Short Report on
Image Analysis of Microstructure of Concrete

1. Introduction

In Basheer et al. (1999) it is explained how concrete is taken as a three phase material, consisting of
  1. aggregate particles,
  2. cement matrix - paste, and
  3. the interfacial transition zone (ITZ).
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.

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.

2. De-Speckling

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 (MR/1, 1999) 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 scales.

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.

3. Segmenting

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 examination.

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.

4. Conclusion

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.

References

  1. P.A.M. Basheer, L. Basheer, D.A. Lange and A.E. Long, "Reliability of thresholding to determine the size of interfacial transition zone", preprint.
  2. 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.
  3. G. Celeux and G. Govaert, "Gaussian parsimonious clustering models", Pattern Recognition, 28, 781-793, 1985.
  4. R.E. Kass and A.E. Raftery, "Bayes factors", Journal of the American Statistical Association, 90, 773-795, 1995.
  5. MR/1 Multiresolution Analysis Software, User Manual, 1999.
  6. D. Stanford, enhanced xv (J. Bradley, University of Pennsylvania) Version 3.10a, 1998.