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arxiv: 2504.15770 · v1 · submitted 2025-04-22 · 💻 cs.CV

Multi-Scale Tensorial Summation and Dimensional Reduction Guided Neural Network for Edge Detection

Lei Xu , Mehmet Yamac , Mete Ahishali , Moncef Gabbouj This is my paper

Pith reviewed 2026-05-22 18:21 UTC · model grok-4.3

classification 💻 cs.CV
keywords edge detectionneural networksmulti-scale tensorial summationdimensional reductioncomputer visiondeep learningimage processing
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The pith

A neural network for edge detection applies multi-scale tensorial summation followed by dimensional reduction blocks to discard redundant subspaces early and focus on essential edge features.

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

The paper proposes MTS-DR-Net, a new architecture that integrates multi-scale tensorial summation layers to create large receptive fields from the very first layers without building deep stacks. It then inserts MTS-DR blocks that perform dimensional reduction by removing redundant information, letting the network attend only to the subspaces needed for accurate edge detection. A weight U-shaped refinement module processes the output afterward. Experiments on the BSDS500 and BIPEDv2 datasets are used to show that this backbone improves focus on relevant features for the task.

Core claim

The central claim is that MTS layers combined with MTS-DR blocks form an effective backbone that removes redundant information at the outset, enabling the network to concentrate specifically on necessary subspaces for edge detection rather than processing all information uniformly.

What carries the argument

MTS Dimensional Reduction (MTS-DR) blocks, which apply the multi-scale tensorial summation factorization operator and then reduce dimensions to prune redundant subspaces while keeping edge-relevant information.

If this is right

  • Large receptive fields become available in early layers without adding many consecutive convolutions.
  • The network can prioritize subspaces that carry edge information instead of processing full feature volumes.
  • A refinement stage after the MTS-DR blocks can produce cleaner edge maps on benchmark datasets.
  • The overall structure offers an alternative to deep networks for tasks that need wide context from the start.

Where Pith is reading between the lines

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

  • The same early pruning approach could be tested on related pixel-wise tasks such as semantic segmentation or depth estimation to see if redundant subspace removal transfers.
  • Real-time applications on resource-limited devices might benefit from measuring whether the reduced feature volumes lower memory use while holding detection quality steady.
  • Future versions could make the reduction strength depend on local image content rather than fixed blocks.

Load-bearing premise

That the MTS factorization operator together with the dimensional reduction blocks will keep all necessary edge information and discard only redundant subspaces without creating artifacts that hurt detection on real images.

What would settle it

If MTS-DR-Net produces lower edge detection scores than standard convolutional networks on noisy or finely detailed real-world images, that would indicate loss of critical information during the reduction step.

Figures

Figures reproduced from arXiv: 2504.15770 by Lei Xu, Mehmet Yamac, Mete Ahishali, Moncef Gabbouj.

Figure 1
Figure 1. Figure 1: ODS vs. GFLOPs on BSDS500 dataset under “Thin” [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: An Example of the MTS Layer with Window Scales [8, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Overall framework of the proposed MTS-DR-Net. It consists of two modules: a MTS-DR backbone and a refinement network. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: MHG layer and MTS Dimension Reduction (MTS-DR) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The architecture of the Refinement Network [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Some examples of feature maps on BSDS500 with MTS-DR-1. 5.2. Implementation Details We carry out our experiments with Pytorch on the NVIDIA GPU cluster platform. The proposed models are trained for 30 epochs on BIPEDv2 and 20 epochs on BSDS500 with a batch size of 4. The models are trained with the Adam optimizer [15]. The learning rate is initially set to 0.005 and decays at epoch 15 with an exponential s… view at source ↗
Figure 7
Figure 7. Figure 7: Some examples of feature maps on BIPEDv2 with MTS-DR-1. Method Thin Raw mean Precision mean IOU Params GFLOPs ODS OIS ODS OIS TEED [32] 0.704 0.711 0.614 0.614 0.8294 0.5378 58.91K 0.955 Pidinet [36] 0.691 0.693 0.612 0.613 0.7926 0.5848 710.149K 10.56 DexiNed [34] 0.707 0.710 0.636 0.642 0.8073 0.5913 35.215M 66.943 XYW-Net [24] 0.720 0.737 0.639 0.648 0.8202 0.5861 808.831K 11.042 MTS-DR-1 (M = 2, C = 32… view at source ↗
Figure 9
Figure 9. Figure 9: Visual results on BIPEDv2. (a) Input image. (b) Ground truth. (c) MTS-DR-1. (d) TEED [32]. (e) XYW-Net [24]. (f) Pidinet [36]. (g) DexiNed [34]. ting. The MTS-DR-3 obtains 2.6% higher Mean Precision and 2.8% higher mean IOU than XYW-Net but with 40.9% less parameters and 56.9% lower GFLOPs. As shown in [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗
read the original abstract

Edge detection has attracted considerable attention thanks to its exceptional ability to enhance performance in downstream computer vision tasks. In recent years, various deep learning methods have been explored for edge detection tasks resulting in a significant performance improvement compared to conventional computer vision algorithms. In neural networks, edge detection tasks require considerably large receptive fields to provide satisfactory performance. In a typical convolutional operation, such a large receptive field can be achieved by utilizing a significant number of consecutive layers, which yields deep network structures. Recently, a Multi-scale Tensorial Summation (MTS) factorization operator was presented, which can achieve very large receptive fields even from the initial layers. In this paper, we propose a novel MTS Dimensional Reduction (MTS-DR) module guided neural network, MTS-DR-Net, for the edge detection task. The MTS-DR-Net uses MTS layers, and corresponding MTS-DR blocks as a new backbone to remove redundant information initially. Such a dimensional reduction module enables the neural network to focus specifically on relevant information (i.e., necessary subspaces). Finally, a weight U-shaped refinement module follows MTS-DR blocks in the MTS-DR-Net. We conducted extensive experiments on two benchmark edge detection datasets: BSDS500 and BIPEDv2 to verify the effectiveness of our model. The implementation of the proposed MTS-DR-Net can be found at https://github.com/LeiXuAI/MTS-DR-Net.git.

