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Enhancing Medical Image Segmentation via Heat Conduction Equation

Rong Wu, Yim-Sang Yu

TL;DR

This work tackles the challenge of efficient global context modeling in medical image segmentation by introducing a hybrid architecture, UMH, that combines Mamba state-space modules for long-range reasoning with heat conduction–based diffusion in the bottleneck via Heat Conduction Operators. The frequency-domain diffusion is implemented through DCT/IDCT transforms with an adaptively learned diffusion coefficient, achieving a computational profile of $O(N^{1.5})$ while maintaining interpretability. Across multimodal abdominal CT/MRI datasets, UMH delivers state-of-the-art or competitive results in 3D segmentation and demonstrates robustness for boundary refinement and global context propagation. Ablation studies confirm the complementary benefits of Mamba and HCO components, highlighting a scalable pathway that blends physics-inspired diffusion with modern sequence models for biomedical image analysis.

Abstract

Medical image segmentation has been significantly advanced by deep learning architectures, notably U-Net variants. However, existing models struggle to achieve efficient global context modeling and long-range dependency reasoning under practical computational budgets simultaneously. In this work, we propose a novel hybrid architecture utilizing U-Mamba with Heat Conduction Equation. Our model combines Mamba-based state-space modules for efficient long-range reasoning with Heat Conduction Operators (HCOs) in the bottleneck layers, simulating frequency-domain thermal diffusion for enhanced semantic abstraction. Experimental results on multimodal abdominal CT and MRI datasets demonstrate that the proposed model consistently outperforms strong baselines, validating its effectiveness and generalizability. It suggest that blending state-space dynamics with heat-based global diffusion offers a scalable and interpretable solution for medical segmentation tasks.

Enhancing Medical Image Segmentation via Heat Conduction Equation

TL;DR

This work tackles the challenge of efficient global context modeling in medical image segmentation by introducing a hybrid architecture, UMH, that combines Mamba state-space modules for long-range reasoning with heat conduction–based diffusion in the bottleneck via Heat Conduction Operators. The frequency-domain diffusion is implemented through DCT/IDCT transforms with an adaptively learned diffusion coefficient, achieving a computational profile of while maintaining interpretability. Across multimodal abdominal CT/MRI datasets, UMH delivers state-of-the-art or competitive results in 3D segmentation and demonstrates robustness for boundary refinement and global context propagation. Ablation studies confirm the complementary benefits of Mamba and HCO components, highlighting a scalable pathway that blends physics-inspired diffusion with modern sequence models for biomedical image analysis.

Abstract

Medical image segmentation has been significantly advanced by deep learning architectures, notably U-Net variants. However, existing models struggle to achieve efficient global context modeling and long-range dependency reasoning under practical computational budgets simultaneously. In this work, we propose a novel hybrid architecture utilizing U-Mamba with Heat Conduction Equation. Our model combines Mamba-based state-space modules for efficient long-range reasoning with Heat Conduction Operators (HCOs) in the bottleneck layers, simulating frequency-domain thermal diffusion for enhanced semantic abstraction. Experimental results on multimodal abdominal CT and MRI datasets demonstrate that the proposed model consistently outperforms strong baselines, validating its effectiveness and generalizability. It suggest that blending state-space dynamics with heat-based global diffusion offers a scalable and interpretable solution for medical segmentation tasks.

Paper Structure

This paper contains 12 sections, 10 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Preliminaries
  4. Overview
  5. Experiments
  6. Dataset and Experiment Setting
  7. Evaluation Metrics and Implementation Details
  8. Main Results
  9. Ablation studies
  10. Conclusions
  11. COMPLIANCE WITH ETHICAL STANDARDS
  12. Acknowledgment

Figures (2)

  • Figure 1: Overall pipeline. (a) Encoder–Decoder design: the upper encoder uses Mamba blocks for local and long-range feature extraction, while the two bottleneck layers are replaced by HCOs to enhance global context modeling through frequency-domain diffusion. (b) Each HCO transforms features via DCT/IDCT and applies an adaptive thermal diffusion filter, simulating heat conduction for efficient global information propagation.
  • Figure 2: Semantic segmentation results for UMH and its competitors.