Statistical Models for Landmark Coordinate Data - An Invariant Approach to Statistical Analysis of Shapes - page 84

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Figure 3.3. Fifty Gaussian random observations generated for the sample of Ts65Dn
aneuploid mice (left) and the sample of Ts65Dn normal littermates (right). The random
observations for each sample were generated using the mean form and variance-
covariance matrix estimated from the landmark coordinate data (after Richtsmeier et
al., 2000). This graphical depiction of the variability for each sample is not invariant
with respect to the coordinate system as we are viewing the three-dimensional data
from a given perspective. A mouse hemi-mandible is shown to indicate approximate
location of landmarks on the mean form.

project the mean form is arbitrary, and that the visual impression of
the simulated data can change with the coordinate system. Generation
of the hypothetical data is simply a tool to help visualize variability
local to landmarks.
It is important to understand that within any sample, estimation of
K * changes depending upon the landmarks included in its estimation.
Suppose that instead of analyzing all eleven landmarks on the aneu-
ploid Ts65Dn mouse mandible, we decide to analyze a subset of the
original group of landmarks, say landmarks 1, 2, 3, 5, 7, and 10. The
estimate of the parameters of interest using only those data for the
landmark subset are given in Tables 3.2a-c.