Topo-VM-UNetV2: Encoding Topology into Vision Mamba UNet for Polyp Segmentation

Bin Fu; Diego Adame; Fabian Vazquez; Haoteng Tang; Huimin Li; Jose A. Nunez; Nayeli Gurrola; Pengfei Gu

REVIEW 3 major objections 5 minor 28 references

Topo-VM-UNetV2: Encoding Topology into Vision Mamba UNet for Polyp Segmentation

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Persistence-based attention maps improve Mamba U-Net polyp segmentation on five public datasets.

desk verdict Consistent empirical gains, but the topology story is likely wrong; needs revision before it should be trusted. read the letter →

arxiv 2505.06210 v1 pith:7XVOVBCF submitted 2025-05-09 eess.IV cs.CV

Diego Adame , Jose A. Nunez , Fabian Vazquez , Nayeli Gurrola , Huimin Li , Haoteng Tang , Bin Fu , Pengfei Gu This is my paper · ORCID

classification eess.IVcs.CV

keywords polypsegmentationpersistenthomologytopologyattentionMambastatespacemodelsVM-UNetV2medicalimage

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 show that encoding topological features into a Mamba U-Net improves polyp segmentation beyond what the base architecture achieves. It proposes a two-stage method: first train VM-UNetV2 to produce probability maps, convert those maps into topology attention maps via persistent homology, then re-train the network with those attention maps integrated into its feature-fusion module. The claim is that this yields state-of-the-art Dice, IoU, and MAE scores on all five datasets, with up to a 3.29% DSC improvement over VM-UNetV2 on ETIS. If correct, it shows that persistence-based topology is a useful, cheaply computable prior for medical image segmentation.

What carries the argument

The central mechanism is the Topo-SDI module: a per-scale Hadamard product between the encoder's features (after CBAM attention and a 1x1 convolution) and a resized topology attention map, followed by the same resolution-aligned multi-scale fusion as the original SDI. The attention map itself is built from a persistence diagram: significant 0- and 1-dimensional features of a probability map are selected by a 50th-percentile filter, each feature's persistence value is placed at the pixel(s) whose filtration value is 'very close' to the feature's birth value, and the resulting score map is sigmoid-activated into [0,1].

What would settle it

Recompute the topology attention maps while sweeping the 'very close' tolerance and the 50th-percentile significance filter across a coarse grid; if the reported Dice gains vanish or the maps reduce to generic edge detectors on synthetic images with known component counts, the improvement does not stem from persistent homology.

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Extended reading notes

Core claim

Topo-VM-UNetV2 claims that replacing the plain SDI module in VM-UNetV2 with a topology-guided version that multiplies each multi-scale feature map by a persistence-derived attention map consistently improves polyp segmentation. The attention maps are generated by computing persistence diagrams of the model's probability maps under a sublevel filtration, filtering to the top 50% by persistence, assigning each surviving feature's persistence value to its birth location, and passing those scores through a sigmoid. The paper reports that this addition outperforms VM-UNetV2 on all five datasets and also beats a control in which raw probability maps, rather than topology-derived maps, are used for the same attention mechanism.

Load-bearing premise

The method assumes that the pixels whose probability values are very close to a topological feature's birth value are exactly where that feature is born, yet that tolerance is never defined and a sublevel filtration actually births a 0-dimensional component at a single local minimum pixel, not across a plateau.

Editorial extensions

If this is right

The reported gains suggest that a lightweight topological prior computed once per image can sharpen boundaries and reduce false positives without changing the backbone or the inference-time architecture.
The same Topo-SDI idea could be grafted onto other U-Net-style segmenters, since the attention maps are model-agnostic once probability maps exist.
Because the topology maps are computed offline in Stage 1, adding them does not increase the model's parameter count or inference cost during deployment.
The method's behavior on hard datasets such as ETIS and ColonDB indicates the largest payoff appears exactly where the base model struggles most with under- and over-segmentation.
The ablation against PM-SDI, where raw probability maps replace the topology maps, indicates that the improvement comes from persistence information rather than from simply adding any auxiliary spatial signal.

