Sketch of Derivation

Histograms represent the values taken on by p(x) over various spatial regions. Section 3 describes the histogram equation for a normalized histogram of data values within a region. Section 4 describes how the histogram equation can be used to create basis functions that model histograms taken over small, voxel-sized regions. These basis functions model histograms for regions consisting of single materials and for regions consisting of mixtures of two materials. Using Bayes' theorem, the histogram of an entire dataset, the histogram model basis functions, and a series of approximations, Section 5 derives an estimate of the most likely set of materials within an entire dataset. Similarly, given the histogram of a voxel-sized region, Section 6 derives an estimate of the most likely density for each material in that voxel. The classification process is illustrated in Fig. 7.

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