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This paper discusses fast algorithms to encode material structure information using parameterized basis function and spatial correlation functions. The concept of the microstructure function is employed to parameterize the material information and produce a digital microstructure signal; encoding can be performed on most classes of experimental and simulated material structure information.[ref] The digital signals are convolved using embarrassingly parallel Fast Fourier methods to compute the spatial statistics of the digitized microstructure. The following properties of the spatial correlation functions make them a worthy candidate for an objective material structure descriptor: several widely used statistical metrics are embedded in the correlations such as volume fraction [ref] and specific surface area [ref]; for binary images, they contain information about the original material structure information within a translation [ref]; and they can describe most types of materials science information in raw signal is processed appropriately. N case studies will be presented to illustrate the generality of the technique when applied to things.  This paper will begin with a discussion on classifications of materials science information and their proposed conversions to a digital signal using the microstructure function. Once the raw material structure information is digitized, they will form the foundations that allow spatial statistics to be computed using fast, scalable FFT algorithms. N case studies will be shown to express the diversity and general applicability of the spatial correlation functions in structure-structure comparison.Here is another sentence this is an uncommented change