🤖 AI Summary
To address under-segmentation in instance segmentation of scanning electron microscopy (SEM) images caused by fragmented cell contours, this paper proposes an end-to-end learnable Deep Contour Operator (DCO)—the first differentiable geometric contour-closure operator explicitly modeled as a topology-aware neural operator and embedded within a U-Net architecture for joint boundary restoration and segmentation optimization. The method integrates a self-supervised contour completeness loss, a differentiable morphological closing module, and SEM-specific synthetic data augmentation, eliminating the need for post-processing. Evaluated on multi-source biological SEM datasets, our approach achieves a 12.6% improvement in mean average precision (mAP) and reduces under-segmentation error by 37% compared to state-of-the-art methods including Mask R-CNN and CellPose. It significantly decreases reliance on manual correction, demonstrating robustness and practical utility in high-precision biomedical image analysis.