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Data-efficient crack quantification in lithium-ion cathodes using foundation model transfer

Thorsten Tegetmeyer-Kleine, Thomas Schmitt, Phillip Aquino, Christiane Rahe, Dirk Uwe Sauer, Weihan Li

arXiv:2608.27162v1cond-mat.mtrl-scics.CVcs.LG

TL;DR

Quantifying particle cracking in lithium-ion cathodes is limited by destructive microscopy and labor-intensive expert annotation. This paper uses frozen foundation-model features with lightweight decoding and iterative annotation to measure crack morphometrics, finding substantially more late intergranular cracking and tortuous networks after cycling than after initial or calendar-aged conditions.

  • Problem

    Quantifying particle cracking in lithium-ion cathodes is bottlenecked by destructive cross-sectional microscopy and labor-intensive expert annotation.

    Source: §1 · pp. 2–3

  • Method

    A frozen self-supervised vision-transformer encoder, lightweight decoder, and iterative model-assisted annotation infer per-particle morphometrics across three crack classes.

    Source: §1 · p. 4, Multi-class segmentation of crack types · p. 15

  • Results

    4.58% late intergranular crack area fraction occurred in the cycled-aged sample versus 0.52% initially and 0.49% after calendar aging, with more tortuous networks after cycling.

    Source: Per-particle morphometric quantification · p. 9, §3 · p. 11

  • Takeaways & Limitations

    A single destructive cross-section can provide population-scale per-particle crack statistics for battery lifetime research and aging assessment.

    Source: §1 · p. 4, §4 · p. 14

    Because only one SEM cross-section represented each aging condition, the statistics describe within-cross-section heterogeneity rather than cell- or lot-level population inference.

    Source: §3 · p. 14

Abstract

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Battery lifetime is central to sustainable electrification, yet the particle cracking that drives lithium-ion cathode aging is hard to measure: quantitative microscopy of this degradation is bottlenecked by annotation, because each destructive electron-microscopy cross-section spans hundreds of megapixels and pixel-level expert labelling requires hours per image. We show that a frozen self-supervised vision-transformer encoder, combined with a lightweight trainable decoder and iterative model-assisted annotation, turns this sparse labelling budget into population-scale degradation measurements. Applied to three 120-megapixel NMC cathode cross-sections representing initial, cycled-aged and calendar-aged states, the framework distinguishes intragranular cracks from early- and late-stage intergranular cracks and yields per-particle distributions of crack width, tortuosity and area fraction. Late intergranular crack coverage reaches 4.6% in the cycled sample versus 0.5% in the initial and calendar-aged samples, forming more tortuous, higher-coverage networks, consistent with degradation from repeated electrochemical cycling rather than elevated-temperature storage alone. A single destructive image yields the population-level statistics needed for lifetime-extending design, aging assessment and second-life decisions.

1. Introduction · 2. Results · Multi-class segmentation performance

The study addresses destructive, annotation-intensive crack quantification in NMC cathodes with a sparse-label framework using a frozen self-supervised vision-transformer encoder and lightweight decoder. Applied to three aging conditions, the model resolves three crack classes with population-scale morphometric potential despite contrast variation.

1. Introduction

  • Destructive high-resolution microscopy and labour-intensive expert annotation limit quantitative tracking of cathode cracking and degradation evolution.FIB-SEM and nano-CT resolve fine details but are destructive, whereas laboratory micro-CT is repeatable but generally lacks resolution for small cracks.Source: §1 · pp. 2–3
  • Three crack classes distinguish intragranular, early intergranular, and late intergranular morphologies associated with different structural locations and degradation mechanisms.Intragranular cracks traverse individual grains, while intergranular cracks propagate along grain boundaries; the framework targets semantically distinct early- and late-stage intergranular cracks.Source: §1 · pp. 2–4
  • The framework freezes a self-supervised vision-transformer encoder and trains only a lightweight decoder, concentrating scarce annotation on task-specific adaptation.An iterative model-assisted workflow expands 79 hand-labelled SEM tiles into a larger expert-corrected dataset.Source: §1 · pp. 3–4

2. Results

  • Three SEM cross-sections represented initial, cycled-aged, and calendar-aged NMC cathodes, each spanning approximately 17k×7k pixels at 22.3 nm/px.The samples showed condition-dependent differences in SEM contrast, brightness, and crack density, with pixel-level annotations defining the three crack classes.Source: §2 · p. 4, Figure 1 · p. 5

