chord_length_distribution

chord_length_distribution(im, bins=10, log=False, voxel_size=1, normalization='count')

Determines the distribution of chord lengths in an image containing chords.

Parameters:

• im (ndarray) – An image with chords drawn in the pore space, as produced by apply_chords or apply_chords_3d. im can be either boolean, in which case each chord will be identified using scipy.ndimage.label, or numerical values in case it is assumed that chords have already been identifed and labeled. In both cases, the size of each chord will be computed as the number of voxels belonging to each labelled region.

• bins (scalar or array_like) – If a scalar is given it is interpreted as the number of bins to use, and if an array is given they are used as the bins directly.

• 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.

• normalization (string) –

  Indicates how to normalize the bin heights. Options are:

  ’count’ or ‘number’

  (default) This simply counts the number of chords in each bin in the normal sense of a histogram. This is the rigorous definition according to Torquato [1].

  ’length’

  This multiplies the number of chords in each bin by the chord length (i.e. bin size). The normalization scheme accounts for the fact that long chords are less frequent than shorert chords, thus giving a more balanced distribution.

• 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.

Returns:

result – A custom object with the following data added as named attributes:

Attribute	Description
L or LogL	Chord 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:

Results object

References

[1] Torquato, S. Random Heterogeneous Materials: Mircostructure and Macroscopic Properties. Springer, New York (2002) - See page 45 & 292

Examples

Click here to view online example.