# lineal_path_distribution¶

`lineal_path_distribution`(im, bins=25, voxel_size=1, log=False)[source]

Determines the probability that a point lies within a certain distance of the opposite phase along a specified direction

This relates directly the radial density function defined by Torquato [1], but instead of reporting the probability of lying within a stated distance to the nearest solid in any direciton, it considers only linear distances along orthogonal directions.The benefit of this is that anisotropy can be detected in materials by performing the analysis in multiple orthogonal directions.

Parameters
• im (ND-array) – An image with each voxel containing the distance to the nearest solid along a linear path, as produced by `distance_transform_lin`.

• bins (int or array_like) – The number of bins or a list of specific bins to use

• voxel_size (scalar) – The side length of a voxel. This is used to scale the chord lengths into real units. Note this is applied after the binning, so `bins`, if supplied, should be in terms of voxels, not length units.

• log (boolean) – If `True` (default) the 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.

Returns

result

L or LogL

Length, equivalent to `bin_centers`

pdf

Probability density function

cdf

Cumulative density function

relfreq

Relative frequency chords in each bin. The sum of all bin heights is 1.0. For the cumulative relativce, use cdf which is already normalized to 1.

bin_centers

The center point of each bin

bin_edges

Locations of bin divisions, including 1 more value than the number of bins

bin_widths

Useful for passing to the `width` argument of `matplotlib.pyplot.bar`

Return type

named_tuple

References

[1] Torquato, S. Random Heterogeneous Materials: Mircostructure and Macroscopic Properties. Springer, New York (2002)

Examples