Abstract. We introduce Minkowski functionals to characterise, reconstruct and discriminate different complex material microstructures, for instance, experimental data sets generated from X-ray computer tomography imaging; samples include a suite of Fontainebleau sandstone, and a heterogeneous cross-bedded sandstone. Three distinct classes of digitised complex microstructure are considered: particle based Boolean models, structures generated by level-cuts through Gaussian fields, and models based on a Voronoi tesselation of space. One can define a set of measures for random composite media from a single image at any phase fraction φ which allows one to accurately reconstruct the medium for all other phase fractions and to predict, for instance, the percolation threshold pc. The evolution of the Minkowski functions during erosion and dilation operations on non-convex morphologies leads to a very accurate discrimination of morphologybetter than commonly used techniques such as structure functions or chord length distributions.
Spatial Structures: Experimental Data and Stochastic ModelsThe structure of a disordered material -an oil bearing rock, a piece of paper, or a polymer composite -is a remarkably incoherent concept. Despite this, scientists and engineers are asked to predict the properties of a disordered material based on the "structure" of its constituent components. A major shortcoming in the understanding of processes involving complex materials has been an inability to accurately characterize microstructure. The specification of "structure" requires topological as well as geometric descriptors to characterize the connectivity and the shape of the spatial configuration. In oil recovery from petroleum reservoir rocks, an area of particular interest to the authors, recovery depends crucially on the topology of the pore space and on the mean curvature of the surfaces where immiscible phases meet at a contact angle. To determine accurate flow models and to devise intelligent recovery strategies requires an accurate characterization of reservoir rocks in terms of topology and geometry.To date, the main toolkit used to quantify complex structures has been primarily that of the statistical physicist and not the advanced techniques developed in spatial statistics [11,59]