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REVIEW 4 major objections 6 minor 55 references

EDMB: Edge Detector with Mamba

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A Mamba-based edge detector reaches top BSDS500 accuracy while generating multi-granularity edges without multi-label data.

desk verdict Solid Mamba-based edge detector with competitive single-granularity results, but the multi-granularity claim rests on unvalidated learned variance and test-set-selected gamma. read the letter →

arxiv 2501.04846 v1 pith:C75U6HFH submitted 2025-01-08 cs.CV

Yachuan Li , Xavier Soria Poma , Yun Bai , Qian Xiao , Chaozhi Yang , Guanlin Li , Zongmin Li This is my paper · ORCID
classification cs.CV
keywords edgedetectionMambastatespacemodelmulti-granularityedgesevidencelowerboundlearnableGaussiandistributionssingle-labellearningBSDS500
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

This paper tries to show that a vision-Mamba backbone can replace the Transformer in edge detection without sacrificing accuracy, and that multi-granularity edges do not require multiple human label sets. It reports an edge detector, EDMB, that reaches an ODS F-measure of 0.837 on BSDS500 at single granularity and 0.851 when granularity is varied, using no multi-scale testing and no extra PASCAL-VOC data. The same detector works on single-label datasets NYUDv2 and BIPED, where prior multi-granularity methods could not be applied. If true, this makes high-quality edge detection cheaper and makes granularity control available for datasets annotated by only one person.

What carries the argument

The load-bearing object is the learnable Gaussian distributions (LGD) decoder. It turns fused global, fine-grained, and high-resolution features into per-pixel parameters $(\mu, \sigma^2)$; the edge map is a sample from $\mathcal{N}(\mu, \sigma^2)$, and granularity is controlled by the scalar formula $p_\gamma = \mu + \gamma \sigma^2$. The ELBO loss—a weighted cross-entropy term for the sample plus a KL term that regularizes each pixel distribution toward $\mathcal{N}(0,1)$—is what lets one binary label supervise the variance, removing the need for multiple human annotations. Without this decoder, the network still detects edges but cannot produce multi-granularity outputs.

What would settle it

Train EDMB on BSDS500 and inspect the learned $\sigma^2$: if the average variance on edge pixels is not larger than on non-edge pixels, or if it does not correlate with the spread of human annotations across the 4–9 ground-truth maps, then the learned distribution is not encoding edge uncertainty and the multi-granularity claim fails. A simpler check is to fix $\gamma$ at several values and compute the mean distance between the resulting edge maps; near-zero distance means $\gamma$ does not control granularity.

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Extended reading notes

Core claim

EDMB's central claim is that Mamba's selective state-space model can serve as the core of a state-of-the-art edge detector when paired with a global-local architecture and a probabilistic decoder. The network uses a global Mamba encoder for long-range context, a fine-grained Mamba encoder over non-overlapping windows for local detail, and a lightweight CNN high-resolution encoder to preserve precise location information. A learnable Gaussian distributions decoder fuses these features to predict per-pixel means and variances, and multi-granularity edges are obtained by sampling $p_\gamma = \mu + \gamma \sigma^2$. The Evidence Lower Bound loss—weighted cross-entropy on a sampled edge map plus a KL divergence pushing each pixel distribution toward $\mathcal{N}(0,1)$—supervises the distribution so that a single binary label is enough. The paper reports ODS 0.837/0.851 on BSDS500 without multi-scale testing or extra PASCAL-VOC data, and ODS 0.783 on NYUDv2 and 0.906 on BIPED for the multi-granularity version, claiming the first Mamba-based edge detector and the first multi-granularity edge results on single-label datasets.

Load-bearing premise

The multi-granularity capability rests on the assumption that a per-pixel Gaussian variance, learned from a single binary edge label through the ELBO loss, actually captures meaningful edge uncertainty; if the variance is degenerate or unrelated to annotation disagreement, the granularity slider $p_\gamma = \mu + \gamma \sigma^2$ produces no real granularity variation.

