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

arXiv: https://arxiv.org/abs/2504.15770 · HTML: https://mlsanity.com/paper/2504.15770/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 72 references that are in the map.
- First posted on arXiv 22 Apr 2025.

## Builds on (most cited first, 30 of 32)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Semantic Understanding of Scenes through the ADE20K Dataset](https://mlsanity.com/paper/1608.05442/) (2016)
- [GLaM: Efficient Scaling of Language Models with Mixture-of-Experts](https://mlsanity.com/paper/2112.06905/) (2021)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Holistically-Nested Edge Detection](https://mlsanity.com/paper/1504.06375/) (2015)
- [GhostNet: More Features from Cheap Operations](https://mlsanity.com/paper/1911.11907/) (2019)
- [CondConv: Conditionally Parameterized Convolutions for Efficient Inference](https://mlsanity.com/paper/1904.04971/) (2019)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Pixel Difference Networks for Efficient Edge Detection](https://mlsanity.com/paper/2108.07009/) (2021)
- [Richer Convolutional Features for Edge Detection](https://mlsanity.com/paper/1612.02103/) (2016)
- [Dense Extreme Inception Network: Towards a Robust CNN Model for Edge Detection](https://mlsanity.com/paper/1909.01955/) (2019)
- [Feature Pyramid and Hierarchical Boosting Network for Pavement Crack Detection](https://mlsanity.com/paper/1901.06340/) (2019)
- [Stable Low-rank Tensor Decomposition for Compression of Convolutional Neural Network](https://mlsanity.com/paper/2008.05441/) (2020)
- [FastFCN: Rethinking Dilated Convolution in the Backbone for Semantic Segmentation](https://mlsanity.com/paper/1903.11816/) (2019)
- [Rigid-Motion Scattering for Texture Classification](https://mlsanity.com/paper/1403.1687/) (2014)
- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Towards Efficient Tensor Decomposition-Based DNN Model Compression with Optimization Framework](https://mlsanity.com/paper/2107.12422/) (2021)
- [DeepEdge: A Multi-Scale Bifurcated Deep Network for Top-Down Contour Detection](https://mlsanity.com/paper/1412.1123/) (2014)
- [RINDNet: Edge Detection for Discontinuity in Reflectance, Illumination, Normal and Depth](https://mlsanity.com/paper/2108.00616/) (2021)
- [DiffusionEdge: Diffusion Probabilistic Model for Crisp Edge Detection](https://mlsanity.com/paper/2401.02032/) (2024)
- [Learning Deep Structured Multi-Scale Features using Attention-Gated CRFs for Contour Prediction](https://mlsanity.com/paper/1801.00524/) (2018)
- [Tiny and Efficient Model for the Edge Detection Generalization](https://mlsanity.com/paper/2308.06468/) (2023)
- [RankED: Addressing Imbalance and Uncertainty in Edge Detection Using Ranking-based Losses](https://mlsanity.com/paper/2403.01795/) (2024)
- [Deep Crisp Boundaries: From Boundaries to Higher-level Tasks](https://mlsanity.com/paper/1801.02439/) (2018)
- [Dynamic Group Convolution for Accelerating Convolutional Neural Networks](https://mlsanity.com/paper/2007.04242/) (2020)
- [Delving into Crispness: Guided Label Refinement for Crisp Edge Detection](https://mlsanity.com/paper/2306.15172/) (2023)
- [Generalized Tensor Summation Compressive Sensing Network (GTSNET): An Easy to Learn Compressive Sensing Operation](https://mlsanity.com/paper/2108.03167/) (2021)
- [PNT-Edge: Towards Robust Edge Detection with Noisy Labels by Learning Pixel-level Noise Transitions](https://mlsanity.com/paper/2307.14070/) (2023)

## Built on by (most cited first, 1 of 1)

- [MTS-CSNet: Multiscale Tensor Factorization for Deep Compressive Sensing on RGB Images](https://mlsanity.com/paper/2602.07056/) (2026)

## Abstract (arXiv)

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.