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

arXiv: https://arxiv.org/abs/2505.05806 · HTML: https://mlsanity.com/paper/2505.05806/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 47 references that are in the map.
- First posted on arXiv 9 May 2025.

## Builds on (most cited first, 21 of 21)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2001.05566/) (2020)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [Visual Saliency Based on Multiscale Deep Features](https://mlsanity.com/paper/1503.08663/) (2015)
- [Adversarial Regularizers in Inverse Problems](https://mlsanity.com/paper/1805.11572/) (2018)
- [Segment Anything Model for Medical Image Segmentation: Current Applications and Future Directions](https://mlsanity.com/paper/2401.03495/) (2024)
- [Learning deep structured active contours end-to-end](https://mlsanity.com/paper/1803.06329/) (2018)
- [Structure preserving deep learning](https://mlsanity.com/paper/2006.03364/) (2020)
- [DARNet: Deep Active Ray Network for Building Segmentation](https://mlsanity.com/paper/1905.05889/) (2019)
- [On learning optimized reaction diffusion processes for effective image restoration](https://mlsanity.com/paper/1503.05768/) (2015)
- [PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural Networks](https://mlsanity.com/paper/2307.09039/) (2023)
- [Reformulating Level Sets as Deep Recurrent Neural Network Approach to Semantic Segmentation](https://mlsanity.com/paper/1704.03593/) (2017)
- [CNN-based Semantic Segmentation using Level Set Loss](https://mlsanity.com/paper/1910.00950/) (2019)
- [Double-well Net for Image Segmentation](https://mlsanity.com/paper/2401.00456/) (2023)
- [Connections between Operator-splitting Methods and Deep Neural Networks with Applications in Image Segmentation](https://mlsanity.com/paper/2307.09052/) (2023)

## Built on by (most cited first, 1 of 1)

- [Robust Variational Model Based Tailored UNet: Leveraging Edge Detector and Mean Curvature for Improved Image Segmentation](https://mlsanity.com/paper/2512.07590/) (2025)

## Abstract (arXiv)

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.