For computing a percolation threshold, the pore space was isolated from the segmented image (fig. S6A). A local thickness map was computed from the pore space voxels (using ImageJ software). For this computation, the algorithm inserts spheres (using a distance map in the pore space), with a radius that can fit into the pore space along the medial axis (fig. S6B). An interactive thresholding (using Avizo-9 software) was then applied to find the minimum (threshold) radius of the sphere at which the pore space is connected across the image axes. Figure S8C shows the image of the spheres (converted to voxel data) that have a minimum (threshold) radius of 17 μm at which the pore space is connected across the vertical axis. Different colors represent disconnected clusters of the pore space at this particular threshold. The connected cluster is then isolated using an axis connectivity algorithm (fig. S6D). The connected cluster from fig. S6D is masked on fig. S6B to obtain the radius distribution of the connected and percolating pore space (fig. S6E). Figure S6F shows the image with a threshold radius of 17.5 μm at which the pore space is not connected across any axis. The disconnection is marked by a dashed (white) circle. The image processing protocol in fig. S6 shows an example for computing a percolation threshold radius in two-dimensional pore space. In three dimensions, a higher threshold radius is expected as we show in Results.

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