find_porosity_threshold#

This function dilates the solid phase iteratively until the void space no longer percolates. The percolating porosity is used in a popular tortuosity correlation by Tomadakis and Sotirichos [1]:

\[ tau = \bigg(\frac{1-\varepsilon}{\varepsilon - \varepsilon_p}\bigg)^{\alpha}\]
import matplotlib.pyplot as plt

import porespy as ps

im#

im = ps.generators.blobs([100, 100], porosity=0.7, blobiness=0.5, seed=1)

fig, ax = plt.subplots(figsize=[4, 4])
ax.imshow(im)
ax.axis(False);
../../../_images/fb7a91e7fa68323a220dc94a6832d3e3c8ff85d3c2698dee160dae91e2d2b351.png 
r = ps.metrics.find_porosity_threshold(im)
print(r)

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Results of find_porosity_threshold generated at Sat Jul 12 16:19:56 2025
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eps_orig                  0.7
eps_orig_perc             0.6771
eps_thresh                0.2843
eps_thresh_perc           0.2179
R                         7
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The function returns a Results object with several attributes. eps_orig is the original porosity of im while eps_orig_perc is the fraction of the original porosity that percolates between the inlet and outlet faces (which default to the x=0 and x=-1 faces). eps_thresh is the total porosity of the image at the percolation threshold, meaning that if the solid were dilated one more time that the image would no longer percolate. eps_thresh_perc is the fraction of the void space at the percolation threshold which is connected to the percolating cluster(s).

Lastly, R is for reproducing the percolating image. This is possible since the dilation is done by thresholding the distance transform of the void space. For instance:

edt = ps.tools.get_edt()
dt = edt(im)

fig, ax = plt.subplots(1, 3, figsize=[12, 4])
ax[0].imshow(dt/im)
ax[0].axis(False)
ax[1].imshow((dt >= r.R)/im)
ax[1].axis(False)
ax[2].imshow((dt >= (r.R + 1))/im)
ax[2].axis(False);
../../../_images/2f80837d878a49c2e5498999dd50509d71466864e167cd07ab04e1fad5cb34e8.png

‘axis’#

Percolation is a direction dependent phenomena. By default the function considers the x-direction, but this can be specified:

r = ps.metrics.find_porosity_threshold(im, axis=1)
print(r)

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Results of find_porosity_threshold generated at Sat Jul 12 16:19:56 2025
――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――――
eps_orig                  0.7
eps_orig_perc             0.6771
eps_thresh                0.4754
eps_thresh_perc           0.4693
R                         4
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Percolation is reached in the y-direction sooner due to the relatively small opening on the right hand side which closes at R==4.

fig, ax = plt.subplots(1, 3, figsize=[12, 4])
ax[0].imshow(dt/im)
ax[0].axis(False)
ax[1].imshow((dt >= r.R)/im)
ax[1].axis(False)
ax[2].imshow((dt >= (r.R + 1))/im)
ax[2].axis(False);
../../../_images/6cc607bd0a35d11e61ee0adba31723da3121d5ec3dcceba7e5a23ae0e173660d.png

conn#

The connectivity of the pixels/voxels can also be specified as either min or max, meaning 4 or 8 neighbors in 2D, and 6 or 26 in 3D.