用深度学习分析磁性条纹演化，揭示两种不同形态的形成机制。
Geometric Analysis of Magnetic Labyrinthine Stripe Evolution via Deep Learning Segmentation
- 基于U-Net模型实现噪声与遮挡下的条纹图像精准分割。
- 从444张图像中量化出条纹长度与曲率变化，发现两类演化模式。
- 适用于复杂无序结构分析，适合材料物理与图像算法研究者。
蜿蜒条纹在多种物理系统中普遍存在，但因其缺乏长程有序性，定量表征困难。本文研究铋掺杂钇铁石榴石（Bi:YIG）薄膜在磁场退火条件下的条纹演化过程。采用基于合成噪声（含高斯白噪声和Simplex噪声）训练的U-Net深度学习模型，实现对实验磁光图像的鲁棒分割，克服了噪声与遮挡问题。在此基础上，构建基于骨架化、图映射与样条拟合的几何分析流程，通过长度与曲率测量量化局部条纹传播行为。结合12组退火实验共444张图像，分析从“淬火态”到更平行连贯的“退火态”的转变过程，识别出受磁场极性影响的两种不同演化模式（类型A与类型B）。研究提供了磁性条纹几何与拓扑特性的定量分析方法，揭示其局部结构演化规律，并建立了一套通用的复杂蜿蜒系统分析工具。
原文摘要 · Abstract (English)
Labyrinthine stripe patterns are common in many physical systems, yet their lack of long-range order makes quantitative characterization challenging. We investigate the evolution of such patterns in bismuth-doped yttrium iron garnet (Bi:YIG) films subjected to a magnetic field annealing protocol. A U-Net deep learning model, trained with synthetic degradations including additive white Gaussian and Simplex noise, enables robust segmentation of experimental magneto-optical images despite noise and occlusions. Building on this segmentation, we develop a geometric analysis pipeline based on skeletonization, graph mapping, and spline fitting, which quantifies local stripe propagation through length and curvature measurements. Applying this framework to 444 images from 12 annealing protocol trials, we analyze the transition from the "quenched" state to a more parallel and coherent "annealed" state, and identify two distinct evolution modes (Type A and Type B) linked to field polarity. Our results provide a quantitative analysis of geometric and topological properties in magnetic stripe patterns and offer new insights into their local structural evolution, and establish a general tool for analyzing complex labyrinthine systems.
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