Morphometric Data - An Invariant Approach to Statistical Analysis of Shapes - page 19

2.1.4 Landmarks
A landmark is a point in two- or three-dimensional space that corre-
sponds to the position of a particular feature on an object of interest.
For example, in the study of osteological remains, a landmark might be
defined as the point that marks the scar of a muscle insertion on a
bone, the intersection of two or more bones at a cranial suture, or the
foramen that marks the path of a neurovascular bundle. We choose to
focus on landmark data because we want to analyze data that have
unambiguous correspondence between the forms being compared.
Issues relating to correspondence are discussed below. The mathemat-
ical reasons for preferring landmark data are developed later in this
book (see especially Part 2 of Chapters 3 and 4 ).
One of the first decisions that a researcher must make is the selec-
tion of landmarks for approaching a research question. This choice is
necessary but subjective. Landmarks should be chosen in order to pro-
vide an adequate representation of the object under study, but the
research question will also dictate the landmarks chosen for study.
There are no concrete rules for making this choice. Our rules of thumb
include: 1) know your specimens, 2) make a list of all potential land-
marks, 3) collect data from as many landmarks as are feasible. Once
data are collected and analyses are underway, the number of land-
marks can be reduced on the basis of measurement error studies, or
redundancy of information from landmarks.
Landmarks collected from biological objects may be classified into
three general groups discussed below. Similar groups can probably be
formed from landmarks taken from nonbiological objects but our lack of
experience with non-biological data sets discourages us from generalizing.
a) Traditional landmarks
Traditional landmarks are precisely delineated points corresponding to
the location of features of some biological significance. There are two
classes of traditional landmarks: those whose definition is not dependent
upon a coordinate system, and those whose definition is tied to a partic-
ular orientation or a coordinate system. Examples of the first class
include landmarks such as nasion and nasale. Nasale is defined as the
distal end of the internasal suture, while anterior nasal spine is defined
as the intersection of the right and left nasal spines of the maxilla
( Figure 2.3 ) . Both of these points can be located on a skull regardless of
the orientation of the skull or its position in the laboratory. The exact