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The shear properties of natural granular particles such as sand are significantly dependent on the shapes of the particles in the mixture. This is important from a practical viewpoint, because a measurement and characterization technique for the 3-D shapes of such particles can lead to an improved understanding of soil stability and influence the design of structural foundations. Previous techniques that have been developed for this purpose have proven to be complex, and the associated instrumentation has proven to be expensive. Furthermore, conventional 2-D shape measurement and description methods do not readily lend themselves to parsimonious 3-D representations. The situation is further complicated by the fact that, to parameterize the relationship between shape and shear characteristics, a single numerical descriptor is required to model the 3-D shapes of multiple particles in a natural sand particle mixture. This paper describes an optical tomography technique for the measurement of particle data that is then characterized using statistical 3-D shape descriptors. The algebraic reconstruction technique (ART) is used to synthesize 3-D particle shapes from 2-D tomography projections. It is shown that the measurement and characterization techniques used can provide distinct features for differently shaped particle mixtures and can be used to synthesize 3-D composite particles representative of the entire mix. The novelty of the technique described in this paper is that numerical shape descriptors can be obtained for not only a single 3-D object but also an entire collection of 3-D objects. Furthermore, the statistical nature of the 3-D shape descriptor of a particle mixture can be used to synthesize a mixture containing an arbitrary number of particles that have similar but not identical shapes. Results demonstrating the efficacy of the method on a set of natural sand particle mixtures are presented.