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An interesting theoretical approach to generating 3-D images is to generate a representative 3-D porous medium from a single 2-D view of the system, such as that provided by a conventional micrograph illustrating the pore system. Based on the work of Joshi [89], Quiblier has developed a computational technique for creating a three-dimensional microstructure based on 2-point correlation function (S2) analysis of a 2-D image [90]. The main principle is that a 3-D image is produced that has the same 1-point and 2-point correlation functions as did the real material, as determined in the 2-D image. In essence, S2 obtained from the 2-D image is introduced into a 3-D image by convoluting an initial image consisting of Gaussian noise. The resulting image is then filtered so as to have the same S2 as the original image. This involves solving a large number of non-linear equations [90]. In his original paper, Quiblier performed some stress calculations on a slice of the generated 3-D medium. Adler et al. [91] have utilized this technique to generate 3-D images of Fontainebleau sandstones. They have computed permeabilities [91] and conductivities [92] but the results were consistently lower than measurements on real samples. This is probably due to differences in the pore space connectivity since S2 does not contain such information. The evidence of this weakness is the difference in percolation thresholds. Pores in sandstone are known to become disconnected at a few percent porosity, but the 3-D generated images tend to have percolation thresholds near 10% porosity [91].