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The similarity ranking of three
distinct points [IMAGE ] can be formalized
via the notion of their simple ratio, defined as [IMAGE ]. Obviously, a mapping [IMAGE ]
preserves distance ranks iff it preserves [IMAGE ] for any choice of points. A bijective
mapping S with this property must be a similitude, that is, a
mapping of the form [IMAGE ], where [IMAGE ], and [IMAGE ] is an orthogonal
transformation [Reshetnyak, 1989]. Thus, the requirement of rank
preservation is quite restrictive in the class of mappings it allows.
Edelman Shimon
Tue Nov 28 13:24:55 IST 1995