LHMCF-Net: A Learned Hyperbolic Mean Curvature Flow Network for Medical Images Segmentation

2026-08-21

AI Summary

该研究提出LHMCF-Net，通过结合双曲平均曲率流与深度学习，解决医学图像分割中低对比度和模糊边界的问题。

Abstract

Motivated by the classical Chan-Vese model and the ability of deep priors to capture complex spatial structures, we develop a segmentation model that leverages learned hyperbolic mean curvature flow (LHMCF) as a mathematical foundation for integrating feature space data fidelity and deep structural priors within a unified high-dimensional framework. The proposed LHMCF model is governed by a second-order dissipative hyperbolic PDE, where the introduction of a velocity field provides inertia and momentum to the evolving interface. This hyperbolic mechanism enables the contour to bypass noise-induced local minima and propagate coherently through low-contrast or ambiguous regions, addressing limitations inherent to first-order parabolic flows. To solve the continuous LHMCF model, we construct a deep unfolding network, named LHMCF-Net, which maps the iterative numerical procedure of the PDE into a sequence of discrete evolution stages. Each stage corresponds to one physically interpretable update of the underlying dynamical system, allowing the network to inherit the stability and geometric consistency of the PDE while supporting end-to-end optimization. Comprehensive experiments on three publicly available medical segmentation datasets demonstrate that LHMCF-Net achieves superior performance, particularly in challenging scenarios with low contrast and unclear boundaries. These results highlight the effectiveness of embedding hyperbolic geometric evolution into deep unfolding architectures and underscore the potential of physically inspired models for robust medical image segmentation.

Problem

• Medical Image Segmentation
• Low Contrast
• Unclear Boundaries
• Hyperbolic Mean Curvature Flow

Innovation

• Learned Hyperbolic Mean Curvature Flow
• Deep Unfolding Network
• Second-order Dissipative Hyperbolic PDE
• Medical Image Segmentation