A Deep Learning Approach for Semantic Segmentation of Unbalanced Data in Electron Tomography of Catalytic Materials

Heterogeneous catalysts possess complex surface and bulk structures, relatively poor intrinsic contrast, and often a sparse distribution of the catalytic nanoparticles (NPs), posing a significant challenge for image segmentation, including the current state-of-the-art deep learning methods. To tackle this problem, we apply a deep learning-based approach for the multi-class semantic segmentation of a $\gamma$-Alumina/Pt catalytic material in a class imbalance situation. Specifically, we used the weighted focal loss as a loss function and attached it to the U-Net's fully convolutional network architecture. We assessed the accuracy of our results using Dice similarity coefficient (DSC), recall, precision, and Hausdorff distance (HD) metrics on the overlap between the ground-truth and predicted segmentations. Our adopted U-Net model with the weighted focal loss function achieved an average DSC score of 0.96 $\pm$ 0.003 in the $\gamma$-Alumina support material and 0.84 $\pm$ 0.03 in the Pt NPs segmentation tasks. We report an average boundary-overlap error of less than 2 nm at the 90th percentile of HD for $\gamma$-Alumina and Pt NPs segmentations. The complex surface morphology of the $\gamma$-Alumina and its relation to the Pt NPs were visualized in 3D by the deep learning-assisted automatic segmentation of a large data set of high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) tomography reconstructions.