Data-efficient U-Net for Segmentation of Carbide Microstructures in SEM Images of Steel Alloys

TL;DR

This work tackles carbide segmentation in SEM images of reactor-pressure-vessel steels where gray-level overlap makes thresholding unreliable. It introduces a data-efficient segmentation pipeline based on a lightweight U-Net trained on only $10$ annotated images and augmented with uncertainty calibration via temperature scaling. The model achieves a Dice coefficient of $0.98$ on held-out test data, substantially outperforming a classical image-analysis baseline, and generalizes to a different steel type with a Dice of $0.94$, suggesting robust applicability for rapid, automated microstructure quantification. The approach offers practical impact for alloy design and structural integrity assessments, while reducing labeling effort by an order of magnitude compared to prior data-efficient baselines.

Abstract

Understanding reactor-pressure-vessel steel microstructure is crucial for predicting mechanical properties, as carbide precipitates both strengthen the alloy and can initiate cracks. In scanning electron microscopy images, gray-value overlap between carbides and matrix makes simple thresholding ineffective. We present a data-efficient segmentation pipeline using a lightweight U-Net (30.7~M parameters) trained on just \textbf{10 annotated scanning electron microscopy images}. Despite limited data, our model achieves a \textbf{Dice-Sørensen coefficient of 0.98}, significantly outperforming the state-of-the-art in the field of metallurgy (classical image analysis: 0.85), while reducing annotation effort by one order of magnitude compared to the state-of-the-art data efficient segmentation model. This approach enables rapid, automated carbide quantification for alloy design and generalizes to other steel types, demonstrating the potential of data-efficient deep learning in reactor-pressure-vessel steel analysis.

Figures (6)

• Figure 1: Data and model architecture. SEM images (top) of a RPV steel (JFL) acquired with SE and InLens detectors (top left and top center, respectively) and the corresponding manually annotated target label mask is overlaid in cyan onto the SEM image (top right). Red squares indicate the example tile shown in the bottom row as the two input channels (bottom left) for the U-net (bottom center; adapted from Ronneberger_2015) and the network output and corresponding labels (bottom right).
• Figure 2: Model training. (left) Training and validation loss curves over 110 epochs. (right) Dice-Sørensen coefficient on the validation set.
• Figure 3: Segmentation results. (top) Example segmentation results on the test set. The model accurately segments carbides of varying sizes and shapes. (bottom) Box plot of Dice-Sørensen coefficients on the test set for the classical image-analysis baseline and our U-Net model. The U-Net significantly outperforms the baseline (Wilcoxon signed-rank test $p<0.001$).
• Figure 4: Model generalization. Application of the trained U-Net to SEM images from a different steel (ANP-3). Accurate segmentation of carbides confirms that the model generalizes beyond the training dataset. The baseline achieved a Dice-Sørensen coefficient of 0.90, while the U-Net achieved 0.94.
• Figure 5: Uncertainty estimation (top right) Reliability diagram before and after temperature scaling. The reliability diagram shows the relationship between predicted probabilities and observed frequencies of the positive class (carbide pixels). The diagonal line represents perfect calibration, where predicted probabilities match observed frequencies. After applying temperature scaling with $T=1.87117$ (orange line), the predictions are better calibrated than without any calibration (blue line) and also better calibrated than with mean-variance estimation (green line), as shown by the curve being closer to the diagonal line. (top center) input image, (top right) target label, (bottom center) model output after temperature scaling, (bottom right) model output with mean-variance estimation. The colors represent the model's confidence in its predictions, with dark green representing pixels classified as true with low confidence, light green medium confidence and yellow high confidence (as indicated in the color bar in the bottom right).