LHMCF-Net：用于医学图像分割的学习型双曲平均曲率流网络
LHMCF-Net: A Learned Hyperbolic Mean Curvature Flow Network for Medical Images Segmentation
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- Zhejiang Normal University（浙江师范大学）
- College of Mathematical Medicine, Zhejiang Normal University（浙江师范大学数学医学院）
- School of Mathematical Sciences, Zhejiang University（浙江大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。
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中文总结 AI 辅助
该研究提出了基于学习型双曲平均曲率流的LHMCF-Net深度展开网络，将双曲几何演化与端到端优化结合，在公开医学分割数据集上的低对比度、边界模糊场景中实现了优异的分割性能。
中文摘要 AI 辅助
受经典Chan-Vese模型以及深度先验捕捉复杂空间结构能力的启发，我们开发了一种分割模型，该模型利用学习型双曲平均曲率流（LHMCF）作为数学基础，在统一的高维框架内整合特征空间数据保真度与深度结构先验。所提出的LHMCF模型由二阶耗散双曲偏微分方程（PDE）控制，其中速度场的引入为演化界面提供了惯性和动量。这种双曲机制使轮廓能够绕过噪声诱导的局部极小值，并在低对比度或模糊区域连贯传播，解决了一阶抛物流固有的局限性。为求解连续LHMCF模型，我们构建了一个名为LHMCF-Net的深度展开网络，该网络将PDE的迭代数值过程映射为一系列离散演化阶段，每个阶段对应底层动力学系统的一次物理解释性更新，使网络既能继承PDE的稳定性和几何一致性，又支持端到端优化。在三个公开可用的医学分割数据集上进行的综合实验表明，LHMCF-Net实现了优异的性能，尤其是在低对比度和边界不清晰的挑战性场景中。这些结果凸显了将双曲几何演化嵌入深度展开架构的有效性，并强调了受物理启发的模型在鲁棒医学图像分割方面的潜力。
英文摘要
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.
