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

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.

💡 Research Summary

Edge detection (ED) is a cornerstone of computer vision, providing structural cues for higher‑level tasks such as segmentation, object recognition, and scene understanding. While deep neural networks have dramatically improved quantitative performance on benchmark datasets, most existing ED models still produce edge maps that are visually blurry or contain excessive false positives, limiting their usefulness in downstream intelligent systems. The authors identify the root cause as the loss function: conventional Binary Cross‑Entropy (BCE) and its weighted variant (WBCE) address class imbalance by assigning higher static weights to edge pixels, but they ignore a fundamental property of human perception—an asymmetry in decision making. Human annotators tend to label a pixel as an edge only when strong evidence is present, whereas non‑edge decisions are made more liberally. This perceptual asymmetry implies that edge predictions should be evidence‑driven and conservative, while non‑edge predictions can tolerate lower confidence.

To bridge this gap, the paper proposes Symmetrization Weighted Binary Cross‑Entropy (SWBCE), a novel loss that combines the class‑balancing effect of WBCE with a prediction‑guided dynamic weighting scheme. Specifically, for each pixel with predicted probability p, a dynamic weight g(p)=α·p+β·(1−p) is computed, where α and β are hyper‑parameters controlling the emphasis on high‑confidence edge and non‑edge predictions respectively. The final loss is:

L_SWBCE = –