## 5 Conclusions  
In this paper, we propose DEPANet, an encoder-decoder architecture for strip steel surface defect segmentation. The encoder consists of three key components: a backbone, a Differentiable Edge Feature Pyramid (DEFP) network, and Edge-aware Feature Aggregation Modules (EFAMs). The backbone utilizes ResNet34 to extract comprehensive features from the strip steel surface. The DEFP network extracts multi-scale edge features through a series of Adaptive Feature Smoothing Filters (AFSFs). Each AFSF incorporates two learnable components: a Laplacian operator for edge feature extraction and a Gaussian blur mechanism for feature smoothing and enhancement. The multiple proposed EFAMs are employed to generate edge-enhanced features, with each EFAM designed to integrate the global backbone features with the edge components from DEFP at the corresponding level. In addition, we incorporate a Convolutional Block Attention Module (CBAM) to ensure effective fusion of global context and fine edge detail. Experimental results demonstrate that DEPANet effectively enhances defect segmentation accuracy in complex industrial environments.  
In future work, we will focus on two key improvements: (1) developing a lightweight variant of DEPANet for real-time defect detection in resource-constrained industrial settings and (2) extending our framework to handle temporal information from production line videos to better capture transient defect patterns.  
Y.S.: conceptualization, methodology, writing--review & editing, supervision; S.G.: validation, formal analysis, writing--original draft, visualization; H.G.: writing--review & editing, supervision; C.Z.: writing--review & editing, supervision; Y.F.: conceptualization, formal analysis, resources, writing--review & editing; C.X.: formal analysis, data curation. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the Teacher Education Curriculum Reform Projects of Henan Province under Grant 2024-JSJYZD-008; in part by the Henan Province Key Research and Development Project under Grants 241111212200 and 252102220046; in part by the Henan Joint Fund for Science and Technology Research under Grant 20240012; in part by the Key Scientific Research Projects of Higher Education Institutions in Henan Province under Grant 25B520004; and in part by the Open Fund of the Engineering Research Center of Intelligent Swarm Systems, Ministry of Education under Grant ZZU-CISS-2024004.  
**Data Availability Statement:** Our code and experimental results are available at [[https://github.com/hpguo1982/DFPANet](https://github.com/hpguo1982/DFPANet)]([https://github.com/hpguo1982/DFPANet](https://github.com/hpguo1982/DFPANet)), accessed on 26 March 2025.  
**Conflicts of Interest:** The authors declare that there are no conflicts of interest.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Methods** & **MAE \(\downarrow\)** & **SM \(\uparrow\)** & **\(E_{\text{max}}\uparrow\)** & **\(F_{\text{max}}\uparrow\)** & **Parameters (M) \(\downarrow\)** \\ \hline C2 FNet [53] & 0.0207 & 0.8982 & 0.9701 & 0.8835 & **26.4** \\ CPD [36] & 0.0254 & 0.8884 & 0.9627 & 0.8777 & 29.6 \\ DACNet [37] & 0.0226 & 0.8855 & 0.9570 & 0.8722 & 98.2 \\ EDRNet [39] & 0.0229 & 0.8651 & 0.9603 & 0.8769 & 49.4 \\ BC [34] & 0.1356 & 0.6004 & 0.6704 & 0.4976 & — \\ F3 Net [40] & 0.0208 & 0.8977 & 0.9663 & **0.8910** & 35.8 \\ MINet [43] & 0.0221 & 0.8885 & 0.9604 & 0.8798 & 48.3 \\ RCRR [49] & 0.2194 & 0.5633 & 0.6198 & 0.4377 & — \\ CorrNet [54] & 0.0243 & 0.8776 & 0.9532 & 0.8785 & 39.3 \\ PiCANet [46] & 0.0449 & 0.8490 & 0.9317 & 0.8337 & 49.1 \\
**Ours** & **0.0202** & **0.9007** & **0.9654** & 0.8860 & 47.6 \\ \hline \hline \end{tabular}
\end{table}
Table 3: DEPANet is comprehensively evaluated against 10 state-of-the-art methods on the ESDIs-SOD dataset, with optimal results highlighted in bold.