Biology Reference
In-Depth Information
the only information extracted from the semilandmarks is about the bowing of the curve
(displacement perpendicular to the tangent) because any variation along the curve is treated
as non-shape (nuisance) information resulting from the arbitrary choices made when digitiz-
ing the semilandmarks. The outcome is shown in
Figure 3.11
all the semilandmarks line
up on their respective perpendiculars.
RESISTANT-FIT SUPERIMPOSITION
Resistant-fit superimposition methods (RFTRA) are similar to GPA but there is no
goodness-of-fit criterion to be minimized. In recognition of the general similarity, the
resistant-fit methods have also been characterized as “Procrustes methods” (see
Chapman,
1990
). The rationale for such methods is that GPA, like any method that uses least squares,
is very sensitive to large displacements at few landmarks. In statistical procedures like
regression, a few cases with unusually large deviations from the general pattern (i.e. “outliers”
or “influential observations”) can have a large effect on the results of a procedure that
minimizes the sum of the squared deviations. In shape analysis, a large change limited to one
or a few influential landmarks is sometimes called the Pinocchio effect, although those
influential landmarks need not be at the tip of a long process. When GPA is used to super-
impose landmark configurations, the Pinocchio effect can have a large effect because the
least squares criterion distributes the displacements of the few landmarks across all the
other landmarks. In graphical displays, the Pinocchio effect appears to be “smeared out”
over all landmarks, which can be unsettling for some workers.
Figure 3.12
shows a
hypothetical example in which the only shape change in a tree squirrel scapula is the ventral
displacement of the three most ventral landmarks. The more severe consequence is that
FIGURE 3.12
Hypothetical example of
the Pinocchio effect as exemplified by ven-
tral displacements of the three most ventral
landmarks of a tree squirrel scapula.
(A) Configurations superimposed by a resis-
tant-fit method (RFTRA); (B) configurations
superimposed by GLS. The outline of the
scapula is approximated by lines connecting
the landmarks.