Multi-class segmentation performance

  • 79 expert-labelled seed tiles produced a mean Dice score of 0.49 before model-assisted correction expanded the dataset to 482 expert-corrected tiles.The expanded set contained 79 fully manual seed tiles and 403 model-assisted tiles distributed across the three cross-sections.Source: Figure 2 · p. 6, Multi-class segmentation performance · p. 8
  • 0.580 mean Dice was achieved across the three classes, with intragranular 0.575, early intergranular 0.513, and late intergranular 0.653.Mean precision was 0.729 and mean recall was 0.485 on the expert-corrected tile set (n=482; τ=0.1), while outputs resolved all classes across the three conditions.Source: Figure 3 · p. 7, Multi-class segmentation performance · p. 8
  • 0.587 mean clDice and boundary F1 increasing from 0.446 at d = 1 px tolerance to 0.600 at d = 2 px indicate that narrow-crack errors are partly boundary-shift effects.Many cracks are only 2–5 pixels wide, making pixel-exact Dice conservative for morphology-preserving predictions.Source: Multi-class segmentation performance · p. 8
  • SAM2 achieved binary Dice scores of 0.019 without prompts and 0.025 with Otsu-derived point prompts, and cannot directly resolve the required crack morphologies.The evaluation used the same 482-tile reference set with a binary crack-versus-background target.Source: Multi-class segmentation performance · pp. 8–9

Per-particle morphometric quantification

Per-particle distributions of crack width, tortuosity, and area fraction distinguish degradation morphologies beyond pixel-overlap metrics. Cycling particularly increases and complicates late-stage intergranular cracking, while the measurements describe within-cross-section heterogeneity rather than population-level inference.

Morphometric measurements

  • Per-particle width, tortuosity, and area-fraction distributions extracted from class maps resolved degradation morphologies that pixel-overlap metrics alone could not capture.The framework therefore provided morphology-sensitive measurements at the particle level.Source: Per-particle morphometric quantification · p. 9

Late intergranular cracking

  • 4.58% late intergranular area fraction in the cycled-aged sample exceeded 0.52% initially and 0.49% after calendar aging, an approximately ninefold increase over initial.This pattern is consistent with progressive grain-boundary degradation during repeated electrochemical cycling.Source: Per-particle morphometric quantification · p. 9
  • Late intergranular cracks in the cycled-aged sample were markedly more tortuous, indicating more interconnected grain-boundary crack networks than in the initial and calendar-aged samples.Mean late-crack width increased modestly from 159 ± 22 nm initially to 167 ± 39 nm after cycling, without statistical significance.Source: Per-particle morphometric quantification · p. 9

Condition-level distributions

  • Combined-class distributions retained the cycled-aged shift toward larger widths and tortuosities, including a broader late-intergranular width tail beyond 200 nm.These condition-level trends persisted across threshold reruns.Source: Per-particle morphometric quantification · p. 10

Scope and sampling

  • ROI-level statistics characterized within-cross-section morphometric heterogeneity rather than cell- or lot-level population inference because each condition used a single cross-section.Intergranular ROIs included 97 initial, 69 cycled-aged, and 49 calendar-aged particle-scale regions; intragranular ROIs included 446, 610, and 623 connected components, respectively.Source: Per-particle morphometric quantification · pp. 9, 11

3. Discussion

The discussion links cycling to enriched late intergranular cracking and greater crack coverage and tortuosity, while presenting sparse-label morphometric inference as a population-scale measurement framework. It also emphasizes robustness, broader applicability, and limitations from the three-cross-section case study.

Degradation interpretation

  • Cycling strongly enriches late intergranular cracking in NMC, unlike elevated-temperature calendar aging, with greater crack area fraction and geometric tortuosity.The findings are consistent with progressive grain-boundary degradation during repeated electrochemical lithiation–delithiation and the development of more interconnected crack networks.Source: §3 · p. 11
  • Anisotropic lattice evolution during cycling is consistent with mechanically incompatible strain between differently oriented primary grains and intergranular crack development.The described evolution involves in-plane lattice contraction and c-axis expansion followed by collapse near the H2→H3 transition at high state of charge.Source: §3 · p. 11

Methodological contribution

  • The framework extracts per-particle crack width, tortuosity and area-fraction distributions from sparse, imperfect SEM annotations using a frozen self-supervised encoder and lightweight decoder.Per-pixel class probabilities provide the intermediate representation for deriving these morphometrics while concentrating expert labeling on the scientific question.Source: §3 · p. 11

