Ann Zumwalt writes:
> I am especially interested in testing for differences in the rugosity (ie,
> "bumpiness")
> of the surfaces, but am interested in *any* method that would help me analyze these
> surfaces. I have 3D grid data (x,y,z) that represents the surfaces (I am scanning
> the
> bones with a 3D laser scanner to obtain this data).
One possible suggestion: topographic roughness is often quantified by the power
spectrum
of the elevation plotted on a log-log scale as a function of the wavenumber (the
cycles per
km, or in your case, cm) in the horizontal direction along a profile. (The power law
that this
exhibits is often, but is not always, a self-affine fractal.) The roughness is
characterized by
the slope and the intercept (at some reference wavenumber) of a least-squares linear
fit to
the power spectrum. The measurement is repeated for multiple transects at regular
horizontal spacing; in your case, this would correspond to profiles measures a few
degrees
apart as the bone is rotated about its axis. Examples of the application of this
technique
to topographic profiles are given in, e.g., "Fractals and chaos in geology and
geophysics"
by Donald Turcotte (Cambridge University Press, 1992). Once a quantitative measure is
assigned (some way or another!) to the bones, then discriminant analysis can be applied
to determine the separation (if any) between the populations ("exercised" vs. "no
exercise").
Wilmer Rivers
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