M-tortuosity (2D/3D)

Associated article: Chaniot J., Moreaud M., Sorbier L., Fournel T. and Becker J.-M. (2019). "Tortuosimetric operator for complex porous media characterization", Image Analysis & Stereology 38(1) :25-41

Specifications:
  • scalable topological descriptor; informations of different dimensions

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

  • the M-tortuosity is translation, rotation and homothety invariant. Moreover, it is stable for periodic microstructures.
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) displays the difference between the two sampling methods.
  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. M-coefficients: set of mean morphological tortuosities, each one connected to a specific location, i.e. a random point.
    A M-coefficient can be seen as either a viewpoint of the microstructure from this location, or the mean accessibility of this point for any random point.
  5. M-scalar: The M-tortuosity value, named the M-scalar, is an assessment of the morphological tortuosity. It aggregates information of each M-coefficient into a scalar value.
    The M-scalar is a global viewpoint of the microstructure, or the mean accessibility of any random point for any other random point.

Input:

  • binary microstructure

Outputs:

  • M-tortuosity value  (*.txt file)
  • set of M-coefficients (*.txt file)
  • map of the mean relative tortuosities (*.fda file)
  • optional: "Euclidean distance/geodesic distance/ morphological tortuosity" for each points pair (*.txt file)
  • optional: maps associated to each starting point (*.fda file)

Parameters:

  • sampling choice (1D-sampling or stratified-sampling)
  • number of random points N
  • boolean 'Save Dist/Tor' (optional output): save information for each points pair; distances and tortuosity (*.txt file)
  • boolean 'Save Data' (optional output): maps associated to each starting point (*.fda file) . Additional parameters (if checked):
  1. 'Maps': morphological tortuosities map of each point
  2. 'Paths': geodesic paths associated to each point
  3. '...': selection of the save directory

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

Associated article: Chaniot J., Moreaud M., Sorbier L., Fournel T. and Becker J.-M. (2019). "Tortuosimetric operator for complex porous media characterization", Image Analysis & Stereology 38(1) :25-41

Specifications:

  • M-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 M-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.

Input:

  • binary microstructure
  • optional: microstructure skeleton

Outputs:

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

Parameters:

  • sampling choice (1D-sampling or stratified-sampling)
  • 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

Deterministic M-tortuosity (2D/3D)

Associated article: Batista A.T.F., Baaziz W., Taleb A.-L., Chaniot J., Ersen O., Moreaud M., Legens C., Aguilar-Tapia A., Proux O., Hazemann J.-L., Diehl F., Chizallet C., Gay A.-S. and Raybaud P. (2020). "Atomic scale insight into the formation, size and location of platinum nanoparticles supported on γ-alumina", ACS Catalysis 10(7):4193–4204

Specifications:

  • M-tortuosity with an imposed set of starting points
  • image of objects with volume bigger than 1 voxel can be used to define the imposed set of starting points

Computation:
The steps are identical to the M-tortuosity, except for some pre-processing steps linked to the definition of the imposed set of starting points.
As objects can be used, real particles can be considered to define the starting locations. Nevertheless, they have to be reduced to a unique voxel, their center of mass. Due to some approximations, some starting points may not belong to the microstructure. The orthogonal projection can fix this issue, computing the closest feature point to each starting point outside to the microstructure.

'Center of Mass' and 'Orth. Projection' can be used combined; first center of mass computation then orthogonal projection, or separately, center of mass or orthogonal projection.

'Maps' and 'Paths' can be used combined; the geodesic paths are displayed over the morphological tortuosities maps, or separately; the morphological tortuosities maps or the geodesic paths.

Inputs:

    • binary microstructure
    • imposed set of starting points

    Outputs:

    • deterministic M-tortuosity value (*.txt file)
    • set of M-coefficients (*.txt file)
    • map of the mean relative tortuosities (*.fda file)
    • optional: "Euclidean distance/geodesic distance/ morphological tortuosity" for each points pair (*.txt file)
    • optional: maps associated to each starting point (*.fda file)

    Parameters:

    • '...': selection of the imposed set of starting points (*.txt OR an image *.tif or *.fda)
    • boolean 'Image', if an image is used for the starting points. Additional parameters (if checked):
    1. boolean 'Center of Mass': computation of the center of mass of each object
    2. boolean 'Orth. Projection': orthogonal projection of each point on the microstructure
    • boolean 'Save Dist/Tor' (optional output): save information for each points pair; distances and tortuosity (*.txt file)
    • boolean 'Save Data' (optional output): maps associated to each starting point (*.fda file). Additional parameters (if checked):
    1. 'Maps': morphological tortuosities map of each point
    2. 'Paths': geodesic paths associated to each point
    3. '...': selection of the save directory