radial_density_distribution(dt, bins=10, log=False, voxel_size=1)¶
Computes radial density function by analyzing the histogram of voxel values in the distance transform. This function is defined by Torquato  as:\[\int_0^\infty P(r)dr = 1.0\]
where P(r)dr is the probability of finding a voxel at a lying at a radial distance between r and dr from the solid interface. This is equivalent to a probability density function (pdf)
The cumulative distribution is defined as:\[F(r) = \int_r^\infty P(r)dr\]
which gives the fraction of pore-space with a radius larger than r. This is equivalent to the cumulative distribution function (cdf).
dt (ND-array) – A distance transform of the pore space (the
edtpackage is recommended). Note that it is recommended to apply
find_dt_artifactsto this image first, and set potentially erroneous values to 0 with
dt[mask] = 0where
mask = porespy.filters.find_dt_artifaces(dt).
bins (int or array_like) – This number of bins (if int) or the location of the bins (if array). This argument is passed directly to Scipy’s
histogramfunction so see that docstring for more information. The default is 10 bins, which reduces produces a relatively smooth distribution.
log (boolean) – If
Truethe size data is converted to log (base-10) values before processing. This can help to plot wide size distributions or to better visualize the in the small size region. Note that you should not anti-log the radii values in the retunred
tuple, since the binning is performed on the logged radii values.
voxel_size (scalar) – The size of a voxel side in preferred units. The default is 1, so the user can apply the scaling to the returned results after the fact.
result – A named-tuple containing several 1D arrays:
- R or LogR
Radius, equivalent to
Probability density function
Cumulative density function
The center point of each bin
Locations of bin divisions, including 1 more value than the number of bins
Useful for passing to the
- Return type
Torquato refers to this as the pore-size density function, and mentions that it is also known as the pore-size distribution function. These terms are avoided here since they have specific connotations in porous media analysis.
 Torquato, S. Random Heterogeneous Materials: Mircostructure and Macroscopic Properties. Springer, New York (2002) - See page 48 & 292
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