Robustness

  • Robust morphometric trends persist across thresholds and descriptors, because width and tortuosity average over crack geometry rather than relying on exact pixel overlap.This supports degradation signatures beyond pixel-level segmentation metrics despite local annotation uncertainty.Source: §3 · p. 13

Broader implications

  • Each destructive cross-section yields hundreds of per-particle morphometric measurements, enabling population-level crack characterization and potential application to other destructive-microscopy domains.The framework is presented as relevant to manufacturing quality assurance, aging diagnostics and quantification of single-crystal NMC designs.Source: §3 · pp. 13–14

Limitations

  • The case study evaluates one frozen vision-transformer encoder and lightweight decoder across only three SEM cross-sections, leaving systematic architecture and training-seed benchmarking for future work.The authors frame the sparse-label morphometric-inference framework, rather than optimization of a specific segmentation architecture, as the primary focus.Source: §3 · p. 14

4. Conclusions · 5. Methods · Multi-class segmentation of crack types

The paper introduces a sparse-label framework that uses frozen self-supervised vision-transformer features and a trainable decoder to infer per-particle crack morphometrics. Crack typing is formulated as three-class semantic segmentation, supported by iterative expert-corrected annotation and calibrated operating-point evaluation.

4. Conclusions

  • The framework converts few expert annotations into per-particle crack morphometrics while concentrating annotation effort on quantification rather than representation learning.It uses frozen self-supervised vision-transformer features rather than learning the representation from scratch.Source: §4 · p. 14
  • 79 hand-labelled tiles grew into a 482-tile expert-corrected reference set through iterative model-assisted annotation across three NMC cathode cross-sections.The framework resolved intragranular as well as early crack categories in the supplied conclusion passage.Source: §4 · p. 14

Multi-class segmentation of crack types

  • Pixel-wise crack typing is formulated as three-class semantic segmentation with intragranular, early intergranular, and late intergranular labels.The intragranular class reflects defect-induced crack initiation within primary particles.Source: Multi-class segmentation of crack types · p. 15
  • 85.7 M frozen parameters and 768-dimensional patch embeddings come from the DINOv3 ViT-B/16 encoder, while the DeepLabV3+ decoder has 17.8 M trainable parameters.Each greyscale 1024 × 1024 px SEM tile is replicated to three channels and produces a 64×64×768 feature map from 16 × 16 patches.Source: Multi-class segmentation of crack types · p. 15
  • τ=0.1 was selected on the validation precision–recall curve, after which binary masks were obtained by thresholding class probabilities.Training minimised a weighted sum of binary cross-entropy, mean-squared-error, and Dice losses.Source: Multi-class segmentation of crack types · p. 15
  • 80%/20% per-image partitioning yielded 96 held-out validation tiles from the 482-tile pool, comprising 79 manual seed tiles and 403 model-assisted, expert-corrected tiles.The 403 corrected tiles were distributed as 160 cycled-aged, 81 calendar-aged, and 162 initial tiles; metrics on all 482 tiles served operating-point calibration.Source: Multi-class segmentation of crack types · p. 15

Baseline evaluation using SAM2 · Inference and overlay mask generation · Segmentation mask analysis pipeline

The section evaluates SAM2 against the DINOv3 framework on binary crack segmentation, then describes full-resolution inference, overlay generation, and morphometric extraction from predicted masks. The pipeline converts likelihood maps into calibrated particle-level crack geometry and width measurements.

Baseline evaluation using SAM2

  • SAM2 was evaluated using automatic dense-grid mask generation and prompted segmentation with Otsu-thresholded dark-region point prompts.The comparison used facebook/sam2.1-hiera-large in two configurations.Source: Baseline evaluation using SAM2 · p. 15
  • Because SAM2 is class-agnostic, the three reference classes were collapsed into a binary crack-versus-background target for comparison.This binary evaluation allowed comparison with the DINOv3 framework.Source: Baseline evaluation using SAM2 · p. 15
  • Dice = 0.77 was achieved by the DINOv3 framework against SAM2 values reported in Table A.1 on the binary metric.The reported metric is for crack-versus-background segmentation rather than the original three-class target.Source: Baseline evaluation using SAM2 · p. 15

Inference and overlay mask generation

  • Full-resolution inference on ∼17,000×7,000 px images used overlapping sliding windows with per-class prediction averaging across overlapping tiles.This strategy was applied to the initial, calendar-aged, and cycled-aged probes.Source: Inference and overlay mask generation · p. 16
  • Final per-class binary masks were thresholded and rendered as alpha-blended overlays at native resolution for side-by-side probe comparison.The overlays supported visual comparison across the three aging states.Source: Inference and overlay mask generation · p. 16

