Introduction to porosity analysis

Method note
MCT-059
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2. Introduction
CTAn allows for the analysis of porosity in micro-CT dataset of any kind of
material. This method note will firstly introduce the concepts of pores and
related topics, and illustrate how to perform a 3D porosity calculation. In
addition a list of all pores and their exact size, position,…. is extracted. Even
more, a size distribution is calculated from the pore network. In the second
part is demonstrated how to make such measurements automatically, by
using a tasklist. This will introduce the use of the Custom processing page
in CTAn. This page opens up a wide range of tools, specifically dedicated to
noise removal of images and for advanced as well as automated porosity
analysis.

3. Introduction to Porosity Analysis in 3D

A micro-CT image of a porous material is shown in the image below. In this
method note a rock example is used.

Parameter of interest are porosity, open porosity, closed porosity, pore size
distributions,… for which the impact of 2D versus 3D thinking is significant.
As illustrated below, on a 2D microscopic image a void might appear as a
closed pore (right), however considering 3D information it might be that
this pore is in fact connected to the empty space outside of the object. This
difference is one of the key advantages of a 3-dimensional micro-CT dataset
over conventional 2D imaging methods.

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In 3D:
void is connected to
space outside of the
object
In 2D:
Isolated void

Image analysis consists of the following steps which are explained below:
choosing an appropriate volume of Interest (VOI), image segmentation,
….The region of interest (ROI) refers to the selected region, on a single
crossection image. The volume of interest (VOI) refers to the integration
of all the ROIs across all the selected image levels, and defines the sub-
volume of the dataset within which procedures will be performed such as
model construction and morphometric calculation. Tools are provided for
highly flexible volume of interest (VOI) delineation. As example a dataset
of a porous rock is chosen for which a cylindrical shape is applicable.

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To proceed with the data within the selected VOI, we will create a new
dataset by saving the images inside the ROI. This dataset is smaller in size
and will free up space in the memory. There’s a tick-box that enables you
to save the actual ROI-shape (used to cut the large data) as well.
Additionally, you can automatically restart with this newly generated
dataset. CTAn will also automatically load the automatically generated ROI-
file of this sub-dataset.

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This 8-bit reconstructed image contains 256 grey values. Each voxel has a
greyscale intensity from 0 to 255. For morphometric analysis, a binarised
image is needed. To this end each pixel needs to become either black or
white. This procedure is called segmentation and CTAn offers a range of
methods are available, from global to adaptive methods, both manual and
automated algorithms. For simple segmentation, a user must define a
threshold value. Voxels with a grey value higher than this value become
white and are considered as solid objects. Voxels with a grey value below
this threshold will be black and considered as part of the background.

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In case your image is displayed in red/green colors, switch of the half-tone

view with the icon indicated with the green arrow.
For porosity analysis it is important to understand two basic concepts in
CTAn. Any group of white pixels (solid space) is considered as an object1.
Any group of black pixels (background), entirely surrounded by white pixels
is considered a pore2. Moving on to the Morphometry-page, the 2D porosity
analysis is immediately displayed in the final tab, where porosity for
individual objects in 2D is defined as the volume of any spaces fully
surrounded by solid, as a percent of the volume of solid plus closed pores.

1 A discrete 3D object is a connected assemblage of solid (white) voxels

fully surrounded on all sides in 3D by space (black) voxels
2 closed pore in 3D is a connected assemblage of space (black) voxels that
is fully surrounded on all sides in 3D by solid (white) voxels.

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3D
Porosi 2D
ty Porosity

To enable the porosity analysis in 3D, one first needs to activate the
’Additional Values’. Porosity analysis is contained in the final check box for
‘number of Objects’.

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The result can be seen by scrolling down in the pop-up. Additionally, CTAn
calculates and reports parameters as open and closed porosity in the same
window. The output is automatically saved as a file in the same location as
the dataset, with the extension *_3d.csv.
A closed pore in 3D is a connected assemblage of space (black) voxels that
is fully surrounded on all sides in 3D by solid (white) voxels. Percent closed
porosity is the volume of closed pores as a percent of the total of solid plus
closed pore volume, within the VOI. An open pore is defined as any space
located within a solid object or between solid objects, which has any
connection in 3D to the space outside the object or objects. Total porosity
is the volume of all open plus closed pores as a percent of the total VOI
volume.

