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

TL;DR

The paper tackles the gap between numerical edge-detection accuracy and perceptual edge quality by introducing SWBCE, a perception-inspired loss that extends WBCE with prediction-guided symmetry to capture human-like asymmetry in edge decisions. SWBCE combines a label-driven recall term with a prediction-driven precision term, formalized as $L_{SWBCE}=\frac{L_{Label}(\hat{Y},Y)+b\cdot L_{Pred}(\hat{Y},Y)}{1+b}$, and weights predictions through per-pixel factors to penalize overconfident false edges. Across multiple ED architectures (e.g., HED, BDCN, Dexi, EdgeNat) and datasets (BIPED2, BRIND, UDED, NYUD2), SWBCE consistently improves perceptual metrics such as SSIM (e.g., roughly +15% on BRIND with HED-EES) while maintaining or enhancing standard ED scores, demonstrating robust generalization. A new Edge Ratio metric is introduced to evaluate continuous edge precision without binarization, and experiments reveal that SWBCE provides a generally applicable principle for perceptually grounded optimization in soft computing and neural learning. The work suggests that explicit modeling of perceptual asymmetry can bridge statistical optimization and human visual reasoning, with potential benefits for downstream vision tasks requiring reliable edge cues.

Abstract

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 \textit{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.

Figures (10)

• Figure 1: Qualitative comparisons on HED-EES for the four loss functions. Although tracing loss also provides clear results, it preserves more unwanted artifacts, such as in the middle of the tire (bottom), while the proposed method yields cleaner results, filtering such artifacts.
• Figure 2: Qualitative comparisons on BDCN-EES for the four loss functions. While the tracing loss avoids the pollution in the middle of the tire (bottom), SWBCE still yields more perceptual results, which is thinner and smoother, consistent with the performance on HED-EES.
• Figure 3: Qualitative comparisons on Dexi-EES for the four loss functions. Previous loss functions introduce artifacts, such as in the middle of the tire (bottom), and glitches in the words (middle), while SWBCE yields more perceptual and smooth results.
• Figure 4: Qualitative comparisons on EdgeNat for the four loss functions. All loss function seems not to perform well, indicating that this model may not be suitable for this dataset (BIPED2). However, SWBCE results still look better.
• Figure 5: Stability of the hyperparameter $b$ balancing between $L_{Label}$ and $L_{Pred}$ on BRIND