# Robust Variational Model Based Tailored UNet: Leveraging Edge Detector and Mean Curvature for Improved Image Segmentation

arXiv: https://arxiv.org/abs/2512.07590 · HTML: https://mlsanity.com/paper/2512.07590/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Visual Saliency Based on Multiscale Deep Features](https://mlsanity.com/paper/1503.08663/) (2015)
- [Deep Semantic Segmentation of Natural and Medical Images: A Review](https://mlsanity.com/paper/1910.07655/) (2019)
- [Segment Anything Model for Medical Image Segmentation: Current Applications and Future Directions](https://mlsanity.com/paper/2401.03495/) (2024)
- [Optimizing the Dice Score and Jaccard Index for Medical Image Segmentation: Theory & Practice](https://mlsanity.com/paper/1911.01685/) (2019)
- [PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural Networks](https://mlsanity.com/paper/2307.09039/) (2023)
- [Double-well Net for Image Segmentation](https://mlsanity.com/paper/2401.00456/) (2023)
- [ℓ1DecNet+: A new architecture framework by ℓ1 decomposition and iteration unfolding for sparse feature segmentation](https://mlsanity.com/paper/2203.02690/) (2022)
- [Image Segmentation via Variational Model Based Tailored UNet: A Deep Variational Framework](https://mlsanity.com/paper/2505.05806/) (2025)

## Abstract (arXiv)

To address the challenge of segmenting noisy images with blurred or fragmented boundaries, this paper presents a robust version of Variational Model Based Tailored UNet (VM_TUNet), a hybrid framework that integrates variational methods with deep learning. The proposed approach incorporates physical priors, an edge detector and a mean curvature term, into a modified Cahn-Hilliard equation, aiming to combine the interpretability and boundary-smoothing advantages of variational partial differential equations (PDEs) with the strong representational ability of deep neural networks. The architecture consists of two collaborative modules: an F module, which conducts efficient frequency domain preprocessing to alleviate poor local minima, and a T module, which ensures accurate and stable local computations, backed by a stability estimate. Extensive experiments on three benchmark datasets indicate that the proposed method achieves a balanced trade-off between performance and computational efficiency, which yields competitive quantitative results and improved visual quality compared to pure convolutional neural network (CNN) based models, while achieving performance close to that of transformer-based method with reasonable computational expense.