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2 important remarks should be made:

• Closed Porosity is a “material porosity”, and is calculated differently
from of open porosity and total porosity, where the denominator is
total VOI volume.)
• Closed porosity in 2D is usually much larger than the equivalent
parameter measured in 3D; a space region is more likely to be
surrounded by solid in a single crossectional plane in 2D than in all
directions in 3D.
•

4. Extracting a list of all pores with their properties

One of the reported values in the 3D analysis is the number of closed pores.
To quantify each pore individually an individual object analysis can be
performed to calculate properties of each pore individually.

As indicated by the name, this type of analysis is performed on objects only,

known in CTAn as a group of white pixels. Hence one needs to binarise the
pore space to create appropriate objects. The easiest way to invert the
thresholding level is to use the sliders.

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Now that the pore phase can be identified as objects, an individual object
analysis can be done in 3D by moving back to the morphometry-page. A
list is displayed showing parameters such as volume, surface, x-y-z-
coordinates of the centroid,… Each parameter in this list is well documented
and the description can be found in the document ‘CTAN03.pdf’, which is
available from the website. (http://www.skyscan.be/next/CTAn03.pdf). By
double clicking on the column label the objects can be sorted increasingly
or decreasingly according to volume, position,…. The object of interest can
be indicated by clicking on it, while enabling the tick box ‘navigate to
position of object centroid’. In the screenshot below the objects are
organized by their volume to display the largest one. The list can be saved

as an Excell-file.

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1 important remarks should be made:

• The highlighted point may be located in black space. Remember that
the object centroid is highlighted, which can be outside of the actual
object. A banana is a very intuitive example of this.

5. Calculating a Pore Size Distribution

Size can be calculated of object space (white pixels) or of pore space (black pixels) by the
structure thickness or separation respectively, one of the additional values in the 3D analysis.
The calculation of a size distribution involves 2 steps. Firstly, a “skeletonisation” is performed
to identify the medial axis of all structures. Secondly, a “sphere-fitting” measurement is made
for all the voxels lying along this axis. Local thickness for a point in solid is defined as the
diameter of the largest sphere which fulfills two conditions:
• the sphere encloses the point (but the point is not necessarily the
center of the sphere);
• the sphere is entirely bounded within the solid surfaces.
The key advantage of the local thickness measurement is that the bias from
the 3D orientation of the structure is kept to a minimum.

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More details about this size distribution calculations, and how to generate
color-coded images from these distributions were discussed in Academy
Newsletter issue 1.
The outcome of the analysis is a distribution as shown below, with 4
columns, representing the Range (in µm-depending on the settings in
‘Preferences’), Mid-range value, the volume of (object or pore) space within
that range and the percentage of space within that range. Below the
distribution one can find the standard deviation.

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Opening the *_3d.csv file in a spreadsheet like Excel allows to generate

representative graphs.

Structure thickness distribution

Percent volume in range (%)

25
20
15
10
5
0

Range (µm)

Advances in Porosity Analysis using Custom Processing

The first four pages have been explored for the purpose of porosity analysis
in 3D. The fifth page is called ‘custom processing’ and serves 2 goals: for
advanced tools in image analysis (this section) as well as for automation of
analysis (next section). The Custom processing page contains a number of
plugins, which can be performed on one crossection (in 2D) or on the entire
dataset (3D). To apply a plugin, one can press the play button. When
opening this page, a copy is made of data in the ‘raw image’ page and the
‘ROI’ page. Make sure you are looking at your raw image by activating the
‘image’ view. All steps performed in the previous sections are accessible
from this window as well.

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The first step in our porosity analysis is to apply a thresholding. For this
example automatic thresholding by means of the Otsu algorithm is selected.

Up to now, we have been demonstrating techniques how to perform

porosity analysis. Prior to the actual analysis, one needs to consider the
level of noise and appropriate ways to deal with this. After all, the binarised
image may now contain some black or white speckles which are caused by
noise.
To remove ‘black’ noise, a despeckle operation can be applied.

