# LMS-Net: A Learned Mumford-Shah Network For Few-Shot Medical Image Segmentation

arXiv: https://arxiv.org/abs/2502.05473 · HTML: https://mlsanity.com/paper/2502.05473/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 8 Feb 2025.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [PANet: Few-Shot Image Semantic Segmentation with Prototype Alignment](https://mlsanity.com/paper/1908.06391/) (2019)
- [CHAOS Challenge -- Combined (CT-MR) Healthy Abdominal Organ Segmentation](https://mlsanity.com/paper/2001.06535/) (2020)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Multivariate mixture model for myocardium segmentation combining multi-source images](https://mlsanity.com/paper/1612.08820/) (2016)
- [Self-Supervision with Superpixels: Training Few-shot Medical Image Segmentation without Annotation](https://mlsanity.com/paper/2007.09886/) (2020)
- [Denoising Prior Driven Deep Neural Network for Image Restoration](https://mlsanity.com/paper/1801.06756/) (2018)
- [Recurrent Mask Refinement for Few-Shot Medical Image Segmentation](https://mlsanity.com/paper/2108.00622/) (2021)
- [Anomaly Detection-Inspired Few-Shot Medical Image Segmentation Through Self-Supervision With Supervoxels](https://mlsanity.com/paper/2203.02048/) (2022)
- [Intermediate Prototype Mining Transformer for Few-Shot Semantic Segmentation](https://mlsanity.com/paper/2210.06780/) (2022)
- [Deep Convolutional Neural Networks with Spatial Regularization, Volume and Star-shape Priori for Image Segmentation](https://mlsanity.com/paper/2002.03989/) (2020)
- [Few-Shot Medical Image Segmentation via a Region-enhanced Prototypical Transformer](https://mlsanity.com/paper/2309.04825/) (2023)
- [Unfolded proximal neural networks for robust image Gaussian denoising](https://mlsanity.com/paper/2308.03139/) (2023)

## Abstract (arXiv)

Few-shot semantic segmentation (FSS) methods have shown great promise in handling data-scarce scenarios, particularly in medical image segmentation tasks. However, most existing FSS architectures lack sufficient interpretability and fail to fully incorporate the underlying physical structures of semantic regions. To address these issues, in this paper, we propose a novel deep unfolding network, called the Learned Mumford-Shah Network (LMS-Net), for the FSS task. Specifically, motivated by the effectiveness of pixel-to-prototype comparison in prototypical FSS methods and the capability of deep priors to model complex spatial structures, we leverage our learned Mumford-Shah model (LMS model) as a mathematical foundation to integrate these insights into a unified framework. By reformulating the LMS model into prototype update and mask update tasks, we propose an alternating optimization algorithm to solve it efficiently. Further, the iterative steps of this algorithm are unfolded into corresponding network modules, resulting in LMS-Net with clear interpretability. Comprehensive experiments on three publicly available medical segmentation datasets verify the effectiveness of our method, demonstrating superior accuracy and robustness in handling complex structures and adapting to challenging segmentation scenarios. These results highlight the potential of LMS-Net to advance FSS in medical imaging applications. Our code will be available at: https://github.com/SDZhang01/LMSNet