boxcount#

A method for measuring the fractal dimension of an image

import matplotlib.pyplot as plt
import numpy as np
import porespy as ps

The arguments and their defaults for this function are:

import inspect
inspect.signature(ps.metrics.boxcount)
<Signature (im, bins=10)>
im = ps.generators.sierpinski_foam(dmin=5, n=5, ndim=2)
fig, ax = plt.subplots(1, 1, figsize=[6, 6])
ax.imshow(im, interpolation='none', origin='lower')
ax.axis(False);
../../../_images/308838144227d64968417f555b835087e1a1b3917fa6a508b397e5e39fa8bba8.png

im#

The image which is to be analzyed. Can be 2D or 3D.

b = ps.metrics.boxcount(im=im)
print(b)
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Item                      Description
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size                      Array of size (10,)
count                     [6505, 4095, 1435, 552, 206, 77, 24, 9, 4, 1]
slope                     Array of size (10,)
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The returned object is like a dataclass with each computed value stored in an attribute. The result can be printed for inspection. The results can also be plotted as follows:

fig, ax = plt.subplots(1, 2, figsize=[12, 6])
ax[0].loglog(b.size, b.count)
ax[0].set_xlabel('box length')
ax[0].set_ylabel('number of partially filled boxes')

ax[1].semilogx(b.size, b.slope)
ax[1].plot([0, 1000], [1.9, 1.9])
ax[1].set_xlabel('box length')
ax[1].set_ylabel('slope')
ax[1].set_ylim([0, 3]);
../../../_images/7c71172cf92b023b26a81690ad1ed7eb39acfcb4e5c1fb03120944220a6e7851.png

bins#

The box sizes to use. The default is 10. If an integer is given it computes the range of box sizes. If an array is given, these are used directly

b = ps.metrics.boxcount(im=im, bins=20)
fig, ax = plt.subplots(1, 2, figsize=[12, 6])
ax[0].loglog(b.size, b.count)
ax[0].set_xlabel('box length')
ax[0].set_ylabel('number of partially filled boxes')

ax[1].semilogx(b.size, b.slope)
ax[1].plot([0, 1000], [1.9, 1.9])
ax[1].set_xlabel('box length')
ax[1].set_ylabel('slope')
ax[1].set_ylim([0, 3]);
../../../_images/70ddb586f23f979095d8a7e9a4dae96432fc9f5bb83bf47b9227cdaecdbe22df.png