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A clever way to remove ‘white’ noise in a many porous materials is a sweep

function, also available from the ‘despeckle’ plugin. As the white pixels are
representing the selection of rock all solid space should be connected as
one object. Any other objects present in the dataset are by default caused
by noise and can be removed by sweeping all except the largest object in
3D.

The empty space is now thresholded as black pixels ( pores). The 3D

analysis can include a structure separation calculation.

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6. Automated Porosity Analysis using the BATchMANager

(BATMAN)

To reduce the user interaction in image analysis, all steps in the analysis
protocol can be automated. After applying a plugin one can add it to a task
list by clicking on the plus-button. The task list of the 3D porosity analysis
as discussed in the previous section would consist of 4 steps: thresholding,
2 x despeckling and 3D analysis. When applying a tasklist to a dataset, all
plugins will be applied to the dataset in order of appearance in the list from
top to bottom. The dataset can be restored by clicking the first button on
the left of the menu. One can now easily modify the analysis protocol and
repeat it without having to go manually go through all steps.

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The BATchMANager (BATMAN) can now be accessed to apply this tasklist to

several datasets (indicated by red arrow). The list of datasets can be saved
as a list file (.ctl), particularly convenient when analyzing a large number of
datasets. If any modification in analysis protocol is desirable afterwards,
loading the list file will load all datasets at once. New in CTAn 1.14, it is
possible to load several task lists to all datasets. Several Batchmanagers
can run simultaneously, the feasibility will depend on the size of your
datasets and your hardware configuration. If you have resized the dataset
for faster experimenting with the analysis protocol, here is an opportunity
to reload the dataset to repeat your analysis at high resolution.

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7. Advanced Automated Porosity Analysis using ‘bitwise

operations’

Up to now, we have carefully ignored the individual object analysis in the

automatic protocol, as this requires a whole new set of functions, called the
‘bitwise operations’.
In the ‘image’ and ‘ROI’ views one can see the active image, as well as ROI,
that is considered for analysis. Note that in the latest release of CTAn
(version 1.14), an additional ‚clipboard‘ function is available where data can
be stored temporarily during a task list (see icons below). These data can
be reloaded at any point in the tasklist either as image or region of interest,
which makes the clipboard a handy tool to make a task list more time-
efficient. In addition, it allows you to make more complicated tasklists and
even to combine different tasklists into 1 instead of running them
separately.
The buttons on the right side of the screen in the custom processing page
now appear as:
: image view
: image inside ROI view
: ROI view
: clipboard view
At this point, all views should look like indicated below.
Image inside
Image ROI Clipboard
ROI

Bitwise operations will apply any logical operation on the image, the ROI or
a combination of both. For this application, first the NOT operation is applied
to the image to invert the segmentation.

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The outcome is shown below.

Image Image inside ROI ROI Clipboard

A logical combination of the Image AND the ROI is used to cut the white
pixels outside of the sample. This function will include in the ‘new image’
only those white pixels which are white in my ‘old image’ AND my ‘old ROI’.
The outcome is also shown below.

Image Image inside ROI ROI Clipboard

In this way, an automatic segmentation of pores is generated in the ‘image’

view, whichis now ready for individual object analysis in either 2D or 3D, or
for generating a 3D model thereof by means of surface rendering.

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Introducing the clipboard function created opportunities to simplify certain

analysis request. In case you have copied your greyscale images to this
clipboard, you can now use that data as a source to calculate the density of
each particle as identified in the ‘image’ data and restricted to the VOI.
Additionally, one can also use this function to save the color-coded images
for size distribution so they become immediately available for viewing
and/or using in the analysis protocol. These functions will be demonstrated
in more detail in future separate method notes. Your final task list will look
as below and will provide you with analytical result for following
parameters:
• Porosity calculation
• Pore size distribution
• Open versus closed porosity calculation
• A list of all pores and their individual properties such as
volume, surface, and centroid location. .

Techniques for extracting only 1 pore phase, either open or closed pores,
and for respective visualization are discussed in a separate method note
(MN060).

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