[Insight-developers] Renaming frenzy

[Paul Hughett]

Miller, James V (CRD) hath spake unto us, saying:

> I'm assuming that you are saying that it is not a metric in the strict
> mathematical sense of one-to-one, if a > b, ax > bx, etc....

For the record, a metric on a set X is a function d() from pairs of
elements of X to non-negative real numbers such that for any x,y,z in
X:

(1) d(x,y) = d(y,x);

(2) d(x,y) = 0 implies x = y; and

(3) d(x,z) <= d(x,y) + d(y,z).

You can call the function D(x) = d(x,0) a metric without causing me to
cringe too much, but I won't let you generalize to any measurment.

> I tend to call anything that takes a "measurement" a "metric" (though
> this is not always appropriate). So a term like Calculator, Estimator,
> or Measurement is probably more appropriate.

Actually, the term "statistic" is perfectly appropriate, since you can
consider an image as a member of the population of all images of a
given size and intensity statistics.  (A statistic is simply some
function of a random variable.)  Alternatively, you can consider the
center of gravity and central moments as the mean and covariance matrix
of the image considered as a probability distribution.

All in all, though, I'm inclined to stick with ImageMomentCalculator;
calling it a statistic will probably confuse almost as many people as
calling it a metric.  Image moments are perfectly well defined in
themselves; the people who really need to know its relationship to
statistics probably already know it.

Paul Hughett