Reading between the lines

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

The same persistence-to-attention recipe might transfer to other medical imaging tasks like tumor or organ segmentation, where boundary accuracy and the number of connected components are clinically meaningful.
A natural testable extension is to sweep the 'very close' tolerance and the 50th-percentile filter per dataset; if the improvements are stable across a wide range, the method is robust, and if they collapse, the reported gains may be implementation-specific.
The attention mechanism effectively acts as a boundary-and-structure prior, so it could be combined with other priors such as shape constraints or anatomical atlases to push further.
One implicit consequence is that the quality of the Stage-1 probability maps bounds the quality of the topology; retraining Stage 1 with better segmenters might yield even larger gains.

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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: this is a competent engineering paper with consistent DSC gains, but the topology story is probably wrong. The sublevel filtration maps birth locations to low-probability background minima, not to the polyp, so the attention maps may be a boundary/background signal. The gains over VM-UNetV2 are still real, but they may come from the extra probability-map conditioning rather than from topology. The paper deserves peer review because the empirical result is worth checking, but it needs major revision.

What's new: the specific design of computing persistence diagrams from a trained model's probability maps, thresholding persistence at the 50th percentile, mapping persistence to birth pixels, and injecting the result into the SDI module of VM-UNetV2. The ablation against PM-SDI is a reasonable control, and the gains are consistent across five datasets. The computational cost is reported (187 seconds for 1450 images), which is useful.

The soft spots: first, the filtration direction. The paper explicitly constructs a sublevel filtration: pixels activate when p_ij <= t_n. Under that filtration, 0D homology classes are born at local minima of the probability map, which are typically background regions. The birth-location mapping then assigns high persistence to those background minima, not to the polyp. The paper's Figure 5 shows attention at boundaries, which is consistent with a boundary artifact rather than a genuine topological signal. This is not a minor concern; it undercuts the paper's central claim that topology is being encoded. The authors should re-run with a superlevel filtration (or at least justify why sublevel minima are the right birth locations), and they should define the 'closely match' tolerance.

Second, the evaluation is missing error bars. They ran five seeds but only report averages, with no standard deviations or significance tests. Some of the reported differences are small (e.g., PM-SDI vs Topo-SDI on ClinicDB is 0.79 DSC points), and without variance we cannot tell whether the topology part contributes meaningfully.

Third, no code is released, and the persistence threshold (50th percentile) and sigmoid scaling are not sensitivity-tested. The claim of SOTA is also overstated given that they compare against only four baselines.

Who this is for: anyone working on topology-aware segmentation will be interested, but should read the ablation table with care. It is a useful empirical data point, not a settled method.

Recommendation: send to peer review, but require the authors to fix or reframe the filtration issue, add error bars/significance tests, release code, and run a sensitivity analysis. If the gains survive those changes, the paper becomes a solid application; if not, it is a cautionary tale about conflating extra inputs with topological understanding.

Referee Report

3 major / 5 minor

Summary. The paper proposes Topo-VM-UNetV2, a two-stage method for polyp segmentation that injects topology-aware attention into VM-UNetV2, a Mamba-based U-Net. In Stage 1, a trained VM-UNetV2 produces probability maps (PMs) for training and test images; these PMs are then processed via persistent homology to generate topology attention maps. The pipeline constructs a sublevel filtration of each PM, computes persistence diagrams for 0- and 1-dimensional features, filters features by persistence at the 50th percentile, assigns each surviving feature's persistence to its birth-location pixels, and applies a sigmoid to obtain attention weights in [0,1]. In Stage 2, these maps are multiplied with the multi-scale features inside the SDI module of VM-UNetV2, forming a Topo-SDI module. Experiments on Kvasir-SEG, ClinicDB, ColonDB, ETIS, and CVC-300 report consistent DSC, IoU, and MAE improvements over VM-UNetV2, with the largest gain on ETIS (3.29% DSC). An ablation compares Topo-SDI against a PM-SDI variant that uses sigmoid-transformed raw PMs as attention maps, showing larger gains for Topo-SDI. The authors state that each experiment is run five times with different seeds, but only averaged results are reported.

