FIGURE 12 A volume-rendering image of a human hand dataset. The opacity of different materials is decreased above cutting planes to show details of the classification process within the hand. See also Plate 19.

forms of basis functions are derived: one for single, pure materials; another for two-material mixtures that arise due to partial-volume effects in sampling. Equation (1), the histogram equation, is h' <" = /

and measures a histogram of the function p(x) over a region defined by '(x). x ranges over spatial locations, and v over feature space. Note that if p(x) contains additive noise, n(x; s), with a particular distribution, kn(v; s), then the histogram of p with noise is the convolution of kn(v; s) with p(x) — n(x; s) (i.e., p(x) without noise). kn(v; s) is, in general, a normal distribution. Thus, h'(v) = kn(v; s)* ( M(x)8((p(x) — n(x; s)) — v)dx. (10)

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