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The second set of models are what we call artificial image models. In Section 4, the measured 2-point correlation function, S2, measured on a 2-D digital image of a real material, was used to convolve a random noise image to obtain an artificial 3-D microstructure that had approximately the same porosity and functional form of S2 as did the 2-D image. There are other ways of operating directly on random images to produce artificial structures. These methods are not based on the actual formation processes of the real material, and they may not even use a real image in the convolution algorithm. They are, however, useful because they can be easily generated and often bear reasonable resemblances to real microstructures.
One method is take a random white noise image, convolve it with some other function, and then threshold it to solid and pore phases to give the desired porosity. This has been done using a Gaussian convolution function, and, remarkably, gives images that resemble thin sections of carbonate rock [111]. If the convolution function is the Laplacian of a Gaussian, the resulting images exhibit features of VycorTM [111,112]. The microstructures in Fig. 4 are from Gaussian convolutions of a white noise image.
A variation of the above method uses two thresholds, x1 and x2. All pixels with values of x, 0 < x < 1, below x1 and above x2 are designated pores, and pixels with x1 < x < x2 are designated as solid. This algorithm turned out to generate images that resembled foam and aerogel-like structures [113,114]. The conductivity of these structures has been computed along with the two and three-point correlation functions and resulting three-point bounds, and has shown reasonable agreement with experimental measurements [113,115].
This kind of model shows that as long as the correlation functions are similar to the real materials, artificial image models can be used productively to understand other material properties.