Significance. If the mechanism is correct, the work is a useful and inexpensive way to incorporate global topological structure into Mamba-based segmentation networks, and it addresses a recognized limitation of SSM architectures in capturing connected components and loops. The main strengths are the clear two-stage design, the evaluation across five public datasets with consistent gains, the inclusion of a PM-SDI ablation as a first-step control for the extra probability-map input, and the reporting of topology-attention computation cost. These elements make the empirical claim concrete and reproducible if code is released. The principal risk is that the topology attention maps may not actually encode the polyp's topology, because the birth-location heuristic in the sublevel filtration is conceptually questionable and empirically unvalidated; this concern must be resolved before the contribution can be fully credited.

major comments (3)

[II-A2, Steps 1-3] The sublevel filtration defined in Step 1 activates pixels when p_ij <= t_n, so 0-dimensional homology classes are born at local minima of the probability map. In polyp segmentation, these minima are located in the background, not on the polyp. The birth-location mapping in Step 3 then assigns persistence values to 'cells whose filtration values closely match the feature's birth value,' but for a 0D class the birth cell is a single local-minimum pixel or a tied plateau, not a band of close-valued pixels, and the matching tolerance is never defined. Consequently, the topology attention maps may highlight background minima rather than polyp structures, which would mean the reported gains do not come from encoding polyp topology. Please validate this step by (i) overlaying birth locations on the PMs, (ii) re-running the pipeline with a superlevel filtration (activating p_ij >= t_n, where 0D classes are born at local maxima), or (iii) otherwise demonstrating that the birth-localization heuristic is correct for the claimed purpose.
[II-A2, Step 3 and Table II] The persistence significance filter is fixed at the 50th percentile with no sensitivity analysis, and the PM-SDI ablation does not isolate the persistence geometry. PM-SDI uses a smooth sigmoid of the raw PM, whereas the topology maps, as the paper's own Fig. 5 states, emphasize boundaries and transitions; the observed Topo-SDI gains could therefore arise from a boundary-emphasis or high-frequency signal rather than from persistent homology. Please add at least one additional control whose spatial distribution matches the topology maps but whose values are not persistence-derived (e.g., an edge-filtered or randomly shuffled version of the same attention maps), and report results across a small grid of persistence thresholds (e.g., 40th, 50th, 60th percentiles) to show the 50th percentile choice is not load-bearing.
[III-B and Table I] The manuscript reports that each experiment is run five times with different seeds, but Table I and Table II list only point estimates with no standard deviations, confidence intervals, or significance tests. Given that the gains on Kvasir-SEG (1.20% DSC) and ClinicDB (1.76% DSC) are small relative to typical seed-to-seed variability in medical segmentation models, the claim of consistent improvement is not statistically supported as presented. Please report per-seed results or standard deviations, and, if possible, paired statistical tests between Topo-SDI and VM-UNetV2 on the same data splits.

minor comments (5)

[III-C / Table I] The comparison table omits PraNet, SANet, and Polyp-PVT with only a sentence explaining that U-Net v2 already outperforms them; please state this explicitly in the table caption or in the main text so readers do not interpret the table as a complete SOTA comparison.
[Fig. 3 caption] The caption says 'As the threshold value increases or decreases,' but the sublevel filtration only uses an increasing threshold; please adjust the wording to avoid ambiguity.
[III-E] The computational complexity section reports wall-clock time for 1450 images but not the per-image breakdown or the memory footprint; adding those details would make the cost claim easier to assess.
[II-A2] The terms 'sub-level' and 'sublevel' are used inconsistently; please use one spelling throughout.
[References] Reference [22] is formatted inconsistently with the other entries (missing conference/journal and year formatting); please check the bibliographic style.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central claim is an empirical benchmark comparison, and the topology-attention input is not by construction equal to the predicted segmentation.

full rationale

The paper's derivation chain is empirical rather than analytic. Stage 1 trains VM-UNetV2 to produce probability maps, then computes persistence diagrams of those probability maps via a sublevel filtration, assigns persistence values to birth locations, and applies a sigmoid to obtain attention maps. Stage 2 inserts those maps into the SDI module of the same architecture and retrains. The reported gains are benchmark results, not consequences of an equation that reuses its own output. The ablation PM-SDI is a direct control for the extra probability-map input: feeding sigmoid(PM) as attention yields only small gains, whereas Topo-SDI yields larger gains, so the improvement is not forced by construction. Although the attention maps are computed from the model's own probability maps, this is a standard self-conditioning input rather than a fitted parameter renamed as a prediction; the final segmentation is not equal to the probability map or to a persistence transform of it. The undefined 'very close' tolerance in Birth Location Mapping and the untested 50th-percentile filter are potential correctness risks, but they are heuristic implementation choices, not circular steps. Cited prior work supplies the baseline architecture, the SDI module, and the persistent-homology background, and the authors' earlier self-citations are not load-bearing for the central claim. No specific reduction of a prediction to its own input by construction is present, so the circularity score is 0.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests mainly on the choice of persistence threshold, the unspecified birth-location matching tolerance, the sigmoid transform, and the assumption that a VM-UNetV2 probability map is a trustworthy substrate for topology extraction. No new physical or conceptual entities are postulated; the attention maps are computed from existing probability maps.