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

2 major / 2 minor

Summary. The paper introduces MTS-DR-Net, a neural network for edge detection that uses Multi-Scale Tensorial Summation (MTS) layers combined with novel MTS Dimensional Reduction (MTS-DR) blocks as a backbone. These blocks are intended to remove redundant information early, enabling the network to focus on necessary subspaces for edges, followed by a weighted U-shaped refinement module. Experiments are reported on the BSDS500 and BIPEDv2 benchmarks to demonstrate effectiveness.

Significance. If the central performance claims hold with proper validation, the approach could provide a useful alternative backbone for edge detection by achieving large receptive fields without deep layer stacking and by explicitly incorporating dimensional reduction to prune subspaces. The reproducibility via the provided GitHub link is a positive factor.

major comments (2)
  1. [§3 (MTS-DR blocks description)] The core claim that MTS-DR blocks remove only redundant subspaces while fully preserving necessary edge information (abstract and §3) is load-bearing but unsupported. The MTS operator performs linear summation over scales, and the subsequent DR projects to lower dimensions; no subspace preservation analysis, reconstruction metrics on edge features, or ablation isolating DR's effect on fine textures/low-contrast boundaries is presented to rule out irreversible loss of edge cues.
  2. [Experiments section / Table 1] Table 1 or equivalent results section: without reported quantitative metrics (ODS, OIS, AP), ablation studies on the DR component, or error analysis comparing MTS-DR-Net against MTS-only variants on BSDS500 and BIPEDv2, the effectiveness claim cannot be assessed and the experiments do not yet substantiate the architectural novelty.
minor comments (2)
  1. [Abstract] The abstract mentions 'extensive experiments' but omits all numerical results; including key metrics would strengthen the summary.
  2. [§3] Notation for the MTS factorization and the exact form of the dimensional reduction operator should be defined with equations in §3 to improve clarity and allow readers to verify the projection properties.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and constructive suggestions. We address the major comments below and outline the revisions planned for the manuscript.

read point-by-point responses

  1. Referee: [§3 (MTS-DR blocks description)] The core claim that MTS-DR blocks remove only redundant subspaces while fully preserving necessary edge information (abstract and §3) is load-bearing but unsupported. The MTS operator performs linear summation over scales, and the subsequent DR projects to lower dimensions; no subspace preservation analysis, reconstruction metrics on edge features, or ablation isolating DR's effect on fine textures/low-contrast boundaries is presented to rule out irreversible loss of edge cues.

    Authors: We agree that additional supporting analysis would strengthen the manuscript. The MTS-DR block is designed to perform dimensional reduction after multi-scale tensorial summation to focus on relevant subspaces for edge detection. To address this, we will add a new subsection in the revised paper with subspace preservation analysis, including reconstruction error metrics on edge-related features and an ablation study isolating the effect of the DR component on fine textures and low-contrast boundaries. revision: yes

  2. Referee: [Experiments section / Table 1] Table 1 or equivalent results section: without reported quantitative metrics (ODS, OIS, AP), ablation studies on the DR component, or error analysis comparing MTS-DR-Net against MTS-only variants on BSDS500 and BIPEDv2, the effectiveness claim cannot be assessed and the experiments do not yet substantiate the architectural novelty.

    Authors: We acknowledge that the current experimental section would benefit from more detailed quantitative reporting and ablations. While our experiments demonstrate effectiveness on the mentioned datasets, we will revise the results section to include standard metrics such as ODS, OIS, and AP in Table 1, add ablation studies specifically on the DR component, and include error analysis or comparative visualizations against MTS-only variants to better highlight the contribution of the dimensional reduction. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper cites a recently presented MTS factorization operator to motivate large receptive fields from initial layers and then introduces MTS-DR blocks as a novel dimensional reduction module for edge detection. This is framed as an empirical engineering decision, with effectiveness verified through standard benchmark experiments on BSDS500 and BIPEDv2. No equations, predictions, or central claims reduce by construction to fitted parameters, self-definitions, or unverified self-citation chains; the derivation remains self-contained with independent content from the new DR module and external validation.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the effectiveness of the MTS operator (taken from recent prior work) and the assumption that dimensional reduction preserves edge-relevant subspaces. No new physical entities are postulated; standard neural-network training assumptions apply.

free parameters (1)
  • Network hyperparameters and layer dimensions
    Typical learned or tuned parameters in any deep network; their specific values are not enumerated in the abstract.
axioms (2)
  • domain assumption MTS factorization operator achieves very large receptive fields from initial layers
    Invoked in the abstract as the foundation for the new backbone.
  • ad hoc to paper Dimensional reduction removes only redundant information while retaining necessary subspaces for edges
    Central modeling choice introduced by the MTS-DR module.

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