Segmentation mask analysis pipeline

  • The morphometric pipeline cleans each likelihood map into a binary crack mask, extracts particle-level ROIs, and derives skeleton-based width and geometry distributions.ROIs represent individual cathode secondary particles or small clusters.Source: Segmentation mask analysis pipeline · p. 16
  • Measurements are computed in pixel units and converted to physical units through SEM calibration after thresholding m(x) at τ into B(x) = 1{m(x) ≥τ}.The thresholded binary field forms the basis for subsequent crack measurements.Source: Segmentation mask analysis pipeline · p. 16
  • Skeletonisation reduces each ROI’s binary crack mask to one-pixel centrelines, while distance-transform sampling estimates crack width from maximal inscribed disks.Non-finite or nonpositive samples are excluded from summary statistics but retained as zeros in visualisation maps.Source: Segmentation mask analysis pipeline · p. 16

Geometric descriptors and width distributions

The section defines geometric descriptors for crack morphology, including topology, orientation, anisotropy, tortuosity and transverse roughness. It also characterizes crack-width distributions using descriptive statistics, histograms, ECDFs and quartiles for cross-ROI comparison.

Geometric descriptors

  • Topology classifies crack pixels by 3 × 3 neighbour degree into endpoints, branch points, and isolated pixels.Endpoints have degree 1, branch points degree ≥3, and isolated pixels degree 0.Source: Geometric descriptors and width… · p. 16
  • Orientation and anisotropy are derived from covariance eigenpairs of centered skeleton coordinates.Orientation is reported over [0°, 180°).Source: Geometric descriptors and width… · p. 16
  • Geometric tortuosity is the centreline-length-to-projected-span ratio along the principal direction, distinct from effective pore-network transport tortuosity.Because length uses a raw skeleton-pixel count, near-linear cracks can produce tortuosity marginally below unity without indicating measurement error.Source: Geometric descriptors and width… · p. 17

Width distributions

  • Crack widths are summarized by minimum, maximum, mean, median, and standard deviation, with histograms and ECDFs visualizing their distributions.The ECDF gives the fraction of centreline length with width ≤t.Source: Geometric descriptors and width… · p. 17
  • Quartiles P25, P50, and P75 are marked to support cross-ROI comparison and aggregated ECDF analysis.Aggregated ECDFs are presented across multiple panels of Fig. 5.Source: Geometric descriptors and width… · p. 17

Statistical analysis · Reporting and assumptions · CRediT authorship contribution statement

The analysis compares per-ROI crack morphometrics across aging conditions with non-parametric tests and multiple-comparison correction, while reporting calibrated pixel-based measurements and threshold sensitivity. Contributions span conceptualization, methodology, analysis, data curation, supervision, funding, and manuscript review, with all authors approving the final manuscript.

Statistical analysis

  • Per-ROI area fraction, mean width, and geometric tortuosity distributions were compared between aging conditions.Source: Statistical analysis · p. 17
  • Two-sided Mann–Whitney U tests assessed differences between aging conditions.Source: Statistical analysis · p. 17
  • Cliff’s δ provided a non-parametric effect-size estimate, with Benjamini–Hochberg correction controlling family-wise multiple comparisons.Source: Statistical analysis · p. 17

Reporting and assumptions

CRediT authorship contribution statement

Appendix A. Extended data … S1. Training configuration

The appendix validates threshold selection, compares segmentation baselines, and tests morphometric sensitivity, while supplementary methods specify sample preparation, SEM imaging, and frozen-encoder training configuration. Full-resolution inference uses overlapping windows, stitching, optional intensity gating, cleanup, and particle-level ROI extraction.

Appendix A. Extended data

  • A low operating threshold reflects extreme foreground–background imbalance, with crack pixels comprising <1% of the image.Per-class precision–recall curves and Dice-versus-threshold plots support threshold selection.Source: Figure A.1 · p. 19
  • Zero-shot SAM2 configurations were evaluated against fine-tuned DINOv3 on the same 482-tile reference set using binary Dice and IoU.Reference labels were collapsed from three classes to crack versus background, retaining the higher filtered or unfiltered SAM2 value per tile; confidence intervals used 1000 bootstrap resamples.Source: Table A.1 · p. 19
  • Area fraction decreases monotonically as threshold τ increases, whereas mean crack width and tortuosity remain more stable across τ ∈ {0.05, 0.1, 0.2, 0.3, 0.5}.The appendix attributes this contrast to suppression of low-confidence pixels and skeleton-based averaging over retained crack pixels.Source: Figure A.2 · p. 20
  • Morphometric statistics are reported by sample and crack class as mean ± std across ROIs at a pixel size of 22.3 nm.These statistics support the per-condition morphometric comparisons in the main article.Source: Table A.2 · p. 20

