## 2 Materials and Methods
### Protocols for 3D Image Analysis  
3D image analysis was performed using Dragonfly (version 2022), a software package by Object Research Systems [67]. A multi-stage protocol originally developed and tested in the earlier brick porosity study [51] was applied:  
1. Intensity calibration of each micro-CT image at the outset brought the set of images closer to each other in intensity values with the goal of reducing the number of segmentation models that had to be developed by machine learning/deep learning; since then, some models worked well for multiple images. 2. A Region of Interest (ROI) for each micro-CT image was created, selected to remove the background and to exclude any surface roughness area (Figure 2, left). Some of the ceramic samples also have a slip or a glaze layer, or both a glaze and a thin slip beneath it. These layers were excluded from the ROI since the purpose here is to characterize pores within the ceramic body itself. 3. A segmentation model was developed that could separate the pore areas from the silica-rich particles and from the ceramic matrix. Since simple thresholding does not work well with these images, the Dragonfly tool for \"segment with artificial intelligence\" was used. Beginning with one slice, a large frame was created. Initial Otsu thresholding [68] was used to separate the image into the pore, silica particle, and matrix classes. Errors in that initial thresholding were corrected using a manual paintbrush tool. Several different machine learning and deep learning models were then trained using the data in the initial frame, as it is known that such models can improve the accuracy of segmentation when grey-level thresholding does not work well [49]. Once the models were trained, the results were viewed on a second slice, and the best-performing model used for further training, after additional manual corrections were applied with the paintbrush tool. Training followed by manual corrections continued until we had a model that gave good segmentation with no further corrections needed. We could usually stop after three slices; the maximum that was ever needed was five slices. The final fully trained model was then applied to the entire ROI (Figure 2, center). Individual models only needed to be developed about one-third of the time; initial intensity calibration of images meant that some models worked well for multiple images. 4. The pore class was extracted from the segmentation result (Figure 2, right). It was processed to eliminate any speckling noise or other imaging artifacts. The total pore volume percentage was then calculated. 5. The percentage of the pores that are accessible to any surface versus the percentage of inaccessible interior-only ones was calculated. This was carried out by overlaying a single-pixel-wide shell of the ROI and calculating what percentage of pores touch the shell in any slice (so are accessible to a surface) and what percentage do not (interior-only pores). 6. A multi-ROI was created for the pores in each image by automatically grouping the voxels into components based on connectivity. Then, 16 statistical properties related to various shape and size parameters were calculated for the individual pores in each image. These variables were selected based on properties found to be significant in the previous brick micro-CT study [51]. 7. A sparse graph of pores was created for each image (Figure 3). This is a pore system model with spheres representing the pores and straight lines representing the connections between them (also called pore throats). These provided data primarily useful for quantitative connectivity data. Four variables were recorded: maximum and mean connectivity for the pores in each image, the connectivity standard deviation, and the percentage of pores that are completed isolated and unconnected to any other pores in the system. 8. Additional data related to pore connections were obtained from a dense graph of pores.