free parameters (3)

Persistence significance threshold (percentile) = 50th percentile
The paper filters persistence values at the 50th percentile to retain significant features; this threshold is not justified and no sensitivity analysis is given.
Birth-location matching tolerance = Not specified
The paper assumes cells with filtration values 'very close' to the birth value are birth locations, but no tolerance is defined.
Sigmoid scaling for persistence scores = Not specified
Raw persistence values are passed through a sigmoid, but no scaling or normalization is described, so the attention weights depend on an unspecified transform.

assumptions (6)

domain assumption Persistent homology on sublevel filtrations of probability maps captures topologically meaningful polyp structures.
The paper assumes that persistent features in the probability map correspond to relevant polyp topology; this is stated in Section II-A2 and supported only by qualitative examples.
ad hoc to paper Birth locations of topological features can be recovered as pixels with probability values close to the feature's birth value.
Section II-A2 Step 2 states this closeness assumption without defining a tolerance or justifying it theoretically.
ad hoc to paper The 50th percentile persistence filter separates significant topology from noise.
Section II-A2 Step 3 uses this cutoff without sensitivity analysis or per-dataset justification.
domain assumption The sigmoid of persistence scores maps to useful attention weights in [0,1].
Used in Section II-A2 Step 4; no scaling or normalization is specified, yet this mapping determines the attention values.
standard math The Gudhi library computes correct persistence diagrams for cubical complexes.
The paper reports using Gudhi in Section III-E; correctness of the library is a background assumption.
domain assumption Stage 1 probability maps generated by VM-UNetV2 are reliable enough for computing topology attention maps.
The two-stage design in Section II-A1 uses VM-UNetV2's outputs as the only source for attention maps; if those probability maps are poor, the attention signal is poor.

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Cite this review

Pith. "Pith review of Topo-VM-UNetV2: Encoding Topology into Vision Mamba UNet for Polyp Segmentation." pith.science (2026). https://pith.science/paper/7XVOVBCF

@misc{pith2026250506210,
  author       = {Pith},
  title        = {Pith review of: Topo-VM-UNetV2: Encoding Topology into Vision Mamba UNet for Polyp Segmentation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7XVOVBCF}},
  note         = {Machine review of arXiv:2505.06210}
}

read the original abstract

Convolutional neural network (CNN) and Transformer-based architectures are two dominant deep learning models for polyp segmentation. However, CNNs have limited capability for modeling long-range dependencies, while Transformers incur quadratic computational complexity. Recently, State Space Models such as Mamba have been recognized as a promising approach for polyp segmentation because they not only model long-range interactions effectively but also maintain linear computational complexity. However, Mamba-based architectures still struggle to capture topological features (e.g., connected components, loops, voids), leading to inaccurate boundary delineation and polyp segmentation. To address these limitations, we propose a new approach called Topo-VM-UNetV2, which encodes topological features into the Mamba-based state-of-the-art polyp segmentation model, VM-UNetV2. Our method consists of two stages: Stage 1: VM-UNetV2 is used to generate probability maps (PMs) for the training and test images, which are then used to compute topology attention maps. Specifically, we first compute persistence diagrams of the PMs, then we generate persistence score maps by assigning persistence values (i.e., the difference between death and birth times) of each topological feature to its birth location, finally we transform persistence scores into attention weights using the sigmoid function. Stage 2: These topology attention maps are integrated into the semantics and detail infusion (SDI) module of VM-UNetV2 to form a topology-guided semantics and detail infusion (Topo-SDI) module for enhancing the segmentation results. Extensive experiments on five public polyp segmentation datasets demonstrate the effectiveness of our proposed method. The code will be made publicly available.

Figures

Figures reproduced from arXiv: 2505.06210 by the authors.

**Figure 2.** The pipeline of our proposed framework. (a) Stage 1: VM-UNetV2 [ [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Illustrating the sub-level filtration process. (a) An example image and its probability map generated by VM-UNetV2. (b) Four thresholded binary [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Examples of segmentations from five polyp segmentation datasets. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Examples of different attention maps computed from probability maps. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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