Biology Reference
In-Depth Information
Coplanarity of Landmarks
This is the sole criterion that is specific to two-dimensional data, and it arises from the dis-
tortion caused by projecting a three-dimensional organism into a two-dimensional plane. To
minimize this distortion, specimens must be consistently oriented under the camera, and one
particular plane must be chosen for that orientation. Points not in that plane may be inconsis-
tently oriented or difficult to interpret. The two-dimensional analysis will suggest that the
points have moved within the plane of photography, but it is possible that they actually have
moved toward or away from that plane. What you will see is the projection of a change that is
actually in the third dimension onto the plane of the photograph. Foreshortening can look
like shortening. The distortions resulting from projection can be a serious problem, as it
turned out to be in the analysis of cotton rat (Sigmodon fulviventer) skull ontogeny (
Zelditch
et al., 1992
). One characteristic feature of mammalian skull ontogeny is the change in orienta-
tion of the skull base: points that initially are on the posterior end of the ventral surface move
dorsally, out of the picture plane. Some points could not be included in the data set because
they were not visible at all ages (in consistently oriented photographs) but worse, other points
apparently on the lateral boundary of the skull (in the photograph) are actually on the lateral
surface of the skull. It was not possible to tell if they moved in the anteroposterior and medio-
lateral directions (the plane of photography) or if they instead moved dorsoventrally. In hind-
sight, those lateral points should have been excluded as too ambiguous.
BOOKSTEIN'S TYPOLOGY OF LANDMARKS
Bookstein (1991)
introduced an influential classification of landmarks into three catego-
ries: Type 1, Type 2 and Type 3 (see
Roth, 1993
, for another discussion of these types).
According to this scheme, Type 1 landmarks are optimal, Type 2 are more problematic
and Type 3 might not even be considered landmarks at all. The classification is based
on two interrelated considerations: one is that landmarks ought to be locally defined, the
other is the type of explanation into which they can enter. The first consideration is
relatively easy to summarize because it is a matter of the degree to which landmarks are
locally defined. The second consideration, however,
is more difficult
to summarize
because it depends on a classification of explanations.
Bookstein categorizes Type 1 landmarks as points at discrete juxtapositions of tissues,
which need not be juxtapositions of different tissue types
by his usage, the juxtaposition of
three bones is a juxtaposition of tissues, and a foramen is also a Type 1 landmark, although it
is not a juxtaposition of observed tissues so much as the consequence of the passage of neural
or vasculature tissue through the bone. Type 1 landmarks may be more clearly distinguished
as points whose definition refers solely to structures close to the point. For example, the inter-
section between three bony sutures is locally defined, as is a foramen. For Type 1 landmarks
you do not need to mention any structures far away from that point. They are surrounded by
tissue on all sides. At the other extreme are Type 3 landmarks. The definition of these points
depends on structures far removed from the landmark, and meaningful variation is usually
limited to a single direction, the one stipulated by the definition. Type 3 landmarks are often
constructed geometrically. For example,
Figure 2.6
shows a classic measurement scheme for