Supplementary Notes

  • Three NMC cathode conditions were prepared from commercial Ni-rich NCM pouch cells: formation-only initial, K100 after 100 charge–discharge cycles, and K187 stored at 45°C.One cell per condition was prepared for post-mortem cross-sectioning.Source: Cell, aging, and post-mortem sample… · p. 22

Cross-section SEM imaging

  • SEM cross-sections were acquired at 10 kV using a ZEISS Supra 55 BSE detector, with tiles assembled without line or frame averaging at approximately 22.3 nm/px.The supplied passage also reports per-sample pixel sizes of 22.29 nm/px for K100, 22.38 nm/px for K187, and 22.28 nm/px for the initial sample.Source: Cross-section SEM imaging · p. 22

S1. Training configuration

  • Only the decoder and output head were trained while the encoder remained fixed, using AdamW with η=10^-4, β1=0.9, β2=0.98, ε=10^-9, and λ=10^-3.Training used a cosine-cyclical schedule with 4 warm-restart cycles and a minimum learning rate of 5×10^-5.Source: S1. Training configuration · p. 22
  • Training ran for up to 500 epochs with patience 20 early stopping, batch size 4 at 1024×1024 px in FP32, seed 42, and checkpoint selection at epoch 465.The objective combined per-channel weighted BCE, MSE, and Dice losses with equal weights λBCE = λMSE = λDice = 1.Source: S1. Training configuration · p. 23

S3. Segmentation operating point and threshold selection

All quantitative results use a decision threshold of τ=0.1, selected from the validation precision–recall curve to maximize class-averaged Dice for highly imbalanced thin-crack segmentation. Crack pixels comprise less than 1% of tile area, and higher thresholds reduce recall faster than false positives.

Threshold selection

S4. Supplementary morphometric definitions

The pipeline uses standard morphometric conventions for skeleton topology and crack-width distributions. Skeleton pixels are classified by local eight-connected neighbourhood degree, while width ECDFs are summarized with robust quartiles.

Skeleton topology

  • Skeleton pixels are classified on an eight-connected 3×3 window by neighbourhood degree: degree 1 endpoints, degree ≥3 branch points, and degree 0 isolated pixels excluded from path-length statistics.This is the standard medial-axis classification used throughout connected-component morphometry.Source: S4. Supplementary morphometric… · p. 25

Width statistics

  • Width statistics use the empirical cumulative distribution function, defined as the fraction of centreline length with width ≤t.The width values are derived from the Euclidean distance transform.Source: S4. Supplementary morphometric… · p. 25
  • Width ECDFs are summarized by P25, P50, and P75 rather than mean and standard deviation because distributions are typically heavy-tailed and right-skewed by junction pixels.These quartiles are used as robust descriptors for cross-ROI comparisons.Source: S4. Supplementary morphometric… · p. 25

S5. Spatial overlap quantification · S6. SAM2 baseline details · S7. Statistical-analysis bookkeeping

The supplementary analyses define how spatial overlap, SAM2 baseline outputs, and multiple-comparison statistics were handled. Validation metrics reflect overlapping within-image tiles, SAM2 was evaluated class-agnostically, and the headline cycling-versus-baseline claim survived FDR adjustment at q < 0.001 in both test families.

S5. Spatial overlap quantification

  • Each validation tile was assigned an overlap fraction computed over training tiles from the same SEM cross-section.The tiling used 50%-overlap sliding windows.Source: S5. Spatial overlap quantification · p. 25
  • 50% adjacent-tile area sharing and the random 80/20 partition made the median overlap fraction across 96 validation tiles ≈0.50 by construction.The stated probability that all four cardinal neighbours are validation tiles is 0.24 ≈0.002.Source: S5. Spatial overlap quantification · p. 25
  • Image-disjoint splits were omitted because only three SEM cross-sections were available, one per aging condition, making leave-one-condition-out validation infeasible without losing condition coverage.A rotating image-disjoint sensitivity analysis was left for future work pending additional independent cross-sections per condition.Source: S5. Spatial overlap quantification · pp. 25–26

