基于变分模型的定制UNet图像分割：一种深度变分框架
Image Segmentation via Variational Model Based Tailored UNet: A Deep Variational Framework
AI总结：
本文提出VM_TUNet框架，结合变分模型与UNet，通过数据驱动操作和定制有限点法提升图像分割精度与可解释性。
摘要：
传统图像分割方法，如基于偏微分方程（PDE）的变分模型，具有强数学可解释性和精确边界建模能力，但往往易受参数设置敏感性和计算成本高所限。相比之下，参数相对较少的深度学习模型如UNet在自动特征提取方面表现优异，但缺乏理论可解释性和需要大量标注数据。为融合两种范式的优势，我们提出变分模型基于的定制UNet（VM_TUNet），一种新颖的混合框架，将第四阶修改的Cahn-Hilliard方程与UNet的深度学习主干相结合，结合变分方法的可解释性和边缘保留特性与神经网络的自适应特征学习能力。具体而言，引入了数据驱动的操作符以取代手动参数调整，并结合定制有限点法（TFPM）以强制高精度边界保留。在基准数据集上的实验结果表明，VM_TUNet相比现有方法在分割性能上表现更优，特别是在细边界界定方面。
英文摘要：
Traditional image segmentation methods, such as variational models based on partial differential equations (PDEs), offer strong mathematical interpretability and precise boundary modeling, but often suffer from sensitivity to parameter settings and high computational costs. In contrast, deep learning models such as UNet, which are relatively lightweight in parameters, excel in automatic feature extraction but lack theoretical interpretability and require extensive labeled data. To harness the complementary strengths of both paradigms, we propose Variational Model Based Tailored UNet (VM_TUNet), a novel hybrid framework that integrates the fourth-order modified Cahn-Hilliard equation with the deep learning backbone of UNet, which combines the interpretability and edge-preserving properties of variational methods with the adaptive feature learning of neural networks. Specifically, a data-driven operator is introduced to replace manual parameter tuning, and we incorporate the tailored finite point method (TFPM) to enforce high-precision boundary preservation. Experimental results on benchmark datasets demonstrate that VM_TUNet achieves superior segmentation performance compared to existing approaches, especially for fine boundary delineation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
