Image Segmentation via Variational Model Based Tailored UNet: A Deep Variational Framework

TL;DR

This paper introduces VM_TUNet, a hybrid deep learning and variational model framework that improves image segmentation accuracy and boundary preservation by integrating PDE-based methods with UNet architecture.

Contribution

It presents a novel hybrid framework combining variational PDE models with UNet, including a data-driven operator and TFPM for enhanced boundary accuracy.

Findings

Superior segmentation performance on benchmark datasets

Enhanced boundary delineation accuracy

Effective integration of variational models with deep learning

Abstract

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.