Histogram Basis Functions for Pure Materials and Mixtures

This section describes basis functions that model histograms of regions consisting of pure materials and regions consisting of pairwise mixtures of materials. Other voxel contents are also possible and are discussed in Section 10. The parameters of the basis functions specify the expected value, c, and standard deviation, 5, of each material's measurements (see Fig. 8).

Equation (1) can be used to derive these basis functions, which are subsequently fitted to histograms of the data. The equations provide reasonable fits to typical MR data, which gives confidence that the assumptions about the measurement r~-\

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