlow trajectory on a DRIVE image: (a) input, (b-f) evolution of the predicted segmentation over time, from an initial noisy state (𝑡=0) to the final prediction (𝑡=1), including intermediate steps at 𝑡= 0.25, 0.33, 0.67, and (g) ground truth. HD95 and clDice scores indicate that CurvSegFlow better preserves structural continuity and reduces fragmentation compared to other architectures, particularly… view at source ↗
read the original abstract

Accurate segmentation of curvilinear structures remains challenging in biomedical imaging due to their thin geometry, complex topology, and sensitivity to noise. This is particularly critical for microscopy images of cytoskeletal network, where low signal-to-noise ratios and dense filament crossings often lead to fragmented or inaccurate segmentation. In this work, we propose CurvSegFlow, a segmentation framework based on time-conditioned flow matching. Instead of predicting a segmentation mask in a single pass, the method models segmentation as a dynamic process that progressively refines a noisy initialization into the target structure through a learned velocity field. The proposed model combines a U-Net backbone with triple-term loss function and temporal embeddings to guide the refinement process across reconstruction stages. This formulation enables gradual error correction and improves the continuity of thin structures. CurvSegFlow is evaluated on multiple synthetic and real microtubule datasets, as well as on public benchmarks of retinal vessels, corneal nerves and coronary arteries. Across datasets, the method achieves competitive or superior performance compared to established segmentation models, with consistent improvements in precision and structural continuity, particularly under low signal-to-noise conditions. These results show that flow-based iterative refinement provides a robust and general framework for curvilinear structure segmentation. Overall, the proposed approach improves segmentation quality in challenging imaging conditions and generalizes effectively across modalities without architectural changes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript proposes CurvSegFlow, a segmentation framework that models curvilinear structure segmentation as a dynamic, time-conditioned flow matching process. A U-Net backbone augmented with temporal embeddings and a triple-term loss learns a velocity field that iteratively refines a noisy initialization into the target mask. The method is evaluated on synthetic and real microtubule datasets plus public benchmarks for retinal vessels, corneal nerves, and coronary arteries, with claims of competitive or superior performance in precision and structural continuity, especially under low SNR, and effective generalization across modalities without architectural changes.

Significance. If the experimental results, ablations, and visualizations hold, the work provides a generalizable iterative refinement strategy for thin-structure segmentation in noisy biomedical images. The flow-matching formulation for progressive error correction on curvilinear topologies could be of interest to the biomedical CV community as an alternative to single-pass or post-processing-heavy approaches.

minor comments (2)
  1. [Abstract] Abstract: the triple-term loss is described only at a high level; a brief enumeration of the three terms (or reference to the equation that defines them) would improve readability for readers who encounter the abstract first.
  2. [Abstract] The claim that the framework 'generalizes effectively across modalities without architectural changes' would be strengthened by an explicit statement of the training protocol (e.g., whether the same hyper-parameters and temporal embedding schedule are used on all datasets).

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. The referee's description of the method and results is accurate.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The abstract and visible description present CurvSegFlow as a modeling choice: a U-Net backbone augmented with temporal embeddings and a triple-term loss to learn a time-conditioned velocity field that iteratively refines an initial noisy mask. No equations, fitted parameters, self-citations, or derivation steps are supplied that reduce any claimed prediction or uniqueness result to the inputs by construction. The central claim of flow-based iterative refinement therefore remains an independent architectural proposal rather than a tautological restatement of fitted quantities or prior self-referential results. This is the expected non-finding for a high-level methods description lacking explicit mathematical reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no free parameters, axioms, or invented entities are explicitly stated or derivable from the given text.

pith-pipeline@v0.9.1-grok · 5804 in / 1054 out tokens · 26889 ms · 2026-06-26T14:39:21.822498+00:00 · methodology

discussion (0)

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