Geometric Analysis of Magnetic Labyrinthine Stripe Evolution via U-Net Segmentation

Abstract

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.

Figures (15)

• Figure 1: Magnetic stripe pattern in Bi:YIG film.
• Figure 2: Magnetic field annealing transition. The crops are from the same region at different demagnetization steps.
• Figure 3: (a) The image is segmented with a U‑Net. (b) Threshold is applied to binarize the image. (c) The border path of the dark regions are extracted through contour finding. (d) A spline is fitted to the contour for modeling the real space contour. (e) Topological defects are detected with TM-CNN. (f) Medial skeletonization is performed to characterize the inner path along the dark regions. (g) The skeletons are mapped into a graph. (h) Spline fitting is performed for modeling the real space paths between defects. (i) The real space length of the border and inner paths are used to characterize the magnetic labyrinthine patterns.
• Figure 4: Field annealing protocol for positive and negative sequences. Images “Type A” are obtained after applying upward-pointing magnetic field (orange) and images “Type B” are obtained after applying downward-pointing magnetic field (blue).
• Figure 5: Regions with low noise and distinct patterns (yellow) extracted from the magnetic stripe image for U-Net model training. Purple areas represent high-noise regions that were excluded from the training dataset.