Editorial extensions

If this is right

  • Mamba can replace Transformers in edge detection: on BSDS500, EDMB reports a higher ODS than DiffusionEdge while using roughly one-third the parameters and about half the GFLOPs.
  • Multi-granularity edge maps become available on single-label datasets such as NYUDv2 and BIPED, removing a previous dependency on multiple human annotations.
  • Granularity is controlled at inference time by one scalar $\gamma$, so a single trained model can serve tasks that want coarse boundaries or fine detail without retraining.
  • The reported gains on BSDS500 are achieved without multi-scale testing or extra PASCAL-VOC data, so they come from the architecture and loss rather than test-time augmentation.

Reading between the lines

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

  • If the learned variance truly reflects per-pixel edge uncertainty, the same $\sigma^2$ could guide active re-annotation by pointing at pixels where annotators most disagree; the paper does not explore this use.
  • The $\gamma$ schedule is selected after evaluating several schedules and reporting the best ODS on the test set; a stricter protocol that fixes $\gamma$ on validation data would be needed to know whether the 0.851 multi-granularity number is robust.
  • Because the ELBO head resembles a variational autoencoder, a natural extension is to condition $\gamma$ on a task embedding so downstream systems could request coarse or fine edges explicitly instead of tuning a scalar.
  • A promising test of the method's generality is to apply it to domains with deliberately coarse annotation styles, such as medical or remote-sensing boundaries, where multi-label training data is rarely available.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper proposes EDMB, an edge detector built on vision Mamba, combining a global Mamba encoder, a fine-grained Mamba encoder, and a lightweight CNN high-resolution encoder. A decoder predicts per-pixel Gaussian distributions N(mu, sigma^2), supervised by an ELBO loss composed of a weighted cross-entropy term and a KL divergence to N(0,1). Multi-granularity edges are generated as p_gamma = mu + gamma*sigma^2. Experiments on BSDS500, NYUDv2, and BIPED report single-granularity ODS 0.837 and multi-granularity ODS 0.851 on BSDS500, with further multi-granularity results on single-label datasets. The paper claims to be the first Mamba-based edge detector and the first to produce multi-granularity edges without multi-label training data.

Significance. If the reported results are sound, EDMB is significant in two respects: it demonstrates that a Mamba-based backbone can reach the top of the BSDS500 leaderboard without multi-scale testing or extra PASCAL-VOC data, and it extends multi-granularity edge generation to single-label datasets, removing the multi-label-data requirement of prior work such as UAED and MuGE. The paper is also commendable for providing source code, an honest ablation showing that the proposed decoder alone does not improve single-granularity accuracy, and a correct closed-form KL divergence in Eq. (8). The main risk is that the central multi-granularity claim rests on an unvalidated learned variance and on a gamma schedule chosen directly from test-set performance; these issues need to be resolved before the significance can be fully assessed.

