H-tortuosity (2D/3D)

Associated article: Chaniot J., Moreaud M., Sorbier L., Jeulin D., Becker J.-M. and Fournel T. (2020). "Heterogeneity assessment based on average variations of morphological tortuosity for complex porous structures characterization", Image Analysis & Stereology 39(1):111-128

Specifications:
  • scalable topological descriptor; informations of different dimensions at distinct scales

  • random points sampling, handling disconnections and applicable on complex multi-scale microstructures, especially when entries and exits are delicate to impose

  • H-tortuosity values, named H-scalars, assessing the average variations of the peripheral morphological tortuosity
Computation:
  1. Optional step: skeletonization
  2. Sampling: definition of the set of N random points; 1D-sampling method (a), stratified-sampling method (b) (Fig.(a-b)). An additional sub-step is imposed in the case of biphasic images, avoiding boundary issues; a sampling area is defined to remove potentially problematic points (turquoise disk Fig.(c)).
  3. Distance transforms: At this step, the map of mean relative tortuosities and the maps associated to each points, if 'Save Data' checked, are computed.
  4. H-coefficients: set of mean morphological tortuosities, each one connected to a specific location, i.e. a random point, and a scale, i.e. a Euclidean distance (shades of purple Fig.(d)).
    A H-coefficient can be seen as either a viewpoint from this location at a specific distance, or the mean accessibility of this point for any other point located at this distance.
  5. H-scalars: set of viewpoints according to a distance d (from 1 to Dmax). Contrarily to the M-tortuosity, the H-tortuosity focuses on local features by quantifying them thanks to the local variations of the morphological tortuosity.
    A H-scalar, connected to a specific distance, is the mean tortuosity of a pair of random points with this distance as only constraint.

Input:

  • binary microstructure

Outputs:

  • H-tortuosity values (*.txt file)
  • map of the mean relative tortuosities (*.fda file)
  • optional: maps associated to each starting point (*.fda file)

Parameters:

  • sampling choice (1D-sampling or stratified-sampling)
  • maximal distance Dmax (Fig.(d))
  • number of random points N
  • boolean 'Save Data', to save tortuosity maps associated to each starting point (*.fda file). Additional parameter (if checked):
  1. "...": selection of the save directory.

H-tortuosity-by-iterative-erosions (2D/3D)

Associated article: Chaniot J., Moreaud M., Sorbier L., Jeulin D., Becker J.-M. and Fournel T. (2020). "Heterogeneity assessment based on average variations of morphological tortuosity for complex porous structures characterization", Image Analysis & Stereology 39(1):111-128

Specifications:

  • H-tortuosity as seen by a spherical particle of given radius which increases step by step
  • linked to constrictivity, characterizing the bottleneck effect and/or the hindrance
Computation:

The steps defining the H-tortuosity are applied to the microstructure, which is eroded step by step. The iterative erosions using a unit sphere as structuring element, allow to consider a large interval of radii, representing the size of the hypothetic percolating particle.

Inputs:

  • binary microstructure
  • optional: microstructure skeleton

Outputs:

  • H-tortuosity values as a function of the radius (*.txt file)
  • map of the mean relative tortuosities (*.fda file)

Parameters:

  • sampling choice (1D-sampling or stratified-sampling)
  • maximal distance Dmax
  • number of random points N
  • boolean 'Use skeleton', when the microstructure skeleton is considered (loaded using 'Open' button). Additional parameter (if checked):
  1. "...": selection of the microstructure