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Assume a digital image of a cut through a porous material has been obtained,
in the form of a gray scale image. Often the first
step is to make it into a two-phase black and white image.
There are many ways this can be done, based on analysis of the gray
scale histogram (distribution) of the image [18]. This histogram
simply tells what fraction of the pixels have which gray scale value. If
the density of the solid phase is known, then the porosity can also be directly
measured from some kind of physical bulk density measurement.
If 
s is the
solid density, and is the measured
empty-pore or bulk density,
then the porosity
is simply 
=
1 - /
s.
A threshold gray scale can then be chosen, so that all pixels with
gray levels above this threshold are white (solid), and all below are
black (porosity), such that
the correct porosity is achieved.
Once a correct binary image has been made, then further
analysis can be carried out. Often, one will want to remove isolated pixels
due to noise in the image acquisition process.
Median filtering or other image processing algorithms can be utilized for
this purpose [18].
The left image in Fig. 4a shows an example of a
random image, generated by convolving a Gaussian
function with a random noise image (see Section 3). Figure
4b shows the gray
scale histogram for this image, with dashed lines marking the gray scales
of 93 and 110. In the graph, there is a single maximum at a gray
scale of about 125, out of 255. Many porous material images would have
two peaks in the gray scale histogram, one for each phase.
The middle image of Fig. 4a shows the
result of choosing a threshold
gray level of 93, where every pixel
with a gray scale lower than this is turned to black, and every other pixel is
turned to white. The resulting porosity (black phase) is about
22%. If the threshold is chosen to be 110, in the right image in Fig.
4a,
then the porosity turns out to
be about 41%. In these 2-D sections,
the pore phase is isolated and the solid phase is connected.
The isolated islands of solid trapped within the
pore phase is a 2-D artifact.
Figure 4(a): Left--showing an artificial gray scale image,
generated from a Gaussian
convolution process. Middle--
showing same image thresholded at a gray level of 93, so
that all pixels with a gray level less than or equal to 93 are turned
black, all others turned white, black area fraction = 22%.
Right--
same image thresholded at a gray level of 110, with
black area fraction of 41%.
Figure 4(b): Bottom--
gray scale histogram of the original image. The y-axis is
the area fraction of the image having a given gray scale, and the gray
scale runs from 0 to 255. The values of 93 and 110 are marked by
dashed lines.
Next: Stereology mathematical morphology,
Up: Main
Previous: Digital images