major comments (4)
  1. [Section 4.3, Table 3] The text states that on BIPED "EDMB* achieves 0.924 ODS, which is the new SOTA method and 0.7% higher than the second best DiffusionEdge," but Table 3 reports EDMB* ODS of 0.906 and DiffusionEdge ODS of 0.899 for BIPED. The two numbers (0.924 and 0.906) are inconsistent, and the claimed 0.7% improvement matches the 0.906 vs. 0.899 difference, not the 0.924 value. Please correct this inconsistency and, if 0.924 was obtained under a different evaluation setting, describe that setting explicitly.
  2. [Section 3.6, Eq. (14), Table 5] The headline multi-granularity ODS of 0.851 on BSDS500 is obtained by selecting the gamma schedule "Random n/2 - 5" from Table 5, which reports test-set ODS values between 0.845 and 0.851 for different schedules. No held-out validation set is used to select gamma, so the reported improvement from single-granularity 0.837 to multi-granularity 0.851 may reflect test-set overfitting rather than a genuine granularity-control benefit. Please report how gamma was selected (e.g., on a validation split) and, ideally, the variance of the results over multiple runs.
  3. [Sections 3.4-3.6, Eq. (14)] The multi-granularity mechanism assumes that the learned per-pixel variance sigma^2 encodes meaningful edge uncertainty, so that p_gamma = mu + gamma*sigma^2 produces genuine granularity variation. The paper does not provide any direct evidence for this: no statistics on the learned sigma^2 (e.g., whether it is spatially structured or nearly constant), no correlation with per-pixel annotator disagreement on BSDS500, and no ablation that replaces sigma^2 with a constant or a hand-crafted uncertainty proxy. If sigma^2 is degenerate, Eq. (14) reduces to a global bias and the claimed ability to control granularity on single-label data does not follow. Please add such validation analyses.
  4. [Section 3.5, Eq. (10)] The ELBO loss depends on "a sampling p of the distributions," but the paper does not state how p is sampled during training, e.g., whether the reparameterization trick is used, how many samples are drawn per iteration, or whether the sampling is performed on the full-resolution output. This implementation detail is essential for reproducing the training procedure and for the claim that Eq. (10) is a valid ELBO. Please clarify the sampling procedure in the implementation details.
minor comments (6)
  1. [Eq. (8)] The integral derivation of the KL divergence is malformed in the typeset text (missing integral signs and unclear exponent placement). The final closed form is correct, but the derivation should be typeset properly for readability.
  2. [Section 3.6] The term "sampling" is used both for random draws from the Gaussian during training and for the deterministic operation in Eq. (14), which may confuse readers. Consider using "granularity modulation" or "deterministic shifting" for the inference-time operation.
  3. [Section 4.3, Table 3] The text says EDMB* "can match" RankED on NYUDv2, but Table 3 shows EDMB* ODS 0.783 above RankED's 0.780; this could be phrased more precisely as a slight improvement.
  4. [Section 4.3] The statement that ODS and OIS are improved by "0.3%" over DiffusionEdge should say "0.3 percentage points" (i.e., 0.003 in the reported metrics), to avoid ambiguity between relative and absolute improvement.
  5. [Figure 3] The caption of Figure 3 appears to be duplicated, and some subfigure labels (e.g., (g), (m)) are repeated. Please clean up the figure caption and subfigure numbering.
  6. [Section 1] The claim that EDMB is "the first Mamba-based edge detector" should be verified against concurrent work, since the field is rapidly evolving; if any prior Mamba-based edge detector exists, the claim should be adjusted.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the multi-granularity formula and ELBO loss are standard/external, and the empirical benchmark claims are self-contained.

full rationale

The paper's derivation chain is self-contained and not circular. The learnable Gaussian decoder (Sec. 3.4, Eq. 7) predicts means and variances from global and fine-grained features; the ELBO loss (Sec. 3.5, Eq. 10) combines a standard closed-form KL divergence (Eq. 8) with a weighted cross-entropy term (Eq. 9); multi-granularity outputs are then obtained by the explicitly inherited shift rule p_gamma = mu + gamma sigma^2 (Eq. 14), which the paper attributes to the external MuGE method [53], not to the authors' own prior work. No equation defines its output in terms of the reported ODS/OIS numbers, and no fitted parameter is relabeled as a prediction. The only self-citations ([27], [37], [38] by co-author Xavier Soria Poma) concern dataset details and implementation practice and are not load-bearing for the central novelty. The main weaknesses are empirical rather than circular: the learned variance sigma^2 is not directly validated as encoding per-pixel uncertainty, and the headline multi-granularity ODS 0.851 in Table 5 is obtained by selecting the best gamma schedule on the BSDS500 test set. These are validation/test-selection concerns, not reductions of the claimed result to its inputs. The appended limitation statement notes a lack of downstream-task discussion, which is a scope limitation, not a circular step.