S6. SAM2 baseline details

  • SAM2 was evaluated in automatic mode with a 64 × 64 dense point grid and in prompted mode with Otsu-derived centroid prompts, allowing up to 128 prompts per tile.Prompted candidates were area-bounded and selected by lowest mean intensity, with candidate area ≤0.25 of the tile as stated in the passage.Source: S6. SAM2 baseline details · p. 26
  • SAM2 outputs were compared against a binary crack-versus-background target by collapsing the three-class reference, while heuristic width-based class assignment was rejected.The rejection avoided conflating SAM2 segmentation quality with the supervised classifier.Source: S6. SAM2 baseline details · p. 26

S7. Statistical-analysis bookkeeping

  • 27 comparisons covered 3 ROI subsets, 3 morphometric metrics, and 3 condition pairs, with Benjamini–Hochberg-adjusted q-values reported within this family.ROI counts were 194/138/98 for the intergranular early subset as stated in the passage.Source: S7. Statistical-analysis bookkeeping · p. 26
  • The separate 9-test intergranular-late family also used Benjamini–Hochberg adjustment, and the headline cycling-versus-baseline claim survived FDR adjustment at q < 0.001 in both families.The intergranular-late ROI counts were 97/69/49.Source: S7. Statistical-analysis bookkeeping · p. 26

S8. Software environment and reproducibility · Supplementary Figures

The supplementary materials specify the training environment, model configuration, augmentation and inference settings, and automated ROI-extraction criteria. Supplementary figures document skeleton-based morphometrics, boundary-F1 behavior, method diagnostics, ROI detection, and segmentation performance across crack densities.

S8. Software environment and reproducibility

  • All models ran on a single NVIDIA A100 80 GB PCIe GPU under Ubuntu 22.04.5 LTS with Python 3.10.13 and the listed deep-learning and image-analysis packages.The environment used PyTorch 2.4.0 with CUDA 12.1 and cuDNN 9.1.0, torchvision 0.19.0, PyTorch-Lightning 2.0.8, timm 0.9.6, scikit-image 0.25.2, SciPy 1.15.3, NumPy 1.26.4, and OpenCV.Source: S8. Software environment and… · p. 26
  • The frozen DINOv3 ViT-B/16 encoder fed a DeepLabV3+ decoder with ASPP dilation rates 6/12/18 and low-level stride 2.The configuration had 17.8 M trainable parameters and 85.7 M frozen parameters.Source: S8. Software environment and… · p. 27
  • Training used online augmentation only on the training split, while validation data remained unaltered.The Dice loss used smoothing constant ε=1, and augmentation operations were independently sampled at their specified probabilities, including random affine transforms at probability 0.5 with rotation up to ±45◦.Source: S8. Software environment and… · p. 27
  • Inference binarised per-class probability maps at τ=0.1 and extracted particle ROIs using blurred backscatter thresholding, morphological closing, fragment merging, and minimum component criteria.The pipeline used a 5 × 5 Gaussian pre-blur, a 5×5 elliptical kernel, a 50 px merge radius, particle area ≥10,000 px, crack area ≥1000 px, and skeleton length ≥100 px.Source: S8. Software environment and… · p. 27

Supplementary Figures

  • Skeleton-based extraction converted segmented crack masks within each ROI into medial-axis skeletons with branch points and endpoints for morphometric analysis.Supplementary Figure S1 illustrates the procedure for an intergranular late ROI, where the crack mask covered 16.1% of pixels, or 17 666 px.Source: Figure S1 · p. 28
  • Median boundary-F1 was 0.45–0.46 per class at 1-pixel tolerance and 0.58–0.62 at 2-pixel tolerance, indicating that 1–2-pixel boundary misalignment drives moderate pixel-exact Dice.The comparison covers intragranular, early intergranular, and late intergranular crack classes.Source: Figure S2 · p. 29
  • Supplementary diagnostics compare expert references with SAM2-auto, SAM2-prompted, and fine-tuned DINOv3 predictions using binary Dice and error maps.The diagnostic is shown for tile 100_0000_00038, the Fig. 1 sample tile, with cyan true positives, magenta false positives, amber false negatives, and black true negatives.Source: Figure S3 · p. 30
  • Across 482 expert-corrected tiles, Dice and IoU were plotted against foreground pixel fraction for intragranular, early intergranular, and late intergranular cracks, with Pearson r = 0.21–0.32.The supplementary figures also show the automated ROI-detection workflow and its thresholding, post-merge, and rejected-component stages for the cycled-aged image.Source: Figure S4 · p. 31, Figure S5 · p. 32

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