# Symmetrization Weighted Binary Cross-Entropy: Modeling Perceptual Asymmetry for Human-Consistent Neural Edge Detection

arXiv: https://arxiv.org/abs/2501.13365 · HTML: https://mlsanity.com/paper/2501.13365/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 60 references that are in the map.
- First posted on arXiv 23 Jan 2025.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Holistically-Nested Edge Detection](https://mlsanity.com/paper/1504.06375/) (2015)
- [SparseDrive: End-to-End Autonomous Driving via Sparse Scene Representation](https://mlsanity.com/paper/2405.19620/) (2024)
- [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)
- [VerilogCoder: Autonomous Verilog Coding Agents with Graph-based Planning and Abstract Syntax Tree (AST)-based Waveform Tracing Tool](https://mlsanity.com/paper/2408.08927/) (2024)
- [Learning to predict crisp boundaries](https://mlsanity.com/paper/1807.10097/) (2018)
- [Fast Edge Detection Using Structured Forests](https://mlsanity.com/paper/1406.5549/) (2014)
- [Dense Extreme Inception Network for Edge Detection](https://mlsanity.com/paper/2112.02250/) (2021)
- [Towards Accurate One-Stage Object Detection with AP-Loss](https://mlsanity.com/paper/1904.06373/) (2019)
- [EDTER: Edge Detection with Transformer](https://mlsanity.com/paper/2203.08566/) (2022)
- [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)
- [Unmixing Convolutional Features for Crisp Edge Detection](https://mlsanity.com/paper/2011.09808/) (2020)
- [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)
- [ N4 -Fields: Neural Network Nearest Neighbor Fields for Image Transforms](https://mlsanity.com/paper/1406.6558/) (2014)
- [Practical Edge Detection via Robust Collaborative Learning](https://mlsanity.com/paper/2308.14084/) (2023)
- [EdgeNAT: Transformer for Efficient Edge Detection](https://mlsanity.com/paper/2408.10527/) (2024)
- [One-Stage Deep Edge Detection Based on Dense-Scale Feature Fusion and Pixel-Level Imbalance Learning](https://mlsanity.com/paper/2203.09387/) (2022)
- [Generative Edge Detection with Stable Diffusion](https://mlsanity.com/paper/2410.03080/) (2024)
- [Boosting Edge Detection with Pixel-wise Feature Selection: The Extractor-Selector Paradigm](https://mlsanity.com/paper/2501.02534/) (2025)
- [SDC-HSDD-NDSA: Structure Detecting Cluster by Hierarchical Secondary Directed Differential with Normalized Density and Self-Adaption](https://mlsanity.com/paper/2307.00677/) (2023)

## Built on by (most cited first, 2 of 2)

- [Binarization-Aware Adjuster for Discrete Decision Learning with an Application to Edge Detection](https://mlsanity.com/paper/2506.12460/) (2025)
- [Edge-Boundary-Texture Loss: A Tri-Class Generalization of Weighted Binary Cross-Entropy for Enhanced Edge Detection](https://mlsanity.com/paper/2507.06569/) (2025)

## Abstract (arXiv)

Edge detection (ED) is a fundamental perceptual process in computer vision, forming the structural basis for high-level reasoning tasks such as segmentation, recognition, and scene understanding. Despite substantial progress achieved by deep neural networks, most ED models attain high numerical accuracy but fail to produce visually sharp and perceptually consistent edges, thereby limiting their reliability in intelligent vision systems. To address this issue, this study introduces the Symmetrization Weighted Binary Cross-Entropy (SWBCE) loss, a perception-inspired formulation that extends the conventional WBCE by incorporating prediction-guided symmetry. SWBCE explicitly models the perceptual asymmetry in human edge recognition, wherein edge decisions require stronger evidence than non-edge ones, aligning the optimization process with human perceptual discrimination. The resulting symmetric learning mechanism jointly enhances edge recall and suppresses false positives, achieving a superior balance between quantitative accuracy and perceptual fidelity. Extensive experiments across multiple benchmark datasets and representative ED architectures demonstrate that SWBCE can outperform existing loss functions in both numerical evaluation and visual quality. Particularly with the HED-EES model, the SSIM can be improved by about 15% on BRIND, and in all experiments, training by SWBCE consistently obtains the best perceptual results. Beyond edge detection, the proposed perceptual loss offers a generalizable optimization principle for soft computing and neural learning systems, particularly in scenarios where asymmetric perceptual reasoning plays a critical role.