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

Lei Xu, Mehmet Yamac, Mete Ahishali, Moncef Gabbouj

TL;DR

This paper introduces MTS-DR-Net, a backbone for edge detection based on Multi-Scale Tensorial Summation and Dimensional Reduction to suppress redundant information and emphasize necessary subspaces. The architecture combines a light MTS-DR backbone with a three-scale refinement network, employing MTS layers and Multi-Head Gate (MHG) gates to achieve strong representational power with reduced parameters. Experiments on BSDS500 and BIPEDv2 show state-of-the-art performance without post-processing or pretraining, validating the method’s efficiency and effectiveness. The results suggest that learning and operating in the essential subspaces via tensorial summation can outperform traditional multi-scale CNNs and lightweight models while maintaining practicality for real-world deployment.

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.

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

TL;DR

This paper introduces MTS-DR-Net, a backbone for edge detection based on Multi-Scale Tensorial Summation and Dimensional Reduction to suppress redundant information and emphasize necessary subspaces. The architecture combines a light MTS-DR backbone with a three-scale refinement network, employing MTS layers and Multi-Head Gate (MHG) gates to achieve strong representational power with reduced parameters. Experiments on BSDS500 and BIPEDv2 show state-of-the-art performance without post-processing or pretraining, validating the method’s efficiency and effectiveness. The results suggest that learning and operating in the essential subspaces via tensorial summation can outperform traditional multi-scale CNNs and lightweight models while maintaining practicality for real-world deployment.

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.

Paper Structure

This paper contains 19 sections, 7 equations, 9 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related works
  3. Edge Detection
  4. Efficiency in Neural Networks
  5. Learnable Tensor Decomposition
  6. MTS Layer for multi-linear feature extraction
  7. MHG Layer as Activation Free Non-linear Operator
  8. Methods
  9. MTS-DR-Net Framework
  10. MTS-DR Blocks
  11. Refinement Network
  12. Loss Function
  13. Experiments
  14. Datasets
  15. Implementation Details
  16. ...and 4 more sections

Figures (9)

  • Figure 1: ODS vs. GFLOPs on BSDS500 dataset under "Thin" setting.
  • Figure 2: An Example of the MTS Layer with Window Scales [8, 16, 32]
  • Figure 3: Overall framework of the proposed MTS-DR-Net. It consists of two modules: a MTS-DR backbone and a refinement network.
  • Figure 4: MHG layer and MTS Dimension Reduction (MTS-DR) block implementations
  • Figure 5: The architecture of the Refinement Network
  • ...and 4 more figures