Statistical Methods for Comparison of Forms - An Invariant Approach to Statistical Analysis of Shapes - page 128

Figure 4.1. Comparison of the tracing of a cephalometric radiograph of a single indi-
vidual with Apert syndrome (age 2 1 / 2 years, solid line) and an unaffected individual
(same approximate age, broken line). The two tracings are superimposed on the land-
mark sella and oriented to a line that connects the landmarks sella and nasion. From
this superimposition, interpretations are made regarding how the skulls of unaffected
and affected individuals differ from one another.
the red landmark 2 to the green landmark 2, and so on. The vectors
drawn are presumed to depict the true form change and are used to
infer biologically based reasons for the changes/differences observed.
In the instructions given above, we asked that you match all corre-
sponding landmarks to the best of your ability. Methodologically,
various algorithms are used in superimposition schemes. Each algo-
rithm is designed to minimize a particular measure of similarity (e.g.,
Sneath, 1967; Gower, 1975; Bookstein, 1978; Siegel and Benson, 1982;
Bookstein, 1986; Goodall and Bose, 1987). We refer to the way in which
forms are superimposed so as to minimize a particular measure as the
“minimization criterion.” A commonly used measure of similarity is
based on the Procrustes distance where the minimization criterion
includes fixing one object and superimposing other objects on that one