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

2025-02-08

AI Summary

To address the limited interpretability and inadequate anatomical structure modeling in few-shot medical image segmentation, this paper proposes an end-to-end unrolled network that integrates physical priors with deep learning. The core innovation lies in the first deep unrolling of the Mumford–Shah variational model into learnable alternating optimization modules, augmented with a prototype-matching mechanism to enable geometrically aware and physically interpretable segmentation of semantic regions. The framework synergistically combines the structural priors of variational models with data-driven adaptability, overcoming key limitations of conventional few-shot methods in anatomical consistency and lesion robustness. Evaluated on three public medical benchmarks, the method achieves state-of-the-art performance, significantly improving segmentation accuracy and generalization for complex anatomical structures and low-contrast lesions.

Technology Category

• Computer Vision: Segmentation
• Machine Learning: Multimodal Learning
• Reasoning under Uncertainty: Graphical Models

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

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

Problem

• Enhancing interpretability in medical image segmentation
• Integrating physical structures into few-shot segmentation
• Improving accuracy in complex medical segmentation tasks

Innovation

• Learned Mumford-Shah Network
• Deep unfolding network
• Alternating optimization algorithm