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

The load-bearing pieces of the multi-granularity claim are imported from prior work: the granularity formula comes from MuGE, and the Gaussian distribution idea from UAED. The paper's own contribution is the combination with Mamba and the ELBO supervision for single-label data. No new physical or mathematical entities are introduced.

free parameters (4)
  • lambda (WCE balance) = 1.1 (BSDS500/BIPED), 1.3 (NYUDv2)
    Weights positive vs negative samples in the weighted cross-entropy; set per dataset following prior work.
  • phi (KL weight in ELBO loss) = not reported
    Balances reconstruction and KL terms in Eq. 10; no value or tuning procedure is given in the paper.
  • alpha2 (auxiliary ELBO weight) = 0.4
    Weight for the fine-grained auxiliary loss in Eq. 13.
  • gamma (granularity control) = n/2 - 5, n in {0..10} for the best result
    Controls edge granularity in Eq. 14; the reported 0.851 ODS is chosen from several schedules in Table 5, i.e., selected on the test set.
assumptions (4)
  • domain assumption Edge granularity can be controlled by p_gamma = mu + gamma * sigma^2
    Taken directly from MuGE [53]; the paper does not derive or independently validate this mapping for its own learned distributions.
  • ad hoc to paper A single binary label plus ELBO loss yields a meaningful per-pixel variance
    Central assumption in Sec. 3.5 that makes multi-granularity work on single-label data; supported only by qualitative figures and test-set-selected ODS.
  • domain assumption Vision Mamba (ViM) is an effective backbone for edge detection
    The encoder follows ViM [55] and relies on its ImageNet pre-training and selective-scan design.
  • standard math The closed-form KL divergence between two Gaussians is correct
    Eq. 8 is the standard result; the integrals are correct despite typographical garbling in the rendering.

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Cite this review

Pith. "Pith review of EDMB: Edge Detector with Mamba." pith.science (2026). https://pith.science/paper/C75U6HFH

@misc{pith2026250104846,
  author       = {Pith},
  title        = {Pith review of: EDMB: Edge Detector with Mamba},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C75U6HFH}},
  note         = {Machine review of arXiv:2501.04846}
}
read the original abstract

Transformer-based models have made significant progress in edge detection, but their high computational cost is prohibitive. Recently, vision Mamba have shown excellent ability in efficiently capturing long-range dependencies. Drawing inspiration from this, we propose a novel edge detector with Mamba, termed EDMB, to efficiently generate high-quality multi-granularity edges. In EDMB, Mamba is combined with a global-local architecture, therefore it can focus on both global information and fine-grained cues. The fine-grained cues play a crucial role in edge detection, but are usually ignored by ordinary Mamba. We design a novel decoder to construct learnable Gaussian distributions by fusing global features and fine-grained features. And the multi-grained edges are generated by sampling from the distributions. In order to make multi-granularity edges applicable to single-label data, we introduce Evidence Lower Bound loss to supervise the learning of the distributions. On the multi-label dataset BSDS500, our proposed EDMB achieves competitive single-granularity ODS 0.837 and multi-granularity ODS 0.851 without multi-scale test or extra PASCAL-VOC data. Remarkably, EDMB can be extended to single-label datasets such as NYUDv2 and BIPED. The source code is available at https://github.com/Li-yachuan/EDMB.

Figures

Figures reproduced from arXiv: 2501.04846 by the authors.

Figure 1
Figure 1. The EDMB’s framework. N(µ, σ2 ) means learnable Gaussian distributions, where the means µ and variances σ 2 are predicted by the mean decoder and variance decoder, respectively. Mamba. To date, modeling Mamba’s long-range and short￾range dependencies simultaneously and efficiently remains an open problem. The computational efficiency of Mamba is between Transformer and CNN. To further improve the efficiency of the m… view at source ↗
Figure 2
Figure 2. The detailed architecture of the LGD decoder. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Qualitative comparisons on challenging samples in the BSDS500 test set. MuGE produces diverse results with edge granularity [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Results of different multi-label handling methods. The [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

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Pith tools

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