Surface Area

The objective of this notebook is to familiarize new users with the main datastructures that stand at the basis of the PuMA project, and outline the functions to compute material properties (please refer to these papers (1, 2) for more details on the software).

Installation setup and imports

The first code block will execute the necessary installation and package import.

If you are running this jupyter notebook locally on your machine, assuming you have already installed the software, then the installation step will be skipped.

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# for interactive slicer
%matplotlib widget
import pumapy as puma
import os

if 'BINDER_SERVICE_HOST' in os.environ:  # ONLINE JUPYTER ON BINDER
    from pyvirtualdisplay import Display
    display = Display(visible=0, size=(600, 400))
    display.start()  # necessary for pyvista interactive plots
    notebook = True

else:  # LOCAL JUPYTER NOTEBOOK
    notebook = False  # when running locally, actually open pyvista window

Tutorial

In this tutorial we demonstrate how to calculate the surface area of a microstructure

We import or generate the microstructure

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ws_fiberform = puma.import_3Dtiff(puma.path_to_example_file("200_fiberform.tif"), 1.3e-6)

The calculation of the surface area requires the value for the voxel length to be set. The voxel length can be set during import, as shown above. The voxel length can also be set for the workspace directly, as shown below:

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ws_fiberform.voxel_length = 1.3e-6  # setting the voxel length in meters

For an accurate calculation of the surface area, it is recommended to use an unsegmented domain. In a segmented domain, each phase is defined by a single grayscale value (i.e. 0 for void and 1 for solid). In an unsegmented domain, the material phases are specified by a range of grayscale value. In the case of the imported tomography, the void range is [0,89] and the solid range is [90,255], as shown by the plotted slice below:

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puma.plot_slices(ws_fiberform)

An unsegmented domain is recommended because the surface area relies on the marching cubes triangulation of the isosurface, which is much more accurate for an unsegmented domain than a segmented domain.

To calculate the surface area, we use the puma.compute_surface_area function: The function returns both the raw area and the specific surface area. The specific surface area is the more often used quantity, and defines the surface area divided by the volume of the domain, with units of 1/m.

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cutoff = (90, 255)  # specifying the grayscale range of the phase of interest

area_us, specific_area_us = puma.compute_surface_area(ws_fiberform, cutoff)
print("Unsegmented:",area_us,specific_area_us)

If a segmented image must be used, a Gaussian blur can be utilized to help smooth out the triangulation for the surface area calculation. Note, however, that this blurring would smear any sharp features present in the microstrucutre. It is more appropriate for segmented images of microstrucutres with smooth features. As an example, the above domain is segmented and the surface area calculated with and without the Gaussian blur.

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ws_fiberform.binarize(90)  # segmenting the domain. [0,89] --> 0 and [90,255] --> 1
cutoff = (1, 1)  # updating the cutoff now that the domain is segmented

area, specific_area = puma.compute_surface_area(ws_fiberform, cutoff, flag_gaussian=False)
print("Segmented:",area,specific_area)
print("Percent Error: ", (specific_area - specific_area_us)/specific_area_us * 100.)

area, specific_area = puma.compute_surface_area(ws_fiberform, cutoff, flag_gaussian=True)
print("Segmented Gaussian:",area,specific_area)
print("Percent Error: ", (specific_area - specific_area_us)/specific_area_us * 100.)