Short Report on
Image Analysis of Microstructure of Concrete
In Basheer et al. (1999) it is explained how concrete is taken as a
three phase material, consisting of
The latter is found in the immediate vicinity of aggregate surface. It
differs from the bulk hydrated cement paste in morphology, composition and
density. Rather than the cement aggregate bond being the major factor
in the strength of concrete, it is asserted that the ITZ has a significant
effect on permeability and durability. In Basheer et al. (1999)
concrete samples of predefined composition were imaged, visually-defined
thresholding was carried out, and porosity measurements were made (based
on greyscale values) within specified thickness bands of coarse aggregate.
- aggregate particles,
- cement matrix - paste, and
- the interfacial transition zone (ITZ).
The aggregate/paste/ITZ is examined using back-scattered electron (bse)
images of polished sections of concrete. Such Scanning Electron Microscope
(SEM) images are subject to significant speckle.
Fig. 1 shows an example, which is a 512x512 cutout of a larger
1024x1024 image, here shown histogram-equalized.
We see two ways to put the procedure of Basheer et al. (1999)
on a more effective footing: firstly,
define the thresholds based on distribution mixture modeling of the
image greyscale intensity distribution; and, secondly, since this cannot
be feasibly done on the available speckled images, first remove this speckle.
Speckle is multiplicative noise, and is typical of synthetic aperture
radar (SAR) or acoustic images. The statistical modeling of speckle is
discussed in Section 5.3 of MR/1 (1999). We used the MR/1 package
to de-speckle the image shown in Fig. 1. The result is shown in
Fig. 2 for the same 512x512
area. De-speckling the 1024x1024 image takes a few seconds elapsed time
on a Sun UltraSparc 10. A wavelet transform is used, with noise
modeling, to allow for speckle filtering on a range of resolution
To compare the input and de-speckled output images, we show a 64x64
subregion here side by side. As before, these images are shown
histogram-equalized to improve the contrast.
The difference in intensity distribution in these images is quite
significant. Fig. 3 shows the
intensity distribution of the given SEM image. It is clear than there
is little by way of heuristic pointers towards where one should place
thresholds leading to image segmentation.
Fig. 4 shows the intensity
distribution, again based on the 1024x1024 image, following filtering
to remove speckle. Here, the distribution is much more amenable to the
fitting of Gaussians.
We may comfortably hypothesize that, by the law
of large numbers, the different constituents of the image each follow a
Gaussian distribution. It is our task to disentangle these, in most cases
partially, superimposed Gaussians. This can be done through an iterative
fitting procedure (Celeux and Govaert, 1995). In Campbell et al. (1999),
this mixture model fitting approach was used for setting thresholds in
images containing various types of production faults in textiles.
Furthermore in Campbell et al. (1999), we select the best model -
helping significantly in selecting the best thresholds - by use of a
Bayesian model selection procedure. One appropriate measure is the
BIC (Bayes Information Criterion), the theory of which was developed in
Kass and Raftery (1995).
We choose a cutout from the given images to facilitate display. The following
shows (left) a cutout of the original image (of dimensions 288 x 274) and
(right) a cutout of the de-speckled image (of dimensions 288 x 267). These
cutout images show approximately, but evidently not exactly, the same region.
In all cases, images are shown histogram-equalized to facilitate
A mixture of Gaussians was fit to the intensity distribution
(Stanford, 1998). In the case
of the original image, the BIC values were -803173, -803094, -803104,
-803089, -803111, -803113, -803065, -803061, -798791, for numbers of
segments = 2, 3, ..., 10. There are relative maxima at 4 and at 7 segments.
We'll take the second of these relative maxima, believing that a larger
number of clusters is more realistic. In the case of the de-speckled image,
the BIC values were -719804, -719893, -719844, -719782, -719782, -719816,
-719859, -719860, -719779, for numbers of segments = 2, 3, ..., 10. The
relative maxima of this criterion, used for segment cardinality selection,
are at 3 and 9. As before, we take the second of these relative maxima.
The segmented images are shown below, (left) original, 7 segments, and
(right) de-speckled, 9 segments.
Overall, this is a very effective procedure,
and since the intensity distribution, only, is being processed it is highly
efficient (a second or two on a normal workstation). It is an approach
which we believe will lead to a solution which is quite robust for
varying lighting conditions, or compositions of the concrete being studied.
It is, as we have seen, capable of providing an objective procedure for the
setting of the thresholds. Finally, we note that it is a novel procedure
encompassing multiplicative noise modeling for speckle filtering, and
mixture modeling of the denoised signal.
- P.A.M. Basheer, L. Basheer, D.A. Lange and A.E. Long, "Reliability
of thresholding to determine the size of interfacial transition zone",
- J.G. Campbell, C. Fraley, D. Stanford, F. Murtagh and A.E. Raftery,
"Model-based methods for textile fault detection", International Journal
of Imaging Systems and Technology, 10, 339-346, 1999.
- G. Celeux and G. Govaert, "Gaussian parsimonious clustering models",
Pattern Recognition, 28, 781-793, 1985.
- R.E. Kass and A.E. Raftery, "Bayes factors", Journal of the
American Statistical Association, 90, 773-795, 1995.
- MR/1 Multiresolution Analysis Software, User Manual, 1999.
- D. Stanford, enhanced xv (J. Bradley, University of Pennsylvania)
Version 3.10a, 1998.