Morphometric Data - An Invariant Approach to Statistical Analysis of Shapes - page 18

skull, a joint articulation, an insect wing, or a granule of grain.
Techniques for quantitative analysis of such data are most commonly
based on either Fourier analysis or on Eigenshape analysis (e.g.,
Ehrlich and Weinberg, 1970; Lestrel, 1982; Ehrlich, Pharr et al., 1983;
Lohmann, 1983; Ferson, Rohlf et al., 1984; Lestrel, 1989; Lohman and
Schweitzer, 1990; MacLeod and Rose, 1993; Rao, 2000).
One major drawback of outline data is that one cannot unambigu-
ously establish correspondence between the outlines of two objects. A
one-to-one correspondence between data sets collected from various
objects is critical to meaningful comparisons. The lack of correspon-
dence between outlines makes it unlikely that the analysis of outlines
will enable the identification of localities that are different between
forms (Cole and Wall, 2000). On the other hand, outlines can provide
certain information about the form (e.g., curvature) that cannot be cap-
tured by landmarks (Bookstein et al., 1982; Ehrlich et al., 1983; Read
and Lestrel, 1986; see Figure 2.2 ) .
A surface is the area of the outer or inner face of an object ( Figure
2.1.d ). A surface can be recorded as an array of points in three-dimen-
sional space. A volume can be thought of as the amount of space within
a closed surface measured as a single number in cubic units ( Figure
2.1.e ) . An alternate measure of volume is the three-dimensional coor-
dinates of points that map the contents of that closed surface. Data
arrays representing surfaces and volumes are large, and statistical
tools for summarizing and comparing the topography or shapes
described by these data sets are not well developed.
Figure 2.2. Outlines can provide certain information about the form (e.g., curvature)
that cannot be captured by landmarks. In this figure identical sets of landmark data
are recorded on two forms. In the example shown here, comparison of the sets of land-
mark data collected from the two forms would determine that the two forms are the
same while outline information shows clear differences between the two forms (after
Read and Lestrel (1986), figure 2).