# Edge-Boundary-Texture Loss: A Tri-Class Generalization of Weighted Binary Cross-Entropy for Enhanced Edge Detection

arXiv: https://arxiv.org/abs/2507.06569 · HTML: https://mlsanity.com/paper/2507.06569/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 35 references that are in the map.
- First posted on arXiv 9 Jul 2025.

## Builds on (most cited first, 20 of 20)

- [Holistically-Nested Edge Detection](https://mlsanity.com/paper/1504.06375/) (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)
- [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)
- [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)
- [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)
- [A Comprehensive Study for Edge Detection: Ideal-Prior Guidance Learning, High-Precision Architecture, and Better Distinguishability Evaluation Benchmark](https://mlsanity.com/paper/2407.19992/) (2024)
- [Symmetrization Weighted Binary Cross-Entropy: Modeling Perceptual Asymmetry for Human-Consistent Neural Edge Detection](https://mlsanity.com/paper/2501.13365/) (2025)

## Abstract (arXiv)

Edge detection (ED) remains a fundamental task in computer vision, yet its performance is often hindered by the ambiguous nature of non-edge pixels near object boundaries. The widely adopted Weighted Binary Cross-Entropy (WBCE) loss treats all non-edge pixels uniformly, overlooking the structural nuances around edges and often resulting in blurred predictions. In this paper, we propose the Edge-Boundary-Texture (EBT) loss, a novel objective that explicitly divides pixels into three categories, edge, boundary, and texture, and assigns each a distinct supervisory weight. This tri-class formulation enables more structured learning by guiding the model to focus on both edge precision and contextual boundary localization. We theoretically show that the EBT loss generalizes the WBCE loss, with the latter becoming a limit case. Extensive experiments across multiple benchmarks demonstrate the superiority of the EBT loss both quantitatively and perceptually. Furthermore, the consistent use of unified hyperparameters across all models and datasets, along with robustness to their moderate variations, indicates that the EBT loss requires minimal fine-tuning and is easily deployable in practice.